business cycle analysis of econometric model simulations · 2017. 5. 5. · business cycle analysis...

This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research

Volume Title: Econometric Models of Cyclical Behavior, Vols. 1 and 2

Volume Author/Editor: Bert G. Hickman, ed.

Volume Publisher: UMI

Volume ISBN: 0-870-14232-1

Volume URL: http://www.nber.org/books/hick72-1

Publication Date: 1972

Chapter Title: Business Cycle Analysis Of Econometric Model Simulations

Chapter Author: Victor Zarnowitz, Charlotte Boschan, Geoffrey H. Moore, Josephine Su

Chapter URL: http://www.nber.org/chapters/c2784

Chapter pages in book: (p. 311 - 542)

BUSINESS CYCLE ANALYSIS OFECONOMETRIC MODELSIMULATIONSVICTOR ZARNOWITZ University of ChicagoCHARLOTTE BOSCHAN • National Bureau of

Economic ResearchGEOFFREY H. MOORE Bureau of Labor

Statisticsassisted by JOSEPHINE SU

IN A pioneering study published ten years ago, Irma Adelman andFrank L. Adelman [2] calculated and analyzed the time paths of themain endogenous variables from the 1955 Klein-Goldberger (KG)econometric model of the United States [22]. They examined severalforms of hypothetical long-term development of this system: (I) non-stochastic simulations based on smooth extrapolations of the exoge-nous variables; (2) stochastic simulations of "Type I." with randomshocks superimposed upon the extrapolated values of the exogenousquantities; and (3) stochastic simulations of "Type II," with randomshocks introduced into each of the fitted equations. Each of these dif-ferent solutions was dynamic, in that it related current values of endog-enous variables to their lagged values generated by the model fromearlier data; each also involved some tentative assumptions about secu-lar economic trends, in that it projected the exogenous variables farbeyond the sample-period base of the KG estimates (1929—52) overone hundred years of the "future." The Adelmans were primarily in-terested in learning whether the KG Model can, internally, generatecyclical movements resembling cycles found historically in the UnitedStates economy. The nonstochastic simulations and those using theType I shocks did not produce such movements, but the stochastic

311

rterly Econoflietric1965.

tr Results. Chicago,

York, Harper and

Analysis of theModels," this vol-

metric Forecasting

:y." American Eco-

ions with an Econo- 1 INTRODUCTION

1.1 BACKGROUND AND PURPOSEnflation and Its Les-Economic A ctivity

A Review Article,"0), 78, pp. 489—525.

me: A Review Ar-(May 1968), 50. pp.

licy and Investmentlurie 1967), 57, pp.

ccelerated Deprecia-nt and General Eco-centives and Invest-

and Its Interactionand Statistics

with Special Refer-w of Economics and

./

32 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR

simulations with shocks of Type 11 did, as the Adelmans concludedfrom comparisons of the time paths computed for the KG Model withthe NBER cycle" measures for the series involved.

Since then—in the 1960's—increasingly ambitious efforts havebeen made to estimate economic relationships with more detailed andcomplex econometric models, and the simulation experiments per-formed upon these models have grown correspondingly in size andscope. Simulations of a quarterly model by Duesenberry, Eckstein,and Fromm [8] were designed to test the proneness to recession of theU.S. economy and the effectiveness of automatic stabilizers. Later.several quarterly models of the postwar U.S. economy were unveiledin quick succession, notably those by L. R. Klein [22], Klein and M. K.Evans [13], M. Liebenberg, A. A. Hirsch, and J. Popkin for the Officeof Business Economics of the Department of Commerce (0 BE) [23],the Brookings Model [9], and most recently, the F RB-MET Model [3],[11], [27]. The last two systems represent efforts by sizable groups ofeconomists, and each consists of a very large number of equations. Atthe NBER, an econometric model of business cycles was formulatedin the last few years by G. C. Chow and G. H. Moore: its early sets ofestimates are currently being evaluated [6].

The present Conference is concerned with these recent models,viewed as instruments for the analysis and prediction of general eco-nomic fluctuations. Our study, in particular, deals with experimentsperformed on some of these systems in a search for answers to the typeof question which Irma and Frank Adelman asked with respect to theKG system. Do these models endogenously generate cyclical behavior,and, if so, to what extent, how, in which sectors, and over what predic-tive span? To what degree are the fluctuations produced by externalimpulses? How do such cycles as may originate in the nonstochasticand stochastic simulations compare with the relationships observed inthe NBER business cycle studies? How do the models differ from eachother in these respects?

The materials that can now be analyzed with a view to clarifyingthese issues are clearly much richer than those available in the late1950's. It has long been recognized, for instance, that annual data arefar less adequate in business cycle analysis than are quarterly or monthlydata. The new quarterly models, therefore, should definitely be more

BUS'

appropriate for thd(such as the KG

4draw on longer exestimationgreater number a'were hardly tappeConference. Suchused primarily forspecific postulatec

Although Siminherent limitationby Irma Adelman,a specificbe investigated" [IPtion results concelas good as the moexample, the Adelin the KG Modelextent this study hwere the major caintially on the qualit(basic

While no simsevidence from student periods, and sqthis weakness. Thuweredence based onthe simulations forjyield similar indictpulses, we wouldshock hypothesissort, a plausible ardiversified coveracycle analysis.

I

concludedthe KG Model with

kes involved.Ibitious efforts have

h more detailed andn experiments per-ndingly in size andsenberry, Eckstein,s to recession of the

stabilizers. Later,were unveiled

22], Klein and M. K.kin for the Office

nmerce (OBE) [23],RB-MIT Model [3],by sizable groups ofber of equations. Atdes was formulated)ore: its early sets of

hese recent models,ction of general eco-Is with experimentsr answers to the type

with respect to thecyclical behavior,over what predic-

roduced by externalin the nonstochasticionships observed indels differ from each

a view to clarifyingavailable in the latethat annual data arequarterly or monthly

definitely be more

L

BUSINESS CYCLE ANALYSIS OF MODEL SIMULATIONS • 313

appropriate for the purposes at hand than are the older annual models(such as the KG equation system). Furthermore, the present modelsdraw on longer experience with, and better knowledge of, econometricestimation methods; and they cover larger data samples and a muchgreater number and variety of macroeconomic relations. These datawere hardly tapped for studies of cyclical behavior before the presentConference. Such simulations as were made with these models wereused primarily for general evaluation and for analyzing the effects ofspecific postulated policy changes [10], [17].

Although simulation is a powerful tool of economic analysis, itsinherent limitations are substantial and should be recognized. As notedby Irma Adelman, "Any simulation experiment produces no more thana specific numerical case history of the system whose properties are tobe investigated" [1, p. 272]. Hence, the inferences drawn from simula-tion results concerning the properties of the economic system are onlyas good as the model which is used as the analogue of that system. Forexample, the Adelmans' study has shown that the cyclical fluctuationsin the KG Model are due to random shocks of a certain type; to whatextent this study has verified the hypothesis that random perturbationswere the major cause of business cycles of experience, depends essen-tially on the quality of the KG equation system as a representation ofbasic relationships in the U.S. economy.

While no simulation study can avoid being limited in this sense,evidence from studies based on different models, applications to differ-ent periods, and so forth, may to some extent cumulate and help reducethis weakness. This would be so if the different applications and modelswere complementary in their substantially valid parts, and if the evi-dence based on them were internally consistent. For example, shouldthe simulations for a variety of differently structured quarterly modelsyield similar indications of the importance of exogenous erratic im-pulses, we would regard this as additional support for the random-shock hypothesis of cyclical behavior. In the light of possibilities of thissort, a plausible argument can be made in favor of comprehensive anddiversified coverage of econometric model simulations in businesscycle analysis. 'I

1.2 PROGRAM AND DATA

According to the original plan for the Conference, the study was tocover five models: Brookings, Wharton-EFU, OBE, FRB-MIT-PENN. and Chow-NBER.' However, no simulation data were re-ceived for the Brookings Model before the time scheduled for deliveryof the Conference papers, and the estimates for the Chow-NBERModel are still incomplete. The Wharton, OBE, and FMP model-builders have supplied us with the large amounts of required data, andhave given us excellent cooperation. In its present version, therefore,our study covers the estimates produced by the current versions ofthese three quarterly models of the postwar U.S. economy.2

Twenty-two variables were selected for the cyclical simulations.The list includes GNP in constant (1958) dollars and five of its compo-nents: consumption, residential construction, nonresidential fixedinvestment, change in business inventories, and net exports. Alsospecified for the investigation were data on GNP, personal income, andcorporate profit in current dollars, employment and the unemploymentrate, average workweek, new and unfilled orders, construction con-tracts and housing starts, the implicit price deflator for GNP, laborcompensation per man-hour and unit of output, money supply, and theshort- and long-term interest rates. These variables were selectedbecause of their importance for macroeconomic theory in general,and business cycle analysis in particular, and in view of their cyclicalsensitivity and timing. With some exceptions and modifications, theyappear in most of the recent econometric models of intermediate orlarge size.

314' ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR

Table 1.1actually used toing systems. Itwith each other in rthere are several dibeen omitted. Thuscontracts. Only thecosts per unit ofnous components ocoverage differ amoOBE uses both newin real terms; Wharand FMF', unfilledcurrent dollars.

Most of theare brought out inmeasurement are atall factors that impaundoubtedly numeidifferences in the v'as in the case of the•

For each of thewere examined. nasix-quarter periodsrecent fluctuationssimulations oversimulationsstarting at the end

Each set of sinous sequences (formates for as many ain the given modelsimulations of typestochastic simulaticquested, with one hto examine the vanconfigurations of ra

'See references in previous section. For brevity, the Wharton Econometric Fore-casting Unit (EFU) Model and the FRB-MLT-PENN Model will henceforth be referredto as the Wharton and FMP Models, respectively.

2 In the process of being developed and revised, each model has been undergoingchanges of varying importance and frequency. Models with relatively long histories, suchas the Wharton Model, have passed through several distinguishable versions. as des-cribed in the paper by Evans. Haitovsky. and Treyz [121. The OBE Model, as used inthis report and identified by the list of its equations in the paper by George Green andassociates [18]. differs from the earlier version introduced in 1966 [23]. The model var-iants on which our analysis is based are those developed by the spring and summer sea-sons of 1969. prior to the time when the simulation data were supplied to us by the model-builders. These models are explained in considerable detail in other reports prepared forthis Conference [l2], [14], [18]; we shall refer to this information as needed, withoutreproducing it at length.

the study was to

OBE, FRB-MIT-data were re-

led for deliverythe Chow-NBERand FMP model-

f required data, andversion, therefore,

current versions of

yclical simulations.nd five of its compo-onresidential fixednet exports. Also

ersonal income, andi the unemployment

construction con-tor for GNP, laborIney supply, and theibles were selected

theory in general,iew of their cyclicalmodifications, they

s of intermediate or

Econometric Fore-henceforth be referred

'del has been undergoinglively long histories, suchiishable versions. as des-e OBE Model, as used inper by George Green and1966 [23]. The model var-

spring and summer sea-Lipplied to us by the model-other reports prepared for

as needed, without


Table 1. 1 gives some descriptive detail and sources for the dataactually used to represent the selected variables in each of the cooperat-ing systems. It shows that, on the whole, the models agree rather wellwith each other in regard to coverage of the specified items. However,there are several differences among models, and some variables havebeen omitted. Thus, none of the three systems includes constructioncontracts. Only the OBE Model estimates housing starts, and laborcosts per unit of real private GiVP; only OBE and FMP have endoge-nous components of money supply. Also, the concepts and industrialcoverage differ among the models for certain variables. For example,OBE uses both new and unfilled orders for durable-goods manufacturesin real terms; Wharton, deflated unfilled orders for all manufacturing;and FMP, unfilled orders for machinery and equipment industries, incurrent dollars.

Most of the important differences in data definitions and coverageare brought out in Table 1. 1, and some minor discrepancies in units ofmeasurement are also annotated, but we do not claim to have identifiedall factors that impair comparisons across the models. Such factors areundoubtedly numerous and some are difficult to detect, notably thedifferences in the vintage of data used, which can be quite significant,as in the case of the frequently revised series for GNP and components.

For each of the models, three types of complete-model simulationswere examined, namely: (a) nonstochastic simulations over selectedsix-quarter periods which include the dates of the turning points ofrecent fluctuations in aggregate economic activity; (/4 nonstochasticsimulations over the entire period covered by the models; (c) stochasticsimulations projecting the models for a period of twenty-five years,starting at the end of the sample period.

Each set of simulations of a particular type consists of discontinu-ous sequences (for a), or continuous time-series (for b and c) of esti-mates for as many of the selected endogenous variables as are includedin the given model. One set per model is sufficient to produce thesimulations of type a; and one run, for those of type b; but for thestochastic simulations (c), as many as fifty runs per model were re-quested, with one hundred quarterly terms in each run. This was doneto examine the variability of responses of a given system to differentconfigurations of random shocks, and to avoid excessive reliance on

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318 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR

SOURCE NOTES FOR TABLE 1.1Line

I. OBE definition. National Income Accounts (NIA) Table 1.1. line 1.2. NIA Table 1.2, line 1.3. Ibid., line 2.4. ibid., line 11. In FMP Model, hundred billion 1958 dollars.5. ibid.. line 8.6. ibid., line 15.7. ibid., line 17.8. NIA Table 2.1, line 1.9. NIA Table 8.l,line I.

10. Based on monthly BLS figures. In Wharton Model, includes armed forces.II. Ibid. In FMP Model, labor-force base includes armed forces.12. Corporate profits before taxes, including inventory valuation adjustment.13. Based on monthly BLS figures. OBE: 1957—59= 1.00. Wharton: 40

hours = 1 .00 (manufacturing and nonmanufacturing).14. Unpublished BLS series.15. Based on monthly Census figures. Deflated by Wholesale Price Index for

durable-goods manufactures.16. Ibid. in Wharton Model, equals unfilled orders for all manufacturing. De-

flated by corresponding Wholesale Price Index series.17. Ibid.18. Ibid.19. Based on monthly Federal Reserve System data.20. Based on monthly Moody's Investors Service series. In FRB-MIT Model,

the A bond yield.21. Based on monthly BLS labor income and man-hours data. in Wharton

Model, wage rate (quarterly earnings at annual rate), weighted averagefor manufacturing and nonmanufacturing. In FMP Model, rate of compen-sation in nonfarm private domestic sector.

22. Based on monthly OBE data.23. Based on monthly Federal Reserve System data.a Seasonally adjusted.

Quarterly, seasonally adjusted.

the results of any particular distribution of the shocks that could wellbe highly idiosyncratic.

The sections that follow deal successively with these three typesof simulations, thus proceeding from the shortest to the longest ones.The six-quarter simulations (a) can be viewed as conditional predictionsover selected, relatively short periods. They are conditioned on theex post values of the exogenous factors, and on the structure of the

t

model estimateding point episodesperiod values inThe sample-periodsame sense, but thproximately) II, IModels, respectiveinitial conditions asfuture: a period witime yet—unknownprojections (controvarious assumptionjworking purposes

or consulInstead, their functistics of the modebperiments with the

1.3 SOME PRORLE

Differentanalyticalaround businessreproduction oftudes of cyclical ssegments of theperiod simulationscycle patterns.some results of timsion analysis, to saccuracy of predicinto the futureactuals are made iirelative size of movvariables is

BUSINESS CYCLE ANALYSIS OF MODEL SIMULATIONS 319

Table I. I. line 1.

58 dollars.

includes armed forces.-med forces-y valuation adjustment.9 = 1.00. Wharton: 40ng).

holesale Price index for

r all manufacturing. De-

es. In FRB-MIT Model,

hours data. In Whartonrate), weighted averageModel, rate of compen-

hocks that could well

these three typesst to the longest ones.onditional predictionsre conditioned on then the structure of the

model estimated from the sample-period data, which include the turn-ing point episodes covered here. Being reinitiated from actual base-period values in each new run, they predict six successive quarters.The sample-period simulations (b) are conditional, or ex post, in thesame sense, but they have much longer predictive spans: up to (ap-proximately) II, 14, and 20 years, for the FMP, OBE, and WhartonModels, respectively. Finally, the stochastic simulations (c) start frominitial conditions as of the end of the sample-period, and look into thefuture: a period which is for the most part unknown and—for a longtime yet—unknowable. These simulations are based on nonstochasticprojections (control solutions) of each of the models, which embodyvarious assumptions—some, reasonably well founded; others, made forworking purposes only. In a purely formal sense, these simulations areex ante model forecasts over a long stretch of time, but they were notintended, or constructed, to serve any practical forecasting purposes.Instead, their function is to help us evaluate some important character-istics of the models and to compare the evolution charted in these ex-periments with the historical movements of the economy.

1.3 SOME PROBLEMS OF MEASUREMENT AND INTERPRETATION

Different types and aspects of simulations require differentanalytical methods and measures. For the six-quarter simulationsaround business cycle turning points (Part 2), the emphasis is on thereproduction of turning points, the timing of these turns, and the ampli-tudes of cyclical swings—all in comparison with the correspondingsegments of the actual series. The measures applied to the sample-period simulations (Part 3) range widely, from the NBER reference-cycle patterns, cyclical timing and amplitude comparisons, throughsome results of time-series decomposition and correlation and regres-sion analysis, to selected summary measures of absolute and relativeaccuracy of prediction. For the long stochastic simulations extendinginto the future (Part 4), broad comparisons with the sample-periodactuals are made in terms of the average frequencies, durations, andrelative size of movements. The relative timing of the various simulatedvariables is analyzed, and an attempt is made to find out whether the

-J


simulated series can be classified as leaders, coinciders, and laggers—in the same way in which the historical indicators were classified.

This diversification of the techniques and tools used (still under-stated in the above summary) reflects the difficulty of any attempt toestablish the degree of verisimilitude of a model as an analogue of theeconomic system in motion. The task is necessarily intricate, for itinvolves study of relationships of various kinds, between differenteconomic processes and over time. Incomplete knowledge of the past,and ignorance of the future, reduce the potential attainments of theanalysis. Recurrent, diverse, cumulative, and widely diffused expan-sions and contractions in economic activities, which underlie aggrega-tive cyclical fluctuations, have been a persistent feature of highlydeveloped capitalistic economies of the modern era. To what extentthey will continue in this role in the future, no one can predict withconfidence: it depends on structural changes in the economy, thesuccess of economic policies (and of the underlying forecasts), inter-national developments, and so on. All we have as a measurable criterionfor evaluating the model-results is the past evolution of the economy.This compels a particularly cautious interpretation of any findings forthe long-term simulations.

The results for the different models are not directly comparablefor at least two reasons. First, there are differences between the sampleperiods (e.g., the simulations start late in 1948 for the Wharton Model,in 1953 for OBE, and in 1956 for FMP). This can strongly affect therelative performance of the models. As a task for the future, it would bemost desirable to recalculate the simulations with one common sampleperiod for all included models. Secondly, models differ in coverage: inparticular, what is endogenous in one model may be exogenous inanother. This is a major problem for comparing models of differentscope, with respect to their predictive performance [7, Sec. E- 1], but itis not so serious for our study, which concentrates on a subset ofselected variables that are basically common to, and endogenous in, allof the models covered. However, some points of difference ought to benoted. Comprehensive aggregates, such as GNP, include certain exog-enous components in each case, but they are not always exactly thesame across the models. Thus, in the Wharton Model, the parts of realGNP originating in the farm sector, and in the government sector, are

r

exogenous; in the 01goods and services,are treated exogenoof expgovernment purcha[18], [25]. FurtherWharton, while exptary imports). Of vthe money supplysists of currency(endogenous). Themonetary factorstreatment of thethe Wharton Modelt

Because of thdparts of thisever, comparisonssome of them mayhave something to s'different types of si

2 SIX-QUARTEIREFERENCE'

BUILDERS ofmodels are short-t1would tend toously for manyto test the efficacyrationale for this cosuch as consumptistructurally differetype of model shoUtime-spans. Since si4without any

t

OR

ciderS. and laggers—were classified.

lois used (still under-of any attempt to

5 an analogue of thearily intricate, for its. between different

of the past,attainments of the

dely diffused expan-ch underlie aggrega-fl feature of highlyera. To what extentne can predict withthe economy, the

ing forecasts), inter-measurable criterionion of the economy.

'n of any findings for

directly comparablebetween the sample

the Wharton Model,n strongly affect theie future, it would beone common sample

in coverage: inay be exogenous inmodels of different[7, Sec. E-lJ, but it

ates on a subset ofFid endogenous in, all

ought to beinclude certain exog-t always exactly thedel, the parts of real'ernment sector, are

BUSINESS CYCLE ANALYSIS OF MODEL SIMULATIONS • 32 1

exogenous; in the OBE Model, in addition to government purchases ofgoods and services, and investment in farm structures, housing servicesare treated exogenously; and in the FMP Model, only the federal partof government expenditures is exogenous, while the state and localgovernment purchases are handled essentially as endogenous [13],[18], [25]. Furthermore, exports and imports are endogenous forWharton, while exports are exogenous for OBE and FMP (as are mili-tary imports). Of variables other than real expenditure components,the money supply (M) deserves attention. In the OBE Model, M con-sists of currency outside banks (exogenous) and demand deposits(endogenous). The FMP Model, which is particularly concerned withmonetary factors and financial markets, also adopts this differentialtreatment of the two components of M. The variable does not appear inthe Wharton Model.

Because of these differences in sample-periods and scope, largeparts of this report deal with each of the models separately. How-ever, comparisons between the models will inevitably be made, andsome of them may be justified if they are framed with caution. We shallhave something to say on this subject in summarizing the results of thedifferent types of simulation.

2 SIX-QUARTER SIMULATIONS AROUNDREFERENCE TURNS

BUILDERS of cyclical models have stressed—correctly-—that theirmodels are short-term models, that cumulations of short-run errorswould tend to distort the results of simulations which are run continu-ously for many quarters, and that, therefore, it would be inappropriateto test the efficacy of the models by long-run simulations only. Anotherrationale for this contention is the argument that dynamic relationships,such as consumption responses to cyclical swings of income, may bestructurally different in the short run and in the long run. Thus, thistype of model should be tested for its efficacy over relatively shorttime-spans. Since such tests may not be very interesting over stretcheswithout any cyclical turns, we tested the models by a more stringent

r y

322 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR BUSIN

criterion; that is, by their performance during six-quarter periods whichinclude cyclical turns in general business conditions. Specifically,simulations were carried out for six-quarter periods beginning, alterna-tively, three quarters, two quarters, and one quarter before each busi-ness cycle turn. In these simulations, the endogenous variables werederived by using actual values for the quarter preceding the simulationand letting the model determine subsequent values; exogenous vari-ables were used throughout the simulation period at their historicallevels. The resulting configurations of twenty specified variables werecompared with the actual behavior of these variables during the cor-responding periods. The following three behavioral characteristics ofthe simulated and actual series were investigated: (a) Did cyclicalturns occur in simulated and actual behavior? (b) If so, what were thetiming relations between simulated and actual turns? (c) What were thecomparative amplitudes of simulated and actual cycle phases?

2.1 INCIDENCE OF TURNING POINTS

For the Wharton Model, the sample period starts in the thirdquarter of 1948 and ends in the fourth quarter of 1964, but the simula-tions are extended through the first quarter of 1968. Thus, they includefour reference troughs (1949-IV, 1954-Ill, 1958-11, and 196 1-1) andthree reference peaks (1953-lI, 1957-111, and 1960-lI). The Office ofBusiness Economics (OBE) sample period starts in 1953-lI and ends in1966-I V. including three troughs and two peaks. The Federal Reserve-MIT-PENN (FMP) Model has the shortest sample period, extendingfrom 1956 to 1966 and covering two troughs and two peaks only.

61.1For each variable and for each turning point covered by a given

model, we compared the simulated behavior produced in the three 550 -simulation runs with the actual behavior of the particular variable.Chart 2. 1 contains a selection of these comparisons. We reproduced 525 -

charts only for those variables and turning points which were common—

to the three models. The charts are arranged in such a way that theWharton Model is on the left, the OBE in the middle, and the FMP on 475the right. The top panel shows comparisons for the 1957 peak; thesecond panel, for the 1958 trough; and so on. In each diagram, the

t

kiarter periods whichSpecifically,

Is beginning, alterna-ker before each busi-

variables wereeding the simulationes: exogenous van-

d at their historicalified variables werebles during the cor-al characteristics ofd: (a) Did cyclicalIf so, what were thes? (c) What were the'cle phases?

starts in the third964, but the simula-• Thus, they includeII, and 196 1-1) and0-lI). The Office of

1953-11 and ends in

Federal Reserve-

le period, extendingnd two peaks only.covered by a given

in the threeparticular variable.

bns. We reproducedIv hich were common

a way that theand the FMP on

the 1957 peak; theh each diagram, the

I


CHART 2.1

(Vonstoc/,astic Six—Quarter Sun tim tions

500 -

475 —

450 -

Wharton

57-3

425

4(5'l

FMP

57-3

I I

58-

I I

500

475 -

450 -

425 -

0400 —

550 —0

— 525 —

Gross National Product

08E57-3

- 58-2

60-2

- 61-1

- 58-2

I I I I I I I I I I I

I

61-1

2 4 4 2 0 2 4Number of quarters before and after turning points

(continued)

I


500

475

450

425

0400

CHART 2. I (continued)

Gross National Product, 1958 Dollars

— I

I I

I I I I I I I I

r

Wharton OBE FMP57-3 — 57-3 — 57-3500 -

I'll'— 58-258-2

— 50-2C 5500

525Co

500

475

60—2

— 58-2

— 60—2

1_ I I

61-1

4 2 0 2 4

550 - 61-1

525 -

500 -

475

450 I I ,4 2 0

61-1

___________________________

2 4Number of quarters before and after turning points

4 2 0 2 4


CHART 2.1 (conti,zued)

Investment in Nonfarm Residential Structures

FMP

- 57-3

24 -Wharton OBE FMP

57-3 — 57-3 — 57-3

11111111I I

58-2t2522 -a° 19c 260

23

— 58-

60-2

- 60—2

I I I

—

I I I I

61-1

Number of quarters before and after turning points

(continued)

4


Wharton57-3

I I I


Investment in Plant and Equipment

r

BUSINE

Wharton

55—

50 -

x45 -

35

50 — 58-2

45

x

30 I I _I

C 55 60-20

-50

—

OBE FMP

57-3 — 57-3

111111 liii liii58-2

II liii

58—2

II I I60-2 — 60-2

liii I 1111111161-1. - 61-1

II liii III 112 0 2 44 2 0 2 4

45

40

0

C

0

50

45

40

- 61-1

4 2 0 2 4Number of quarters before and after turning points

4 2 0

L

Wharton57-3

-- I I I

I

I

FMP

57-3



Change in Business Inventories

10

5

0

—5

OBE

- 57-3

I I I I

FMP- 57-3

58-2- 58-2

- 60-2

1111

__j_I II— 60-2

I I I I

61-1

I I I

4 2 0 2 4

— 60-2

61-1 61-1 61-1

I I I I I I

Number of quarters before and after turning points

(continued)

4 2 0 2

I

4 2 0

FMP57-3

I I I I

58-2

I I_J

- 60-2

I328 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR

CHART 2.1 (continued)

Total C,viJian Employment

r

70

68

66

64

Wharton- 57-3

I I I

B US IN

Wharton

10

8

6

4

2

10

S

6

4

C

OBE

57-3

I I I

58-2

I I I

- 60-2

I I I

- 61-1

70 - 58-2

0 64 -

62 I I I

60-2

o I

64 I I

72 - 61-1

70 -

68X

66 -

I 24 42 024 4 2 0 2 4Number of quarters before and after turning points 't 2 0 2

1'


FMP

57-3

C HART 2. I (continued)

Unemployment Rate

OBE57-3

10

8

6

4

2

Wharton57-3

FMP— 57-3

III

I

58-2

I I I I

58-2

6

I I I I

I

I I

61-1

I I

4

I I I I

4

—

I I I I I I I

2 42 0 2 4Number of quarters before and after turning points

(continued)


CHART 2.1 (continued)

Corporate Profits and Inventory Valuation Adjustment

r

Wharton

55 — 57-3

55 -

50

45

40

035

60

55

61-1

E

40 I

FMP

57-3x


C HART 2. 1 (continued

Average Yietd, Short Term

5

4

3

OBE57-3

Wharton- 57-3

I I

FMP57-3

2

III5

58-2

4

3

58-2

2 / 58-2I II I

60-2

TN60—2

5

60-2

4

I I I

60—2

3

61-1

I I I I I I

6

5

4

61-1

3Z_4

61-1

2 0 2 4 4 2 0 2 4 4 2 0 2 4Number of quarters before and after turning points

(continued)

RIJSIN1

actual is shown asbefore the turn istwo quarters

before theare connected to thtin the actuals are rn

Our investigatiomust begin with thtask, never an easy othe data refer to shouse

existing computlion period makes itrection are cyclicallof short duration.turns fall close to thcausing the observalindeed. Third, it isof the amplitude ofqualify as a cyclicadeciding in favor of

The determinatimay require conside,to a puzzlingor after the six-quartltion be considered sUseries experiences ashould it because during the simicircumvented this prway is to take onlyturns occurred in ththem with turns in thsample by utilizing oshortly before and afshowed a peak shorand the simulated s

r

Wharton

5.0 -FMP57-3

I I I I I I I

5.0-- 58-2

3.5 -

3.0 I


CHART 2.1 (conc/ttded)

Average Yield, Long Term

OBE

- 57-3

— 58-2

__________ ___________

I I I I I I

— 60-2

I I I I

61-1

__________

I I

C

5.5 -

5.0

4,5

58-2

- I I_______60-2

I I I I

60-2

4.0 -

I I I

— 61-1

4.0 -

3". I I I I4

61-1

I I I I I

2 0 2 420 4 4 2 0Number of quarters before and after turning points

2 4


actual is shown as a solid line; the simulation starting three quartersbefore the turn is delineated by boxes (LII): the simulation startingtwo quarters before the turn by x's; and the simulation starting onequarter before the turn by asterisks. In each case, the simulation resultsare connected to the last available actual observation. Turning pointsin the actuals are marked by X's.

Our investigation of the incidence of successfully simulated turnsmust begin with the determination of cyclical turning points. Thistask, never an easy one, is complicated by several circumstances. First,the data refer to short, nonconnected periods, making it impossible touse existing computer programs. Second, the shortness of the simula-tion period makes it difficult to decide whether observed changes in di-rection are cyclically significant or merely reflect random movementsof short duration. This is particularly difficult whenever the suspectedturns fall close to the beginning or the end of the six-quarter period,causing the observable part of one of the phases to become very shortindeed. Third, it is difficult to determine whether the observable partof the amplitude of a particular movement is large enough for it toqualify as a cyclical phase. We resolved these problems largely bydeciding in favor of recognizing turns if this seemed at all reasonable.

The determination of turning points for the six-quarter simulationsmay require consideration of events outside this period. This gives riseto a puzzling problem: if actual series experience turning points beforeor after the six-quarter period chosen for simulation, should a simula-tion be considered successful when it shows a turn because the actualseries experiences a turn—albeit not within the six-quarter period? Orshould it be considered successful when it does not show a turn, be-cause during the simulation period the actual shows no turn either? Wecircumvented this problem by using two types of counts: the simplestway is to take only those instances of the actual series where cyclicalturns occurred in the six-quarter period under observation and matchthem with turns in the simulations. Alternatively, we used an increasedsample by utilizing our knowledge of the behavior of the actual seriesshortly before and after the simulation period. Thus, if the actual seriesshowed a peak shortly before the beginning of the simulation period

points and the simulated series continued downward, the simulation was

FMP57-3

I

334 ECONOMETRIC MODELS OF CYCLICAL BEHAVIORBUSINE

presumed to have produced a peak.3 Unfortunately, this procedure hasto be modified for series with long lags extending beyond the end of thesimulation period. In such situations, only those simulations which stillshowed a turn in the sample period could be recognized as successful.No assumptions could be made about simulated turns that might occurbeyond the sample period. The incidence of successfully simulatedturns is summarized in Table 2. 1. The upper panel refers to the larger LLsample, including the inferred prior turning points; the lower panelrefers only to those turns which actually occurred in the six-quarterperiod.

On the whole, all three models were fairly successful in reproduc-ing cyclical turns in the neighborhood of business cycle turns, particu-larly when the more liberal definition—which includes inferred turningpoints—was used. In almost all cases, the simulated series successfullyshowed "no turns" whenever there were no turns in the actual series. —We, therefore, based the "attainment rate" forthe simulation of cyclicalreversals on the number of actual turning points. —

We expected simulations starting one quarter before referenceturns to reproduce more turning points than those starting two or morequarters before. We had this expectation because we thought that onequarter before a reference turn the cumulative strains before peaks,and the gradual restoration of profits before troughs, are included inthe data used in the simulation. Conversely, data truncated as much as

'Take, for example, the unemployment rate at the 1957 reference peak (Chart2.1). The actual series has a trough in the first quarter of 1957. i.e.. two quarters '.before the reference peak. For the Wharton Model (furthest left in the chart) the sim-ulation starting in 1956-tV, i.e., three quarters before the turn, also shows a trough in1957-I. This is unproblematic. For the simulation starting two quarters before the ref-erence turn, a trough can be found in the first simulated observation if we connect thesimulations with the last available actual before the start of the simulation. This troughis still located within the six-quarter simulation period and is counted as a turn in thelarger. as well as in the more restrictive, sample. The last simulation, however. starts in1957-Il, i.e., one quarter after the trough in the actual. Although one can infer the exist-ence of a trough from the upward direction of the simulated series, it did not occur duringthe simulation period. Hence, this simulation is counted as having successfully repro-duced a turning point in the larger sample, but neither the actual nor the simulated turnis counted in the sample which is restricted to the six-quarter period.

The case is still more complicated for a configuration like that of the OBE simulationsof this series at the same turning point (upper panel, middle row). Here all three of thesimulations are higher than the last actual, so that in each case the inferred trough occursin the quarter before the simulation starts. All are counted in the extended sample; noneof the simulations and only the first two actuals are counted in the smaller sample.

IR BUSINESS CYCLE ANALYSIS OF MODEL SIMULATIONS 335

this procedure hasthe end of the

knulations which stillas successful.

ms that might occurcessfully simulated

-I refers to the largerts: the lower paneld in the six-quarter

cessful in reproduc-cycle turns, particu-des inferred turningd series successfullyin the actual series.

jrnulationofcyclical —

er before reference -.iLU

starting two or morewethoughtthatonetrains before peaks, F-,

ghs, are included inruncated as much as

7 reference peak (Chart1957. i.e.. two quarters

left in the chart) the sim-m. also shows a trough in'o quarters before the ref-rvation if we connect thee simulation. This troughcounted as a turn in the

ulation, however, starts in-Cgh one can infer the exist-

ies,itdidnotoccurduringlaying successfully repro-ual nor the simulated turnperio .

at of the OBE simulationsow). Here all three of thethe inferred trough occurshe extended nonein the smaller sample.

LU

C

?

E

<

E'

E(.1)

c.

Z

v

,

a—

a•C,')

©

r—

r—

— — —

I..

.0 .0

—

— r,4 e•-i

.

._-.

•

.•I—

— —

v v

v

oV )V.0 .0 .0

—

'I'

i

E

E

'-C.

C..E

.9—

.E

v—

336 ECONOMETRIC MODELS OF CYCLICAL BEHAVIORB 1) SINE

three quarters before changing business conditions should not be ex-pected to reflect, to the same extent, the dynamic processes precedingcyclical turns. As it turns out, these expectations have not generallybeen met, either by the six-quarter periods (lower panel), or by theextended sample periods (upper panel). The reason may be as follows:as the beginning of the six-quarter period approaches the referenceturn, fewer specific turning points occur, both in the actual series and inthe simulated ones. This is because more specific turns occur twoquarters before reference turns (the quarter omitted as we go fromthe second to the third simulation) than four quarters after referenceturns (the quarter added). This is true for the actual series (see Table2.1, second panel, columns 1, 4, and 7), as well as for the simulatedseries (columns 2, 5, and 8). Whenever the simulated series lead theactuals, as seems to be the prevailing tendency for the Wharton Model(see Section 2.2 below), more turns get lost in the simulations than inthe actual. For the extended sample period, no turns are actuallycut off in the beginning by shifting the sample period. All the same, itseems that for the Wharton Model, simulations starting one quarterbefore peaks showed fewer turns (actual or imputed) than those startingtwo quarters before. One series for which this happens rather consist-ently is the average workweek, which is known to be a leading series.

We also expected the simulations to be more successful in repro-ducing troughs than in reproducing peaks. The reasons for this expecta-tion are basically that the contours of troughs are often more sharplydefined, and that the turning points are more closely clustered aroundreference troughs than around reference peaks. This can be observedparticularly during the postwar period and is largely due to long-termupward trends, government intervention to end recessions, the absenceof "drag" factors (such as backlogs, contractual obligations, gestationperiods—as they exist at peaks), and the rapid expectational changes,based on these elements. We thought that these characteristics mightbe reflected in the structure of the models and would certainly be im-posed upon the simulations by actual reversals in the exogenous van-ables—rnuch more decisively than in the neighborhood of referencepeaks. We expected that all of these elements would increase the likeli-hood of reversals in the neighborhood of troughs falling within oursix-quarter simulation period.

t


0

C

LU

C

C

C

IOR

should not be ex-processes precedinghave not generally

panel), or by themay be as follows:

oaches the referencehe actual series and in:ific turns occur two

as we go fromarters after referencetual series (see TableI as for the simulatedulated series lead the

the Wharton Modelie simulations than in

turns are actuallyeriod. All the same, it

starting one quartered) than those startingappens rather consist-to be a leading series.e successful in repro-

asons for this expecta-re often more sharplysely clustered aroundThis can be observedgely due to long-term

ecessions, the absenceobligations, gestation

changes,characteristics might

vould certainly be im-in the exogenous van-borhood of reference

kuld increase the likeli-falling within our

—

0I-H

—


TABLE 2.3

,Vo,,stocliastic Six-Quarter Simulations: Relative Frequencyof Inferred Prior Peaks and Troughs

(as per cent of a/I turns)"

StartWharton

of Simulations Model(1)

OBEModel

(2)

FMPModel

(3)

I

2

3

3

2

I

At reference troughsQ before troughs 3Q before troughs 14Q before troughs 37

3

Ii37

68

8

4

5

6

3

2

1

At reference peaksQ before peaks 14Q before peaks 15Q before peaks 42

505048

192558

7

8

9

3

2

I

At a/i reference turnsQ before turns 8Q before turns 15Q before turns 39

21

2741

13

16

29

"The inferred prior turning points in simulations (see text andTable 2.1, note a) are expressed as percentages of all turningpoints in the simulations (as listed in Table 2. 1, lines 1 to 3,columns 2, 5, and 8).

However, the evidence summarized in Table 2.2 does not showany systematic difference between successful duplication of peaks andof troughs.4 Perhaps we should investigate to what extent this may re-flect the failure of the models to distinguish the difference in cyclicaldynamics in the neighborhood of peaks and troughs; and to what extentit portrays the relative weakness of the exogenous variables in im-posing characteristic cyclical behavior on the simulation patterns.

r

BUSINE1

Although thereasons stated in Sectof reproducing turnrates. The reason

for the period IModel is retained e'based on this shorterperformance is causwith a shorter sampl

2.2 TIMING COMPA1

For Tables 2.4points in the actualserved cyclical turnswe neglect the instalwere inferred.

The majority ofquarter of those in th1turns of theseries, those onein the actual series.

The relativespan — centered aroutsimulations andtroughs.

Given the sma]ldof troughs, we wouk4closer to the actualevidence does not rperhaps because thelags (which are moretion. Alternatively. ttroughs may be aused by the models.

The incidence oil

"There is a facet of this experiment where the wider spread of turning points in theneighborhood of peaks does cause the six-quarter periods before troughs to differ fromthe six-quarter periods before peaks: for the actual, as well as the simulated, series moreturns had to be inferred before peaks than before troughs, relative to the turns actuallyoccurring in the six-quarter period. (See Table 2.3.)

21 13

27 16

41 29

ons text andes of all turning

lines Ito 3,

le 2.2 does not showlication of peaks andat extent this may re-difference in cyclicalis; and to what extent

hous variables in im-simulation patterns.

rad of turning points in thetroughs to differ from

the simulated, series moreto the turns actually

r

OR

jire FrecilteJlL"

BE FMPodel Model

(2)

3 6

II 8[37 8

50 19

50 25

48 58


Although the three models cannot be directly compared—for thereasons stated in Section .3 above — it must be noted that in the matterof reproducing turning points, the FMP Model has higher attainmentrates. The reason for this is not that fluctuations are more easily simu-lated for the period 1957—61, since the better performance of the FMPModel is retained even when comparisons for the three models arebased on this shorter period. Nevertheless, it is possible that the betterperformance is caused, at least partly, by the better fits associatedwith a shorter sample period.

2.2 TIMING COMPARISONS

For Tables 2.4 and 2.5; timing comparisons between the turningpoints in the actual and the simulated time-series are based on ob-served cyclical turns falling into the six-quarter periods only. That is,we neglect the instances in which turns falling outside those periodswere inferred.

The majority of turns in the simulated series occurred within onequarter of those in the actual series. Table 2.4 shows the percentages ofturns of the simulated series which coincided with turns in the actualseries, those one quarter away, and those yet further away from turnsin the actual series.

The relative frequency of simulated turns outside the three-quarterspan—centered around the turn in the actual—is lowest in the FMPsimulations and highest in the Wharton Model, both for peaks and fortroughs.

Given the smaller dispersion of turning points in the neighborhoodof troughs, we would have expected simulated turns at troughs to becloser to the actual ones than simulated peaks are to actual peaks. Theevidence does not show any systematic difference in performance,perhaps because the simulation period is so short that long leads andlags (which are more frequent at peaks) fall outside the span of observa-tion. Alternatively, the unexpected similarity of behavior at peaks andtroughs may be a consequence of the constancy of the lag structureused by the models.

The incidence of leads and of lags is different for the three models.

N

L

00a)

C,,

a)

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C_. 5#5

a) 00C,

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00

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I

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340 ECONOMETRIC MODELS

C',

E

H

OF CYCLICAL

r— NN

BEHAVIOR

NN — —

•

00

I

The Wharton Modelof simulated series cdModel shows moreany systematic preferin the simulations

—

0

streference turns, withone quarter before).

One important qi.

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which exithose shown by the ain the simulatedcoinciders coincidewere classified intohistorical performanctleads), coincidences,that can be matched2.6. The evidence revlated series. For the

C',

00

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N S 0

N — N

a)a)a)I.. C..

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series in all three gromost of the simulated

.

series show a tendenduces more leads thaicentage of leadersthan that in the actuall

The bias toward Itbefore the start offerred turns of the sir4shows that for theseriously affected by Igroup IS reducedabout half (if only th(few long leads—i.e.,

Wharton Model, leadiniGNP58, C. YP, LE. UN:same as Wharton. plus.series: same as Wharton pl

— N N 00 0\OUME: coinciding series:ton.

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The Wharton Model shows a clear preponderance of leads in the turnsof simulated series compared to those in the actual ones; the FMPModel shows more lags than leads; and the OBE Model does not showany systematic preference for leads or lags (leads being more frequentin the simulations starting three quarters and two quarters beforereference turns, with lags predominating in the simulations startingone quarter before). The numerical findings are given in Table 2.5.

One important question is whether the models generate simulatedtime-series which exhibit the same general timing characteristics asthose shown by the actual variables. In other words, do turning pointsin the simulated leading series lead business-cycle turning points? Docoinciders coincide and laggers lag? The series included in each modelwere classified into leaders, coinciders, and laggers, according to theirhistorical performance.5 For each group, leads (including inferredleads), coincidences, and lags—expressed as a percentage of all turnsthat can be matched with business-cycle turns—are shown in Table2.6. The evidence reveals a distinct bias toward early turns in the simu-lated series. For the Wharton Model, the majority of the simulatedseries in all three groups lead at reference turns. In the OBE Model,most of the simulated leading and coinciding series lead, while laggingseries show a tendency to coincide. The FMP Model generally pro-duces more leads than lags, but the bias is a little less strong. The per-centage of leaders in the simulated leading series is actually smallerthan that in the actual leading series.

The bias toward leads is substantially reduced if we exclude turnsbefore the start of the six-quarter period (actual turns as well as in-ferred turns of the simulations). The evidence, presented in Table 2.7,shows that for the actual series only those classified as leaders areseriously affected by this exclusion. The proportion of leads for thisgroup is reduced from about two-thirds (if all turns are considered) toabout half (if only those in the six-quarter period are counted). Sincefew long leads—i.e., turns before the start of the six-quarter simulation

Wharton Model, leading series: IH. II. CPR,AWWS UMD: coinciding series: GNP.GNP58, C, YP, LE. UN. lagging series: ISE, RS, RL. OBE Model, leading series:same as Wharton. plus OMD. HS, and M; coinciding series: same as Wharton: laggingseries: same as Wharton plus LC/O. FMP Model. leading series: IH. 11. CPR. LH andOUME; coinciding series: GNP, GNP58. C. Y. LE. UN: lagging series: same as Whar-ton.

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)

C z m ci) rn z ci) ci) 0 m 0 rn ci, C > H 0 z ci,

344 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR BUSINESS

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period—occur in the acentage distributions fo'the simulated series, oicoincident series, as wtoward leads isfrom the count.period only, leads are rJin the actuals for all grdthe leaders in the FMp;

On the whole, thenjbetween theview of the importanceit should benection between thein the simulations.

2.3 AMPLITUDES

Amplitude measur€tion—can obviously de!contractions whichspite of this truncation,systematic differences Iand actual amplitudes:variously timed simulati

A glance at the chafthe patterns of the simutudes which are morefinding is that the pattedother than to the actualltime-staggered simulatioften true across modelulations may be explarelatively slowly and, tiulations are fairly similare typically more succ

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SUSINESS CYCLE ANALYSIS OF MODEL SIMULATIONS • 345

period—occur in the actual coinciding and lagging series, the per-—

centage distributions for those two groups are not much affected. Forthe simulated series, on the other hand, long leads were inferred forcoincident series, as well as for some lagging ones. Thus, the bias

. . .— — toward leads is somewhat reduced by eliminating the inferred turnsfrom the count. However, even for turns occurring in the six-quarterperiod only, leads are relatively more frequent in the simulations thanin the actuals for all groups except the laggers in the OBE Model andthe leaders in the FMP Model.

On the whole, then, the simulations discriminate only very weaklybetween the historically leading, coinciding, and lagging variables. Inview of the importance of lead-lag relationships in economic dynamics,it should be worthwhile to investigate whether there exists any con-nection between the model formulations and the timing biases observed

C C — in the simulations.o

2.3 AMPLiTUDESc)

Amplitude measures—in the framework of the present investiga-lion—can obviously describe only those segments of expansions andcontractions which occur during the six-quarter simulation periods. Inspite of this truncation, it is of interest to establish whether there aresystematic differences between the observable portions of simulatedand actual amplitudes: among different variables, cyclical phases, andvariously timed simulations.

A glance at the charts shows one fact quite clearly: in most cases,the patterns of the simulated series are flatter—i.e., they have ampli-tudes which are more shallow than those of the actual series. A relatedfinding is that the patterns of simulated phases are more similar to eachother than to the actual ones. This is particularly striking for the threetime-staggered simulations produced by the same model: but it is alsooften true across models. The similarity among the time-staggered sim-

E ulations may be explained by the fact that cyclical conditions varyE relatively slowly and, therefore, the initial conditions for the three sim-

ulations are fairly similar. Furthermore, forecasts for the first quarterare typically more successful than those for later quarters. The family


resemblance of simulations produced by different models may be dueto the fact that all models reflect only the systematic portion of cy-clical interactions, which during any historical period, represent only apart of economic reality. It is. of course, also possible that the threemodels have some common biases and that this is the reason why theyresemble each other more than they resemble reality.

In order to give some precision to these impressions, amplitudeswere computed for the observable part of expansions and contractionsin the actual and the simulated series for each simulation that containeda cyclical turning point.6 As a first step in the analysis. we determinedthe frequencies with which simulated amplitudes were smaller than,similar to, or larger than, those of the actual series. Differences of onepercentage point and less (for UN, II, RS, and RL. differences of 10per cent and less in the absolute differences) were regarded as negligi-ble, and the amplitudes were tabulated as similar. The frequencies aresummarized in Table 2.8. For each model, for each type of time-stag-gered simulation, and for all expansions and all contractions, the fre-quencies are expressed as a percentage of all comparisons feasible inthat class.

On the whole, simulated amplitudes underestimate actual ampli-tudes more often than they overstate or equal actual amplitudes. As thetable shows, this is equally true for expansions and contractions, foreach of the time-staggered simulations, and for each model.1 The oneexception occurred in the Wharton Model, for which this tendency isgenerally somewhat less pronounced. The incidence of underestima-tion amounts usually to more than half of all cases, except in the Whar-ton Model, where the incidence of underestimating expansions is onlyabout 40 per cent.

Let us turn from the analysis of incidences to that of measured am-plitudes. Table 2.9 presents average expansion and average contrac-

6 Since no direct comparisons between expansion and contraction amplitudes wereintended, the percentage-base bias of amplitude measures could be neglected. and rela-tive amplitudes could simply be measured as percentage changes from initial levels. Incase of rates and differences (for UN, Ii. RS. and RL). absolute changes rather thanpercentage changes were computed.

It is also true for each cycle, for phases before and after the turn, and for most activi-ties. A minor exception, not shown in the summary table, is theexpansion preceding the1958 peak for the FMP Model, where the simulations overestimated amplitudes foralmost all variables.

BUS IN

tion amplitudes of alliThe average amplituimodel cover all incilthus, thethe differentthere is a correspon4sponding actual phasulations included inThe comparisonsages of the simulatedamplitudes: forare more than 20 perjulations seem to undare difficult to make,amplitude averages.

In order to incriof those cycle phaselnod and the same wIattempt to increase cja sharp reduction in1plicity, and in view otisimulations, we usedreference turns. The:the incidence of undipervasive, particularltimation varylarge variation inprovides averages fosolute and relative dithe smaller amplitudshows that for the s1very close to actual athe FMP Model giv

6Since the average of pedifferences which may be.expansion phase in Table 3amplitudes (which gives lai

[OR

4-


models may be due

:matiC portion of cy-iod, represent only a)ssible that the three

the reason why they

ressiofl5, amplitudesons and contractionsilation that containedtlysis. we determineds were smaller than,

s. Differences of onedifferences of 10

regarded as negligi-The frequencies are

ch type of time-stag-the fre-

nparisons feasible in

timate actual ampli-at amplitudes. As the

md contractions, forach model.7 The onehich this tendency ispnce of underestima-

except in the Whar-expansions is only

that of measured am-Lnd average contrac-

traction amplitudes wereId be neglected, and rela-ges from initial levels. In

olute changes rather than

e turn, and for most activi-e expansion preceding theestimated amplitudes for

tion amplitudes of all variables included, irrespective of comparability.The average amplitude measures presented for each variable in eachmodel cover all incidents for which amplitudes could be measured:thus, the composition of the measures is not strictly comparable amongthe different variables or models. Comparability exists only insofar asthere is a corresponding expansion for each contraction, and a corre-sponding actual phase for each simulation phase. The number of sim-ulations included in each average amplitude is indicated in the table.The comparisons show that for a large majority of variables, the aver-

• ages of the simulated amplitudes are smaller than those of the actualamplitudes; for about 60 per cent of the possible comparisons, they

• are more than 20 per cent below the actuals. The Wharton Model sim-ulations seem to underestimate less than the others, but comparisonsare difficult to make, because of the heterogeneous composition of theamplitude averages.

In order to increase comparability, we present comparisons onlyof those cycle phases which could be measured for the same time pe-riod and the same well-defined economic process in all models. Thisattempt to increase comparability from model to model brought abouta sharp reduction in sample size. Furthermore, for the sake of sim-plicity, and in view of the observed similarity among the time-staggeredsimulations, we used only the simulations starting two quarters beforereference turns. The results appear in Table 2.10. Again we find thatthe incidence of underestimation of amplitudes by the simulations ispervasive, particularly for contractions. The magnitudes of underes-timation vary widely. In spite of problems of summarization, due to thelarge variation in size among the amplitudes themselves, Table 2. 11provides averages for simulated and actual amplitudes, and for ab-solute and relative differences.8 Again, the summary measures showthe smaller amplitudes of the simulations. Intermodel comparisonshows that for the simulations included, the Wharton Model comesvery close to actual amplitudes during expansions. During contractionsthe FMP Model gives closer approximations than do the other two

8Since the average of percentage differences gives a large weight to large percentagedifferences which may be based on very small amplitudes (see, for instance, the lastexpansion phase in Table 2.10). we also provide the percentage difference of the averageamplitudes (which gives larger weight to large amplitudes, e.g., corporate profits).


models. However, comparisons among models remain very uncertain,even for this less heterogeneous selection, since the sample is smalland the differences not very pronounced.

A major analytical interest concerns the reasons for the sweepingtendency toward underestimation of amplitudes shown by most simula-tions. It has been argued that most of the explanation can be found in

All Phases

Per Cent of All Phases

Start of Simulations

Numberof PhasesCompared

(1)

Compared

S < A S A S > A(2) (3) (4)

Wharton Model,1949-1961

1 3 Q before turn 104 36 28 362 2 Q before turn 96 51 27 223 1 Q before turn 70 44 34 224 All simulations 270 44 29 27

OBE Model5 3 Q before turn 90 64 29 76 2 Q before turn 84 67 27 67 1 Q before turn 76 59 30 118 All simulations 250 63 29 8

FMP Model9 3 Q before turn 62 62 19 19

10 2 Q before turn 72 67 15 1811 1 Q before turn 66 61 27 1212 All simulations 200 63 21 16

NOTE: S and A denote amplitudes of simulated and actual series, respec-tively. For UN, 11, RS, and RL, amplitudes were computed as absolutechanges between two turning points; for all other series, as percentage changesfrom initial levels.

B US IN

the systemic tendelchanges. Also, thereselecting turningted as peaks; and rastatement of the cylated series, on the

Comparisons Betweenci,icI 0

Nonstochastic Six-Quarter Simulations: A mplitudeIncidence of Underestimation

TABLE 2.8

Expansiol

Per Cl

S

kiain very uncertain,the sample is small

bns for the sweepingbwn by most simula-[lion can be found in

TABLE

niiilations: A mplitudee of

Eases

bent of All PhasesCompared

S>A(3) (4)

28 3627 2234 2229 27

29 727 630 1129 8

19 19

15 18

27 1221 16


the systemic tendency of regression techniques to underestimatechanges. Also, there is some bias inherent in the method used forselecting turning points. Randomly high observations tend to be selec-ted as peaks; and randomly low ones, as troughs—leading to an over-statement of the cyclical component of actual amplitudes. The simu-lated series, on the other hand, are constructed without imposition of

2.8

Comparisons Between A cow! and Simulated Series;and Overestimation

Expansions Contractions

Per Cent of All Per Cent of AllNumber Compared Phases

of PhasesCompared S < A S A S > A

Numberof PhasesCompared

Compared Phases

S.< A S A S > A(5) (6) (7) (8) (9) (10) (11) (12)

52 33 29 39 52 40 27 3348 52 19 29 48 50 35 1535 40 37 23 35 49 31 20

135 42 27 31 l35 46 31 23

45 65 24 11 45 65 33 2142 72 21 7 42 62 33 538 66 24 10 38 53 37 10

125 67 23 10 125 60 34 6

31 49 19 32 31 75 19 636 64 14 22 36 69 17 1433 67 21 12 33 55 33 12

100 60 18 22 100 66 23 11

actual series, respec-computed as absoluteas percentage changes

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business cycle analysis of econometric model simulations · 2017. 5. 5. · business cycle analysis...

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