Trade Growth and Trade Growth and InequalityInequality

Professor Christopher BlissProfessor Christopher BlissHilary Term 2004Hilary Term 2004

Fridays 10-11 a.m.Fridays 10-11 a.m.

Why the Poor Stay Why the Poor Stay PoorPoor

Chapter 3 of the bookChapter 3 of the book

(circulated)(circulated)

The Persistence of PovertyThe Persistence of Poverty

What are the transmission properties What are the transmission properties of income at t to income at t+1?of income at t to income at t+1?

Friedman (1992) regression to the Friedman (1992) regression to the meanmean

Incomes normally distributed and:Incomes normally distributed and:Positions randomPositions randomPositions fixedPositions fixed

Are All Agents the Same?Are All Agents the Same?

Herrnstein and Murray (The Bell Herrnstein and Murray (The Bell Curve)Curve)

Income=F(IQ)Income=F(IQ) They claim that technological change They claim that technological change

has been such that:has been such that:F(IQ))/F(100) has been falling over F(IQ))/F(100) has been falling over time for values of IQ well below the time for values of IQ well below the mean=100 mean=100

Adam SmithAdam Smith•Little else is requisite to carry a Little else is requisite to carry a

state to the highest degree of state to the highest degree of opulence from the lowest opulence from the lowest barbarism but peace, easy taxes, barbarism but peace, easy taxes, and a tolerable administration of and a tolerable administration of justice: all the rest being brought justice: all the rest being brought about by the natural course of about by the natural course of things. (Lecture 1775)things. (Lecture 1775)

Karl MarxKarl Marx

• The country that is more developed The country that is more developed industrially only shows to the less industrially only shows to the less developed the image of its own developed the image of its own future. (quoted by Myrdal 1968, p. future. (quoted by Myrdal 1968, p. 674) 674)

The Kuznets ModelThe Kuznets Model

• Initially population in low-level Initially population in low-level equalityequality

• Growth takes the form of movement Growth takes the form of movement to higher level “modern” productivityto higher level “modern” productivity

• While some move but not others, While some move but not others, inequality increasesinequality increases

• As all eventually modernize inequality As all eventually modernize inequality declinesdeclines

Problems with the Problems with the Kuznets storyKuznets story• The cross-section evidence does not The cross-section evidence does not

confirm it confirm it

• The idea of low-level equality is also The idea of low-level equality is also not in accord with the evidencenot in accord with the evidence

• The curve is caused by differential The curve is caused by differential adjustment rates – why does this adjustment rates – why does this happen?happen?

The Stiglitz MASS The Stiglitz MASS ModelModel

•Solow-Swan with many Solow-Swan with many agentsagents

•All supply same labour and All supply same labour and save the same proportion of save the same proportion of

all incomeall income

Stiglitz Model Stiglitz Model ResultResult

Let k* satisfy:Let k* satisfy:

s.F[k*,1]-s.F[k*,1]-g.k*=0g.k*=0

All agents converge to holding All agents converge to holding k*k*

Weakening Stiglitz Weakening Stiglitz assumptionsassumptions• The quantity of labour supplied by an The quantity of labour supplied by an

individual may vary with capital individual may vary with capital owned by that agent. It must have a owned by that agent. It must have a positive limit as positive limit as k k goes to zerogoes to zero..

• The share of saving in total income The share of saving in total income may vary monotonically with capital may vary monotonically with capital owned by the agent. It must have a owned by the agent. It must have a positive limit as positive limit as k k goes to zerogoes to zero..

Convergence and the Convergence and the Discount Rate Discount Rate • Utility and Consumption Discount Utility and Consumption Discount

Rates DistinguishedRates Distinguished

• Endogenous Discount RatesEndogenous Discount Rates

• Do the poor have high discount Do the poor have high discount rates?rates?

Discount Rates and Discount Rates and Dynamic Dynamic InconsistencyInconsistency• It is not necessary to assume that It is not necessary to assume that

the poor discount utility at a high the poor discount utility at a high rate (see below)rate (see below)

• Endogenous discount rates give Endogenous discount rates give inconsistency (Strotz)inconsistency (Strotz)

Strotzian Strotzian InconsistencyInconsistencyPeriodPeriod

ChoiceChoice

1 1 22 33

II 9595 2020 2525

IIII 9595 2222 2222

IIIIII 100100 1818 1818

Strotzian Strotzian Inconsistency cont.Inconsistency cont.• With consumption in the range 99 to 100 the With consumption in the range 99 to 100 the

discount factor (the weighting of future utility discount factor (the weighting of future utility against current) is approximately 0.9 per against current) is approximately 0.9 per period.period.

• With consumption in the range 20 to 22 it is With consumption in the range 20 to 22 it is not less than 0.5 per period.not less than 0.5 per period.

• Viewed from time 1 the present value of utility Viewed from time 1 the present value of utility for respectively I, II and III is 133.25, 132.65 for respectively I, II and III is 133.25, 132.65 and 130.78. In each case these totals are and 130.78. In each case these totals are arrived at using weights (1,0.9,0.81). arrived at using weights (1,0.9,0.81).

Strotzian Dynamic Strotzian Dynamic Inefficiency cont.Inefficiency cont.Now the discount Now the discount

factor is 0.5, hence factor is 0.5, hence the present values the present values of the part of the part sequences I and II sequences I and II are respectively are respectively 32.5 and 33. 32.5 and 33.

PeriodPeriod

ChoicChoicee

22 33

II 2020 2525

IIII 2222 2222

The Elasticity of Inter-The Elasticity of Inter-temporal Substitution temporal Substitution

(EIS)(EIS)

ηη =-c(d =-c(d22U/dcU/dc22)/dU/dc)/dU/dcIf dU/dc = uIf dU/dc = u

ηη =-c(du/dc)/u =-c(du/dc)/u

The Optimal Growth The Optimal Growth ConditionCondition-(du/dt)/u = F-(du/dt)/u = F11[k,1] – [k,1] – δδ

ηη(dc/dt)/c = F(dc/dt)/c = F11[k,1] – [k,1] – δδEIS*growth consumptionEIS*growth consumption= MPK – U discount rate= MPK – U discount rate

The Diamond Capital The Diamond Capital ModelModel• Consumer lives two periodsConsumer lives two periods• Supplies 1 unit of labour in Period 1Supplies 1 unit of labour in Period 1• Divides the wage between Divides the wage between

consumption and savingconsumption and saving• Aggregate saving is the economy Aggregate saving is the economy

capital stockcapital stock• That capital plus the return is Period That capital plus the return is Period

2 consumption2 consumption

Diamond Model:Diamond Model:kkt-1t-1 determines k determines ktt

• Max U[cMax U[ctt] + ] + U[cU[ct+1t+1]]

• Subject to:Subject to:

• cctt +(1/1+r +(1/1+rtt) c) ct+1t+1 k kt t +w+wtt

• wwtt = F = F22[k[kt-1t-1,1],1]

• 1+r1+rtt = F = F11[k[ktt,1],1]

Diamond ModelDiamond ModelThe fundamental The fundamental theoremtheorem•TheoremTheorem

•kkt t increases with kincreases with kt-1t-1

•This makes possible This makes possible multiple multiple equilibriaequilibria

Diamond MultiplicityDiamond Multiplicityand Poverty Trapsand Poverty Traps• This idea is not influential: Why not?This idea is not influential: Why not?

• Seldom realised in connection with Seldom realised in connection with two popular model features:two popular model features:stability of SS solutions of intereststability of SS solutions of interestsimple standard functional formssimple standard functional forms

Diamond Model:Diamond Model:The Corner Steady The Corner Steady StateState• Are there zero-capital economies?Are there zero-capital economies?

The Empty Quarter of Saudi Arabia?The Empty Quarter of Saudi Arabia?

• Any Corner solution can be converted Any Corner solution can be converted to a positive income SS by allowing to a positive income SS by allowing production with zero-capital production with zero-capital

Diamond ModelDiamond ModelMultiple Solution IMultiple Solution I• Cobb-Douglas preferencesCobb-Douglas preferences

•U[cU[ctt,c,ct+1t+1] = c] = cttλλ..cct+1 t+1

λλ-1-1

•Where Where λλ > 0.5 > 0.5 gives discounting gives discounting•Then: Then: kkt t = = λλ.F.F22[k[kt-1t-1,1],1]

• In SS: In SS: kk = = λλ.F.F22[k,1][k,1]•Both sides increase with k.Both sides increase with k.•Strict concavity requires Strict concavity requires FF211211[k,1] < 0[k,1] < 0

The Concavity The Concavity ConditionConditionwith Cobb-Douglaswith Cobb-Douglas• With Cobb-DouglasWith Cobb-Douglas

FF22[k,1] = A(1-[k,1] = A(1-αα)k)kαα

• FF211211[k,1] = -A[k,1] = -Aαα(1-(1-αα))22kkαα-2 -2 < 0< 0

• So in the Cobb-Douglas case we have So in the Cobb-Douglas case we have uniquenessuniqueness

Diamond modelDiamond modeland the elasticity of inter-temporal and the elasticity of inter-temporal substitutionsubstitution

• With Cobb-Douglas production and a With Cobb-Douglas production and a constant EIS there is a unique non-constant EIS there is a unique non-degenerate steady statedegenerate steady state

• With a variable EIS this is no longer With a variable EIS this is no longer the case (see the next figure)the case (see the next figure)

Which ModelWhich ModelDiamond or Ramsey?Diamond or Ramsey?• Diamond allows a SS poverty trap, Diamond allows a SS poverty trap,

which the one-agent Ramsey model which the one-agent Ramsey model excludes.excludes.

• Diamond is most clearly appropriate Diamond is most clearly appropriate for a rich country with large funded for a rich country with large funded pension schemes.pension schemes.

• In poor countries, however, parents In poor countries, however, parents invest for their children, by buying invest for their children, by buying education or land.education or land.

Implications for PolicyImplications for Policy

• Solow style models do not support the Solow style models do not support the Kuznets view of inequalityKuznets view of inequality

• Non-concave models permit poverty Non-concave models permit poverty trapstraps

• Even when all agents converge Even when all agents converge inequality may not be monotonicinequality may not be monotonic

• Convergence is not a justification for Convergence is not a justification for inaction inaction

Ch. 4 Convergence in Ch. 4 Convergence in Practice and TheoryPractice and Theory• Cross-section growth empirics starts Cross-section growth empirics starts

with Baumol (1986)with Baumol (1986)

• He looks at He looks at ββ-convergence-convergence

• ββ-convergence v. -convergence v. σσ-convergence - -convergence - Friedman (1992)Friedman (1992)

• De Long (1988) – sampling biasDe Long (1988) – sampling bias

Barro and Sala-i-MartinBarro and Sala-i-Martin

• World-wide comparative growthWorld-wide comparative growth• ““Near complete” coverage (Summers-Near complete” coverage (Summers-

Heston data) minimizes sampling biasHeston data) minimizes sampling bias• Straight test of Straight test of ββ-convergence-convergence• Dependent variable is growth of per-capita Dependent variable is growth of per-capita

income 1960-85income 1960-85• Correlation coefficient between growth Correlation coefficient between growth

and and lnPCI60lnPCI60 for 117 countries is .227 for 117 countries is .227

Table 4.1 Simple regression Table 4.1 Simple regression result result N=117 F=6.245N=117 F=6.245

VariableVariable CoefficientCoefficient t-valuet-value

ConstantConstant -.0135-.0135 -.998-.998

LnPCI60LnPCI60 .0046.0046 2.502.50

Correlation and CausationCorrelation and Causation

• Correlation is no proof of causationCorrelation is no proof of causation

• BUTBUT

• Absence of correlation is no proof of Absence of correlation is no proof of the absence of causationthe absence of causation

• Looking inside growth regressions Looking inside growth regressions perfectly illustrates this last pointperfectly illustrates this last point

The spurious correlationThe spurious correlation

• A spurious correlation arises purely by A spurious correlation arises purely by chancechance

• Assemble 1000 “crazy” ordered data setsAssemble 1000 “crazy” ordered data sets• That gives nearly half a million pairs of That gives nearly half a million pairs of

such variablessuch variables• Between one such pair there is bound to Between one such pair there is bound to

be a correlation that by itself will seem to be a correlation that by itself will seem to be of overwhelming statistical significance be of overwhelming statistical significance

Most correlations encountered Most correlations encountered in practice are not “spurious”in practice are not “spurious”

• But they may well not be due to a But they may well not be due to a simple causal connectionsimple causal connection

• The variables are each correlated The variables are each correlated causally with another “missing” causally with another “missing” variablevariable

• As when the variables are non-As when the variables are non-stationary and the missing variable is stationary and the missing variable is timetime

Two examples of correlating Two examples of correlating non-stationary variablesnon-stationary variables

• The beginning econometrics The beginning econometrics student’s consumption functionstudent’s consumption functioncctt = = αα + + ββyytt + + εεtt

• But surely consumption is causally But surely consumption is causally connected to incomeconnected to income

• ADADtt = = αα + + ββTSTStt + + εεtt

where where TSTS = teachers’ salaries = teachers’ salariesADAD = arrests for drunkeness = arrests for drunkeness

Regression analysis and Regression analysis and missing variablesmissing variables

• A missing variable plays a part in the A missing variable plays a part in the DGP and is correlated with included DGP and is correlated with included variablesvariables

• This is never a problem with This is never a problem with Classical Classical Regression AnalysisRegression Analysis

• Barro would say that the simple Barro would say that the simple regression of regression of LnPCI60 LnPCI60 on per capita on per capita growth is biassed by the exclusion of growth is biassed by the exclusion of extra “conditioning” variablesextra “conditioning” variables

Table 4,2 Growth and extra Table 4,2 Growth and extra variablesvariablesSources * Barro and Sala-i-Martin (1985)Sources * Barro and Sala-i-Martin (1985) * Barro-Lee data set * Barro-Lee data set

VariableVariable DefinitionDefinition MeanMean Standard Standard deviationdeviation

Growth*Growth* Growth rate per Growth rate per capita income capita income

1960-851960-85

.0226.0226 .0161.0161

LnPCI60*LnPCI60* Log of PCI 1960Log of PCI 1960 7.52017.5201 ,8930,8930

bmp**bmp** Forex black Forex black market premiummarket premium

.1188.1188 ,1675,1675

govsh4**govsh4** Gov. con. / GDP Gov. con. / GDP .1571.1571 .0656.0656

geerec**geerec** Public exp. On Public exp. On Edu./GDPEdu./GDP

.0245.0245 ,0103,0103

I/Y*I/Y* Invest./Invest./GDP ratioGDP ratio

.0968.0968 .1893.1893

pinstab**pinstab** Political Political instabilityinstability

.1916.1916 ,0859,0859

Table 4.3 Regression resultTable 4.3 Regression resultN = 73 F = 8.326 RN = 73 F = 8.326 R22 = .4308 = .4308

VariableVariable CoefficientCoefficient t-valuet-value Partial R-Partial R-squaredsquared

ConstantConstant .0698.0698 3.833.83 .1821.1821

LnPCI60LnPCI60 -.01133-.01133 -3.89-3.89 .1863.1863

BmpBmp .0035.0035 .345.345 .0018.0018

Govsh4Govsh4 -.0419-.0419 -1.66-1.66 .0400.0400

GeerecGeerec .4922.4922 2.712.71 .0999.0999

PinstabPinstab .0003.0003 .029.029 .000.000

I/YI/Y .1673.1673 6,026,02 .3545.3545

Table 4.4 Regression with One Table 4.4 Regression with One Conditioning VariableConditioning Variable

VariableVariable CoefficienCoefficientt

t-valuet-value Partial RPartial R22

ConstantConstant .0281.0281 2.172.17 .0403.0403

LnPCI60LnPCI60 -.0048-.0048 -2.33-2.33 .0463.0463

I/YI/Y .1502.1502 7.087.08 .3092.3092

Looking Inside Growth Looking Inside Growth Regressions IRegressions I

gg is economic growth is economic growth

lyly is log initial per capita income is log initial per capita income

zz is another variable of interest, such is another variable of interest, such as as I/YI/Y, which is itself positively , which is itself positively correlated with growth.correlated with growth.

All these variables are measured from All these variables are measured from their means.their means.

Inside growth regressions IIInside growth regressions II

We are interested in a case in which We are interested in a case in which the regression coefficient of the regression coefficient of gg on on lyly is is near zero or positive. So we have:near zero or positive. So we have:

v{gly}≥0v{gly}≥0

where where vv is the summed products of is the summed products of gg and and lyly

Inside Growth regressions IIIInside Growth regressions III

Thus Thus v{gly}v{gly} is is NN times the co- times the co-variance between variance between gg and and lyly..

Now consider the multiple regression:Now consider the multiple regression:

g=βly+γz+εg=βly+γz+ε (3)(3)

Inside Growth Regressions Inside Growth Regressions IVIV

InsideInside Growth Regressions VGrowth Regressions V

So that:So that:v{glY}=(β)(v{gg})+(γ)(v{gz}) (5)v{glY}=(β)(v{gg})+(γ)(v{gz}) (5)

Then if v{glY}≥0 and v{gz}>0, (5) requires that Then if v{glY}≥0 and v{gz}>0, (5) requires that either β or γ, but not both, be negative. If either β or γ, but not both, be negative. If v{glY}>0 then β and γ may both be positive, but v{glY}>0 then β and γ may both be positive, but they cannot both be negative. One way of they cannot both be negative. One way of explaining that conclusion is to say that a finding explaining that conclusion is to say that a finding of β-convergence with an augmented regressions, of β-convergence with an augmented regressions, despite growth and log initial income not being despite growth and log initial income not being negatively correlated, can happen because the negatively correlated, can happen because the additional variable (or variables on balance) are additional variable (or variables on balance) are positively correlated with initial income. positively correlated with initial income.