saving, growth, and investment: a macroeconomic analysis...

30
SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS USING A PANEL OF COUNTRIES Orazio P. Attanasio, Lucio Picci, and Antonello E. Scorcu* Abstract —This paper provides a descriptive analysis of the long- and short-run correlations among saving, investment, and growth rates for 123 countries over the period 1961–94. Three results are robust across data sets and estimation methods: i) lagges saving rates are positively related to investment rates; ii) investment rates Granger cause growth rates with a negative sign; iii) growth rates Granger-cause investment with a positive sign. I. Introduction and Motivation T HE MAIN AIM of this paper is to provide an exhaustive and careful descriptive analysis of the correlations among saving, investment, and growth rates. We want to establish what are the main (aggregate) ‘‘stylized facts’’ that link these variables. For such a purpose, we use a new data set, gathered by the World Bank that contains a wide range of variables for 150 countries over the post-WWII period. The data set is probably the best panel of countries available to date. In what follows, we analyze both contemporaneous correlations and dynamic models. Most of the analysis, however, is focused on the dynamic relationships among the variables of interest. We will be using the statistical concept of Granger causality to denote the fact that a variable (the caused one) is correlated with lagged values of the other (after controlling for its own lags). Obviously, one should refrain from giving a causal or structural interpretation to these results. We estimate exible dynamic (reduced-form) models and identify long-run and short-run correlations among the variables of interest. The empirical regularities we document should complement those observed in microeconomic data sets and constitute the benchmark against which different models of saving, consumption, and growth are evaluated. While the scope of this paper is not the estimation of a structural model that links growth, saving, and investment rates, it is worth thinking about the implications of some of the standard models for the correlations we consider. The theoretical predictions for both the long-run and short-run correlations among the variables of interest are often ambigu- ous. Nonetheless, measuring such correlations is informa- tive about the relative importance of various factors. A natural theoretical framework that is used to think about the correlation between saving and growth is the lifecycle model. Such a model might imply both a long-run relation- ship between past growth and current saving rates and between future expected growth and current saving. If wealth is accumulated during the rst part of the lifecycle and decumulated during retirement, population and/or pro- ductivity growth might lead to higher aggregate saving, if the saving of the young exceeds the dissaving of the old, in the steady-growth equilibrium. However, it is easy to reverse such prediction if one makes individual earning pro les steep enough and lets the young borrow against their future income. If the borrowing (negative saving) of the young is large enough at the aggregate level, a strong productivity growth might lead to a negative correlation between saving rates and growth rates. The picture is further complicated if one considers the possibility of liquidity constraints, precau- tionary savings, habit formation, and general equilibrium effects on the rate of return. In fact, the sign of the long-run equilibrium correlation depends upon the precise shape of the utility function, the demographic structure, the presence of productivity changes, and other such factors. The lifecycle model, in which individual saving is an explicitly forward-looking variable, also predicts Granger causation, possibly with a negative sign, running from saving to growth. Rational individuals anticipating declines in future income will increase savings. This is the ‘‘saving for a rainy day’’ mechanism illustrated, for instance, by Campbell (1987), and it is worth stressing if nothing else to emphasize that one should use particular caution in interpret- ing Granger causality results. 1 Other saving-to-growth link- ages are also possible through an (almost passive) physical capital accumulation. Obviously, this link is only an indirect one. The considerations of the last three paragraphs clarify the potential utility of measuring saving-growth correlations to establish which of the various factors at play are more likely to be of importance. For the same reason, it is important to distinguish between long- and short-run effects and to identify indirect effects through other variables, such as investment rates. It should also be clear, however, that the evidence we present can constitute only a piece of the puzzle. If one is interested in explaining cross-country differences in saving and growth (and their relationship), the aggregate evidence should be complemented with microeco- nomic evidence on the shape of earning pro les, age distribution, and so forth. The dynamic relationship between saving and growth rates has recently been studied by Carroll Received for publication February 2, 1999. Revision accepted for publication November 29, 1999. * University College London Institute for Fiscal Studies and NBER, Universita` di Bologna, and Universita` di Bologna, respectively. We would like to thank Monica Paiella for skillful research assistance and Manuel Arellano, Steve Bond, Costas Meghir, Klaus Schmidt-Hebbel, Luis Serve ´n, and Farshid Vahid for useful comments. This paper was rst presented at the meeting ‘‘Saving in the World,’’ January 15–16, 1998, at the World Bank in Washington D.C., where we received valuable comments from several participants and from our discussant Chris Carroll. We are also grateful for detailed and useful comments from three anonymous referees and an editor. 1 A short-run negative correlation emerges also in the standard IS-LM framework, because a positive shock to saving leads to a subsequent decline in income and production. The Review of Economics and Statistics, May 2000, 82(2): 182–211 r 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

Upload: others

Post on 17-May-2020

5 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

SAVING GROWTH AND INVESTMENTA MACROECONOMIC ANALYSIS USING A PANEL OF COUNTRIES

Orazio P Attanasio Lucio Picci and Antonello E Scorcu

Abstract mdashThis paper provides a descriptive analysis of the long- andshort-run correlations among saving investment and growth rates for 123countries over the period 1961ndash94 Three results are robust across data setsand estimation methods i) lagges saving rates are positively related toinvestment rates ii) investment rates Granger cause growth rates with anegative sign iii) growth rates Granger-cause investment with a positivesign

I Introduction and Motivation

THE MAIN AIM of this paper is to provide an exhaustiveand careful descriptive analysis of the correlations

among saving investment and growth rates We want toestablish what are the main (aggregate) lsquolsquostylized factsrsquorsquo thatlink these variables For such a purpose we use a new dataset gathered by the World Bank that contains a wide rangeof variables for 150 countries over the post-WWII periodThe data set is probably the best panel of countries availableto date

In what follows we analyze both contemporaneouscorrelations and dynamic models Most of the analysishowever is focused on the dynamic relationships among thevariables of interest We will be using the statistical conceptof Granger causality to denote the fact that a variable (thecaused one) is correlated with lagged values of the other(after controlling for its own lags) Obviously one shouldrefrain from giving a causal or structural interpretation tothese results

We estimate exible dynamic (reduced-form) models andidentify long-run and short-run correlations among thevariables of interest The empirical regularities we documentshould complement those observed in microeconomic datasets and constitute the benchmark against which differentmodels of saving consumption and growth are evaluatedWhile the scope of this paper is not the estimation of astructural model that links growth saving and investmentrates it is worth thinking about the implications of some ofthe standard models for the correlations we consider Thetheoretical predictions for both the long-run and short-runcorrelations among the variables of interest are often ambigu-ous Nonetheless measuring such correlations is informa-tive about the relative importance of various factors

A natural theoretical framework that is used to think aboutthe correlation between saving and growth is the lifecyclemodel Such a model might imply both a long-run relation-ship between past growth and current saving rates andbetween future expected growth and current saving Ifwealth is accumulated during the rst part of the lifecycleand decumulated during retirement population andor pro-ductivity growth might lead to higher aggregate saving ifthe saving of the young exceeds the dissaving of the old inthe steady-growth equilibrium However it is easy to reversesuch prediction if one makes individual earning pro lessteep enough and lets the young borrow against their futureincome If the borrowing (negative saving) of the young islarge enough at the aggregate level a strong productivitygrowth might lead to a negative correlation between savingrates and growth rates The picture is further complicated ifone considers the possibility of liquidity constraints precau-tionary savings habit formation and general equilibriumeffects on the rate of return In fact the sign of the long-runequilibrium correlation depends upon the precise shape ofthe utility function the demographic structure the presenceof productivity changes and other such factors

The lifecycle model in which individual saving is anexplicitly forward-looking variable also predicts Grangercausation possibly with a negative sign running fromsaving to growth Rational individuals anticipating declinesin future income will increase savings This is the lsquolsquosavingfor a rainy dayrsquorsquo mechanism illustrated for instance byCampbell (1987) and it is worth stressing if nothing else toemphasize that one should use particular caution in interpret-ing Granger causality results1 Other saving-to-growth link-ages are also possible through an (almost passive) physicalcapital accumulation Obviously this link is only an indirectone

The considerations of the last three paragraphs clarify thepotential utility of measuring saving-growth correlations toestablish which of the various factors at play are more likelyto be of importance For the same reason it is important todistinguish between long- and short-run effects and toidentify indirect effects through other variables such asinvestment rates It should also be clear however that theevidence we present can constitute only a piece of thepuzzle If one is interested in explaining cross-countrydifferences in saving and growth (and their relationship) theaggregate evidence should be complemented with microeco-nomic evidence on the shape of earning pro les agedistribution and so forth The dynamic relationship betweensaving and growth rates has recently been studied by Carroll

Received for publication February 2 1999 Revision accepted forpublication November 29 1999

University College London Institute for Fiscal Studies and NBERUniversita di Bologna and Universita di Bologna respectively

We would like to thank Monica Paiella for skillful research assistanceand Manuel Arellano Steve Bond Costas Meghir Klaus Schmidt-HebbelLuis Serven and Farshid Vahid for useful comments This paper was rstpresented at the meeting lsquolsquoSaving in the Worldrsquorsquo January 15ndash16 1998 atthe World Bank in Washington DC where we received valuablecomments from several participants and from our discussant Chris CarrollWe are also grateful for detailed and useful comments from threeanonymous referees and an editor

1 A short-run negative correlation emerges also in the standard IS-LMframework because a positive shock to saving leads to a subsequentdecline in income and production

The Review of Economics and Statistics May 2000 82(2) 182ndash211

r 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

and Weil (1994) who explicitly used the concept of Grangercausation We will analyze Carroll and Weil results in detailpartly for their intrinsic interest and partly to illustrate someof the methodological points that we want to make

When considering the association between saving andinvestment rates it is natural to think in terms of theintegration (or lack of) of international nancial marketsIndeed in an in uential contribution Feldstein and Horioka(1980) interpreted the cross-country correlation betweensaving and investment rates as evidence of low internationalcapital mobility In this case saving is likely to be a limitingfactor for investment A saving-to-investment link couldtherefore arise because lsquolsquoan increase in national saving has asubstantial effect on the level of investmentrsquorsquo (Feldstein andBacchetta (1991)) as investment must be supported bysaving and domestic rms compete for the ow of availabledomestic saving

This interpretation has often been challenged In fact inthe long run technological variables and the demographicstructure of the population could drive both variablesthereby inducing positive correlation even with perfectcapital mobility (Baxter and Crucini (1992) Taylor (1994)2

Our results show that the correlation between saving andinvestment is indeed a robust nding Moreover we showthat such a correlation has an important dynamic compo-nent in that lagged saving rates are strongly correlated withcurrent investment rates It is therefore interesting to estab-lish whether such a correlation survives also the introductionof various controls

Obviously Granger causation running from investment tosaving is also possible While the exact mechanisms at workare hard to spell out in detail if an increased demand forcapital goods stimulates savingmdashmaybe through interestrate effects or the endogenous development of the nancialinstruments that permit the mobilization of savingmdashsavingmight adjust to investment

The positive contemporaneous association between rateof investment and growth is usually explained in terms of acausal link running from the former variable to the latterSeveral well-known theoretical explanations can be offeredfor such a link Some growth models for instance suggestthat a rise in productivity growth causes both growth ratesand investment rates to move together (possibly coupledwith the accumulation of human capital) This is the type ofmechanism mentioned for instance by Barro (1991) whenconsidering the simultaneous determination of growth andinvestment rates (as well as fertility rates) and investigatedempirically more recently by Caselli Esquirrel and Lefort(1995) and Islam (1996) In what follows we stress onceagain the dynamic nature of the relationship betweeninvestment and growth and show that the dynamic correla-tion can be quite different from the contemporaneous ones

A dynamic link running from growth to investment mightalso hold Higher growth might drive saving up leading in

turn to higher investment However Blomstrom Lipsey andZejan (1996) suggest that accumulation might be a conse-quence of the growth process ignited by the growth-basedsaving change Furthermore higher growth can enhancefuture growth expectations and returns on investmentProvided that saving (possibly raised by the growth process)is not a limiting factor the accumulation of physical capitalwill nally take place

While in recent years several authors have used panels ofcountries to study a variety of phenomena no standardeconometric methodology has been developed for the analy-sis of this type of data a relative large panel of countriesThe second contribution of our paper is a methodologicalone We precede the empirical analysis with a discussion ofalternative econometric techniques and of the related meth-odological issues

In standard panel data analysis the presence of xedeffects correlated with the variables on the right-hand side ofthe equations of interest constitutes an important concernThe issue is particularly serious in the analysis of dynamicsystems in which the hypothesis of strong exogeneity of theindependent variables is obviously untenable Howeverwhile these problems are certainly relevant the analysis of apanel of countries puts the researcher in a slightly differentenvironment than that faced by an econometrician studyinglarge panels of individual observations The main differenceis in the fact that unlike with household-level data in whichtypically N (the number of individuals) is large and T (thenumber of periods) is small in analyzing a panel ofcountries N and T tend to have the same order of magnitudeFurthermore it is more natural to think about the asymp-totics of the problem as T-asymptotics rather thanN-asymptotics This will have an effect on the choice oftechniques used in the analysis Finally if one is interested incharacterizing the dynamic relationship among several vari-ables it is more natural to use concepts from the time-seriesliterature and use the N dimension of the sample to allow fordifferences among countries that can be of independentinterest

The rest of the paper is organized as follows In section IIwe discuss some methodological issues relevant for theeconometric analysis of dynamic models using panels ofcountries In section III we brie y describe the data set andpresent some evidence on the static correlations among thevariables of interest In section IV we analyze the robustnessof the Carroll and Weill results by using their estimators onthe new data set and also considering different econometrictechniques and different frequencies of the data In section Vinstead we switch to the analysis of annual data and applythree different types of estimators We rst assume that thetotal number of time observations we have is large enough toallow us to use lsquolsquobig Trsquorsquo asymptotic approximations We thenpresent some results obtained using a lsquolsquo xed T rsquorsquo estimatorNext we allow for across-country heterogeneity in thedynamic effects that link the three variables of interestFinally we present the estimates of a trivariate model in

2 Arguments based on the intertemporal countryrsquos budget constraint leadto the same conclusion (Argimon and Roldan (1994))

183SAVING GROWTH AND INVESTMENT

which we consider the variables of interests and theirinteractions simultaneously We conclude the section byanalyzing the effects of introducing various controls nor-mally used in the literature In section VI we summarize andinterpret the main results

II The Statistical Model and its Econometric Estimation

Preliminary to the empirical analysis we discuss someeconometric issues that are relevant to the study of thedynamic relationship between two or more variables ob-served over a relatively long time horizon and for a ratherlarge number of countries

A general representation of a dynamic model linking twovariables x and y is

yit 5 a 0 1 oj 5 1

q

a it jy yit 2 j

1 oj 5 1

p

b it jy xit 2 j 1 c t

y f iy 1 uit

y

(1)

xit 5 b 0 1 oj 5 1

m

a it jx yit 2 j

1 oj 5 1

n

b it jx xit 2 j 1 c t

x f ix 1 uit

x

(2)

Obviously such a system cannot be estimated withoutimposing some restrictions on its parameters This can bedone either in the time series or in the cross-sectionaldimension If the time-series variability is deemed sufficientto obtain reasonably precise estimates one could specify themodel by assuming that the parameters are constant overtime and might be variable across countries On the otherhand if one wants to exploit the cross-sectional variabilityone might let the parameters differ over time while beingconstant across countries Which of the two choices isfeasible is often dictated by the data available Howeverwhen the time and cross-sectional dimensions are roughly ofthe same order of magnitude (as it is in the case at hand) onefaces a real choice whose solution should be dictated by thenature of the phenomenon one is studying

An alternative way of thinking about the choice ofestimation techniques is to consider whether the cross-sectional or the time-series dimension has to increase inorder to derive the asymptotic distributions used in hypoth-esis testing In the analysis of country panels it is conceptu-ally awkward to consider N that goes to in nity On the otherhand the analysis that lets T go to in nity is the standardpractice in time-series analysis3 Furthermore if one is

interested in studying the dynamic relationship between twoor more variables either by testing the existence of Grangercausality or more generally by characterizing the dynamicrelationship between the variables under study it seemsnatural to consider a model that is exible but stable overtime The analysis of heterogeneity in impluse-responsefunctions across countries might be also interesting in itsown right

A Large N ( xed T) Models

Many recent studies of data sets similar to the one we usehave followed the microeconometric literature and appliedestimators that rely on the cross-sectional variability toidentify the model of interest This amounts to imposingconstancy of the parameters in equation (1) and (2) acrosscountries while at least in principle allowing them to varyover time Typically estimators with xed effects such asthose proposed by Holtz-Eakin Newey and Rosen (1988)(HNR hereafter) and Arellano and Bond (1991) (AB hereaf-ter) are used The model is often specialized to thefollowing expression to impose constancy of the parametersnot only across equations but also over time4

yit 5 a 0 1 oj 5 1

q

a jyyit 2 j 1 o

j 5 1

p

b jyxit 2 j 1 f i

y 1 ui ty (1a)

xi t 5 b 0 1 oj 5 1

m

a jxyit 2 j 1 o

j 5 1

n

b jxxit 2 j 1 f i

x 1 uitx (2a)

The coefficients a jx are relevant for the Granger causality

running from y to x while the coefficients b jy are relevant for

the Granger causality running in the opposite direction Weassume that the residuals of the two equations of the systemare uncorrelated with the variables on the right side and areiid The two variables however are in principle correlatedat a point in time that is the covariance between uit

x and u ity

is not necessarily zero Notice that because of the presenceof xed effects none of the observable variables on theright-hand side of the two equations is strongly exogenous

To eliminate the bias caused by the presence of xedeffects these equations are typically estimated in rstdifferences As rst-differencing induces MA(1) residualsone has to use some instrumental-variable technique HNRand AB stress that when the cross-sectional dimensionidenti es the model all the orthogonality restrictions im-plied by the dynamics of the system can be exploited toachieve efficiency5 In particular at each point in time t one

3 Also from a practical point of view it is often not obvious thatincreasing the number of the included countries provides additionalinformation when the quality of the data decreases as more countries areconsidered

4 As such a system is typically estimated using N-asymptotics The latterassumption can be easily relaxed (See HNR (1988) for instance)

5 Notice that in both equations we need to instrument both the(one-period) lagged yrsquos and the lagged xrsquos If one is willing to assume thatthe residuals of the two equations are contemporaneously uncorrelatedone can instrument the lagged yrsquos in equation (1) and the lagged xrsquos inequation (2)

184 THE REVIEW OF ECONOMICS AND STATISTICS

can use as valid instruments all the variables from time 1 totime t 2 s 2 1 (where s 5 max (m n p q) 6

While the application of the HNR or AB estimators isconceptually straightforward a few important caveats are inorder when the time dimension is not small and when thefocus is on a dynamic phenomenon such as Grangercausality As T increase the number of admissible instru-ments increases very quickly In our application for in-stance with two variables whose lags are valid instrumentsm 5 n 5 p 5 q 5 1 t 5 35 and N 5 50 (as it isapproximately the case in some of the results presentedbelow) by the time we get to the end of the sample there areclose to seventy valid instruments for no more than ftycross-sectional observations It is obvious that one cannotuse all of them In cases like this it is advisable to use only alimited number of lagged variables as instruments

An alternative way to tackle the problem which has oftenbeen employed is to use n-year averages (with n usuallyequal to 5 or 10) therefore arti cially reducing the time-series dimension of the sample This ltering is meant tocapture long-run relationships and abstract from uctuationsof business-cycle frequencies We favor the use of methodsthat explicitly use the time-series variation and possiblyexplore the existence of heterogeneity across countriesEven if one wants to use the lsquolarge Nrsquo estimators we argue infavor of annual observations rather than n-year averagesSome of the reasons follow7

1 Annual data provide information that is lost whenaveraging

2 Even if one is interested in identifying long-runrelationships it is not obvious that averaging over xed intervals will effectively eliminate business-cycle uctuations and make easier the emergence ofthe relationships of interest The length of the intervalover which averages are computed is arbitrary andthere is no guarantee that business cycles are cut in theright way as their length varies over time and acrosscountries

3 By averaging one commits oneself to the use ofcross-sectional variability to estimate the parametersof interest and discards the possibility of consideringcross-sectional heterogeneity in the parameters Thislimitation might be particularly severe when oneanalyzes several countries that could differ in manydimensions

4 By averaging an overall effect over a given timewindow is measured In the case at hand what weknow about the economic relationship among the

variables involved indicates that contrasting forces areoften at work The dynamic interplay of these forcescould well result in signi cant but opposed effectsmaybe acting with different lags that might eventuallycancel out once averaged Focusing only on thelong-run effect provided averaging does that pre-cludes the analysis of such short-run effects8

B Large T ( xed N) Models

An alternative to methods based on lsquolarge Nrsquo asymptoticsis to assume that the parameters are constant over time andexploit the time-series variability to estimate them In such asituation we can introduce exibility in the cross-sectionaldimension and let the coefficients of interest vary acrosscountries

The coefficients of our model represent the lagged effectsof growth saving and investment on the same variablesHowever the underlying mechanisms linking those vari-ables could differ across countries possibly due to institu-tional reasons or differences in preferences9 The questionthen is to determine whether the econometric techniquesthat we have illustratedmdashall assuming constancy acrosscountries of the underlying parametersmdashare still appropriatein the case in which those parameters are heterogeneous

The answer to this question obviously depends on thenature of the variation and on the general properties of themodel As discussed by Pesaran and Smith (1995) (PShereafter) if the coefficients of equation (1) and (2) areconstant over time but vary across countries techniques thatimpose parameter homogeneity do not yield consistentestimates Responsible of the biasmdashwhich persists regard-less of the size of N T and of any choice of instrumentsmdashisthe dynamic nature of the model On the other hand a meangroup estimator obtained by averaging the individual coun-tries estimates is unbiased and consistent

While wrongly assuming parameter constancy acrosscountries implies biased estimates of the underlying averageeffects a parsimoniously parameterized model yields more-precise estimates Within this familiar tradeoff betweenconsistency and efficiency the choice between homoge-neous lsquolsquopooledrsquorsquo estimators and their heterogeneous counter-parts does not reside in a formula but boils down to acase-by-case problem of model selection10

6 By using a GLS-type transformation to account for the MA structure ofthe residuals one obtains a further gain in efficiency Arellano and Bover(1995) show that one can express the model in terms of orthogonaldeviations to obtain a simple way of computing the HNR or AB estimator

7 The same considerations arise also in different frameworks Forexample the Feldstein-Horioka type regressions have been recentlyestimated on annual series rather than on the more conventional timeaverages See among others Sinn (1992)

8 It has also been argued that the consideration of time averages reducesthe relevance of measurement error Of course this argument is valid onlyif measurement errors are not perfectly correlated over time

9 In such a situation rather than in the complete characterization of thecoefficients in all countries one might be interested in the averagecoefficient

10 Baltagi and Griffin (1997) compare out-of-sample forecast perfor-mances of an array of homogeneous and heterogeneous estimators They nd that pooled estimators fare relatively well thus showing (for theparticular case at hand) that the heterogeneity inevitably characterizingdifferent countries and the ensuing pooled estimatesrsquo bias should notnecessarily lead to the rejection of the homogeneity assumption

185SAVING GROWTH AND INVESTMENT

C Large N or Large T

As in our data set N and T are roughly of the same order ofmagnitude the presence of a tension between exibility inthe time-series and in the cross-sectional dimension isevident The resolution of this tension absent in the analysisof individual data surveys in which T is typically small andinferences are conducted using lsquolarge Nrsquo asymptotics obvi-ously affects the model speci cation and the choice ofestimators

Given these considerations the best strategy is to estimaterich and exible dynamic models that allow for differencesin short- and long-run coefficients and use estimators thatappeal to lsquolarge T rsquo asymptotics to achieve consistency whileefficiently exploiting all the available information Thesemodels can and should also consider the possibilities that the(dynamic) relationships of interest are different acrosscountries

Obviously the proposed approach imposes different typesof constraints on the researcher The most important is thenecessity to consider coefficients that are constant over timeObviously it is necessary to assume that the availablesample period is long enough to allow for reasonably preciseestimates of time-invariant country coefficients11 Partlybecause of these reasons and partly to make our analysiscomparable to a large body of the literature we presentresults obtained estimating both classes of models discussedin this section

III The Data Set

A The Nature of the Data Set and its Construction

As mentioned in the introduction we use a new panel ofcountries (the World Saving Database) recently gathered atthe World Bank As the data-gathering effort is described indetail by Loayza et al (1998) here we provide a very briefdiscussion of the structure of the panel focusing in particu-lar on those aspects that are relevant for our analysis Withthe exception of total population gures originating fromthe World Bank database all the data are from NationalAccounts and follow their standard conventions The data-base includes 150 countries and spans the years 1960 to1995 However not all variables are available for everycountry and for every year In particular the population datacover the period 1960 to 1994 only As a consequence ouranalysis is restricted to those years

For each country the variables that we use are the rate ofgrowth of annual real per capita gross national product thesaving rate and the rate of investment All these series aremeasured in local currencies The saving rates are computedas nominal gross national saving over nominal gross na-tional income while the investment rates are computed as

nominal gross xed investment over nominal gross nationalproduct Growth is measured as the rate of growth in real percapita GNP (de ated with the GDP de ator)12

We use three different samples of countries The rst is asclose as possible to the whole set of countries included in theWorld Bank database We exclude only those countrieswhose annual income saving or investment were notrecorded at all or are recorded for less than a ve-yearinterval and those countries for which the relevant serieshave missing values in the middle of the sample period Thisprocedure leaves us with a sample consisting of 123countries We call this our lsquolsquowholersquorsquo sample The other twosamples trade-off the T and N dimension The second sampleconsists of the fty countries for which all variables areavailable every year in the interval 1965ndash1993 Our thirdsample consists only of those countries whose variables areavailable every year from 1961 to 1994 Only 38 countriesare included We also use for comparison purposes only theCarroll and Weil (1994) 64-countries sample All countriesin this sample are also in our whole sample with theexception of Tanzania and Zimbabwe which were excludedbecause of the unavailability of data13

In the next section we analyze Carroll and Weilrsquos fullsample results in addition to the analysis based on annualdata We also look at nonoverlapping ve-year averages ofgrowth saving and investment rates for each country14 Theinformation on the number of countries in each of the datasets we use is summarized in table 1

B Contemporaneous Correlations and Rank Correlationsbetween Saving Investment and Growth Rates

We start the analysis of the data set computing somesimple correlation and rank correlation coefficients betweenthe three variables that constitute the main focus of thisstudymdashnamely the saving rate the investment rate and the

11 Another limitation is the fact that one is constrained to consider onlysome classes of error models For instance if the residuals of the model inequation (1) and (2) are of the autoregressive type and there are xedeffects it is impossible to nd instruments that identify the relationships ofinterest

12 To avoid the loss of a large number of observations we did not performany PPP adjustment The same applies to the de ation of GNP by the GDPde ator

13 Dropping these countries from this sample does not change the resultsin any signi cant way

14 Given the period covered by our sample for each country the rstobservation on average growth is in fact a four-year average If there wereno missing values we would have seven observations for each countryHowever many observations are missing for the rst sample consideredThis implies that for these countries the averaged data can sometimesresult from the averaging of relatively short series Obviously this problemdoes not arise when using the balanced data sets

TABLE 1mdashDESCRIPTION OF THE DATA SET

Number ofCountries

Of Which WithData 1961ndash1994(1965ndash1993 for

Data Set 2)Average Number ofYears Per Country

Data set 1 123 38 24Data set 2 50 50 29Data set 3 38 38 34CW data set 64 64 29 (5-year average)

186 THE REVIEW OF ECONOMICS AND STATISTICS

growth rate Unlike in the rest of the analysis our interesthere is merely for their static relationships

As in any panel our data has set two dimensions thetemporal and the cross-sectional Therefore even whencomputing simple correlations there are several options Foreach of the three pairs of variables we rst consider thewhole data set that is we use each country-year observa-tion We then average for each country all the availableinformation and therefore focus on the cross-sectionalvariability15 Finally we compute for each year the correla-tion coefficient (in the cross section) between the twovariables of interest and consider the variation of thisparameter over time

We start by comparing the coefficient of variation of thethree variables of interest In data set 1 growth rates are byfar the most volatile The coefficient of variation for thisvariable is 330 to be compared with 049 and 035 forsaving and investment rates respectively This ranking invariability is unchanged when we consider country (time-series) averages of the variables In this case the threecoefficients of variations are 173 046 and 029 Noticethat in this case the variability in growth rates as measuredby the coefficient of variation is almost halved while thereduction in the other two variables is modest In data sets 2and 3 whose countries are more similar the coefficients ofvariation while slightly smaller follow the same pattern

In table 2 we report correlation coefficients and Spear-man rank correlation coefficients computed for the threepairs of variables and in the three data sets We report boththe correlations obtained with all annual observations andwith country averages

In the table the correlation coefficients are alwayspositive Typically the coefficients computed on annual dataincrease by 30 to 50 going from data set 1 to data set 3(that is going from a large group of nonhomogeneouscountries to a more restricted number of more similarcountries observed for longer time spans) Saving-growth

correlations are somewhat higher than investment-growthcorrelations but the strongest link turns out to be thatbetween saving and investment We get similar results forrank correlations which should reduce the effect of outliers

When using time-averaged observations correlation coef- cients increase in most cases The only exception is theslight decline in the simple correlation between saving andinvestment rates in data set 1 Even in that case however thecorresponding rank correlation increases if only slightlyThe largest increase is registered for the investment andgrowth rates pair for which the correlations more thandouble

In gure 1 we plot the contemporaneous correlationcoefficients computed using all saving-growth pairs of agiven year against time In the same graph we plot the timeseries obtained using only the countries in the balancedpanel with fty countries The correlation coefficients arepositive for all but four years In the rst half of the periodcorrelation coefficients usually uctuate in the range of 02to 04 for both samples Starting in 1977 however and untilthe end of the sample period the uctuations of thecorrelation coefficients for data set 1 became more marked16

Two effects are likely to be at play On the one hand severaladditional countries lsquolsquoenterrsquorsquo the data set around this periodmoreover the correlation for the preexisting countries mightalso be varying In fact if the same correlations arecomputed using only the countries for which data areavailable over the sample 1965ndash1993 (often middle- andhigh-income countries) a different picture emerges Correla-tion coefficients are somewhat increasing over time and inthe 1980s uctuate around 05 Over that period data set 1correlations drop with respect to the corresponding values ofdata set 2 Short-run linkages turn out therefore quite weakparticularly for those countries that enter the sample

In gure 2 we plot the annual correlations betweengrowth and investment rates (across countries) against timeAgain it must be stressed that the number of countries that

15 As data set 1 is a not balanced panel the country averages and theannual (cross section) correlations are computed using a (possibly)different number of observations

16 The coefficients of variation computed for the two subsamples1961ndash1976 and 1977ndash1994 are respectively 0509 and 0745

TABLE 2mdashCORRELATION COMPUTED ON ANNUAL DATA DATA SETS 1 2 AND 3

CorrelData Set 1Corr Coeff

Data Set 2Corr Coeff

Data Set 3Corr Coeff

Data Set 1Rank Corr Coeff

Data Set 2Rank Corr Coeff

Data Set 3Rank Corr Coeff

S G Annual 0253 0370 0332 0323 0372 0323(0018) (0024) (0026) (0018) (0026) (0028)

Country average 0376 0666 0492 0522 0623 0525(0084) (0108) (0145) (0091) (0143) (0164)

I G Annual 0165 0227 0242 0211 0240 0243(0018) (0026) (0027) (0018) (0026) (0028)

Country average 0319 0601 0652 0409 0585 0650(0086) (0126) (0126) (0091) (0143) (0164)

S I Annual 0483 0592 0658 0614 0613 0665(0016) (0021) (0021) (0018) (0026) (0028)

Country average 0436 0715 0754 0607 0746 0777(0082) (0101) (0109) (0091) (0143) (0164)

annual obs 2986 1450 1292 2986 1450 1292 countries 123 50 38 123 50 38

Notes Spearman rank correlation coefficient se in parentheses

187SAVING GROWTH AND INVESTMENT

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 2: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

and Weil (1994) who explicitly used the concept of Grangercausation We will analyze Carroll and Weil results in detailpartly for their intrinsic interest and partly to illustrate someof the methodological points that we want to make

When considering the association between saving andinvestment rates it is natural to think in terms of theintegration (or lack of) of international nancial marketsIndeed in an in uential contribution Feldstein and Horioka(1980) interpreted the cross-country correlation betweensaving and investment rates as evidence of low internationalcapital mobility In this case saving is likely to be a limitingfactor for investment A saving-to-investment link couldtherefore arise because lsquolsquoan increase in national saving has asubstantial effect on the level of investmentrsquorsquo (Feldstein andBacchetta (1991)) as investment must be supported bysaving and domestic rms compete for the ow of availabledomestic saving

This interpretation has often been challenged In fact inthe long run technological variables and the demographicstructure of the population could drive both variablesthereby inducing positive correlation even with perfectcapital mobility (Baxter and Crucini (1992) Taylor (1994)2

Our results show that the correlation between saving andinvestment is indeed a robust nding Moreover we showthat such a correlation has an important dynamic compo-nent in that lagged saving rates are strongly correlated withcurrent investment rates It is therefore interesting to estab-lish whether such a correlation survives also the introductionof various controls

Obviously Granger causation running from investment tosaving is also possible While the exact mechanisms at workare hard to spell out in detail if an increased demand forcapital goods stimulates savingmdashmaybe through interestrate effects or the endogenous development of the nancialinstruments that permit the mobilization of savingmdashsavingmight adjust to investment

The positive contemporaneous association between rateof investment and growth is usually explained in terms of acausal link running from the former variable to the latterSeveral well-known theoretical explanations can be offeredfor such a link Some growth models for instance suggestthat a rise in productivity growth causes both growth ratesand investment rates to move together (possibly coupledwith the accumulation of human capital) This is the type ofmechanism mentioned for instance by Barro (1991) whenconsidering the simultaneous determination of growth andinvestment rates (as well as fertility rates) and investigatedempirically more recently by Caselli Esquirrel and Lefort(1995) and Islam (1996) In what follows we stress onceagain the dynamic nature of the relationship betweeninvestment and growth and show that the dynamic correla-tion can be quite different from the contemporaneous ones

A dynamic link running from growth to investment mightalso hold Higher growth might drive saving up leading in

turn to higher investment However Blomstrom Lipsey andZejan (1996) suggest that accumulation might be a conse-quence of the growth process ignited by the growth-basedsaving change Furthermore higher growth can enhancefuture growth expectations and returns on investmentProvided that saving (possibly raised by the growth process)is not a limiting factor the accumulation of physical capitalwill nally take place

While in recent years several authors have used panels ofcountries to study a variety of phenomena no standardeconometric methodology has been developed for the analy-sis of this type of data a relative large panel of countriesThe second contribution of our paper is a methodologicalone We precede the empirical analysis with a discussion ofalternative econometric techniques and of the related meth-odological issues

In standard panel data analysis the presence of xedeffects correlated with the variables on the right-hand side ofthe equations of interest constitutes an important concernThe issue is particularly serious in the analysis of dynamicsystems in which the hypothesis of strong exogeneity of theindependent variables is obviously untenable Howeverwhile these problems are certainly relevant the analysis of apanel of countries puts the researcher in a slightly differentenvironment than that faced by an econometrician studyinglarge panels of individual observations The main differenceis in the fact that unlike with household-level data in whichtypically N (the number of individuals) is large and T (thenumber of periods) is small in analyzing a panel ofcountries N and T tend to have the same order of magnitudeFurthermore it is more natural to think about the asymp-totics of the problem as T-asymptotics rather thanN-asymptotics This will have an effect on the choice oftechniques used in the analysis Finally if one is interested incharacterizing the dynamic relationship among several vari-ables it is more natural to use concepts from the time-seriesliterature and use the N dimension of the sample to allow fordifferences among countries that can be of independentinterest

The rest of the paper is organized as follows In section IIwe discuss some methodological issues relevant for theeconometric analysis of dynamic models using panels ofcountries In section III we brie y describe the data set andpresent some evidence on the static correlations among thevariables of interest In section IV we analyze the robustnessof the Carroll and Weill results by using their estimators onthe new data set and also considering different econometrictechniques and different frequencies of the data In section Vinstead we switch to the analysis of annual data and applythree different types of estimators We rst assume that thetotal number of time observations we have is large enough toallow us to use lsquolsquobig Trsquorsquo asymptotic approximations We thenpresent some results obtained using a lsquolsquo xed T rsquorsquo estimatorNext we allow for across-country heterogeneity in thedynamic effects that link the three variables of interestFinally we present the estimates of a trivariate model in

2 Arguments based on the intertemporal countryrsquos budget constraint leadto the same conclusion (Argimon and Roldan (1994))

183SAVING GROWTH AND INVESTMENT

which we consider the variables of interests and theirinteractions simultaneously We conclude the section byanalyzing the effects of introducing various controls nor-mally used in the literature In section VI we summarize andinterpret the main results

II The Statistical Model and its Econometric Estimation

Preliminary to the empirical analysis we discuss someeconometric issues that are relevant to the study of thedynamic relationship between two or more variables ob-served over a relatively long time horizon and for a ratherlarge number of countries

A general representation of a dynamic model linking twovariables x and y is

yit 5 a 0 1 oj 5 1

q

a it jy yit 2 j

1 oj 5 1

p

b it jy xit 2 j 1 c t

y f iy 1 uit

y

(1)

xit 5 b 0 1 oj 5 1

m

a it jx yit 2 j

1 oj 5 1

n

b it jx xit 2 j 1 c t

x f ix 1 uit

x

(2)

Obviously such a system cannot be estimated withoutimposing some restrictions on its parameters This can bedone either in the time series or in the cross-sectionaldimension If the time-series variability is deemed sufficientto obtain reasonably precise estimates one could specify themodel by assuming that the parameters are constant overtime and might be variable across countries On the otherhand if one wants to exploit the cross-sectional variabilityone might let the parameters differ over time while beingconstant across countries Which of the two choices isfeasible is often dictated by the data available Howeverwhen the time and cross-sectional dimensions are roughly ofthe same order of magnitude (as it is in the case at hand) onefaces a real choice whose solution should be dictated by thenature of the phenomenon one is studying

An alternative way of thinking about the choice ofestimation techniques is to consider whether the cross-sectional or the time-series dimension has to increase inorder to derive the asymptotic distributions used in hypoth-esis testing In the analysis of country panels it is conceptu-ally awkward to consider N that goes to in nity On the otherhand the analysis that lets T go to in nity is the standardpractice in time-series analysis3 Furthermore if one is

interested in studying the dynamic relationship between twoor more variables either by testing the existence of Grangercausality or more generally by characterizing the dynamicrelationship between the variables under study it seemsnatural to consider a model that is exible but stable overtime The analysis of heterogeneity in impluse-responsefunctions across countries might be also interesting in itsown right

A Large N ( xed T) Models

Many recent studies of data sets similar to the one we usehave followed the microeconometric literature and appliedestimators that rely on the cross-sectional variability toidentify the model of interest This amounts to imposingconstancy of the parameters in equation (1) and (2) acrosscountries while at least in principle allowing them to varyover time Typically estimators with xed effects such asthose proposed by Holtz-Eakin Newey and Rosen (1988)(HNR hereafter) and Arellano and Bond (1991) (AB hereaf-ter) are used The model is often specialized to thefollowing expression to impose constancy of the parametersnot only across equations but also over time4

yit 5 a 0 1 oj 5 1

q

a jyyit 2 j 1 o

j 5 1

p

b jyxit 2 j 1 f i

y 1 ui ty (1a)

xi t 5 b 0 1 oj 5 1

m

a jxyit 2 j 1 o

j 5 1

n

b jxxit 2 j 1 f i

x 1 uitx (2a)

The coefficients a jx are relevant for the Granger causality

running from y to x while the coefficients b jy are relevant for

the Granger causality running in the opposite direction Weassume that the residuals of the two equations of the systemare uncorrelated with the variables on the right side and areiid The two variables however are in principle correlatedat a point in time that is the covariance between uit

x and u ity

is not necessarily zero Notice that because of the presenceof xed effects none of the observable variables on theright-hand side of the two equations is strongly exogenous

To eliminate the bias caused by the presence of xedeffects these equations are typically estimated in rstdifferences As rst-differencing induces MA(1) residualsone has to use some instrumental-variable technique HNRand AB stress that when the cross-sectional dimensionidenti es the model all the orthogonality restrictions im-plied by the dynamics of the system can be exploited toachieve efficiency5 In particular at each point in time t one

3 Also from a practical point of view it is often not obvious thatincreasing the number of the included countries provides additionalinformation when the quality of the data decreases as more countries areconsidered

4 As such a system is typically estimated using N-asymptotics The latterassumption can be easily relaxed (See HNR (1988) for instance)

5 Notice that in both equations we need to instrument both the(one-period) lagged yrsquos and the lagged xrsquos If one is willing to assume thatthe residuals of the two equations are contemporaneously uncorrelatedone can instrument the lagged yrsquos in equation (1) and the lagged xrsquos inequation (2)

184 THE REVIEW OF ECONOMICS AND STATISTICS

can use as valid instruments all the variables from time 1 totime t 2 s 2 1 (where s 5 max (m n p q) 6

While the application of the HNR or AB estimators isconceptually straightforward a few important caveats are inorder when the time dimension is not small and when thefocus is on a dynamic phenomenon such as Grangercausality As T increase the number of admissible instru-ments increases very quickly In our application for in-stance with two variables whose lags are valid instrumentsm 5 n 5 p 5 q 5 1 t 5 35 and N 5 50 (as it isapproximately the case in some of the results presentedbelow) by the time we get to the end of the sample there areclose to seventy valid instruments for no more than ftycross-sectional observations It is obvious that one cannotuse all of them In cases like this it is advisable to use only alimited number of lagged variables as instruments

An alternative way to tackle the problem which has oftenbeen employed is to use n-year averages (with n usuallyequal to 5 or 10) therefore arti cially reducing the time-series dimension of the sample This ltering is meant tocapture long-run relationships and abstract from uctuationsof business-cycle frequencies We favor the use of methodsthat explicitly use the time-series variation and possiblyexplore the existence of heterogeneity across countriesEven if one wants to use the lsquolarge Nrsquo estimators we argue infavor of annual observations rather than n-year averagesSome of the reasons follow7

1 Annual data provide information that is lost whenaveraging

2 Even if one is interested in identifying long-runrelationships it is not obvious that averaging over xed intervals will effectively eliminate business-cycle uctuations and make easier the emergence ofthe relationships of interest The length of the intervalover which averages are computed is arbitrary andthere is no guarantee that business cycles are cut in theright way as their length varies over time and acrosscountries

3 By averaging one commits oneself to the use ofcross-sectional variability to estimate the parametersof interest and discards the possibility of consideringcross-sectional heterogeneity in the parameters Thislimitation might be particularly severe when oneanalyzes several countries that could differ in manydimensions

4 By averaging an overall effect over a given timewindow is measured In the case at hand what weknow about the economic relationship among the

variables involved indicates that contrasting forces areoften at work The dynamic interplay of these forcescould well result in signi cant but opposed effectsmaybe acting with different lags that might eventuallycancel out once averaged Focusing only on thelong-run effect provided averaging does that pre-cludes the analysis of such short-run effects8

B Large T ( xed N) Models

An alternative to methods based on lsquolarge Nrsquo asymptoticsis to assume that the parameters are constant over time andexploit the time-series variability to estimate them In such asituation we can introduce exibility in the cross-sectionaldimension and let the coefficients of interest vary acrosscountries

The coefficients of our model represent the lagged effectsof growth saving and investment on the same variablesHowever the underlying mechanisms linking those vari-ables could differ across countries possibly due to institu-tional reasons or differences in preferences9 The questionthen is to determine whether the econometric techniquesthat we have illustratedmdashall assuming constancy acrosscountries of the underlying parametersmdashare still appropriatein the case in which those parameters are heterogeneous

The answer to this question obviously depends on thenature of the variation and on the general properties of themodel As discussed by Pesaran and Smith (1995) (PShereafter) if the coefficients of equation (1) and (2) areconstant over time but vary across countries techniques thatimpose parameter homogeneity do not yield consistentestimates Responsible of the biasmdashwhich persists regard-less of the size of N T and of any choice of instrumentsmdashisthe dynamic nature of the model On the other hand a meangroup estimator obtained by averaging the individual coun-tries estimates is unbiased and consistent

While wrongly assuming parameter constancy acrosscountries implies biased estimates of the underlying averageeffects a parsimoniously parameterized model yields more-precise estimates Within this familiar tradeoff betweenconsistency and efficiency the choice between homoge-neous lsquolsquopooledrsquorsquo estimators and their heterogeneous counter-parts does not reside in a formula but boils down to acase-by-case problem of model selection10

6 By using a GLS-type transformation to account for the MA structure ofthe residuals one obtains a further gain in efficiency Arellano and Bover(1995) show that one can express the model in terms of orthogonaldeviations to obtain a simple way of computing the HNR or AB estimator

7 The same considerations arise also in different frameworks Forexample the Feldstein-Horioka type regressions have been recentlyestimated on annual series rather than on the more conventional timeaverages See among others Sinn (1992)

8 It has also been argued that the consideration of time averages reducesthe relevance of measurement error Of course this argument is valid onlyif measurement errors are not perfectly correlated over time

9 In such a situation rather than in the complete characterization of thecoefficients in all countries one might be interested in the averagecoefficient

10 Baltagi and Griffin (1997) compare out-of-sample forecast perfor-mances of an array of homogeneous and heterogeneous estimators They nd that pooled estimators fare relatively well thus showing (for theparticular case at hand) that the heterogeneity inevitably characterizingdifferent countries and the ensuing pooled estimatesrsquo bias should notnecessarily lead to the rejection of the homogeneity assumption

185SAVING GROWTH AND INVESTMENT

C Large N or Large T

As in our data set N and T are roughly of the same order ofmagnitude the presence of a tension between exibility inthe time-series and in the cross-sectional dimension isevident The resolution of this tension absent in the analysisof individual data surveys in which T is typically small andinferences are conducted using lsquolarge Nrsquo asymptotics obvi-ously affects the model speci cation and the choice ofestimators

Given these considerations the best strategy is to estimaterich and exible dynamic models that allow for differencesin short- and long-run coefficients and use estimators thatappeal to lsquolarge T rsquo asymptotics to achieve consistency whileefficiently exploiting all the available information Thesemodels can and should also consider the possibilities that the(dynamic) relationships of interest are different acrosscountries

Obviously the proposed approach imposes different typesof constraints on the researcher The most important is thenecessity to consider coefficients that are constant over timeObviously it is necessary to assume that the availablesample period is long enough to allow for reasonably preciseestimates of time-invariant country coefficients11 Partlybecause of these reasons and partly to make our analysiscomparable to a large body of the literature we presentresults obtained estimating both classes of models discussedin this section

III The Data Set

A The Nature of the Data Set and its Construction

As mentioned in the introduction we use a new panel ofcountries (the World Saving Database) recently gathered atthe World Bank As the data-gathering effort is described indetail by Loayza et al (1998) here we provide a very briefdiscussion of the structure of the panel focusing in particu-lar on those aspects that are relevant for our analysis Withthe exception of total population gures originating fromthe World Bank database all the data are from NationalAccounts and follow their standard conventions The data-base includes 150 countries and spans the years 1960 to1995 However not all variables are available for everycountry and for every year In particular the population datacover the period 1960 to 1994 only As a consequence ouranalysis is restricted to those years

For each country the variables that we use are the rate ofgrowth of annual real per capita gross national product thesaving rate and the rate of investment All these series aremeasured in local currencies The saving rates are computedas nominal gross national saving over nominal gross na-tional income while the investment rates are computed as

nominal gross xed investment over nominal gross nationalproduct Growth is measured as the rate of growth in real percapita GNP (de ated with the GDP de ator)12

We use three different samples of countries The rst is asclose as possible to the whole set of countries included in theWorld Bank database We exclude only those countrieswhose annual income saving or investment were notrecorded at all or are recorded for less than a ve-yearinterval and those countries for which the relevant serieshave missing values in the middle of the sample period Thisprocedure leaves us with a sample consisting of 123countries We call this our lsquolsquowholersquorsquo sample The other twosamples trade-off the T and N dimension The second sampleconsists of the fty countries for which all variables areavailable every year in the interval 1965ndash1993 Our thirdsample consists only of those countries whose variables areavailable every year from 1961 to 1994 Only 38 countriesare included We also use for comparison purposes only theCarroll and Weil (1994) 64-countries sample All countriesin this sample are also in our whole sample with theexception of Tanzania and Zimbabwe which were excludedbecause of the unavailability of data13

In the next section we analyze Carroll and Weilrsquos fullsample results in addition to the analysis based on annualdata We also look at nonoverlapping ve-year averages ofgrowth saving and investment rates for each country14 Theinformation on the number of countries in each of the datasets we use is summarized in table 1

B Contemporaneous Correlations and Rank Correlationsbetween Saving Investment and Growth Rates

We start the analysis of the data set computing somesimple correlation and rank correlation coefficients betweenthe three variables that constitute the main focus of thisstudymdashnamely the saving rate the investment rate and the

11 Another limitation is the fact that one is constrained to consider onlysome classes of error models For instance if the residuals of the model inequation (1) and (2) are of the autoregressive type and there are xedeffects it is impossible to nd instruments that identify the relationships ofinterest

12 To avoid the loss of a large number of observations we did not performany PPP adjustment The same applies to the de ation of GNP by the GDPde ator

13 Dropping these countries from this sample does not change the resultsin any signi cant way

14 Given the period covered by our sample for each country the rstobservation on average growth is in fact a four-year average If there wereno missing values we would have seven observations for each countryHowever many observations are missing for the rst sample consideredThis implies that for these countries the averaged data can sometimesresult from the averaging of relatively short series Obviously this problemdoes not arise when using the balanced data sets

TABLE 1mdashDESCRIPTION OF THE DATA SET

Number ofCountries

Of Which WithData 1961ndash1994(1965ndash1993 for

Data Set 2)Average Number ofYears Per Country

Data set 1 123 38 24Data set 2 50 50 29Data set 3 38 38 34CW data set 64 64 29 (5-year average)

186 THE REVIEW OF ECONOMICS AND STATISTICS

growth rate Unlike in the rest of the analysis our interesthere is merely for their static relationships

As in any panel our data has set two dimensions thetemporal and the cross-sectional Therefore even whencomputing simple correlations there are several options Foreach of the three pairs of variables we rst consider thewhole data set that is we use each country-year observa-tion We then average for each country all the availableinformation and therefore focus on the cross-sectionalvariability15 Finally we compute for each year the correla-tion coefficient (in the cross section) between the twovariables of interest and consider the variation of thisparameter over time

We start by comparing the coefficient of variation of thethree variables of interest In data set 1 growth rates are byfar the most volatile The coefficient of variation for thisvariable is 330 to be compared with 049 and 035 forsaving and investment rates respectively This ranking invariability is unchanged when we consider country (time-series) averages of the variables In this case the threecoefficients of variations are 173 046 and 029 Noticethat in this case the variability in growth rates as measuredby the coefficient of variation is almost halved while thereduction in the other two variables is modest In data sets 2and 3 whose countries are more similar the coefficients ofvariation while slightly smaller follow the same pattern

In table 2 we report correlation coefficients and Spear-man rank correlation coefficients computed for the threepairs of variables and in the three data sets We report boththe correlations obtained with all annual observations andwith country averages

In the table the correlation coefficients are alwayspositive Typically the coefficients computed on annual dataincrease by 30 to 50 going from data set 1 to data set 3(that is going from a large group of nonhomogeneouscountries to a more restricted number of more similarcountries observed for longer time spans) Saving-growth

correlations are somewhat higher than investment-growthcorrelations but the strongest link turns out to be thatbetween saving and investment We get similar results forrank correlations which should reduce the effect of outliers

When using time-averaged observations correlation coef- cients increase in most cases The only exception is theslight decline in the simple correlation between saving andinvestment rates in data set 1 Even in that case however thecorresponding rank correlation increases if only slightlyThe largest increase is registered for the investment andgrowth rates pair for which the correlations more thandouble

In gure 1 we plot the contemporaneous correlationcoefficients computed using all saving-growth pairs of agiven year against time In the same graph we plot the timeseries obtained using only the countries in the balancedpanel with fty countries The correlation coefficients arepositive for all but four years In the rst half of the periodcorrelation coefficients usually uctuate in the range of 02to 04 for both samples Starting in 1977 however and untilthe end of the sample period the uctuations of thecorrelation coefficients for data set 1 became more marked16

Two effects are likely to be at play On the one hand severaladditional countries lsquolsquoenterrsquorsquo the data set around this periodmoreover the correlation for the preexisting countries mightalso be varying In fact if the same correlations arecomputed using only the countries for which data areavailable over the sample 1965ndash1993 (often middle- andhigh-income countries) a different picture emerges Correla-tion coefficients are somewhat increasing over time and inthe 1980s uctuate around 05 Over that period data set 1correlations drop with respect to the corresponding values ofdata set 2 Short-run linkages turn out therefore quite weakparticularly for those countries that enter the sample

In gure 2 we plot the annual correlations betweengrowth and investment rates (across countries) against timeAgain it must be stressed that the number of countries that

15 As data set 1 is a not balanced panel the country averages and theannual (cross section) correlations are computed using a (possibly)different number of observations

16 The coefficients of variation computed for the two subsamples1961ndash1976 and 1977ndash1994 are respectively 0509 and 0745

TABLE 2mdashCORRELATION COMPUTED ON ANNUAL DATA DATA SETS 1 2 AND 3

CorrelData Set 1Corr Coeff

Data Set 2Corr Coeff

Data Set 3Corr Coeff

Data Set 1Rank Corr Coeff

Data Set 2Rank Corr Coeff

Data Set 3Rank Corr Coeff

S G Annual 0253 0370 0332 0323 0372 0323(0018) (0024) (0026) (0018) (0026) (0028)

Country average 0376 0666 0492 0522 0623 0525(0084) (0108) (0145) (0091) (0143) (0164)

I G Annual 0165 0227 0242 0211 0240 0243(0018) (0026) (0027) (0018) (0026) (0028)

Country average 0319 0601 0652 0409 0585 0650(0086) (0126) (0126) (0091) (0143) (0164)

S I Annual 0483 0592 0658 0614 0613 0665(0016) (0021) (0021) (0018) (0026) (0028)

Country average 0436 0715 0754 0607 0746 0777(0082) (0101) (0109) (0091) (0143) (0164)

annual obs 2986 1450 1292 2986 1450 1292 countries 123 50 38 123 50 38

Notes Spearman rank correlation coefficient se in parentheses

187SAVING GROWTH AND INVESTMENT

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 3: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

which we consider the variables of interests and theirinteractions simultaneously We conclude the section byanalyzing the effects of introducing various controls nor-mally used in the literature In section VI we summarize andinterpret the main results

II The Statistical Model and its Econometric Estimation

Preliminary to the empirical analysis we discuss someeconometric issues that are relevant to the study of thedynamic relationship between two or more variables ob-served over a relatively long time horizon and for a ratherlarge number of countries

A general representation of a dynamic model linking twovariables x and y is

yit 5 a 0 1 oj 5 1

q

a it jy yit 2 j

1 oj 5 1

p

b it jy xit 2 j 1 c t

y f iy 1 uit

y

(1)

xit 5 b 0 1 oj 5 1

m

a it jx yit 2 j

1 oj 5 1

n

b it jx xit 2 j 1 c t

x f ix 1 uit

x

(2)

Obviously such a system cannot be estimated withoutimposing some restrictions on its parameters This can bedone either in the time series or in the cross-sectionaldimension If the time-series variability is deemed sufficientto obtain reasonably precise estimates one could specify themodel by assuming that the parameters are constant overtime and might be variable across countries On the otherhand if one wants to exploit the cross-sectional variabilityone might let the parameters differ over time while beingconstant across countries Which of the two choices isfeasible is often dictated by the data available Howeverwhen the time and cross-sectional dimensions are roughly ofthe same order of magnitude (as it is in the case at hand) onefaces a real choice whose solution should be dictated by thenature of the phenomenon one is studying

An alternative way of thinking about the choice ofestimation techniques is to consider whether the cross-sectional or the time-series dimension has to increase inorder to derive the asymptotic distributions used in hypoth-esis testing In the analysis of country panels it is conceptu-ally awkward to consider N that goes to in nity On the otherhand the analysis that lets T go to in nity is the standardpractice in time-series analysis3 Furthermore if one is

interested in studying the dynamic relationship between twoor more variables either by testing the existence of Grangercausality or more generally by characterizing the dynamicrelationship between the variables under study it seemsnatural to consider a model that is exible but stable overtime The analysis of heterogeneity in impluse-responsefunctions across countries might be also interesting in itsown right

A Large N ( xed T) Models

Many recent studies of data sets similar to the one we usehave followed the microeconometric literature and appliedestimators that rely on the cross-sectional variability toidentify the model of interest This amounts to imposingconstancy of the parameters in equation (1) and (2) acrosscountries while at least in principle allowing them to varyover time Typically estimators with xed effects such asthose proposed by Holtz-Eakin Newey and Rosen (1988)(HNR hereafter) and Arellano and Bond (1991) (AB hereaf-ter) are used The model is often specialized to thefollowing expression to impose constancy of the parametersnot only across equations but also over time4

yit 5 a 0 1 oj 5 1

q

a jyyit 2 j 1 o

j 5 1

p

b jyxit 2 j 1 f i

y 1 ui ty (1a)

xi t 5 b 0 1 oj 5 1

m

a jxyit 2 j 1 o

j 5 1

n

b jxxit 2 j 1 f i

x 1 uitx (2a)

The coefficients a jx are relevant for the Granger causality

running from y to x while the coefficients b jy are relevant for

the Granger causality running in the opposite direction Weassume that the residuals of the two equations of the systemare uncorrelated with the variables on the right side and areiid The two variables however are in principle correlatedat a point in time that is the covariance between uit

x and u ity

is not necessarily zero Notice that because of the presenceof xed effects none of the observable variables on theright-hand side of the two equations is strongly exogenous

To eliminate the bias caused by the presence of xedeffects these equations are typically estimated in rstdifferences As rst-differencing induces MA(1) residualsone has to use some instrumental-variable technique HNRand AB stress that when the cross-sectional dimensionidenti es the model all the orthogonality restrictions im-plied by the dynamics of the system can be exploited toachieve efficiency5 In particular at each point in time t one

3 Also from a practical point of view it is often not obvious thatincreasing the number of the included countries provides additionalinformation when the quality of the data decreases as more countries areconsidered

4 As such a system is typically estimated using N-asymptotics The latterassumption can be easily relaxed (See HNR (1988) for instance)

5 Notice that in both equations we need to instrument both the(one-period) lagged yrsquos and the lagged xrsquos If one is willing to assume thatthe residuals of the two equations are contemporaneously uncorrelatedone can instrument the lagged yrsquos in equation (1) and the lagged xrsquos inequation (2)

184 THE REVIEW OF ECONOMICS AND STATISTICS

can use as valid instruments all the variables from time 1 totime t 2 s 2 1 (where s 5 max (m n p q) 6

While the application of the HNR or AB estimators isconceptually straightforward a few important caveats are inorder when the time dimension is not small and when thefocus is on a dynamic phenomenon such as Grangercausality As T increase the number of admissible instru-ments increases very quickly In our application for in-stance with two variables whose lags are valid instrumentsm 5 n 5 p 5 q 5 1 t 5 35 and N 5 50 (as it isapproximately the case in some of the results presentedbelow) by the time we get to the end of the sample there areclose to seventy valid instruments for no more than ftycross-sectional observations It is obvious that one cannotuse all of them In cases like this it is advisable to use only alimited number of lagged variables as instruments

An alternative way to tackle the problem which has oftenbeen employed is to use n-year averages (with n usuallyequal to 5 or 10) therefore arti cially reducing the time-series dimension of the sample This ltering is meant tocapture long-run relationships and abstract from uctuationsof business-cycle frequencies We favor the use of methodsthat explicitly use the time-series variation and possiblyexplore the existence of heterogeneity across countriesEven if one wants to use the lsquolarge Nrsquo estimators we argue infavor of annual observations rather than n-year averagesSome of the reasons follow7

1 Annual data provide information that is lost whenaveraging

2 Even if one is interested in identifying long-runrelationships it is not obvious that averaging over xed intervals will effectively eliminate business-cycle uctuations and make easier the emergence ofthe relationships of interest The length of the intervalover which averages are computed is arbitrary andthere is no guarantee that business cycles are cut in theright way as their length varies over time and acrosscountries

3 By averaging one commits oneself to the use ofcross-sectional variability to estimate the parametersof interest and discards the possibility of consideringcross-sectional heterogeneity in the parameters Thislimitation might be particularly severe when oneanalyzes several countries that could differ in manydimensions

4 By averaging an overall effect over a given timewindow is measured In the case at hand what weknow about the economic relationship among the

variables involved indicates that contrasting forces areoften at work The dynamic interplay of these forcescould well result in signi cant but opposed effectsmaybe acting with different lags that might eventuallycancel out once averaged Focusing only on thelong-run effect provided averaging does that pre-cludes the analysis of such short-run effects8

B Large T ( xed N) Models

An alternative to methods based on lsquolarge Nrsquo asymptoticsis to assume that the parameters are constant over time andexploit the time-series variability to estimate them In such asituation we can introduce exibility in the cross-sectionaldimension and let the coefficients of interest vary acrosscountries

The coefficients of our model represent the lagged effectsof growth saving and investment on the same variablesHowever the underlying mechanisms linking those vari-ables could differ across countries possibly due to institu-tional reasons or differences in preferences9 The questionthen is to determine whether the econometric techniquesthat we have illustratedmdashall assuming constancy acrosscountries of the underlying parametersmdashare still appropriatein the case in which those parameters are heterogeneous

The answer to this question obviously depends on thenature of the variation and on the general properties of themodel As discussed by Pesaran and Smith (1995) (PShereafter) if the coefficients of equation (1) and (2) areconstant over time but vary across countries techniques thatimpose parameter homogeneity do not yield consistentestimates Responsible of the biasmdashwhich persists regard-less of the size of N T and of any choice of instrumentsmdashisthe dynamic nature of the model On the other hand a meangroup estimator obtained by averaging the individual coun-tries estimates is unbiased and consistent

While wrongly assuming parameter constancy acrosscountries implies biased estimates of the underlying averageeffects a parsimoniously parameterized model yields more-precise estimates Within this familiar tradeoff betweenconsistency and efficiency the choice between homoge-neous lsquolsquopooledrsquorsquo estimators and their heterogeneous counter-parts does not reside in a formula but boils down to acase-by-case problem of model selection10

6 By using a GLS-type transformation to account for the MA structure ofthe residuals one obtains a further gain in efficiency Arellano and Bover(1995) show that one can express the model in terms of orthogonaldeviations to obtain a simple way of computing the HNR or AB estimator

7 The same considerations arise also in different frameworks Forexample the Feldstein-Horioka type regressions have been recentlyestimated on annual series rather than on the more conventional timeaverages See among others Sinn (1992)

8 It has also been argued that the consideration of time averages reducesthe relevance of measurement error Of course this argument is valid onlyif measurement errors are not perfectly correlated over time

9 In such a situation rather than in the complete characterization of thecoefficients in all countries one might be interested in the averagecoefficient

10 Baltagi and Griffin (1997) compare out-of-sample forecast perfor-mances of an array of homogeneous and heterogeneous estimators They nd that pooled estimators fare relatively well thus showing (for theparticular case at hand) that the heterogeneity inevitably characterizingdifferent countries and the ensuing pooled estimatesrsquo bias should notnecessarily lead to the rejection of the homogeneity assumption

185SAVING GROWTH AND INVESTMENT

C Large N or Large T

As in our data set N and T are roughly of the same order ofmagnitude the presence of a tension between exibility inthe time-series and in the cross-sectional dimension isevident The resolution of this tension absent in the analysisof individual data surveys in which T is typically small andinferences are conducted using lsquolarge Nrsquo asymptotics obvi-ously affects the model speci cation and the choice ofestimators

Given these considerations the best strategy is to estimaterich and exible dynamic models that allow for differencesin short- and long-run coefficients and use estimators thatappeal to lsquolarge T rsquo asymptotics to achieve consistency whileefficiently exploiting all the available information Thesemodels can and should also consider the possibilities that the(dynamic) relationships of interest are different acrosscountries

Obviously the proposed approach imposes different typesof constraints on the researcher The most important is thenecessity to consider coefficients that are constant over timeObviously it is necessary to assume that the availablesample period is long enough to allow for reasonably preciseestimates of time-invariant country coefficients11 Partlybecause of these reasons and partly to make our analysiscomparable to a large body of the literature we presentresults obtained estimating both classes of models discussedin this section

III The Data Set

A The Nature of the Data Set and its Construction

As mentioned in the introduction we use a new panel ofcountries (the World Saving Database) recently gathered atthe World Bank As the data-gathering effort is described indetail by Loayza et al (1998) here we provide a very briefdiscussion of the structure of the panel focusing in particu-lar on those aspects that are relevant for our analysis Withthe exception of total population gures originating fromthe World Bank database all the data are from NationalAccounts and follow their standard conventions The data-base includes 150 countries and spans the years 1960 to1995 However not all variables are available for everycountry and for every year In particular the population datacover the period 1960 to 1994 only As a consequence ouranalysis is restricted to those years

For each country the variables that we use are the rate ofgrowth of annual real per capita gross national product thesaving rate and the rate of investment All these series aremeasured in local currencies The saving rates are computedas nominal gross national saving over nominal gross na-tional income while the investment rates are computed as

nominal gross xed investment over nominal gross nationalproduct Growth is measured as the rate of growth in real percapita GNP (de ated with the GDP de ator)12

We use three different samples of countries The rst is asclose as possible to the whole set of countries included in theWorld Bank database We exclude only those countrieswhose annual income saving or investment were notrecorded at all or are recorded for less than a ve-yearinterval and those countries for which the relevant serieshave missing values in the middle of the sample period Thisprocedure leaves us with a sample consisting of 123countries We call this our lsquolsquowholersquorsquo sample The other twosamples trade-off the T and N dimension The second sampleconsists of the fty countries for which all variables areavailable every year in the interval 1965ndash1993 Our thirdsample consists only of those countries whose variables areavailable every year from 1961 to 1994 Only 38 countriesare included We also use for comparison purposes only theCarroll and Weil (1994) 64-countries sample All countriesin this sample are also in our whole sample with theexception of Tanzania and Zimbabwe which were excludedbecause of the unavailability of data13

In the next section we analyze Carroll and Weilrsquos fullsample results in addition to the analysis based on annualdata We also look at nonoverlapping ve-year averages ofgrowth saving and investment rates for each country14 Theinformation on the number of countries in each of the datasets we use is summarized in table 1

B Contemporaneous Correlations and Rank Correlationsbetween Saving Investment and Growth Rates

We start the analysis of the data set computing somesimple correlation and rank correlation coefficients betweenthe three variables that constitute the main focus of thisstudymdashnamely the saving rate the investment rate and the

11 Another limitation is the fact that one is constrained to consider onlysome classes of error models For instance if the residuals of the model inequation (1) and (2) are of the autoregressive type and there are xedeffects it is impossible to nd instruments that identify the relationships ofinterest

12 To avoid the loss of a large number of observations we did not performany PPP adjustment The same applies to the de ation of GNP by the GDPde ator

13 Dropping these countries from this sample does not change the resultsin any signi cant way

14 Given the period covered by our sample for each country the rstobservation on average growth is in fact a four-year average If there wereno missing values we would have seven observations for each countryHowever many observations are missing for the rst sample consideredThis implies that for these countries the averaged data can sometimesresult from the averaging of relatively short series Obviously this problemdoes not arise when using the balanced data sets

TABLE 1mdashDESCRIPTION OF THE DATA SET

Number ofCountries

Of Which WithData 1961ndash1994(1965ndash1993 for

Data Set 2)Average Number ofYears Per Country

Data set 1 123 38 24Data set 2 50 50 29Data set 3 38 38 34CW data set 64 64 29 (5-year average)

186 THE REVIEW OF ECONOMICS AND STATISTICS

growth rate Unlike in the rest of the analysis our interesthere is merely for their static relationships

As in any panel our data has set two dimensions thetemporal and the cross-sectional Therefore even whencomputing simple correlations there are several options Foreach of the three pairs of variables we rst consider thewhole data set that is we use each country-year observa-tion We then average for each country all the availableinformation and therefore focus on the cross-sectionalvariability15 Finally we compute for each year the correla-tion coefficient (in the cross section) between the twovariables of interest and consider the variation of thisparameter over time

We start by comparing the coefficient of variation of thethree variables of interest In data set 1 growth rates are byfar the most volatile The coefficient of variation for thisvariable is 330 to be compared with 049 and 035 forsaving and investment rates respectively This ranking invariability is unchanged when we consider country (time-series) averages of the variables In this case the threecoefficients of variations are 173 046 and 029 Noticethat in this case the variability in growth rates as measuredby the coefficient of variation is almost halved while thereduction in the other two variables is modest In data sets 2and 3 whose countries are more similar the coefficients ofvariation while slightly smaller follow the same pattern

In table 2 we report correlation coefficients and Spear-man rank correlation coefficients computed for the threepairs of variables and in the three data sets We report boththe correlations obtained with all annual observations andwith country averages

In the table the correlation coefficients are alwayspositive Typically the coefficients computed on annual dataincrease by 30 to 50 going from data set 1 to data set 3(that is going from a large group of nonhomogeneouscountries to a more restricted number of more similarcountries observed for longer time spans) Saving-growth

correlations are somewhat higher than investment-growthcorrelations but the strongest link turns out to be thatbetween saving and investment We get similar results forrank correlations which should reduce the effect of outliers

When using time-averaged observations correlation coef- cients increase in most cases The only exception is theslight decline in the simple correlation between saving andinvestment rates in data set 1 Even in that case however thecorresponding rank correlation increases if only slightlyThe largest increase is registered for the investment andgrowth rates pair for which the correlations more thandouble

In gure 1 we plot the contemporaneous correlationcoefficients computed using all saving-growth pairs of agiven year against time In the same graph we plot the timeseries obtained using only the countries in the balancedpanel with fty countries The correlation coefficients arepositive for all but four years In the rst half of the periodcorrelation coefficients usually uctuate in the range of 02to 04 for both samples Starting in 1977 however and untilthe end of the sample period the uctuations of thecorrelation coefficients for data set 1 became more marked16

Two effects are likely to be at play On the one hand severaladditional countries lsquolsquoenterrsquorsquo the data set around this periodmoreover the correlation for the preexisting countries mightalso be varying In fact if the same correlations arecomputed using only the countries for which data areavailable over the sample 1965ndash1993 (often middle- andhigh-income countries) a different picture emerges Correla-tion coefficients are somewhat increasing over time and inthe 1980s uctuate around 05 Over that period data set 1correlations drop with respect to the corresponding values ofdata set 2 Short-run linkages turn out therefore quite weakparticularly for those countries that enter the sample

In gure 2 we plot the annual correlations betweengrowth and investment rates (across countries) against timeAgain it must be stressed that the number of countries that

15 As data set 1 is a not balanced panel the country averages and theannual (cross section) correlations are computed using a (possibly)different number of observations

16 The coefficients of variation computed for the two subsamples1961ndash1976 and 1977ndash1994 are respectively 0509 and 0745

TABLE 2mdashCORRELATION COMPUTED ON ANNUAL DATA DATA SETS 1 2 AND 3

CorrelData Set 1Corr Coeff

Data Set 2Corr Coeff

Data Set 3Corr Coeff

Data Set 1Rank Corr Coeff

Data Set 2Rank Corr Coeff

Data Set 3Rank Corr Coeff

S G Annual 0253 0370 0332 0323 0372 0323(0018) (0024) (0026) (0018) (0026) (0028)

Country average 0376 0666 0492 0522 0623 0525(0084) (0108) (0145) (0091) (0143) (0164)

I G Annual 0165 0227 0242 0211 0240 0243(0018) (0026) (0027) (0018) (0026) (0028)

Country average 0319 0601 0652 0409 0585 0650(0086) (0126) (0126) (0091) (0143) (0164)

S I Annual 0483 0592 0658 0614 0613 0665(0016) (0021) (0021) (0018) (0026) (0028)

Country average 0436 0715 0754 0607 0746 0777(0082) (0101) (0109) (0091) (0143) (0164)

annual obs 2986 1450 1292 2986 1450 1292 countries 123 50 38 123 50 38

Notes Spearman rank correlation coefficient se in parentheses

187SAVING GROWTH AND INVESTMENT

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 4: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

can use as valid instruments all the variables from time 1 totime t 2 s 2 1 (where s 5 max (m n p q) 6

While the application of the HNR or AB estimators isconceptually straightforward a few important caveats are inorder when the time dimension is not small and when thefocus is on a dynamic phenomenon such as Grangercausality As T increase the number of admissible instru-ments increases very quickly In our application for in-stance with two variables whose lags are valid instrumentsm 5 n 5 p 5 q 5 1 t 5 35 and N 5 50 (as it isapproximately the case in some of the results presentedbelow) by the time we get to the end of the sample there areclose to seventy valid instruments for no more than ftycross-sectional observations It is obvious that one cannotuse all of them In cases like this it is advisable to use only alimited number of lagged variables as instruments

An alternative way to tackle the problem which has oftenbeen employed is to use n-year averages (with n usuallyequal to 5 or 10) therefore arti cially reducing the time-series dimension of the sample This ltering is meant tocapture long-run relationships and abstract from uctuationsof business-cycle frequencies We favor the use of methodsthat explicitly use the time-series variation and possiblyexplore the existence of heterogeneity across countriesEven if one wants to use the lsquolarge Nrsquo estimators we argue infavor of annual observations rather than n-year averagesSome of the reasons follow7

1 Annual data provide information that is lost whenaveraging

2 Even if one is interested in identifying long-runrelationships it is not obvious that averaging over xed intervals will effectively eliminate business-cycle uctuations and make easier the emergence ofthe relationships of interest The length of the intervalover which averages are computed is arbitrary andthere is no guarantee that business cycles are cut in theright way as their length varies over time and acrosscountries

3 By averaging one commits oneself to the use ofcross-sectional variability to estimate the parametersof interest and discards the possibility of consideringcross-sectional heterogeneity in the parameters Thislimitation might be particularly severe when oneanalyzes several countries that could differ in manydimensions

4 By averaging an overall effect over a given timewindow is measured In the case at hand what weknow about the economic relationship among the

variables involved indicates that contrasting forces areoften at work The dynamic interplay of these forcescould well result in signi cant but opposed effectsmaybe acting with different lags that might eventuallycancel out once averaged Focusing only on thelong-run effect provided averaging does that pre-cludes the analysis of such short-run effects8

B Large T ( xed N) Models

An alternative to methods based on lsquolarge Nrsquo asymptoticsis to assume that the parameters are constant over time andexploit the time-series variability to estimate them In such asituation we can introduce exibility in the cross-sectionaldimension and let the coefficients of interest vary acrosscountries

The coefficients of our model represent the lagged effectsof growth saving and investment on the same variablesHowever the underlying mechanisms linking those vari-ables could differ across countries possibly due to institu-tional reasons or differences in preferences9 The questionthen is to determine whether the econometric techniquesthat we have illustratedmdashall assuming constancy acrosscountries of the underlying parametersmdashare still appropriatein the case in which those parameters are heterogeneous

The answer to this question obviously depends on thenature of the variation and on the general properties of themodel As discussed by Pesaran and Smith (1995) (PShereafter) if the coefficients of equation (1) and (2) areconstant over time but vary across countries techniques thatimpose parameter homogeneity do not yield consistentestimates Responsible of the biasmdashwhich persists regard-less of the size of N T and of any choice of instrumentsmdashisthe dynamic nature of the model On the other hand a meangroup estimator obtained by averaging the individual coun-tries estimates is unbiased and consistent

While wrongly assuming parameter constancy acrosscountries implies biased estimates of the underlying averageeffects a parsimoniously parameterized model yields more-precise estimates Within this familiar tradeoff betweenconsistency and efficiency the choice between homoge-neous lsquolsquopooledrsquorsquo estimators and their heterogeneous counter-parts does not reside in a formula but boils down to acase-by-case problem of model selection10

6 By using a GLS-type transformation to account for the MA structure ofthe residuals one obtains a further gain in efficiency Arellano and Bover(1995) show that one can express the model in terms of orthogonaldeviations to obtain a simple way of computing the HNR or AB estimator

7 The same considerations arise also in different frameworks Forexample the Feldstein-Horioka type regressions have been recentlyestimated on annual series rather than on the more conventional timeaverages See among others Sinn (1992)

8 It has also been argued that the consideration of time averages reducesthe relevance of measurement error Of course this argument is valid onlyif measurement errors are not perfectly correlated over time

9 In such a situation rather than in the complete characterization of thecoefficients in all countries one might be interested in the averagecoefficient

10 Baltagi and Griffin (1997) compare out-of-sample forecast perfor-mances of an array of homogeneous and heterogeneous estimators They nd that pooled estimators fare relatively well thus showing (for theparticular case at hand) that the heterogeneity inevitably characterizingdifferent countries and the ensuing pooled estimatesrsquo bias should notnecessarily lead to the rejection of the homogeneity assumption

185SAVING GROWTH AND INVESTMENT

C Large N or Large T

As in our data set N and T are roughly of the same order ofmagnitude the presence of a tension between exibility inthe time-series and in the cross-sectional dimension isevident The resolution of this tension absent in the analysisof individual data surveys in which T is typically small andinferences are conducted using lsquolarge Nrsquo asymptotics obvi-ously affects the model speci cation and the choice ofestimators

Given these considerations the best strategy is to estimaterich and exible dynamic models that allow for differencesin short- and long-run coefficients and use estimators thatappeal to lsquolarge T rsquo asymptotics to achieve consistency whileefficiently exploiting all the available information Thesemodels can and should also consider the possibilities that the(dynamic) relationships of interest are different acrosscountries

Obviously the proposed approach imposes different typesof constraints on the researcher The most important is thenecessity to consider coefficients that are constant over timeObviously it is necessary to assume that the availablesample period is long enough to allow for reasonably preciseestimates of time-invariant country coefficients11 Partlybecause of these reasons and partly to make our analysiscomparable to a large body of the literature we presentresults obtained estimating both classes of models discussedin this section

III The Data Set

A The Nature of the Data Set and its Construction

As mentioned in the introduction we use a new panel ofcountries (the World Saving Database) recently gathered atthe World Bank As the data-gathering effort is described indetail by Loayza et al (1998) here we provide a very briefdiscussion of the structure of the panel focusing in particu-lar on those aspects that are relevant for our analysis Withthe exception of total population gures originating fromthe World Bank database all the data are from NationalAccounts and follow their standard conventions The data-base includes 150 countries and spans the years 1960 to1995 However not all variables are available for everycountry and for every year In particular the population datacover the period 1960 to 1994 only As a consequence ouranalysis is restricted to those years

For each country the variables that we use are the rate ofgrowth of annual real per capita gross national product thesaving rate and the rate of investment All these series aremeasured in local currencies The saving rates are computedas nominal gross national saving over nominal gross na-tional income while the investment rates are computed as

nominal gross xed investment over nominal gross nationalproduct Growth is measured as the rate of growth in real percapita GNP (de ated with the GDP de ator)12

We use three different samples of countries The rst is asclose as possible to the whole set of countries included in theWorld Bank database We exclude only those countrieswhose annual income saving or investment were notrecorded at all or are recorded for less than a ve-yearinterval and those countries for which the relevant serieshave missing values in the middle of the sample period Thisprocedure leaves us with a sample consisting of 123countries We call this our lsquolsquowholersquorsquo sample The other twosamples trade-off the T and N dimension The second sampleconsists of the fty countries for which all variables areavailable every year in the interval 1965ndash1993 Our thirdsample consists only of those countries whose variables areavailable every year from 1961 to 1994 Only 38 countriesare included We also use for comparison purposes only theCarroll and Weil (1994) 64-countries sample All countriesin this sample are also in our whole sample with theexception of Tanzania and Zimbabwe which were excludedbecause of the unavailability of data13

In the next section we analyze Carroll and Weilrsquos fullsample results in addition to the analysis based on annualdata We also look at nonoverlapping ve-year averages ofgrowth saving and investment rates for each country14 Theinformation on the number of countries in each of the datasets we use is summarized in table 1

B Contemporaneous Correlations and Rank Correlationsbetween Saving Investment and Growth Rates

We start the analysis of the data set computing somesimple correlation and rank correlation coefficients betweenthe three variables that constitute the main focus of thisstudymdashnamely the saving rate the investment rate and the

11 Another limitation is the fact that one is constrained to consider onlysome classes of error models For instance if the residuals of the model inequation (1) and (2) are of the autoregressive type and there are xedeffects it is impossible to nd instruments that identify the relationships ofinterest

12 To avoid the loss of a large number of observations we did not performany PPP adjustment The same applies to the de ation of GNP by the GDPde ator

13 Dropping these countries from this sample does not change the resultsin any signi cant way

14 Given the period covered by our sample for each country the rstobservation on average growth is in fact a four-year average If there wereno missing values we would have seven observations for each countryHowever many observations are missing for the rst sample consideredThis implies that for these countries the averaged data can sometimesresult from the averaging of relatively short series Obviously this problemdoes not arise when using the balanced data sets

TABLE 1mdashDESCRIPTION OF THE DATA SET

Number ofCountries

Of Which WithData 1961ndash1994(1965ndash1993 for

Data Set 2)Average Number ofYears Per Country

Data set 1 123 38 24Data set 2 50 50 29Data set 3 38 38 34CW data set 64 64 29 (5-year average)

186 THE REVIEW OF ECONOMICS AND STATISTICS

growth rate Unlike in the rest of the analysis our interesthere is merely for their static relationships

As in any panel our data has set two dimensions thetemporal and the cross-sectional Therefore even whencomputing simple correlations there are several options Foreach of the three pairs of variables we rst consider thewhole data set that is we use each country-year observa-tion We then average for each country all the availableinformation and therefore focus on the cross-sectionalvariability15 Finally we compute for each year the correla-tion coefficient (in the cross section) between the twovariables of interest and consider the variation of thisparameter over time

We start by comparing the coefficient of variation of thethree variables of interest In data set 1 growth rates are byfar the most volatile The coefficient of variation for thisvariable is 330 to be compared with 049 and 035 forsaving and investment rates respectively This ranking invariability is unchanged when we consider country (time-series) averages of the variables In this case the threecoefficients of variations are 173 046 and 029 Noticethat in this case the variability in growth rates as measuredby the coefficient of variation is almost halved while thereduction in the other two variables is modest In data sets 2and 3 whose countries are more similar the coefficients ofvariation while slightly smaller follow the same pattern

In table 2 we report correlation coefficients and Spear-man rank correlation coefficients computed for the threepairs of variables and in the three data sets We report boththe correlations obtained with all annual observations andwith country averages

In the table the correlation coefficients are alwayspositive Typically the coefficients computed on annual dataincrease by 30 to 50 going from data set 1 to data set 3(that is going from a large group of nonhomogeneouscountries to a more restricted number of more similarcountries observed for longer time spans) Saving-growth

correlations are somewhat higher than investment-growthcorrelations but the strongest link turns out to be thatbetween saving and investment We get similar results forrank correlations which should reduce the effect of outliers

When using time-averaged observations correlation coef- cients increase in most cases The only exception is theslight decline in the simple correlation between saving andinvestment rates in data set 1 Even in that case however thecorresponding rank correlation increases if only slightlyThe largest increase is registered for the investment andgrowth rates pair for which the correlations more thandouble

In gure 1 we plot the contemporaneous correlationcoefficients computed using all saving-growth pairs of agiven year against time In the same graph we plot the timeseries obtained using only the countries in the balancedpanel with fty countries The correlation coefficients arepositive for all but four years In the rst half of the periodcorrelation coefficients usually uctuate in the range of 02to 04 for both samples Starting in 1977 however and untilthe end of the sample period the uctuations of thecorrelation coefficients for data set 1 became more marked16

Two effects are likely to be at play On the one hand severaladditional countries lsquolsquoenterrsquorsquo the data set around this periodmoreover the correlation for the preexisting countries mightalso be varying In fact if the same correlations arecomputed using only the countries for which data areavailable over the sample 1965ndash1993 (often middle- andhigh-income countries) a different picture emerges Correla-tion coefficients are somewhat increasing over time and inthe 1980s uctuate around 05 Over that period data set 1correlations drop with respect to the corresponding values ofdata set 2 Short-run linkages turn out therefore quite weakparticularly for those countries that enter the sample

In gure 2 we plot the annual correlations betweengrowth and investment rates (across countries) against timeAgain it must be stressed that the number of countries that

15 As data set 1 is a not balanced panel the country averages and theannual (cross section) correlations are computed using a (possibly)different number of observations

16 The coefficients of variation computed for the two subsamples1961ndash1976 and 1977ndash1994 are respectively 0509 and 0745

TABLE 2mdashCORRELATION COMPUTED ON ANNUAL DATA DATA SETS 1 2 AND 3

CorrelData Set 1Corr Coeff

Data Set 2Corr Coeff

Data Set 3Corr Coeff

Data Set 1Rank Corr Coeff

Data Set 2Rank Corr Coeff

Data Set 3Rank Corr Coeff

S G Annual 0253 0370 0332 0323 0372 0323(0018) (0024) (0026) (0018) (0026) (0028)

Country average 0376 0666 0492 0522 0623 0525(0084) (0108) (0145) (0091) (0143) (0164)

I G Annual 0165 0227 0242 0211 0240 0243(0018) (0026) (0027) (0018) (0026) (0028)

Country average 0319 0601 0652 0409 0585 0650(0086) (0126) (0126) (0091) (0143) (0164)

S I Annual 0483 0592 0658 0614 0613 0665(0016) (0021) (0021) (0018) (0026) (0028)

Country average 0436 0715 0754 0607 0746 0777(0082) (0101) (0109) (0091) (0143) (0164)

annual obs 2986 1450 1292 2986 1450 1292 countries 123 50 38 123 50 38

Notes Spearman rank correlation coefficient se in parentheses

187SAVING GROWTH AND INVESTMENT

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 5: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

C Large N or Large T

As in our data set N and T are roughly of the same order ofmagnitude the presence of a tension between exibility inthe time-series and in the cross-sectional dimension isevident The resolution of this tension absent in the analysisof individual data surveys in which T is typically small andinferences are conducted using lsquolarge Nrsquo asymptotics obvi-ously affects the model speci cation and the choice ofestimators

Given these considerations the best strategy is to estimaterich and exible dynamic models that allow for differencesin short- and long-run coefficients and use estimators thatappeal to lsquolarge T rsquo asymptotics to achieve consistency whileefficiently exploiting all the available information Thesemodels can and should also consider the possibilities that the(dynamic) relationships of interest are different acrosscountries

Obviously the proposed approach imposes different typesof constraints on the researcher The most important is thenecessity to consider coefficients that are constant over timeObviously it is necessary to assume that the availablesample period is long enough to allow for reasonably preciseestimates of time-invariant country coefficients11 Partlybecause of these reasons and partly to make our analysiscomparable to a large body of the literature we presentresults obtained estimating both classes of models discussedin this section

III The Data Set

A The Nature of the Data Set and its Construction

As mentioned in the introduction we use a new panel ofcountries (the World Saving Database) recently gathered atthe World Bank As the data-gathering effort is described indetail by Loayza et al (1998) here we provide a very briefdiscussion of the structure of the panel focusing in particu-lar on those aspects that are relevant for our analysis Withthe exception of total population gures originating fromthe World Bank database all the data are from NationalAccounts and follow their standard conventions The data-base includes 150 countries and spans the years 1960 to1995 However not all variables are available for everycountry and for every year In particular the population datacover the period 1960 to 1994 only As a consequence ouranalysis is restricted to those years

For each country the variables that we use are the rate ofgrowth of annual real per capita gross national product thesaving rate and the rate of investment All these series aremeasured in local currencies The saving rates are computedas nominal gross national saving over nominal gross na-tional income while the investment rates are computed as

nominal gross xed investment over nominal gross nationalproduct Growth is measured as the rate of growth in real percapita GNP (de ated with the GDP de ator)12

We use three different samples of countries The rst is asclose as possible to the whole set of countries included in theWorld Bank database We exclude only those countrieswhose annual income saving or investment were notrecorded at all or are recorded for less than a ve-yearinterval and those countries for which the relevant serieshave missing values in the middle of the sample period Thisprocedure leaves us with a sample consisting of 123countries We call this our lsquolsquowholersquorsquo sample The other twosamples trade-off the T and N dimension The second sampleconsists of the fty countries for which all variables areavailable every year in the interval 1965ndash1993 Our thirdsample consists only of those countries whose variables areavailable every year from 1961 to 1994 Only 38 countriesare included We also use for comparison purposes only theCarroll and Weil (1994) 64-countries sample All countriesin this sample are also in our whole sample with theexception of Tanzania and Zimbabwe which were excludedbecause of the unavailability of data13

In the next section we analyze Carroll and Weilrsquos fullsample results in addition to the analysis based on annualdata We also look at nonoverlapping ve-year averages ofgrowth saving and investment rates for each country14 Theinformation on the number of countries in each of the datasets we use is summarized in table 1

B Contemporaneous Correlations and Rank Correlationsbetween Saving Investment and Growth Rates

We start the analysis of the data set computing somesimple correlation and rank correlation coefficients betweenthe three variables that constitute the main focus of thisstudymdashnamely the saving rate the investment rate and the

11 Another limitation is the fact that one is constrained to consider onlysome classes of error models For instance if the residuals of the model inequation (1) and (2) are of the autoregressive type and there are xedeffects it is impossible to nd instruments that identify the relationships ofinterest

12 To avoid the loss of a large number of observations we did not performany PPP adjustment The same applies to the de ation of GNP by the GDPde ator

13 Dropping these countries from this sample does not change the resultsin any signi cant way

14 Given the period covered by our sample for each country the rstobservation on average growth is in fact a four-year average If there wereno missing values we would have seven observations for each countryHowever many observations are missing for the rst sample consideredThis implies that for these countries the averaged data can sometimesresult from the averaging of relatively short series Obviously this problemdoes not arise when using the balanced data sets

TABLE 1mdashDESCRIPTION OF THE DATA SET

Number ofCountries

Of Which WithData 1961ndash1994(1965ndash1993 for

Data Set 2)Average Number ofYears Per Country

Data set 1 123 38 24Data set 2 50 50 29Data set 3 38 38 34CW data set 64 64 29 (5-year average)

186 THE REVIEW OF ECONOMICS AND STATISTICS

growth rate Unlike in the rest of the analysis our interesthere is merely for their static relationships

As in any panel our data has set two dimensions thetemporal and the cross-sectional Therefore even whencomputing simple correlations there are several options Foreach of the three pairs of variables we rst consider thewhole data set that is we use each country-year observa-tion We then average for each country all the availableinformation and therefore focus on the cross-sectionalvariability15 Finally we compute for each year the correla-tion coefficient (in the cross section) between the twovariables of interest and consider the variation of thisparameter over time

We start by comparing the coefficient of variation of thethree variables of interest In data set 1 growth rates are byfar the most volatile The coefficient of variation for thisvariable is 330 to be compared with 049 and 035 forsaving and investment rates respectively This ranking invariability is unchanged when we consider country (time-series) averages of the variables In this case the threecoefficients of variations are 173 046 and 029 Noticethat in this case the variability in growth rates as measuredby the coefficient of variation is almost halved while thereduction in the other two variables is modest In data sets 2and 3 whose countries are more similar the coefficients ofvariation while slightly smaller follow the same pattern

In table 2 we report correlation coefficients and Spear-man rank correlation coefficients computed for the threepairs of variables and in the three data sets We report boththe correlations obtained with all annual observations andwith country averages

In the table the correlation coefficients are alwayspositive Typically the coefficients computed on annual dataincrease by 30 to 50 going from data set 1 to data set 3(that is going from a large group of nonhomogeneouscountries to a more restricted number of more similarcountries observed for longer time spans) Saving-growth

correlations are somewhat higher than investment-growthcorrelations but the strongest link turns out to be thatbetween saving and investment We get similar results forrank correlations which should reduce the effect of outliers

When using time-averaged observations correlation coef- cients increase in most cases The only exception is theslight decline in the simple correlation between saving andinvestment rates in data set 1 Even in that case however thecorresponding rank correlation increases if only slightlyThe largest increase is registered for the investment andgrowth rates pair for which the correlations more thandouble

In gure 1 we plot the contemporaneous correlationcoefficients computed using all saving-growth pairs of agiven year against time In the same graph we plot the timeseries obtained using only the countries in the balancedpanel with fty countries The correlation coefficients arepositive for all but four years In the rst half of the periodcorrelation coefficients usually uctuate in the range of 02to 04 for both samples Starting in 1977 however and untilthe end of the sample period the uctuations of thecorrelation coefficients for data set 1 became more marked16

Two effects are likely to be at play On the one hand severaladditional countries lsquolsquoenterrsquorsquo the data set around this periodmoreover the correlation for the preexisting countries mightalso be varying In fact if the same correlations arecomputed using only the countries for which data areavailable over the sample 1965ndash1993 (often middle- andhigh-income countries) a different picture emerges Correla-tion coefficients are somewhat increasing over time and inthe 1980s uctuate around 05 Over that period data set 1correlations drop with respect to the corresponding values ofdata set 2 Short-run linkages turn out therefore quite weakparticularly for those countries that enter the sample

In gure 2 we plot the annual correlations betweengrowth and investment rates (across countries) against timeAgain it must be stressed that the number of countries that

15 As data set 1 is a not balanced panel the country averages and theannual (cross section) correlations are computed using a (possibly)different number of observations

16 The coefficients of variation computed for the two subsamples1961ndash1976 and 1977ndash1994 are respectively 0509 and 0745

TABLE 2mdashCORRELATION COMPUTED ON ANNUAL DATA DATA SETS 1 2 AND 3

CorrelData Set 1Corr Coeff

Data Set 2Corr Coeff

Data Set 3Corr Coeff

Data Set 1Rank Corr Coeff

Data Set 2Rank Corr Coeff

Data Set 3Rank Corr Coeff

S G Annual 0253 0370 0332 0323 0372 0323(0018) (0024) (0026) (0018) (0026) (0028)

Country average 0376 0666 0492 0522 0623 0525(0084) (0108) (0145) (0091) (0143) (0164)

I G Annual 0165 0227 0242 0211 0240 0243(0018) (0026) (0027) (0018) (0026) (0028)

Country average 0319 0601 0652 0409 0585 0650(0086) (0126) (0126) (0091) (0143) (0164)

S I Annual 0483 0592 0658 0614 0613 0665(0016) (0021) (0021) (0018) (0026) (0028)

Country average 0436 0715 0754 0607 0746 0777(0082) (0101) (0109) (0091) (0143) (0164)

annual obs 2986 1450 1292 2986 1450 1292 countries 123 50 38 123 50 38

Notes Spearman rank correlation coefficient se in parentheses

187SAVING GROWTH AND INVESTMENT

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 6: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

growth rate Unlike in the rest of the analysis our interesthere is merely for their static relationships

As in any panel our data has set two dimensions thetemporal and the cross-sectional Therefore even whencomputing simple correlations there are several options Foreach of the three pairs of variables we rst consider thewhole data set that is we use each country-year observa-tion We then average for each country all the availableinformation and therefore focus on the cross-sectionalvariability15 Finally we compute for each year the correla-tion coefficient (in the cross section) between the twovariables of interest and consider the variation of thisparameter over time

We start by comparing the coefficient of variation of thethree variables of interest In data set 1 growth rates are byfar the most volatile The coefficient of variation for thisvariable is 330 to be compared with 049 and 035 forsaving and investment rates respectively This ranking invariability is unchanged when we consider country (time-series) averages of the variables In this case the threecoefficients of variations are 173 046 and 029 Noticethat in this case the variability in growth rates as measuredby the coefficient of variation is almost halved while thereduction in the other two variables is modest In data sets 2and 3 whose countries are more similar the coefficients ofvariation while slightly smaller follow the same pattern

In table 2 we report correlation coefficients and Spear-man rank correlation coefficients computed for the threepairs of variables and in the three data sets We report boththe correlations obtained with all annual observations andwith country averages

In the table the correlation coefficients are alwayspositive Typically the coefficients computed on annual dataincrease by 30 to 50 going from data set 1 to data set 3(that is going from a large group of nonhomogeneouscountries to a more restricted number of more similarcountries observed for longer time spans) Saving-growth

correlations are somewhat higher than investment-growthcorrelations but the strongest link turns out to be thatbetween saving and investment We get similar results forrank correlations which should reduce the effect of outliers

When using time-averaged observations correlation coef- cients increase in most cases The only exception is theslight decline in the simple correlation between saving andinvestment rates in data set 1 Even in that case however thecorresponding rank correlation increases if only slightlyThe largest increase is registered for the investment andgrowth rates pair for which the correlations more thandouble

In gure 1 we plot the contemporaneous correlationcoefficients computed using all saving-growth pairs of agiven year against time In the same graph we plot the timeseries obtained using only the countries in the balancedpanel with fty countries The correlation coefficients arepositive for all but four years In the rst half of the periodcorrelation coefficients usually uctuate in the range of 02to 04 for both samples Starting in 1977 however and untilthe end of the sample period the uctuations of thecorrelation coefficients for data set 1 became more marked16

Two effects are likely to be at play On the one hand severaladditional countries lsquolsquoenterrsquorsquo the data set around this periodmoreover the correlation for the preexisting countries mightalso be varying In fact if the same correlations arecomputed using only the countries for which data areavailable over the sample 1965ndash1993 (often middle- andhigh-income countries) a different picture emerges Correla-tion coefficients are somewhat increasing over time and inthe 1980s uctuate around 05 Over that period data set 1correlations drop with respect to the corresponding values ofdata set 2 Short-run linkages turn out therefore quite weakparticularly for those countries that enter the sample

In gure 2 we plot the annual correlations betweengrowth and investment rates (across countries) against timeAgain it must be stressed that the number of countries that

15 As data set 1 is a not balanced panel the country averages and theannual (cross section) correlations are computed using a (possibly)different number of observations

16 The coefficients of variation computed for the two subsamples1961ndash1976 and 1977ndash1994 are respectively 0509 and 0745

TABLE 2mdashCORRELATION COMPUTED ON ANNUAL DATA DATA SETS 1 2 AND 3

CorrelData Set 1Corr Coeff

Data Set 2Corr Coeff

Data Set 3Corr Coeff

Data Set 1Rank Corr Coeff

Data Set 2Rank Corr Coeff

Data Set 3Rank Corr Coeff

S G Annual 0253 0370 0332 0323 0372 0323(0018) (0024) (0026) (0018) (0026) (0028)

Country average 0376 0666 0492 0522 0623 0525(0084) (0108) (0145) (0091) (0143) (0164)

I G Annual 0165 0227 0242 0211 0240 0243(0018) (0026) (0027) (0018) (0026) (0028)

Country average 0319 0601 0652 0409 0585 0650(0086) (0126) (0126) (0091) (0143) (0164)

S I Annual 0483 0592 0658 0614 0613 0665(0016) (0021) (0021) (0018) (0026) (0028)

Country average 0436 0715 0754 0607 0746 0777(0082) (0101) (0109) (0091) (0143) (0164)

annual obs 2986 1450 1292 2986 1450 1292 countries 123 50 38 123 50 38

Notes Spearman rank correlation coefficient se in parentheses

187SAVING GROWTH AND INVESTMENT

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 7: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

enter in the computation of the correlations changes fromyear to year While short-run uctuations are apparent theinvestment-growth link does not exhibit any trend or struc-tural break A nding similar to gure 1 emerges While thetwo series have similar cyclical patterns in the periodconsidered from 1977 onwards data set 2 exhibits annualcorrelations higher than data set 1 thereby con rming thepotential importance of country heterogeneity factors

In gure 3 we show the contemporaneous correlationcoefficients computed using all saving-investment pairs fordata sets 1 and 2 The correlation coefficients are alwayspositive but a break in the late 1970s is apparent During the1960s and the early 1970s both correlation series show adecreasing trend All of this ended in 1974 and from thatyear the correlation between saving and investment rates uctuates around a constant or possibly slightly rising trendIn fact starting in 1979 and until the end of the sampleperiod the data set 2 series is always higher than the data set1 series an outcome we have already pointed out for thesaving-growth and investment-growth links

The simple facts we present in table 2 and in gures 1 to 3are roughly in accordance with the existing evidence Thisindicates that the data set we are using is at least at a basiclevel not too dissimilar from the object of study of previousstudies While these simple correlations do not allow for anystructural interpretation they are clearly suggestive In theintroduction we have mentioned for instance that thetheoretical prediction of the lifecycle model about the(long-run) correlation between saving and growth are am-biguous The fact that the contemporaneous correlationcoefficients are always positive seems to indicate a predomi-

nance of those factors within the model that make themsuch In terms of the correlation between saving andinvestment the evidence we present is consistent with thatof Feldstein and Horioka (1980) It is somewhat surprisinghowever that as capital markets have developed in recentyears the correlation between saving and investment ratesdoes not seem to decrease and shows if anything a tendencyto increase

We now consider the dynamic correlation among thevariables of interest and the instrument we use is theconcept of Granger causation

IV Carroll and Weilrsquos Result How Robust Is It

In a recent paper Carroll and Weil (1994) (CW hereafter)used the Summers-Heston data set to analyze the dynamiccorrelation between saving and growth rates by testing forthe presence of Granger causality tests between them In thissection we analyze the robustness of their result Besides itsintrinsic interest we also use this discussion as a method-ological example to justify the choice of econometrictechniques in section V

CW perform the analysis on ve-year averages to avoidpicking up business-cycle uctuations and focus instead onlow-frequency movements After performing the test inlevels they discuss the possible presence of xed effects anduse instrumental-variable techniques to estimate the equa-tions in rst differences However they instrument only thelagged dependent variables of the equations they considerAs discussed above this procedure is valid only if theresiduals of the two equations under study are assumed to becontemporaneously uncorrelated17 They report results ob-tained with and without the inclusion of a set of timedummies in their equations

CW report that in the larger of the two data sets they usegrowth (positively) Granger-causes saving while savingdoes not Granger-cause growth In the OECD data setgrowth does not Granger-cause saving while when timedummies are not included saving Granger-causes growthwith a negative sign In this subsection we study the extentto which CWrsquos results depend on the data they use on the

17 CWrsquos analysis is limited to two subsets of the countries contained inthe Summers-Heston data set the OECD countries and those countries thatachieve a grade of at least C in terms of data quality

FIGURE 1mdashSAVING AND GROWTH CORRELATION OVER TIME

FIGURE 2mdashINVESTMENT AND GROWTH CORRELATION OVER TIME

FIGURE 3mdashSAVING AND INVESTMENT CORRELATION OVER TIME

188 THE REVIEW OF ECONOMICS AND STATISTICS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 8: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

econometric technique they employ and on the frequencythey choose to analyze

In table 3 we report the coefficients of lagged growth inthe saving rate equation and lagged saving in the rate-of-growth equation when equation (1) and (2) are estimatedwith m 5 n 5 p 5 q 5 1 but using different methodologiesand different data sets18 The t-values on these coefficientscan be interpreted as Granger causality tests None of thecolumns include time dummies whose effect is discussed inthe text below

We start in column 1 reporting the results obtained usingthe same procedure as CW but on the new data set Weconsider rst differences of equation (1) and (2) the samecountries as CW19 ve-year averages and we instrumentonly the lagged dependent variable of each equation Theresults are slightly different from those in CW (1994)growth does Granger-cause saving with a positive sign butthe coefficient on lagged saving in our growth equation isnegative and unlike in CWrsquos results strongly signi cantThe introduction of time dummies does not change muchthese coefficients

In column 2 we include all 123 countries of the newWorld Bank data set that satis ed the criteria described insection II The results are qualitatively identical to those incolumn 1 Once again they are robust to the inclusion oftime dummies In columns 3 and 4 for the two samples usedin column 1 and 2 respectively we relax the hypothesis thatthe residuals of the two equations are uncorrelated andproceed to instrument both lagged variables in both equa-tions Unlike CW who estimate a just-identi ed model weuse the second and third lag of growth and saving rates toinstrument the rst lag of these variables20 While the signsof the coefficients do not change relative to columns 1 and 2the hypothesis of no Granger causality in either direction isnot rejected in either of the data sets at usual con dencelevels This different result is explained by a large reductionin the point estimated of the coefficients on lagged growth in

the saving equation (that go from 0775 and 0658 to 042and 015) and a considerable increase in the standard errorsof the coefficients on lagged saving in the growth equationThese results as for the other columns are unaffected by theintroduction of time dummies

The experiments in columns 3 and 4 indicate that theassumption about the lack of contemporaneous correlationin the residuals of equation (1) and (2) is potentially quiteimportant and might substantially affect our inferences Itremains to be seen if this is due to a substantive change in thesize of the estimated coefficients or to a reduction in theprecision of our estimates

In columns 5 through 8 we reestimate the speci cationsin the rst four columns but on annual data rather than ve-year averages Once again the results are obtainedwithout time dummies but are robust to their inclusion

The results on annual data are quite different from thoseobtained using ve-year averages First of all using the CWinstrumenting procedure results in saving Granger-causinggrowth with a strong negative sign both in the subset ofcountries used by CW and in the entire sample (columns 5and 6) On the other hand growth does not seem toGranger-cause saving in the larger sample while it takes asigni cant negative sign in the data set containing the CWcountries When one uses the more robust instrumentingprocedure in columns 7 and 8 one nds signi cant causationin both directions when the reduced sample is usedmdashandmarginally signi cant causation in the growth to savingdirection when the larger sample is used Increasing thenumber of instruments does not signi cantly change theresults

We are now in a position to evaluate the evidencepresented by Carroll and Weil (1994) and in particular itsrobustness First when we use the same procedure followedby CW we obtain roughly similar results even though thenegative causation running from saving to growth is largerand signi cant in our data sets

The second feature that emerges perhaps not surprisinglyfrom the table is that the results are not neutral to theinstrumenting scheme used When we allow for the possibil-ity that the residuals of the two equations are correlated theresults change considerably This indicates that the assump-

18 The complete set of results is available upon request19 Zimbabwe is excluded because several observations are missing in the

World Bank data set20 When we estimated a just-identi ed model as for instance in column

7 and 8 we obtain very noisy estimates due to the low explanatory powerof the rst-stage regressions

TABLE 3mdashTHE ROBUSTNESS OF THE GROWTH-SAVINGS GRANGER CAUSALITY TESTS

Five-Year Averages Annual Data

(1) (2) (3)a (4)a (5) (6) (7)b (8)b

D git2 1 in saving eq 0775 0658 0416 0154 2 0196 0004 0122 0058(0292) (0253) (0231) (0226) (0021) (0021) (0037) (0031)

D sit2 1 in growth eq 2 0365 2 0220 2 0477 2 0225 2 0472 2 0253 2 0446 0009(0070) (0037) (0240) (0203) (0055) (0035) (0297) (0159)

of observations in growthsav eq 223243 331383 158158 220221 18331818 17921795 17921795 28792897 of countries 64 123 64 123 64 123 64 123

Notes Standard errors in parenthesesColumns 1 3 5 7 CW data set Columns 2 4 6 8 data set 1Columns 1 2 5 6 CW instrumenting Columns 3 4 7 8 both lags instrumented in both equationsa) Lags two and three used as instrumentsb) Lag two used as instrument

189SAVING GROWTH AND INVESTMENT

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 9: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

tion of uncorrelated residuals in the two equations might betoo strong

Finally and in a sense most importantly by far the mostdramatic changes are obtained when we move from ve-year averages to annual data Not only are the coefficientsestimated with much more precision (even using a relativelyinefficient estimator) producing more-signi cant resultsbut the point estimates (and therefore the pattern of causa-tion) occasionally change sign relative to the results ob-tained on ve-year averages

The considerations above suggest that the results pre-sented in table 3 can be extended in various directions Firstof all given the importance that proper instrumenting has onthe results and the fact that the estimates in columns 3 and 4are relatively imprecise it is worth investigating the use ofmore-efficient estimators such as those proposed by HNRespecially in analyzing ve-year averages On the otherhand as mentioned in the previous paragraph and discussedin section III the use of annual data can be more informativethan that of ve-year averages in uncovering both long- andshort-run relationships between the variable of interest Theanalysis of annual data however calls for the use ofmore- exible and richer dynamic speci cation models thatallow for more- exible effects and especially longer lags Itis to this that we now turn

V Analysis of Annual Data

In this section we estimate a exible dynamic model ofthe variables of interest that allows us to identify both long-and short-run effects As stressed in the introduction and insection II we believe that the most pro table way ofidentifying the dynamic relationships between two or morevariables in a panel of countries is the analysis of annual dataand not time-averaged data In section IV we showed thatthe results using ve-year averages can be dramaticallydifferent from those obtained with annual data In this sectiontherefore we focus on the analysis of the relationship betweensaving growth and investment rates using annual data

As discussed in section II the technique to be useddepends on the type of phenomena one wants to study thedata available and the restrictions on parameters andresiduals of the model one feels comfortable with and on thesize of the T and N dimension relative to the variabilitypresent in the data Because of this we report several sets ofresults obtained using different techniques and assumptions

We start by assuming that the coefficients of interest areconstant across countries and that the time dimension of oursample is large enough for OLS to provide meaningfulestimates even in the presence of xed effects21 We then

relax the latter assumption and use GMM-IV estimators of rst-differenced models In the third set of results we relaxinstead the assumption that the coefficients are homoge-neous across countries In such a situation we have toassume that T is lsquolsquolarge enoughrsquorsquo

We next estimate a trivariate version of our modelsimultaneously considering the three variables of interestFinally we check whether the results we report are robust tothe introduction of a number of controls that are typicallyused in the literature

To present the complete set of results in detail would testthe endurance of the most interested reader We thereforepresent a summary of the main results and relegate thedetailed tables to the appendix In particular we present inthis section mostly the long-run effects and (implicitly) thepersistence of each of the variables of interest We summa-rize the short-run dynamics of the system we have estimatedby plotting impulse-response functions For the sake ofbrevity however we report only the impulse-responsefunctions for our favorite models

A A Dynamic Model with No Country Heterogeneity

In this subsection we present a dynamic model for eachof the three pairs of variables considered above estimatedwith annual data and allowing for four lags of each of thetwo variables considered As discussed above we estimatethe model by OLS with country-speci c intercepts In doingthis we are implicitly assuming that T is large enough

We estimate the model in equation (1) and (2) for each ofthe three pairs of variables considered in section V and onthree data sets the unbalanced panel of 123 countries andthe two balanced panels (of 50 and 38 countries respec-tively) discussed in section II

Rather than exploring for each equation the most-appropriate dynamic speci cation we opt for a commonnumber of lags for all the models we estimate After someexperimentation we settled for a speci cation with four lagsfor each of the variables considered22 The dynamic behaviorof the model we consider can therefore be quite complexWe can separately identify short- and long-run effects andwe can consider short- and long-run Granger causation

While the complete set of estimates can be found in theappendix in table 4 we report a summary of our results Inparticular for each pair of variables y and x we report thesum of the coefficients on the lagged xrsquos in the regression fory along with the p-value corresponding to the test that such asum is zero Moreover we report the long-run effect of x ony and the p-value of the hypothesis that all the coefficients onthe lagged xrsquos are zero This last test corresponds strictlyspeaking to a test of Granger causality running from x to yThe difference between the sum of the lagged coefficients21 It should be stressed once more that the OLS estimator in section V(A)

(a within estimator) also exploits the cross-sectional dimension as itassumes that the coefficients are identical for all countries except for theconstant However as the constants are estimated asymptotics are done bykeeping N xed and letting T go to in nity As is well known the OLS xed-effects estimator is biased when applied to a dynamic panel modelbut the size of the bias tends to zero as T grows (Nickell (1981))

22 As suggested by a referee in order to consider a longer time span forthe detection of dynamic effects we also experimented with eight lags Themain results of the analysis which are available on request wereunchanged Obviously the point estimates became much less precise

190 THE REVIEW OF ECONOMICS AND STATISTICS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 10: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

and the long-run effects indicates the importance of thepersistence in y

In each of the three panels of table 4 we consider a pair ofvariables In the rst panel we report the results for theregressions for saving and growth rates in the second thosefor the saving and investment regressions and in the thirdfor growth on investment So for instance the columnslabeled lsquolsquosavingrsquorsquo in the Saving and Growth panel containsthe sum of the coefficient on lagged growth rates (and thecorresponding long-run effect) in a regression for savingrates that includes lagged saving and growth rates as well as xed effects

The rst important feature of the table is that the resultsseem to be quite robust across data sets (at least in theirqualitative nature) Starting with the savinggrowth pair itseems that growth Granger-causes saving with a positivesign while there is no signi cant effect running from savingto growth The long-run effect of growth on saving is ingeneral considerably larger than the sum of the laggedcoefficients re ecting a certain amount of persistence ofsaving rates The sum of the coefficients on the lagged

dependent variable is between 07 and 08 in the saving rateequations Growth rates on the other hand do not showmuch persistence The sum of lagged coefficient is veryclose to zero in the three samples This is consistent with theevidence presented by Easterly et al (1993)

The negative relation running from saving to growthfound in table 3 disappears and is probably due to thearbitrary truncation of the dynamics to the rst lag Whilethe sum of the coefficients (and the long-run effect) is notsigni cantly different (either economically or statistically)from zero individual lagged coefficients are signi cant as itcan be veri ed in the appendix Finally growth rates do notexhibit much persistence even though some of the indi-vidual coefficients are signi cantly different from zero

Turning now to the relationship between investment andsaving rates we nd a strong relationship running fromlagged saving to investment while we do not nd anylong-run relationship running from investment to savingThe long-run effect of lagged saving rates on investmentrates turns out to be quite large (038 in the unbalanced paneland 040 and 055 in the two balanced panels) as a

TABLE 4mdashANNUAL DATAmdashOLS ESTIMATES

DependentVariable

Saving and Growth

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 01335 00081 01057 00434 00950 2 00203( p-value) (0000) (0719) (0011) (0239) (0027) (0548)Long-runb 04965 00074 05337 00463 04174 2 00258( p-value)c (0000) (0000) (0000) (0623) (0000) (0028)Number of obs 2766 2757 1250 1250 1140 1140

DependentVariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 00326 01174 00120 01105 00607 01179( p-value) (0167) (0000) (0719) (0000) (0113) (0000)Long-runb 01194 03837 00614 04040 02259 05494( p-value)c (0000) (0000) (0013) (0000) (0000) (0000)Number of obs 2649 2638 1250 1250 1140 1140

DependentVariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00959 01678 2 00916 01606 2 00783 02062( p-value) (0001) (0000) (0025) (0000) (00112) (0000)Long-runb 2 00918 06381 2 01003 07521 2 00947 12871( p-value)c (0000) (0000) (0004) (0000) (0000) (0000)Number of obs 2517 2516 1250 1250 1140 1140

Notes Standard errors in parentheses The estimated equations also included country-speci c intercepts not reported here The equation estimated in each column is of the form

yit 5 a 0i1 oj5 1

4

a j yit 2 j 1 oj 5 1

4

b j xit2 j

where y is the variable in the heading of each column in each panel and x is the other variable in each panel For instance in the saving-growth panel saving is the y variable and growth the x one in columns 1 3 and 5while growth is the y variable and saving the x one in columns 2 4 and 6

Notesa) Sum of the b coefficients and p-value of a chi-square test of the hypotheses that such a sum is zerob) The long-run coefficient is obtained as

oj

b j (1 2 oj

xj)

c) The p-value refers to the hypotheses that the b coefficients are jointly zero

191SAVING GROWTH AND INVESTMENT

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 11: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

consequence of the persistence in the investment rateequations The sum of coefficients on the lagged dependentvariable is close to 07 in the rst two data sets and 08 in thethird one23

Even though the sum of the coefficients on laggedinvestment is not signi cant in the saving equation some ofthe individual coefficients are strongly signi cant Howeverdifferent lags are typically equal in size and opposite in signso that the long-run effect is close to zero As in theequations summarized in table 4 saving rates show aconsiderable amount of persistence

The results in the third panel show a strong and positiveeffect of lagged growth on investment Once again thelong-run effect of growth on investment is much larger thanthe sum of the coefficients due to the multiplier effectsinduced by the strong persistence in the investment equa-tion The most surprising result in the third panel of thetable however is the negative relationship between laggedinvestment rates and growth rates This result is in line withother empirical evidence based on different data sets andmethods of estimation such as Blomstrom et al (1996) andPodrecca and Carmeci (1998)

The long-run effect is very similar to the sum of thecoefficients on lagged investment rates due to the very smallautocorrelation in growth rates While there is almost nodynamics in the growth in terms of the lagged dependent-variable equation (as in the results for the growthsavingequation) the coefficient on lagged investment rates varyconsiderably The coefficient on the rst lag is signi cantlypositive in all data sets but the overall long-run effect turnsout to be negative because of the effect of the additional lags

In gure 4 we summarize the short-run behavior of thesystems of equations that we have estimated by using someimpulse-response function These plot the reaction of eachof the variables in a bivariate system to a permanent shock toone of the two variables In each of the three columns weplot the impulse-response function to a shock to each of thethree variables As each variable appears in two systemsthere are two responses to the lsquolsquoownrsquorsquo shocks For instancethe change of growth rates to shock to growth can becomputed looking at the growth-investment or the growth-saving systems Each column of the gure has four panelsfor this reason

Two elements of the gure are of particular interest Firstthe graphs summarize synthetically the short-run dynamicsimplied by our estimates In some cases such as the reactionof growth to its own shocks or the reaction of I to shocks onG this can be quite involved Second the long-run effectsthat emerge from the graphs are different from the long-runmultipliers computed in table 4 as the latter take into accountone equation at a time while the impulse-response functionscompute the effects on each pair of equations simulta-neously In some cases the simultaneous effects can besubstantially larger than the single equation ones For

instance the effect of a permanent shock to saving rates ongrowth rates is very small if one takes the estimates of thegrowth equation (which includes lagged growth and savingrates) However this effect is greatly ampli ed by consider-ing the growth and saving equation simultaneously

B Fixed T Estimator with Annual Data

As discussed above it is possible that the properties of theestimators we use in section V(A) given the size of T in theavailable sample do not approximate well enough those ofthe asymptotic distribution In such a situation one canconsider estimators based on xed T (and large N ) asymptot-ics

With xed T the within group estimator used above is nolonger appropriate A rst obvious choice is to consider themodel in rst differences to eliminate xed effects and useinstrumental variables to take into account the correlation ofthe lagged dependent variables with the MA(1) residualsinduced by the differencing

In table 5 we report a summary of the results obtainedusing a GMM estimator to estimate a model analogous tothat studied in section V(A) (A complete set of results isavailable in the appendix) As above we consider four lagsfor each of the two variables As far as the orthogonalityconditions are concerned given the length of the time periodcovered we cannot use all of them We use four lags(additional to those necessary to just-identify the model) foreach of the two variables in the system

The most noteworthy feature of table 5 is that with fewexceptions the results are similar to those described insection V(A) The similarity is greater for the balancedpanels and in particular for data set 3 which comprises agroup of relatively homogeneous countries over a longinterval This comes as no surprise given that T is probablylarge enough to pull the OLS bias close to zero The maindifference however is that the estimates obtained with thisGMM estimator are not as precise as those discussed insection V(A) If we consider the relationship between savingand growth for instance while we obtain point estimatesthat are not miles apart (especially in the two balancedpanels) in table 5 we always fail to reject the hypothesis ofno Granger causation

This does not mean however that no effect is picked upby this procedure For instance we nd again the result thatsaving Granger-causes investment Furthermore both theshort- and the long-run effects are quite similar to those intable 4 Analogously we nd that growth strongly andpositively Granger-causes investment while we do not ndany evidence of causation going from investment to growth

C Growth and Investment Dynamic Modelwith Country Heterogeneity

One of the main advantages of using data that have areasonably large time dimension is that one can investigate

23 Moreover the rst two lagged investment rates take very largecoefficients close to 1 in the rst and close to 2 03 in the second

192 THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 12: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

FIGURE 4mdashIMPULSE-RESPONSE IN THE BIVARIATE SYSTEMS

193SAVING GROWTH AND INVESTMENT

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 13: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

the possibility that the coefficients of the dynamic modeldiffer in the cross-sectional dimension We now estimate thesame dynamic relationships of the previous two sectionsrelaxing the assumption that their coefficients are equalacross countries24

To summarize the information from the estimated country-speci c parameters we focus on lsquolsquomean grouprsquorsquo estimates ofthe coefficients of interest as proposed by Pesaran andSmith (1995) but also report the three quartiles of thedistribution of each coefficient We also compute as beforethe short- and long-run multipliers for the (possibly) causingvariable25

This framework is suitable for the analysis of heterogene-ity among countries A detailed analysis of the nature ofcross-sectional heterogeneity would be particularly relevantwhenever relaxing the homogeneity assumption leads toqualitatively different results26

Because the procedure we use in this subsection requires alarge T for each country we limit ourselves to the use of thebalanced panel of 38 countries27 We report the estimates ofthe sum of lagged coefficients and of the long-run effects intable 628

Qualitatively the results do not differ sensibly from whatwas found imposing the homogeneity assumption Com-pared to the OLS estimates we note that on average theshort-run multipliers are approximately halved

Long-run multipliers are often in uenced by the presenceof outliers and sometimes their mean estimate divergesconsiderably from the median individual estimate In thesaving-on-growth equation in which the quantilesrsquo informa-tion shows the presence of considerable heterogeneity thelong-run multiplier looses signi cance once we go fromOLS to mean estimates In the investment-on-growth equa-tion the long-run multiplier changes sign and becomesinsigni cantly different from zero In all other cases theresults obtained with the mean estimator are qualitativelyidentical to those obtained with the OLS estimator

We conclude that even if in our data set there is evidenceof parameter heterogeneity across country appropriatelytaking it into account does not modify the general pictureobtained using estimators that erroneously impose homoge-neity

24 A series of F-tests of the null hypothesis that the coefficients are indeedhomogeneous across countries led to the rejection of the hypothesis in allcases for signi cance levels below 1

25 Their signi cance is assessed using a simple test based on the observedrelative frequency of the estimated multipliers taking positive valueswhich is approximately normally distributed For individual coefficientestimates for which standard errors are available we notice that thissimple lsquolsquocount testrsquorsquo yields results similar to those obtained using standardparametric techniques Note that because of the presence of outlierssometimes the mean group estimator is signed differently than the medianindividual estimate Rejecting the null hypothesis in this case would beevidence in favor of an effect signed as the median estimate

26 This is not our case However an informal analysis to identify thosecountries having the sign of the estimated relationships different from thesign of the mean effect did not show the presence of any clearlyidenti able pattern Details are available from the authors

27 We have also carried out the analysis with the fty-country balanceddata set The results (available upon request) are not signi cantly differentfrom the ones that we report

28 A complete set of results is in the appendix where the standard errorsof individual coefficients are computed using a simple extension to thepresent context of the Whitersquos robust variance-covariance estimator

TABLE 5mdashIV-GMM ESTIMATES ANNUAL DATA

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Dependentvariable

Saving and Growth

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

Suma 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-runb 04353 2 00313 08120 01143 04163 2 00647( p-value)c (09804) (08301) (03481) (07014) (05135) (06720)

Dependentvariable

Saving and Investment

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

Suma 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-runb 01371 03449 2 04427 05959 2 00396 06793( p-value)c (00969) (08789) (05089) (0080) (05778) (00573)

Dependentvariable

Growth and Investment

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

Suma 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-runb 2 00346 05006 2 02687 10648 2 01152 17442( p-value)c (07175) (09845) (04649) (00526) (04399) (00075)

Notes See table 4 The estimates reported here are equivalent to those in table 4 Estimates are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

194 THE REVIEW OF ECONOMICS AND STATISTICS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 14: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

D Three-Equation System

So far we have been considering pair-wise tests ofGranger causation However in studying our three variablesthere is no reason not to consider them jointly In order to doso we return to the methodology used in section V(A)mdashOLS regression with country-speci c intercepts Once againwe consider four lags of the variables under study That iswe regress each of our three variables on four of its lags fourlags of the other two variables and country dummies Theresults of this procedure are summarized in table 7 The tablehas nine columns one for each of the three variables in eachof the three data sets Rather than showing all estimates wereport the sum of the coefficients on the four lags consideredand in the case of the variables other than the dependentvariable the long-run effects In addition we report thep-value of the test that each of the four lags (on a givenvariable) has a zero coefficient and of the hypothesis that thesum of the coefficient is zero

The results once more are reasonably homogeneousacross samples This is particularly true for the investmentequation Investment seems to be affected signi cantly andpositively by both lagged growth and saving rates Savingrates on the other hand do not seem to be affected by eitherlagged growth rates or lagged investment rates The onlyexception is the positive effect of lagged growth rates in theunbalanced panel Finally in the growth equation we nd inall samples a negative effect of lagged investment (alreadynoticed in Section V(A)) Saving rates on the other hand

signi cantly affect growth rates only in the balanced samplewith fty countries

If we consider the persistence of the three equations asmeasured by the sum of the coefficients on the lags of thedependent variable we nd that as before growth showsvery little of it while investment and saving rates are verypersistent29

As with the bivariate systems we summarize the short-run dynamics by plotting in gure 5 the impulse-responsefunctions of each of the variables under study to each of thethree shocks Once again as we consider the three variablessimultaneously the cumulate impulse response does notcoincide with the long-run multipliers of table 7 computedusing a single equationrsquos coefficient because they take intoaccount the dynamics of all the variables simultaneously Ingeneral this magni es the size of the effects In the case ofthe effect of a shock to the saving rate regression on growththe effect is rst negative and then mildly positive whichstands in contrast with the pattern shown in gure 4

E An Overall Evaluation and Some Extensions

We have already noticed that our results are within theframework we have used quite stable and robust Inparticular as mentioned above we have experimented withchanging samples and increasing the number of lags in-

29 The only odd nding in this respect is the sum of the coefficients on laginvestment in the unbalanced panel that equals 2 122

TABLE 6mdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependent variable Saving ratesIndependent variable Growth rates

Dependent variable Growth ratesIndependent variable Saving rates

AvgCoeff

1st 2nd and3rd Quantile

AvgCoeff

1st 2nd and3rd Quantile

Suma 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value)b (0003) (1000)Long-runc 2 1428 2 04550 06613 18027 2 03274 2 01859 00519 09897( p-value)d (0004) (0194)

Dependent variable Saving ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Saving rates

Suma 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-runb 2 81049 2 01700 04949 17086 05789 02893 06417 09289( p-value)c (0009) (0000)

Dependent variable Growth ratesIndependent variable Investment rates

Dependent variable Investment ratesIndependent variable Growth rates

Suma 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value)b (0023) (0023)Long-runc 01411 2 03588 00115 03230 36307 05731 13355 28268( p-value)d (1000) (0000) of observations 1292 of countries 38

Notes The model is equivalent to that estimated in table 4 but with country-speci c coefficients p-values from lsquolsquocount testsrsquorsquo are in parenthesesa) Average of the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variableb) p-value of a lsquolsquocount testrsquorsquo of the hypotheses that the fraction of countries for which the sum of the lagged coefficients on the lsquolsquocausingrsquorsquo variable is greater than zero is equal to 12c) The long-run coefficient is the average of the country-speci c long-run effectsd) The p-value of a lsquolsquocount testrsquorsquo of the hypothesis that the fraction of countries for which the long-run coefficient is greater than zero is equal to 12An asterisk next to the p-values of the short- and long-run coefficients indicates that because of the presence of extreme values the estimated coefficientsrsquo most frequent sign is different from the sign of their mean

195SAVING GROWTH AND INVESTMENT

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 15: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

cluded in our regressions Both experiments did not changethe basic nature of our results

In an attempt to control for important differences amongcountries that could affect the relationships of interest manyof the papers that study multicountry data sets such as thegrowth regressions of Barro (1991) and many others haveconsidered a number of variables ranging from measures ofhuman capital to government consumption to measures ofpolitical instability30 While this is certainly important incross-sectional studies it is less so in our case as our focusis on the time dimension Moreover at least the variablesthat do not vary over time are taken care of by the presenceof xed effects However in this subsection we explorewhether the results we obtain are robust to the introductionof a number of control variables that are typical in cross-sectional studies

The control variables we consider are chosen on the basisof two criteria First we want to consider variables that arelikely to be important and have been typically used in themacro (and especially growth) literature Second we do notwant to lose from our data set too many countries because ofdata availability This is an important issue because thecontrols usually included in the growth (cross-sectional)regressions are usually available only at very low frequen-cies

We included four additional controls in data sets 2 and 3the public consumption rate computed as (central) govern-ment consumption over GNP the share of population agedbetween 15 and 65 years a human capital proxy (years ofschooling) and life expectancy at birth As we need annual

controls these series (except public consumption) requiredthe imputation of some missing values To ll the gaps weperformed linear interpolations andor extrapolations basedon the tendency of the nearest six observations of the series

Most of the control variables we consider are stronglysigni cant in most of the speci cations we consider Inparticular the public consumption coefficient is negativeand signi cant in all two- and three-equation systems (withthe exclusion of the regression of investment against laggedsaving using data set 2) This is an unsurprising conclusionin light of previous cross-sectional studies31 The estimatedcoefficient of the share of population aged between 15 and65 is almost always positive and signi cant with theexception of the investment equation in the three-equationsystems and in the investment-growth equation in thetwo-equation systems irrespective of the data set consid-ered In both the two- and three-equation systems thehuman capital control is often imprecisely estimated This istrue especially for the data set of 38 mostly developedcountries in which none of the human capital coefficientsare signi cant perhaps because of the low variability in thesample The effect of the life expectancy is signi cant inmost of the regressions the exception being the investmentequations in the three-equation system and the investmenton lagged growth rates in the case of two equationsHowever the sign of the point estimates are different indifferent equations

The introduction of the control variables however doesnot affect most of our results about the dynamic relationshipamong saving investment and growth For the bivariatesystems (which we do not report but which are availableupon request) this is true for the saving-investment andgrowth-investment cases The short- and long-run effectsalways retain sign and signi cance (or lack of) and are

30 Typically in growth regressions the average growth rate of a countryis explained by means of a set of (supposedly exogenous) controlsconcerning geographical institutional political and more traditionaldemographic factors and economic variablesmdashthe investment rate amongthemmdashevaluated at the beginning of the period or in terms of sampleaverages These controls might also affect the relationships that weanalyze 31 The complete set of results is shown in the appendix

TABLE 7mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 1 (123 Countries) Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Investment coeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

196 THE REVIEW OF ECONOMICS AND STATISTICS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 16: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

remarkably close in size The only important exception is thesaving-growth system While the results for data set 3 areagain unaffected in the case of data set 2 the effect oflagged growth rates on saving changes from positive withoutcontrols to insigni cant (and negative) when controls areintroduced Furthermore when we consider the effect oflagged saving rates on growth we now nd a negative and(marginally signi cant) coefficient

Table 8 summarizes the results of the introduction ofcontrols in the three-equation system considered in theprevious section Let us consider rst the saving equationThe introduction of controls leaves almost unaffected thedegree of persistence of the dependent variable estimated inthe three-equation system without controls Also the esti-mated effect of the lagged investment rates on saving is verysimilar to the corresponding case of table 7 with a long-runmultiplier always positive signi cant and not far from 020for both data sets However the effect of growth is

somewhat different especially in data set 2 In this caseconsistently with the lsquolsquosaving for a rainy dayrsquorsquo argument orwith a more traditional IS-LM model the long-run coeffi-cient is negative and marginally signi cant In the data setincluding 38 of the most-industrialized countries howeverthe effect is insigni cantly different from zero This seems tocon rm Deatonrsquos (1995) statement that lsquolsquothe reverse mecha-nism from growth to saving is at best relatively unimpor-tantrsquorsquo

As for the growth equation to the short- and long-runeffects of lagged investment are again quite preciselyestimated and similar to the estimates of the no-controlsthree-equation system of table 7 for both data sets There-fore the negative short- and long-run investment effects arerobust also to the inclusion of these controls However thesaving effect is less stable than the investment one While intable 7 the short- and the long-run multipliers are positiveand usually signi cant the introduction of controls reduces

FIGURE 5mdashIMPULSE-RESPONSE IN THE TRIVARIATE SYSTEM

197SAVING GROWTH AND INVESTMENT

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 17: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

size and precision of the estimates in data set 2 and changesthe signs in the case of data set 3

The investment equation is unaffected by the inclusion ofcontrols The degree of persistence of the dependent variableis only slightly lower than the one estimated in table 7Investment and growth coefficients both in the short-runand long-run cases are always positive signi cant and veryclose to the corresponding values of the no-control case

In conclusion the results might be consistent with aframework in which the saving-investment and investment-growth relationships are direct and therefore relatively easyto detect On the contrary the (possibly indirect) relationshipfrom saving to growth is in uenced by other factors and istherefore less stable while in the growth-to-saving relation-ship enter opposing (and perhaps offsetting) forces thatre ect different and not completely understood theoreticalmechanisms of consumer behavior

VI Interpretation of the Results and Conclusions

In this section we summarize and interpret our resultsAcross data sets estimation methods and speci cationssaving rates and investment rates show a substantial amountof persistence with the sum of the coefficients on the laggeddependent variable ranging between 06 and 08 On thecontrary growth rates are much less persistent This hasobvious implications on the way in which the shocks arepropagated and on the speed of adjustment The evidence ongrowth rates is consistent with that presented by Easterly etal (1993)

Table 9 provides a simple and selective summary of theimplications of our estimates A plus or a minus signindicates the sign of the long-run coefficients (and thereforeof the long-run effect) in the equation listed in the rstcolumn One asterisk following the sign indicates signi -cance at the 10 level two asterisks indicate signi cance at

the 5 level Within each column are more subcolumnswhen a given estimation technique was used on more thanone sample of countries The number at the head of eachsubcolumn identi es the relevant sample size32

Some clear patterns emerge from the table Three resultsare extremely robust across data sets and estimation meth-ods Lagged saving rates are positively related to investmentrates Investment rates Granger-cause growth rates with anegative sign and growth rates Granger-cause investmentrates with a positive sign These results emerge in allcolumns with the only exceptions being the unbalancedsample with the GMM estimator (which typically yields theless precise estimates) and in one case the heterogeneouscoefficient estimator Also lagged investment positivelyGranger-causes saving in all cases with the exclusion of thetwo smaller samples in GMM estimation in which therelation has a negative and nonsigni cant sign Growth andsaving seem to be mutually and positively related but animportant exception arises once we include additionalcontrols in the three-variable system

In the introduction while discussing the link betweensaving and investment we mentioned the Feldstein andHorioka (1980) and the Feldstein and Bacchetta (1991)papers as relating the positive correlation between savingand investment to the limited mobility of internationalcapital We also mentioned other papers such as that byBaxter and Crucini (1992) who construct a two-countryequilibrium model with perfectly open capital markets thatis able to generate the type of correlation observed in thedata Baxter and Crucinirsquos story seems to be supported bythe evidence on the contemporaneous correlation in section

32 For example the lsquolsquoGrowth on SavrsquorsquomdashlsquolsquoOLSrsquorsquo cell of the table showsthat the long-run coefficient of growth on saving in the OLS estimates andusing the sample with 123 countries is positive and signi cantly differentfrom zero at the 5-signi cance level

TABLE 8mdashA DYNAMIC TRIVARIATE MODEL OF SAVING INVESTMENT AND GROWTH AND CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 2 (50 Countries) Data Set 3 (38 Countries)

Saving(1)

Invest(2)

Grow(3)

Saving(1)

Invest(2)

Grow(3)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Investment coeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coefficientsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

198 THE REVIEW OF ECONOMICS AND STATISTICS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 18: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

III (and especially that in gure 3) which shows that suchcorrelation has been relatively constant in the last thirtyyears while capital markets have been developing andbecoming more integrated However the fact that laggedsaving seems to be strongly related to current investmentposes a more difficult challenge to the type of models thatBaxter and Crucini have been constructing

Turning to the Granger causation running from growth toinvestment one could probably construct models in whichgrowth might create incentives to new investment bymaking future growth more likely This is the mechanismstressed by Blomstrom et al (1996) Such a story howevercontrasts with the low persistence that growth shows in thedata

By far the most difficult piece of evidence to interpret isthe negative Granger causation running from investment togrowth rates This result is extremely robust to changes inthe sample econometric technique model speci cation andinclusion of controls Moreover as already mentioned thisevidencemdashwhich contrasts sharply with the positive correla-tion coefficient typically obtained in growth regressionssuch as those of Barro (1991) and Barro and Lee (1993)mdashisnot inconsistent with that recently presented by Bolstrom etal This negative correlation has been interpreted in terms ofthe adjustment process towards the steady state within theSolow model following a shock on saving (Vanhoudt(1998)) A different possible story might be that savingdecreases anticipating future growth and this constitutes alimiting factor for investment given the limited mobility ofinternational markets This story however is inconsistentwith the fact that in the trivariate system lagged saving isnegatively related to growth only in the smallest data setwhen controls are introduced in the equation Anotherpossibility is that investment is less costly or more produc-tive when growth is high anticipating a decline in growth rms will tend to anticipate investment projects and viceversa

Before turning to the discussion of the relationshipbetween growth and saving a small digression on therelevance of our evidence for the growth regressions initi-ated by the work of Barro (1991) Mankiw Romer and Weil(1992) and others is called for While the evidence on therelationship between growth and investment is relevant forthat literature we should stress that the relation with the

debate on relative convergence is only marginal The mainreason for this is that the convergence regressions aretypically identi ed by cross-sectional variation that in ourregressions that focus mainly on the time series dynamic isto a large extent absorbed by the xed effects

The relationship between saving and growth that consti-tuted the main theme of the Carroll and Weil (1994) work isnot very stable Growth seems to be (positively) Granger-causing saving in many speci cations and data sets butoften the effect is quite weak More importantly theintroduction of controls causes such a correlation to disap-pear In the introduction we mentioned that both thelong-run and short-run implications of the lifecycle modelfor the relationship between growth and aggregate savingare ambiguous and depend on a number of aggregationeffects It is therefore interesting to note thatmdashcontrollingfor some additional variables such as the share of thepopulation in working agemdashthe relationship between laggedgrowth and saving changes from positive to negative Thispiece of evidence is consistent with the importance ofdemographic variables for aggregate saving recently stressedby Behrman Duryea and Szekely (1999)

While there is some evidence of a positive relationshipbetween lagged saving rates and current growth rates it isinteresting to note that a negative and signi cant effect isobtained in the trivariate system when additional controlsare present To identify such a micro effect as the lsquolsquosaving fora rainy dayrsquorsquo implication of the lifecycle model it isnecessary to control for several determinants of heterogene-ity across countries

The long-run coefficients are only a part of the storyhowever because they do not capture short-run dynamiceffects that can be quite complex and relatively long lastingFor instance most of the relationships that exhibit nosigni cant long-run effects are characterized by some signi -cant coefficient on some of the lagged causing variable Thatis even in those cases in which there seems to be nolong-run Granger causation we nd signi cant short-runeffects These results are compatible with the presence of thecontrasting economic forces that are the likely determinantsof the relationships that we have studied and that we havedescribed in the introduction to this work If the timing of theeffects of these forces is different so that they are empirically

TABLE 9mdashSUMMARY OF RESULTS

Number of Countriesin the Sample

OLS(table 4)

HNR GMM(table 5) P-S

(table 6)38

Three Variables(table 7)

Three Variables andControls (table 8)

123 50 38 123 50 38 123 50 38 50 38

Growth on Saving 1 1 1 1 1 1 1 1 1 1 2 1 Saving on Growth 1 1 2 2 1 2 1 1 1 1 1 2 Investment on Saving 1 1 1 1 2 2 1 1 1 1 1 1 Saving on Investment 1 1 1 1 1 1 1 1 1 1 1 1 Investment on Growth 2 2 2 2 2 2 1 2 2 2 2 2 Growth on Investment 1 1 1 1 1 1 1 1 1 1 1 1

Notes A 1 2 sign indicates a positivenegative long-run estimated coefficient Onetwo asterisk(s) indicate(s) signi cance at the 10 (5) level

199SAVING GROWTH AND INVESTMENT

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 19: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

distinguishable (but these effects also tend to cancel out aftertime) then we would exactly expect to nd individuallysigni cant coefficients but a nonsigni cant average effect

In this paper we have experimented with differenteconometric techniques with the purpose of properly treat-ing a panel of data in which both N and T are relatively largeWe have argued that the novelty of using pooled data of thiskind presents the researcher both with new opportunities andwith new problems We have made the point that in ourcase it is more meaningful to think about T rather than Nasymptotics We have also argued that because Grangercausality is an intrinsically dynamic concept the dynamicsof the data is where this relation has to be sought Obviouslythe estimators that one chooses under the assumption that Tis large enough are subject to possible small-sample bias if Tturns out to be not large enough given the variability in thedata Finally we have argued for the use of annual ratherthan time-averaged data and for the construction of exibledynamic models that would allow one to separately modeland identify short- and long-run effects

The comparison of our results obtained using differentestimation techniques also calls for conclusions of a meth-odological type First the instrumental-variables GMMmethod led to less-precise estimates compared to the othermethods The bias of an OLS estimator of a dynamic panelmodel is very small for most data-generating processesbecause it follows a correlation of single observations withtheir time average The lack of precision of our GMMestimates seems to indicate that when T is big enough thebias that comes with an OLS estimator of a dynamic modelis to be preferred to the loss of precision that follows theimplementation of an instrumental-variable procedure

Another issue regards the use of heterogeneous coeffi-cients estimates Even though in all cases we were able toreject the hypothesis of parameter homogeneity when weallowed parameters to vary across countries we ended upwith results that are qualitatively very similar to the onesobtained assuming homogeneity In other words the lack ofparameter homogeneity did not seem to be enough for theensuing bias to invalidate our previous results This resultseems to be further proof of the reliability of pooledestimation techniques and through different means and in adifferent context it adds to the evidence presented byBaltagi and Griffin (1997)

Last a general comment on the issue of large N-large Tpanel data Advocating the use of dynamic models is adifferent way of saying that as the time-series dimension ofthe panel data used in economics tends to grow it becomesincreasingly important to apply the lessons learned fromtime-series econometrics This point has also been forcefullymade by Granger and Ling-Ling (1997)

REFERENCES

Arellano M and S Bond lsquolsquoSome Tests of Speci cation for Panel DataMonte Carlo Evidence and an Application to Employment Equa-tionsrsquorsquo Review of Economic Studies 58 (1991) 277ndash297

Arellano M and O Bover lsquolsquoAnother Look at the Instrumental VariableEstimation of Error-Components Modelsrsquorsquo Journal of Economet-rics 18 (1995) 47ndash82

Argimon I and J M Roldan lsquolsquoSaving Investment and InternationalCapital Mobility in EC Countriesrsquorsquo European Economic Review 38(1994) 59ndash67

Baltagi B H and J M Griffin lsquolsquoPooled Estimators vs Their Heteroge-neous Counterparts in the Context of Dynamic Demand forGasolinersquorsquo Journal of Econometrics 77 (1997) 303ndash327

Barro R J lsquolsquoEconomic Growth in a Cross-Section of CountriesrsquorsquoQuarterly Journal of Economics 106 (1991) 407ndash443

Barro R J and J W Lee lsquolsquoInternational Comparisons of EducationalAttainmentrsquorsquoJournal of Monetary Economics 32 (1993) 363ndash394

Baxter M and M Crucini lsquolsquoExplaining Saving-Investment Correla-tionsrsquorsquo American Economic Review (1993) 416ndash37

Behrman J S Duryea and M Szekely lsquolsquoAging and Economic OptionsLatin America in a World Perspectiversquorsquo manuscript (1999)

Blomstrom M R E Lipsey and M Zejan lsquolsquoIs Fixed Investment the Keyto Economic Growthrsquorsquo Quarterly Journal of Economics 111(1996) 269ndash276

Campbell J lsquolsquoDoes Saving Anticipate Declining Labor Income AnAlternative Test of the Permanent Income Hypothesisrsquorsquo Economet-rica 55 (1987) 1249ndash73

Carroll C D and D Weil lsquolsquoSaving and Growth A Reinterpretationrsquo rsquoCarnegie-Rochester Conference Series on Public Policy 40 (1994)133ndash192

Caselli F G Esquivel and F Lefort lsquolsquoReopening the ConvergenceDebate A New Look at Cross Country Growth Empiricsrsquorsquo Journalof Economic Growth 1 (1996) 363ndash389

Deaton A lsquolsquoGrowth and Saving What Do We Know What Do We Needto Know and What Might We Learnrsquorsquo manuscript World Bank(March 1995)

Easterly W M Kremer L Pritchett and L Summers lsquolsquoGood Policy orGood Luck Country Growth Performance and Temporary ShocksrsquorsquoJournal of Monetary Economics 32 (1993) 459ndash483

Feldstein M and C Horioka lsquolsquoDomestic Savings and InternationalCapital Flowsrsquorsquo Economic Journal 10 (1980) 314ndash329

Feldstein M and P Bacchetta lsquolsquoNational Saving and InternationalInvestmentrsquorsquo in B Douglas Bernheim and J Shoven (Eds)National Saving and Economic Performance (Chicago ChicagoUniversity Press 1991)

Granger C and Ling-Ling H lsquolsquoEvaluation of Panel Data Models SomeSuggestions from Time Seriesrsquorsquo discussion paper 97-10 Universityof California San Diego (1997)

Holtz-Eakin D W Newey and H Rosen lsquolsquoEstimating Vector Autoregres-sions with Panel Datarsquorsquo Econometrica 56 (1988) 1371ndash1395

Islam N lsquolsquoGrowth Empirics A Panel Data Approachrsquorsquo Quarterly Journalof Economics 110 (1995) 1127ndash1170

Loayza N H Lopez K Schmidt-Hebbel and L Serven lsquolsquoSaving in theWorld The Stylized Factsrsquorsquo World Bank mimeograph (1998)

Mankiw N G D Romer and D Weil lsquolsquoA Contribution to the Empirics ofEconomic Growthrsquorsquo Quarterly Journal of Economics 107 (1992)407ndash437

Nickell S lsquolsquoBiases in Dynamic Models with Fixed Effectsrsquorsquo Economet-rica 49 (1981) 359ndash382

Pesaran M H and R Smith lsquolsquoEstimating Long-Run Relationships fromDynamic Heterogeneous Panelsrsquorsquo Journal of Econometrics 68(1995) 79ndash113

Podrecca E and G Carmeci lsquolsquoFixed Investment and Economic GrowthNew Results on Causalityrsquorsquo University of Trieste mimeograph(1998)

Sinn S lsquolsquoSaving-Investment Correlations and Capital Mobility On theEvidence from Annual Datarsquorsquo Economic Journal 102 (1992)1162ndash1170

Taylor A lsquolsquoDomestic Saving and International Capital Flows Reconsid-eredrsquorsquo NBER Working Paper No 4892 (1994)

Vanhoudt P lsquolsquoA Fallacy in Causality Research on Growth and CapitalAccumulationrsquorsquo Economic Letters 60 (1998) 77ndash81

The World Bank Saving Database (1998) ftpmonarchworldbankorg pubPRDDRoutbox

200 THE REVIEW OF ECONOMICS AND STATISTICS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 20: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

Appendix A

This appendix reports the tables with the complete results of the regressions we referred to in the main text In order to facilitate comparisons the numeration ofthe tables of this appendix is the same used in the text

TABLE A4AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0115499 0640135 0645385 0052755 0660285 2 018019(002605) (00204) (0031244) (0045098) (0034705) (0047698)

git 2 2 0005523 0090427 0030299 0012158 0040342 0196364(003044) (002376) (003825) (005521) (0042787) (0058807)

git 2 3 2 008889 2 004794 0026327 2 002583 2 000541 2 005283(00305) (00243) (0040361) (0058257) (0041903) (0057592)

git 2 4 2 002402 0048511 0099913 0004369 0077242 0016326(002608) (002082) (0032765) (0047292) (003239) (0044517)

sit2 1 0025317 0082779 0088442 008095 0161202 0328445(002062) (001614) (0021725) (0031358) (0025508) (0035058)

sit2 2 2 004337 0013104 2 000425 0027619 2 010203 2 009027(002054) (001606) (0021898) (0031607) (002646) (0036366)

sit2 3 2 000905 0058171 0071663 2 000693 0113586 0024084(001997) (001577) (0021856) (0031547) (0026427) (0036321)

sit2 4 2 006747 2 002057 2 005013 2 004076 2 007778 2 005446(001937) (001519) (0021069) (0030411) (0023594) (0032428)

Growth coeffsSum 01335 mdash 01057 mdash 00950 mdash( p-value) (0000) (0011) (0027)Long-run 04965 mdash 05337 mdash 04174 mdash( p-value) (0000) (0000) (0000)

Saving coeffsSum mdash 00081 mdash 00434 mdash 2 00203( p-value) (0719) (0239) (0548)Long-run mdash 00074 mdash 00463 mdash 2 00258( p-value) (0000) (0623) (0028)

of observations 2766 2757 1250 1250 1140 1140

Notes See table 4

201SAVING GROWTH AND INVESTMENT

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 21: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A4BmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH CONTROL

VARIABLES ANNUAL DATA

DependentVariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Growth(4)

Saving(5)

Growth(6)

git 2 1 0047613 0010327 0140069 0268921(0021081) (0030619) (0025084) (0034404)

git 2 2 2 003614 2 003222 2 00973 2 011381(0021145) (0030712) (0025777) (0035355)

git 2 3 0039265 2 006678 0101913 2 001866(0021105) (0030654) (0025754) (0035323)

git 2 4 2 007212 2 009146 2 007862 2 008936(0020419) (0029657) (002319) (0031806)

sit2 1 057426 2 002382 0601141 2 022324(0030251) (0043938) (0034146) (0046833)

sit2 2 0023446 0012066 0031099 018663(0036238) (0052634) (0041145) (0056432)

sit2 3 0027372 2 00194 2 001019 2 004556(0038251) (0055557) (0040337) (0055323)

sit2 4 0089872 2 000505 0071941 0014844(0031141) (0045231) (003115) (0042728)

Publ Cons 2 03807 2 046931 2 034213 2 040405(0036969) (0053695) (0036191) (0049638)

Pop 15ndash65 0003344 0002721 0001447 0002091(0000606) (0000881) (0000493) (0000677)

Hum Cap 2 000307 2 00042 2 000105 2 00016(0002007) (0002915) (0001451) (0001991)

Life Exp 2 000156 2 000294 0000388 2 000158(0000708) (0001029) (0000504) (0000691)

Growth coeffsSum 2 00213 mdash 00661 mdash( p-value) (0618) (0142)Long-run 2 0075 mdash 02159 mdash( p-value) (0000) (0000)

Saving coeffsSum mdash 2 00362 mdash 2 00673( p-value) (0341) (0059)Long-run mdash 2 00307 mdash 2 00707( p-value) (0903) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

202 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 22: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A4CmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 0701393 0107546 067805 0107411 0709031 0114401(002088) (001543) (0029003) (0019293) (0030694) (0021413)

sit2 2 0044949 003632 0011118 0011691 2 006379 0023198(002482) (001848) (0036611) (0024354) (0037283) (0026009)

sit2 3 2 003292 2 004567 0049335 2 001365 0082546 2 003513(002493) (001874) (0038359) (0025517) (0036837) (0025698)

sit2 4 0013751 0019238 0065447 0005032 0003615 0015448(002124) (001577) (0032306) (002149) (003115) (002173)

iit2 1 2 00026 0742666 0073664 0964113 0221524 105534(002696) (001999) (0043308) (0028809) (0043888) (0030616)

iit2 2 0139342 2 000021 0041234 2 024634 2 021374 2 031872(00333) (002507) (0059812) (0039788) (0063564) (0044343)

iit2 3 2 013577 2 009184 2 00579 0049144 0061728 0037378(003297) (002507) (0060084) (0039969) (0063652) (0044404)

iit2 4 0031594 0044129 2 004496 2 004039 2 000884 0011379(00242) (001811) (0043101) (0028672) (0043008) (0030003)

Inv coeffsSum 00326 mdash 00120 mdash 00607 mdash( p-value) (0167) (0719) (0036)Long-run 01194 mdash 00614 mdash 02259 mdash( p-value) (0000) (0013) (0000)

Saving coeffsSum mdash 01174 mdash 01105 mdash 01179( p-value) (0000) (0000) (0000)Long-run mdash 03837 mdash 04040 mdash 05494( p-value) (0000) (0000) (0000)

of observations 2649 2638 1250 1250 1140 1140

Notes See table 4

203SAVING GROWTH AND INVESTMENT

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 23: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A4DmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT

WITH CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(3)

Investment(4)

Saving(5)

Investment(6)

iit2 1 0075511 0954479 0207073 1052369(004101) (0028904) (0042079) (0030578)

iit2 2 0074149 2 024334 2 018473 2 03127(005634) (0039708) (0060976) (004431)

iit2 3 2 004674 0046259 0051483 0035082(005659) (0039884) (0061011) (0044336)

iit2 4 2 004176 2 004 2 000551 0013272(0040787) (0028746) (0041816) (0030387)

sit2 1 0570555 0099757 063258 0098927(0028612) (0020165) (0030372) (0022071)

sit2 2 2 000873 0012924 2 006314 0023208(0034516) (0024326) (0035725) (002596)

sit2 3 0035564 2 001202 0066837 2 003852(0036162) (0025487) (0035335) (0025677)

sit2 4 005856 0011538 0003586 0015635(0030701) (0021638) (002987) (0021706)

Publ Cons 2 039472 2 003267 2 035887 2 0069(0036573) (0025776) (0036649) (0026632)

Pop 15ndash65 0003595 0000103 0001542 0000414(0000613) (0000432) (00005) (0000364)

Hum Cap 2 000156 2 000401 2 000081 2 000074(0002046) (0001442) (0001478) (0001074)

Life Exp 2 000196 0000806 0000163 000082(0000736) (0000519) (0000513) (0000373)

Inv coeffsSum 00611 mdash 00683 mdash( p-value) (0064) (00169)Long-run 01777 mdash 01897 mdash( p-value) (0001) (0000)

Saving coeffsSum mdash 01122 mdash 00992( p-value) (0000) (0000)Long-run mdash 03970 mdash 04682( p-value) (0000) (0000)

of observations 1250 1250 1178 1178

Notes See table 4

204 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 24: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A4EmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 0063251 0092051 0078638 012196 0237738 0156059(002122) (001181) (0029607) (0013695) (0031691) (001607)

git 2 2 2 002297 0059429 0032296 0028082 2 006335 0039476(002126) (001183) (0030451) (0014085) (0033211) (0016841)

git 2 3 2 001722 0001627 0002171 0012899 0051549 000233(002051) (001141) (0030237) (0013986) (0033164) (0016817)

git 2 4 2 006709 0014667 2 002604 2 000234 2 005319 0008317(001962) (001096) (0029562) (0013674) (0031447) (0015946)

iit2 1 0066977 0719835 0132254 0937334 0121781 0999271(003645) (002044) (0063501) (0029373) (006187) (0031373)

iit2 2 2 007657 0014941 2 024183 2 020945 2 032159 2 024987(004461) (002552) (0086259) (00399) (0087388) (0044314)

iit2 3 2 002304 2 00622 0139193 0082148 0210645 0070734(004378) (002555) (0086845) (0040171) (0087391) (0044315)

iit2 4 2 006324 0064476 2 012121 2 002357 2 008918 0019673(003269) (00184) (0062402) (0028865) (0060396) (0030626)

Inv CoeffsSum 2 00959 mdash 2 00916 mdash 2 00783 mdash( p-value) (0001) (0025) (00112)Long-run 2 00918 mdash 2 01003 mdash 2 00947 mdash( p-value) (0000) (0004) (0000)

Growth coeffsSum mdash 01678 mdash 01606 mdash 02062( p-value) (0000) (0000) (0000)Long-run mdash 06381 mdash 07521 mdash 12871( p-value) (0000) (0000) (0000)

of observations 2517 2516 1250 1250 1140 1140

Notes See table 4

205SAVING GROWTH AND INVESTMENT

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 25: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A4FmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH

CONTROL VARIABLES ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 2 001731 0113569 0167132 0150496(002934) (0014264) (0031502) (001651)

git 2 2 2 005582 0020776 2 010837 0039546(0029942) (0014557) (0032582) (0017076)

git 2 3 2 007868 0006057 2 000145 0000674(0029609) (0014395) (0032607) (0017089)

git 2 4 2 009617 2 000797 2 009818 0009741(0028922) (0014061) (0031017) (0016256)

iit2 1 0150473 0935643 0130386 0989416(0060469) (0029398) (006005) (0031472)

iit2 2 2 020543 2 020583 2 029236 2 024637(0081994) (0039863) (0084259) (004416)

iit2 3 0136142 0081233 0189131 0068423(0082518) (0040118) (0084238) (0044149)

iit2 4 2 017482 2 00301 2 009668 0011245(0059575) (0028963) (005848) (003065)

Publ Cons 2 048055 2 004368 2 037454 2 007831(0052234) (0025395) (0047771) (0025037)

Pop 15ndash65 000267 0000659 0001967 0000415(0000839) (0000408) (0000675) (0000354)

Hum Cap 2 000489 2 000274 2 000195 2 000055(0002888) (0001404) (0002005) (0001051)

Life Exp 2 000257 0000287 2 000144 0000388(0001009) (0000491) (0000705) (0000369)

Inv coeffsSum 2 00936 mdash 2 00695 mdash( p-value) (00175) (0031)Long-run 2 0075 mdash 2 0067 mdash( p-value) (0000) (0002)

Growth coeffsSum mdash 01324 mdash 02005( p-value) (0000) (0000)Long-run mdash 06046 mdash 11306( p-value) (0000) (0000)

of observations 1250 1250 1140 1140

Notes See table 4

206 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 26: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A5AmdashA DYNAMIC MODEL OF SAVING AND GROWTH ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Growth(2)

Saving(3)

Growth(4)

Saving(5)

Growth(6)

sit 2 1 07848 00612 05158 2 00483 05220 2 03999(0213) (0240) (0209) (0305) (0172) (0313)

sit 2 2 00315 00606 2 00004 02558 01000 03216(0249) (0335) (0136) (0272) (0134) (0222)

sit 2 3 2 01231 2 00679 00870 2 01975 00004 00011(0279) (0327) (0121) (0283) (0138) (0184)

sit 2 4 01462 2 00822 01276 00986 01636 00272(0190) (0197) (0119) (0187) (0090) (0140)

git 2 1 00140 01036 02159 01878 02687 04206(0213) (0240) (0209) (0305) (0172) (0313)

git 2 2 2 00850 00200 2 00468 2 01536 2 01756 2 00795(0249) (0335) (0136) (0272) (0134) (0222)

git 2 3 01631 2 00658 01081 01226 01280 2 00125(0279) (0327) (0121) (0283) (0138) (0184)

git 2 4 2 00222 00399 2 00579 2 01067 2 01320 2 01021(0190) (0197) (0119) (0187) (0090) (0140)

Sum 00699 2 00283 0213 01086 00891 2 0050( p-value) (07861) (05269) (08105) (04275) (05604) (06593)Long-run 04353 2 00313 08120 01143 04163 2 00647( p-value) (09804) (08301) (03481) (07014) (05135) (06720) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A5BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Saving(3)

Investment(4)

Saving(5)

Investment(6)

sit2 1 07844 00587 05653 01254 06576 01643(0195) (0211) (0310) (0113) (0315) (0108)

sit2 2 00139 00043 2 01142 01167 2 01627 00084(0297) (0297) (0375) (0148) (0322) (0088)

sit2 3 2 00472 2 00642 01787 2 00495 01411 00016(0342) (0295) (0423) (0140) (0294) (0064)

sit2 4 00778 00485 00200 00519 00441 00254(0202) (0180) (0317) (0101) (0167) (0072)

iit2 1 2 00238 09156 2 00019 08938 03372 10742(0195) (0211) (0310) (0113) (0315) (0108)

iit2 2 00401 00077 00632 2 03130 2 04367 2 04216(0297) (0297) (0375) (0148) (0322) (0088)

iit2 3 00567 2 00901 2 00692 00741 01827 01277(0342) (0295) (0423) (0140) (0294) (0064)

iit2 4 2 00496 00296 2 01471 2 00653 2 00958 2 00743(0202) (0180) (0317) (0101) (0167) (0072)

Sum 01100 03449 2 01550 02445 2 00126 01997( p-value) (06145) (04254) (02538) (0024) (09141) (00036)Long-run 01371 03449 2 04427 05959 2 00396 06793( p-value) (00969) (08789) (05089) (0080) (05778) (00573) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

207SAVING GROWTH AND INVESTMENT

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 27: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A5CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT ANNUAL DATA

Dependentvariable

IV-GMM Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Growth(1)

Investment(2)

Growth(3)

Investment(4)

Growth(5)

Investment(6)

git 2 1 01804 00320 01737 02128 01994 01963(0220) (0199) (0393) (0098) (0330) (0083)

git 2 2 00115 00856 2 00593 00651 2 01648 00386(0357) (0193) (0520) (0074) (0489) (0054)

git 2 3 2 01672 2 00754 01481 00430 00195 00226(0281) (0163) (0452) (0079) (0433) (0055)

git 2 4 00009 00165 2 00703 00100 2 00684 00303(0148) (0116) (0283) (0064) (0266) (0049)

iit2 1 00744 09648 01026 09113 03981 10847(0220) (0199) (0393) (0098) (0330) (0083)

iit2 2 2 01271 2 00938 2 05318 2 03398 2 06626 2 03717(0357) (0193) (0520) (0074) (0489) (0054)

iit2 3 2 00083 2 00462 03504 01212 02583 00771(0281) (0163) (0452) (0079) (0433) (0055)

iit2 4 00273 00580 2 01383 2 00035 2 01107 00449(0148) (0116) (0283) (0064) (0266) (0049)

Sum 2 00337 00585 2 02171 03309 2 01169 02878( p-value) (02661) (08234) (01171) (00071) (01135) (0006)Long-run 2 00346 05006 2 02687 10648 2 01152 17442( p-value) (07175) (09845) (04649) (00526) (04399) (00075) of observations

Notes See table 4 The estimates reported here are equivalent to those in table 4 but they are obtained by GMM using the HNR (1988) and AB (1991) estimators Four additional lags are used as instruments in allcolumns

TABLE A6AmdashA DYNAMIC MODEL OF SAVING AND GROWTH WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rates Growth Rates

Avg Coeff(se)

1st 2nd and3rd Quartile

Avg Coeff(se)

1st 2nd and3rd Quartile

sit2 1 07078 04758 07454 08979 2 00854 2 03959 00437 01590(0061) (0097)

sit2 2 00073 2 02130 00658 02249 01264 2 01458 01692 05683(0065) (0104)

sit2 3 2 00030 2 01909 00127 01863 2 00900 2 05703 2 01269 01673(0051) (0089)

sit2 4 00276 2 01963 00118 02165 00398 2 05210 2 00365 03000(0039) (0073)

git 2 1 01547 2 00529 01855 03216 03429 01134 04221 05967(0042) (0065)

git 2 2 2 00274 2 01674 2 00026 00881 2 01280 2 03575 2 01509 00642(0036) (0047)

git 2 3 00551 2 00802 01055 01585 00456 2 01999 01074 03163(0038) (0061)

git 2 4 00030 2 00906 2 00105 00421 2 00891 2 02233 2 01001 00804(0026) (0050)

Sum 00463 2 000964 00390 00993 2 00022 2 00455 00012 00618( p-value) (0003) (1000)Long-run 02204 2 02568 02576 08875 13507 2 01859 00519 09897( p-value) (0105) (0746) of observations 1292 1292

Notes See table 6

208 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 28: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A6BmdashA DYNAMIC MODEL OF SAVING AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Saving Rate Investment Rate

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

sit2 1 07685 05219 06685 10673 01713 00057 02174 03505(0051) (0027)

sit2 2 2 00727 2 02058 2 00558 01367 00548 2 00863 2 00051 02231(0060) (0051)

sit2 3 00975 2 00361 01150 02894 2 00119 2 01426 00220 01243(0065) (0051)

sit2 4 2 00391 2 02006 2 00478 00346 00483 2 00373 00540 01167(0035) (0034)

iit 2 1 00947 2 01758 00876 02055 09599 07766 09783 12263(0059) (0040)

iit 2 2 2 01653 2 05240 2 01951 2 00488 2 03550 2 06684 2 03229 2 00094(0079) (0060)

iit 2 3 2 00888 2 01846 00371 03786 00530 2 01864 00297 02309(0079) (0050)

iit 2 4 2 00488 2 02800 2 00977 00646 2 00643 2 01839 2 000561 01423(0055) (0035)

Sum 2 00077 2 00642 2 00189 00444 00656 00234 00620 01237( p-value) (1000) (0000)Long-run 02549 2 04242 2 00330 05477 01962 2 08175 2 01808 02976( p-value) (0746) (0105) of observations 1292 1292 1292 1292

Notes See table 6

TABLE A6CmdashA DYNAMIC MODEL OF GROWTH AND INVESTMENT WITH HETEROGENEOUS COEFFICIENTS ANNUAL DATA

Dependentvariable

Data Set 338 Countries

Growth Rates Investment Rates

Avg Coeff(se)

1st 2nd and3rd Quantile

Avg Coeff(se)

1st 2nd and3rd Quantile

git2 1 03144 01131 02770 04421 02124 01186 02066 02916(0075) (0026)

git2 2 2 0141 2 03822 2 02205 00095 00483 2 00295 00636 01324(0045) (0024)

git2 3 01258 2 00917 00799 02454 00636 2 00284 00624 01568(0045) (0024)

git2 4 2 00707 2 01924 2 0486 00473 00186 2 00377 00088 01051(0046) (0019)

iit 2 1 2 01990 2 06818 2 00884 02332 09184 07625 09365 10775(0104) (0040)

iit 2 2 00487 2 06855 2 00111 06472 2 02230 2 04556 2 02571 00218(0122) (0061)

iit 2 3 2 00376 2 06079 2 00474 03587 00462 2 01676 00363 03305(0145) (0055)

iit 2 4 00119 2 033480 2 00280 04008 2 00271 2 01416 00492 01897(0099) (0040)

Sum 2 00440 2 01062 2 00644 00106 00857 00279 00815 01271( p-value) (0023) (0023)Long-run 2 01246 2 07449 2 01929 01373 11631 2 07372 00293 1316( p-value) (0105) (1000) of observations 1292 1292 1292 1292

Notes See table 6

209SAVING GROWTH AND INVESTMENT

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 29: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A7mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 1123 Countries

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

Saving(1)

Invest(2)

Growth(2)

git2 1 0090474 0076143 0024328 0082773 0104546 005635 0138821 0160769 0298668(001694) (001247) (002238) (0022407) (0014766) (0032145) (0026493) (0018342) (003635)

git2 2 0015148 0040646 2 005226 2 002062 0006291 0007989 2 012033 2 000052 2 009342(001688) (001238) (002233) (0022942) (0015118) (0032912) (0027723) (0019194) (0038038)

git2 3 0062673 2 000626 2 00209 0056428 0001256 2 000774 0108908 2 001142 0038924(001619) (001184) (002138) (0022719) (0014972) (0032592) (0027629) (0019128) (0037909)

git2 4 2 002922 0000540 2 007362 2 005446 2 001446 2 004567 2 007782 0005581 2 005836(001518) (01117) (002002) (0021468) (0014147) (0030797) (0024174) (0016736) (0033168)

sit 2 1 0671058 0056744 0144853 0642471 0051247 0065979 0651686 0006416 2 015066(002271) (001674) (003005) (0031418) (0020704) (0045071) (0034915) (0024173) (0047906)

sit 2 2 0041783 0042053 2 000248 0031228 0036887 0032961 0032633 0108095 0195221(002619) (001942) (003473) (003849) (0025364) (0055217) (0042666) (0029539) (0058541)

sit 2 3 2 004564 2 002381 2 006429 0023042 2 00086 2 001997 2 002157 2 003789 2 004892(002627) (001964) (003477) (0040375) (0026607) (0057922) (0041877) (0028993) (0057458)

sit 2 4 0053365 0030083 2 000912 0101759 0013313 0047388 0073736 0008791 0067014(002251) (001665) (002982) (003346) (002205) (0048002) (0033464) (0023168) (0045915)

iit2 1 2 004347 0694041 0039478 0048991 092218 0113994 0188093 097931 0107368(002798) (002063) (003703) (0044497) (0029323) (0063834) (0045429) (0031452) (0062333)

iit2 2 0153297 0009941 2 00569 0046829 2 02146 2 02517 2 01781 2 024669 2 031001(003395) (002545) (004474) (0060102) (0039606) (0086221) (0063656) (0044071) (0087341)

iit2 3 2 013416 2 006981 2 004103 2 002721 0073794 0128405 0074803 0055635 0191633(003374) (00255) (004399) (0060516) (0039879) (0086815) (0063465) (0043939) (0087079)

iit2 4 004725 0048684 2 006203 2 00503 2 004601 2 015315 2 002211 0006589 2 011158(002485) (001849) (003295) (004442) (0029272) (0063724) (004461) (0030885) (0061209)

Saving coeffsSum 07206 01051 00690 07985 00928 01264 07364 00854 00627( p-value) (0000) (0000) (0000) (0000) (0000) (0003) (0000) (0000) (0137)Long-run mdash 03313 00614 mdash 03508 01277 mdash 04164 00770( p-value) (0000) (0000) (0000) (0049) (0000) (0000)

Inv CoeffsSum 00229 2 12246 2 01205 00183 07354 2 01625 00627 07948 2 01226( p-value) (0347) (0000) (0000) (0582) (0000) (0001) (0026) (0000) (0001)Long-run 00820 mdash 2 10730 00909 mdash 2 01642 02379 mdash 2 01506( p-value) (0000) (0000) (0111) (0000) (0000) (0000)

Growth coeffsSum 01391 01111 06829 00641 00976 00109 00496 01544 01858( p-value) (0000) (0000) (0000) (0152) (0000) (0865) (0299) (0000) (0000)Long-run 04977 03313 mdash 03182 03689 mdash 01882 07526 mdash( p-value) (0000) (0000) (0000) (0000) (0000) (0000)

of observations 2527 2516 2517 1250 1250 1250 1140 1140 1140

Notes See table 4

210 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT

Page 30: Saving, Growth, and Investment: A Macroeconomic Analysis ...dept.ku.edu/~empirics/Courses/Econ915/papers/savg-growth-inv.pdf · SAVING, GROWTH, AND INVESTMENT: A MACROECONOMIC ANALYSIS

TABLE A8mdashA DYNAMIC MODEL OF SAVING INVESTMENT AND GROWTH WITH CONTROLS ANNUAL DATA

Dependentvariable

OLS Estimates

Data Set 250 Countries

Data Set 338 Countries

Saving(1)

Investment(2)

Growth(2)

Saving(1)

Investment(2)

Growth(2)

git2 1 00395 010118 2 00129 0115431 0161159 0244499(0021561) (0015078) (0031343) (0025982) (001871) (003571)

git2 2 2 00615 0003244 2 005894 2 012116 0003105 2 011978(0022037) (0015411) (0032035) (0027033) (0019467) (0037155)

git2 3 00125 2 00028 2 007862 0090021 2 001048 2 000893(0021872) (0015296) (0031795) (0026989) (0019436) (0037095)

git2 4 2 00816 2 001957 2 010144 2 008338 0008722 2 009158(0020683) (0014464) (0030066) (0023726) (0017085) (0032609)

sit 2 1 05609 0051292 2 001682 0592706 2 00055 2 020505(0030341) (0021219) (0044106) (0034228) (0024648) (0047044)

sit 2 2 00207 0039225 0029692 0023903 0106822 0183714(0036254) (0025354) (0052701) (0040991) (0029518) (0056338)

sit 2 3 00198 2 000459 2 001589 2 002496 2 003958 2 004701(0038048) (0026608) (005531) (0040247) (0028983) (0055316)

sit 2 4 00834 0019516 0033528 0066769 0008833 0053282(0031796) (0022236) (0046221) (0032189) (002318) (0044241)

iit2 1 00796 0915611 0145244 0186539 0975393 0128329(0042122) (0029457) (0061231) (0043837) (0031568) (0060251)

iit2 2 00804 2 021331 2 020919 2 015349 2 024368 2 027482(0056594) (0039578) (0082269) (00612) (0044072) (0084115)

iit2 3 2 00183 0071711 0136593 006485 0055111 0174084(005696) (0039834) (0082801) (0060977) (0043911) (0083808)

iit2 4 2 00777 2 005136 2 018688 2 00282 0002792 2 010717(004194) (002933) (0060966) (0043007) (003097) (0059109)

Publ Cons 2 04036 2 001541 2 047864 2 034153 2 005409 2 039928(0037001) (0025876) (0053787) (0035962) (0025897) (0049427)

Pop 15ndash65 00036 0000018 0002508 0001498 0000288 0002026(0000607) (0000425) (0000883) (000049) (0000353) (0000674)

Hum Cap 2 00021 2 000394 2 000538 2 000097 2 000054 2 000203(0002034) (0001422) (0002956) (0001448) (0001042) (000199)

Life Exp 2 00020 0000991 2 000231 0000148 000033 2 000127(0000732) (0000512) (0001065) (0000511) (0000368) (0000702)

Saving coeffsSum 06847 01054 00305 06584 00706 2 00151( p-value) (0000) (0000) (0500) (0000) (0001) (0072)Long-run mdash 03802 00244 mdash 03354 2 00154( p-value) (0000) (0893) (0000) (0000)

Inv CoeffsSum 00639 07227 2 01142 00697 07896 2 00796( p-value) (0050) (0000) (0016) (0012) (0000) (0039)Long-run 02028 mdash 2 00913 02041 mdash 2 00816( p-value) (0000) (0000) (0000) (0000)

Growth coeffsSum 2 00911 00821 2 02519 00009 01625 00242( p-value) (0046) (0010) (0000) (0985) (0000) (0723)Long-run 2 02891 02958 mdash 00027 07724 mdash( p-value) (0000) (0000) (0000) (0000)

of observations 1250 1250 1250 1140 1140 1140

Notes See table 4

211SAVING GROWTH AND INVESTMENT