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Trade Growth and Trade Growth and Inequality Inequality Professor Christopher Professor Christopher Bliss Bliss Hilary Term 2004 Hilary Term 2004 Fridays 10-11 a.m. Fridays 10-11 a.m.

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Trade Growth and Inequality. Professor Christopher Bliss Hilary Term 2004 Fridays 10-11 a.m. Ch. 4 Convergence in Practice and Theory. Cross-section growth empirics starts with Baumol (1986) He looks at β -convergence β -convergence v. σ -convergence - Friedman (1992) - PowerPoint PPT Presentation

### Transcript of Trade Growth and Inequality

Professor Christopher BlissProfessor Christopher BlissHilary Term 2004Hilary Term 2004

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

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

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

.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

TableTable 4.4 Regression with One 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

LookingLooking Inside Growth Inside Growth Regressions IRegressions I

gg is economic growth is economic growth

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:

vvglYglY=βv=βvgggg + γv + γvgzgz (5) (5)

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

A Growth Regression with A Growth Regression with one additional variableone additional variable

gg lyly I/YI/Y

gg .00034.00034

lyly .00384.00384 .82325.82325

I/YI/Y .00921.00921 .05216.05216 .00780.00780

Growth Regression with I/YGrowth Regression with I/Y

VariableVariable CoefficienCoefficientt

t-valuet-value Partial RPartial R22

Con-Con-stantstant

.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

N=117N=117 RR22=.346=.346 F=29.57F=29.57

From (5) and the From (5) and the variance/covariance matrix variance/covariance matrix above:above:

..00384 = .8232500384 = .82325β + .05216γβ + .05216γ

Now if Now if γγ is positive, is positive, ββ must be must be negativenegative

This has happened because the This has happened because the added variable is positively added variable is positively correlated with g correlated with g

g=βly+γL+εg=βly+γL+ε (7)(7)

The correlation matrix is:The correlation matrix is:

gg lyly LL

gg 11

lyly .17480.17480 11

LL .32184.32184 .73373.73373 11

Growth Regression with LGrowth Regression with L

VariablVariablee

Coeff-Coeff-icienticient

t-valuet-value Partial Partial RR22

Con-Con-stantstant

.01614.0161411

1.031.03 .0092.0092

LnPCI6LnPCI600

-.0008-.000833

-.348-.348 .0011.0011

LL .00043.0004355

3.243.24 .0893.0893

N=117N=117 RR22=.34=.3466

F=29.5F=29.577

Correlation and CauseCorrelation and Cause

1.1. The Barro equation is founded in a The Barro equation is founded in a causal theory of growthcausal theory of growth

2.2. The equation with L cannot have a The equation with L cannot have a causal basiscausal basis

3.3. What is causality anyway?What is causality anyway?4.4. Granger-Sims causality tests. Need Granger-Sims causality tests. Need

time series data. Shocks to causal time series data. Shocks to causal variables come first in timevariables come first in time

Causality and Temporal Causality and Temporal OrderingOrdering1.1. An alarm clock set to ring just before An alarm clock set to ring just before

sunrise does not cause the sun to rise.sunrise does not cause the sun to rise.

2.2. If it can be shown that random shocks to If it can be shown that random shocks to my alarm setting are significantly my alarm setting are significantly correlated with the time of sunrise, the correlated with the time of sunrise, the that is an impressive puzzlethat is an impressive puzzle

3.3. Cause is a (an optional) theory notionCause is a (an optional) theory notion

Convergence TheoryConvergence Theory

The Solow-Swan ModelThe Solow-Swan Model

Solow-Swan Model IISolow-Swan Model II

The model gives convergence in two important The model gives convergence in two important cases:cases:

1.1. Several isolated economies each with the Several isolated economies each with the same saving share. Only the level of per same saving share. Only the level of per capita capital distinguishes economiescapita capital distinguishes economies

2.2. There is one integrated capital markets There is one integrated capital markets economy and numerous agents with the economy and numerous agents with the same saving rate. Only the level of per same saving rate. Only the level of per capita capital attained distinguishes one capita capital attained distinguishes one agnet from another. agnet from another.

Solow-Swan Model IIISolow-Swan Model III

If convergence is conditional on various If convergence is conditional on various additional variables, how precisely do additional variables, how precisely do these variables make their effects these variables make their effects felt?felt?

For country I at time t income is:For country I at time t income is:

AAiiF[KF[Kii(t),L(t),Lii(t)](t)]

A measures total factor productivity, so A measures total factor productivity, so will be called TFPwill be called TFP

Determinants of the Growth Determinants of the Growth RateRate

The growth rate is larger:The growth rate is larger:

• The larger is capital’s shareThe larger is capital’s share

• The larger is the saving shareThe larger is the saving share

• The larger is the TFP coefficientThe larger is the TFP coefficient

• The smaller is capital per headThe smaller is capital per head

• The smaller is the rate of population The smaller is the rate of population growthgrowth

Mankiw, Romer and Weil Mankiw, Romer and Weil (1992)(1992)

• 80% of cross section differences in 80% of cross section differences in growth rates can be accounted for growth rates can be accounted for via effects 2 and 5 by themselvesvia effects 2 and 5 by themselves

• The chief problem for growth The chief problem for growth empirics is to disentangle effects 3 empirics is to disentangle effects 3 and 4and 4

Convergence: The Ramsey Convergence: The Ramsey ModelModel

Ramsey (1928) considered a many-Ramsey (1928) considered a many-agent version of his model (a MARM)agent version of his model (a MARM)

He looked at steady states and noted He looked at steady states and noted the paradoxical feature that if agents the paradoxical feature that if agents discount utility at different rates, discount utility at different rates, then all capital will be owned by then all capital will be owned by agents with the lowest discount rateagents with the lowest discount rate

Two different casesTwo different cases

Just as with the Solow-Swan model the cases are:Just as with the Solow-Swan model the cases are:• Isolated economies each one a version of the Isolated economies each one a version of the

same Ramsey model, with the same utility same Ramsey model, with the same utility discount rate. The level of capital attained at a discount rate. The level of capital attained at a particular time distinguishes one economy particular time distinguishes one economy from anotherfrom another

• One economy with a single unified capital One economy with a single unified capital market, and each agent has the same utility market, and each agent has the same utility function. The level of capital attained at a function. The level of capital attained at a particular time distinguishes one agent from particular time distinguishes one agent from anotheranother

Isolated EconomiesIsolated Economies

Chapter 3 has already made clear that Chapter 3 has already made clear that there is no general connection between there is no general connection between the level of the level of kk and and (1/c)(dc/dt)(1/c)(dc/dt)..

The necessary condition for optimal The necessary condition for optimal growth is:growth is:

{[-c(du/dc)]/u}{(1/c)(dc/dt)}=F{[-c(du/dc)]/u}{(1/c)(dc/dt)}=F11[k(t),1]-r[k(t),1]-r(20)(20)

Where Where uu is is UU11[c(t)][c(t)]

Determinants of the Growth Determinants of the Growth of Consumptionof ConsumptionThe necessary condition for optimal growth is:The necessary condition for optimal growth is:{[-c(du/dc)]/u}{(1/c)(dc/dt)}=F{[-c(du/dc)]/u}{(1/c)(dc/dt)}=F11[k(t),1]-r[k(t),1]-r

When When k(t) k(t) takes a low value the right-hand takes a low value the right-hand side of (20) is relatively large. If the growth side of (20) is relatively large. If the growth rate of consumption is not large, the rate of consumption is not large, the elasticity of marginal utilityelasticity of marginal utility

[-c(du/dc)]/u[-c(du/dc)]/uMust be large.Must be large.The idea that β-convergence follows from The idea that β-convergence follows from

optimal growth theory is suspect.optimal growth theory is suspect.

Growth in the MARMGrowth in the MARM

• With many agents the optimal With many agents the optimal growth condition (20) becomes:growth condition (20) becomes:

FF11[[ΣΣkkiiii(t)),1]=r(t)),1]=rNote the effect of perturbing one Note the effect of perturbing one

agent’s capital holding agent’s capital holding

A non-convergence resultA non-convergence result

In the MARM:In the MARM:1.1. Non-converging steady states are Non-converging steady states are

possiblepossible2.2. Strict asymptotic convergence can Strict asymptotic convergence can

never occurnever occur3.3. Partial convergence (or divergence) Partial convergence (or divergence)

clubs are possible depending on the clubs are possible depending on the third derivative of the utility functionthird derivative of the utility function

What does a MARM What does a MARM maximize?maximize?Any MARM equlibrium is the solution to a problem Any MARM equlibrium is the solution to a problem

of the form:of the form:MaxMax ΣΣNN

11∫∫00∞∞U[cU[cii(t)]dt(t)]dt

Non-convergence is hsown despite the assumptions that:Non-convergence is hsown despite the assumptions that:• All agents have the same tastes and the same utility discount All agents have the same tastes and the same utility discount

raterate• All supply the same quantity of labour and earn the same wageAll supply the same quantity of labour and earn the same wage• All have access to the same capital market where they earn the All have access to the same capital market where they earn the

same rate of returnsame rate of return• All have perfect foresight and there are no stochastic effects All have perfect foresight and there are no stochastic effects

to interfere with convergenceto interfere with convergence

Asymptotic and Asymptotic and ββ--convergenceconvergence• For isolated Ramsey economies we have For isolated Ramsey economies we have

seen that we need not have seen that we need not have ββ-convergence, -convergence, but we must have asymptotic convergencebut we must have asymptotic convergence

• On the other hand we may have On the other hand we may have ββ--convergence without asymptotic convergence without asymptotic convergenceconvergence

lnylnyII = a = aII - b/t+2 - b/t+2 lny lnyIIII = a = aIIII - b/t+1 - b/t+1aaII< a< aIIII

Country I has the lower income and is always Country I has the lower income and is always growing faster growing faster

Strange Accumulation Paths Strange Accumulation Paths can be Optimal can be Optimal

In the Mathematical Appendix it is shown In the Mathematical Appendix it is shown that:that:

Given a standard production function and Given a standard production function and a monotonic time path a monotonic time path k(t)k(t) such that such that kk goes to goes to k*k*, the Ramsey steady state , the Ramsey steady state value, and the implied value, and the implied cc is monotonic, is monotonic, there exists a “well-behaved” utility there exists a “well-behaved” utility function such that this path is Ramsey function such that this path is Ramsey optimal optimal

Optimal Growth with Random Optimal Growth with Random ShocksShocksBliss (2003) discusses the probability density of income Bliss (2003) discusses the probability density of income

levels when Ramsey-style accumulation is shocked levels when Ramsey-style accumulation is shocked each period with shocks large on absolute valueeach period with shocks large on absolute value

Two intuitive cases illustrate the type of result Two intuitive cases illustrate the type of result available:available:

• Low income countries grow slowly, middle income Low income countries grow slowly, middle income countries rapidly and rich countries slowly. If shocks countries rapidly and rich countries slowly. If shocks are large poverty and high income form basins of are large poverty and high income form basins of attraction in which many countries will be found. attraction in which many countries will be found. Compare Quah (1997)Compare Quah (1997)

• If shocks are highly asymmetric this will affect the If shocks are highly asymmetric this will affect the probability distribution of income levels, even if the probability distribution of income levels, even if the differential equation for income is linear. Earthquake differential equation for income is linear. Earthquake shocks.shocks.

The BMS ModelThe BMS Model

Barro, Mankiw and Sala-i-Martin (1995)Barro, Mankiw and Sala-i-Martin (1995)Human capital added which cannot be used as Human capital added which cannot be used as

collateralcollateralOne small country converges on a large world One small country converges on a large world

in steady state (existence is by exhibition).in steady state (existence is by exhibition).A more general case is where many small A more general case is where many small

countries have significant weight. Then if countries have significant weight. Then if they differ some may leave the constrained they differ some may leave the constrained state before others and poor countries may state before others and poor countries may not be asymptotically identicalnot be asymptotically identical

Concluding RemarksConcluding Remarks

1.1. There is no simple statistical association There is no simple statistical association between initial income and subsequent growth, between initial income and subsequent growth, hence no support for hence no support for ββ-convergence from a -convergence from a basic two-variable analysisbasic two-variable analysis

2.2. With multivariate analysis the hypothesis of a With multivariate analysis the hypothesis of a causal connection between initial income and causal connection between initial income and subsequent growth on an other things equal subsequent growth on an other things equal basis is not rejectedbasis is not rejected

3.3. Theoretical models with common technology Theoretical models with common technology often confirm the often confirm the ββ-convergence hypothesis-convergence hypothesis

4.4. Surprisingly the literature neglects “catching-Surprisingly the literature neglects “catching-up”up”