# Trade Growth and Inequality

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

Ch. 4 Convergence in Practice and TheoryCross-section growth empirics starts with Baumol (1986)He looks at -convergence-convergence v. -convergence - Friedman (1992)De Long (1988) sampling bias

Barro and Sala-i-MartinWorld-wide comparative growthNear complete coverage (Summers-Heston data) minimizes sampling biasStraight test of -convergenceDependent variable is growth of per-capita income 1960-85Correlation coefficient between growth and lnPCI60 for 117 countries is .227

Table 4.1 Simple regression result N=117 F=6.245

Correlation and CausationCorrelation is no proof of causationBUTAbsence of correlation is no proof of the absence of causationLooking inside growth regressions perfectly illustrates this last point

The spurious correlationA spurious correlation arises purely by chance Assemble 1000 crazy ordered data setsThat gives nearly half a million pairs of such variablesBetween one such pair there is bound to be a correlation that by itself will seem to be of overwhelming statistical significance

Most correlations encountered in practice are not spuriousBut they may well not be due to a simple causal connectionThe variables are each correlated causally with another missing variableAs when the variables are non-stationary and the missing variable is time

Two examples of correlating non-stationary variablesThe beginning econometrics students consumption function ct = + yt + tBut surely consumption is causally connected to incomeADt = + TSt + t where TS = teachers salaries AD = arrests for drunkeness

Regression analysis and missing variablesA missing variable plays a part in the DGP and is correlated with included variablesThis is never a problem with Classical Regression AnalysisBarro would say that the simple regression of LnPCI60 on per capita growth is biassed by the exclusion of extra conditioning variables

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

Table 4.3 Regression resultN = 73 F = 8.326 R2 = .4308

Table 4.4 Regression with One Conditioning Variable

Looking Inside Growth Regressions Ig is economic growthly is log initial per capita incomez is another variable of interest, such as I/Y, which is itself positively correlated with growth. All these variables are measured from their means.

Inside growth regressions IIWe are interested in a case in which the regression coefficient of g on ly is near zero or positive. So we have:v{gly}0where v is the summed products of g and ly

Inside Growth regressions III Thus v{gly} is N times the co-variance between g and ly. Now consider the multiple regression:g=ly+z+(3)

Inside Growth Regressions IV

Inside Growth Regressions V So that:vglY=vgg + vgz (5) Then if vglY 0 and vg > 0, (5) requires that either or , but not both, be negative. If vglY > 0 then and may both be positive, but they cannot both be negative. One way of explaining that conclusion is to say that a finding of -convergence with an augmented regression, despite growth and log initial income not being negatively correlated, can happen because the additional variable (or variables on balance) are positively correlated with initial income.

A Growth Regression with one additional variable

Growth Regression with I/Y

One additional variable regression From (5) and the variance/covariance matrix above:.00384 = .82325 + .05216Now if is positive, must be negativeThis has happened because the added variable is positively correlated with g

Adding the Mystery Ingredient Lg=ly+L+(7)The correlation matrix is:

glyLg1ly.174801L.32184.733731

Growth Regression with L

VariableCoeff-icientt-valuePartial R2Con- stant.0161411.03.0092LnPCI60-.00083-.348.0011L.0004353.24.0893N=117R2=.346F=29.57

Correlation and CauseThe Barro equation is founded in a causal theory of growthThe equation with L cannot have a causal basisWhat is causality anyway?Granger-Sims causality tests. Need time series data. Shocks to causal variables come first in time

Causality and Temporal OrderingAn alarm clock set to ring just before sunrise does not cause the sun to rise.If it can be shown that random shocks to my alarm setting are significantly correlated with the time of sunrise, the that is an impressive puzzleCause is a (an optional) theory notion

Convergence TheoryThe Solow-Swan Model

Solow-Swan Model IIThe model gives convergence in two important cases:Several isolated economies each with the same saving share. Only the level of per capita capital distinguishes economiesThere is one integrated capital markets economy and numerous agents with the same saving rate. Only the level of per capita capital attained distinguishes one agnet from another.

Solow-Swan Model IIIIf convergence is conditional on various additional variables, how precisely do these variables make their effects felt?For country I at time t income is:AiF[Ki(t),Li(t)] A measures total factor productivity, so will be called TFP

Determinants of the Growth RateThe growth rate is larger:The larger is capitals shareThe larger is the saving shareThe larger is the TFP coefficientThe smaller is capital per headThe smaller is the rate of population growth

Mankiw, Romer and Weil (1992)80% of cross section differences in growth rates can be accounted for via effects 2 and 5 by themselvesThe chief problem for growth empirics is to disentangle effects 3 and 4

Convergence: The Ramsey ModelRamsey (1928) considered a many-agent version of his model (a MARM)He looked at steady states and noted the paradoxical feature that if agents discount utility at different rates, then all capital will be owned by agents with the lowest discount rate

Two different casesJust as with the Solow-Swan model the cases are:Isolated economies each one a version of the same Ramsey model, with the same utility discount rate. The level of capital attained at a particular time distinguishes one economy from anotherOne economy with a single unified capital market, and each agent has the same utility function. The level of capital attained at a particular time distinguishes one agent from another

Isolated EconomiesChapter 3 has already made clear that there is no general connection between the level of k and (1/c)(dc/dt).The necessary condition for optimal growth is:{[-c(du/dc)]/u}{(1/c)(dc/dt)}=F1[k(t),1]-r(20)Where u is U1[c(t)]

Determinants of the Growth of ConsumptionThe necessary condition for optimal growth is:{[-c(du/dc)]/u}{(1/c)(dc/dt)}=F1[k(t),1]-r When k(t) takes a low value the right-hand side of (20) is relatively large. If the growth rate of consumption is not large, the elasticity of marginal utility[-c(du/dc)]/uMust be large.The idea that -convergence follows from optimal growth theory is suspect.

Growth in the MARMWith many agents the optimal growth condition (20) becomes:[-d(du/dc)/dt]/u]=F1[kii(t)),1]-r(23)In steady state (23) becomes:F1[kii(t)),1]=rNote the effect of perturbing one agents capital holding

A non-convergence resultIn the MARM:Non-converging steady states are possibleStrict asymptotic convergence can never occurPartial convergence (or divergence) clubs are possible depending on the third derivative of the utility function

What does a MARM maximize?Any MARM equlibrium is the solution to a problem of the form:MaxN10U[ci(t)]dtNon-convergence is hsown despite the assumptions that:All agents have the same tastes and the same utility discount rateAll supply the same quantity of labour and earn the same wageAll have access to the same capital market where they earn the same rate of returnAll have perfect foresight and there are no stochastic effects to interfere with convergence

Asymptotic and -convergenceFor isolated Ramsey economies we have seen that we need not have -convergence, but we must have asymptotic convergenceOn the other hand we may have -convergence without asymptotic convergencelnyI = aI - b/t+2 lnyII = aII - b/t+1aI< aIICountry I has the lower income and is always growing faster

Strange Accumulation Paths can be Optimal In the Mathematical Appendix it is shown that:Given a standard production function and a monotonic time path k(t) such that k goes to k*, the Ramsey steady state value, and the implied c is monotonic, there exists a well-behaved utility function such that this path is Ramsey optimal

Optimal Growth with Random ShocksBliss (2003) discusses the probability density of income levels when Ramsey-style accumulation is shocked each period with shocks large on absolute valueTwo intuitive cases illustrate the type of result available:Low income countries grow slowly, middle income countries rapidly and rich countries slowly. If shocks are large poverty and high income form basins of attraction in which many countries will be found. Compare Quah (1997)If shocks are highly asymmetric this will affect the probability distribution of income levels, even if the differential equation for income is linear. Earthquake shocks.

The BMS ModelBarro, Mankiw and Sala-i-Martin (1995)Human capital added which cannot be used as collateralOne small country converges on a large world in steady state (existence is by exhibition).A more general case is where many small countries have significant weight. Then if they differ some may leave the constrained state before others and poor countries may not be

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