Trade Growth and Inequality

1. Trade Growth and Inequality Professor Christopher BlissHilary Term 2004Fridays 10-11 a.m.

2. Why the Poor Stay Poor Chapter 3 of the book (circulated)

3. The Persistence of Poverty • What are the transmission properties of income at t to income at t+1? • Friedman (1992) regression to the mean • Incomes normally distributed and:Positions randomPositions fixed

4. Are All Agents the Same? • Herrnstein and Murray (The Bell Curve) • Income=F(IQ) • They claim that technological change has been such that:F(IQ))/F(100) has been falling over time for values of IQ well below the mean=100

5. Adam Smith • Little else is requisite to carry a state to the highest degree of opulence from the lowest barbarism but peace, easy taxes, and a tolerable administration of justice: all the rest being brought about by the natural course of things. (Lecture 1775)

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

7. The Kuznets Model • Initially population in low-level equality • Growth takes the form of movement to higher level “modern” productivity • While some move but not others, inequality increases • As all eventually modernize inequality declines

8. Problems with the Kuznets story • The cross-section evidence does not confirm it • The idea of low-level equality is also not in accord with the evidence • The curve is caused by differential adjustment rates – why does this happen?

9. The Stiglitz MASS Model Solow-Swan with many agents All supply same labour and save the same proportion of all income

10. Stiglitz Model Result Let k* satisfy: s.F[k*,1]-g.k*=0 All agents converge to holding k*

11. Weakening Stiglitz assumptions • The quantity of labour supplied by an individual may vary with capital owned by that agent. It must have a positive limit as k goes to zero. • The share of saving in total income may vary monotonically with capital owned by the agent. It must have a positive limit as k goes to zero.

12. Convergence and the Discount Rate • Utility and Consumption Discount Rates Distinguished • Endogenous Discount Rates • Do the poor have high discount rates?

13. Discount Rates and Dynamic Inconsistency • It is not necessary to assume that the poor discount utility at a high rate (see below) • Endogenous discount rates give inconsistency (Strotz)

14. Strotzian Inconsistency

15. Strotzian Inconsistency cont. • With consumption in the range 99 to 100 the discount factor (the weighting of future utility against current) is approximately 0.9 per period. • With consumption in the range 20 to 22 it is not less than 0.5 per period. • Viewed from time 1 the present value of utility for respectively I, II and III is 133.25, 132.65 and 130.78. In each case these totals are arrived at using weights (1,0.9,0.81).

16. Strotzian Dynamic Inefficiency cont. Now the discount factor is 0.5, hence the present values of the part sequences I and II are respectively 32.5 and 33.

17. The Elasticity of Inter-temporal Substitution (EIS) η =-c(d2U/dc2)/dU/dc If dU/dc = u η =-c(du/dc)/u

18. The Optimal Growth Condition -(du/dt)/u = F1[k,1] – δ η(dc/dt)/c = F1[k,1] – δ EIS*growth consumption = MPK – U discount rate

24. The Diamond Capital Model • Consumer lives two periods • Supplies 1 unit of labour in Period 1 • Divides the wage between consumption and saving • Aggregate saving is the economy capital stock • That capital plus the return is Period 2 consumption

25. Diamond Model:kt-1 determines kt • Max U[ct] + U[ct+1] • Subject to: • ct +(1/1+rt) ct+1 kt +wt • wt = F2[kt-1,1] • 1+rt = F1[kt,1]

26. Diamond ModelThe fundamental theorem • Theorem • kt increases with kt-1 • This makes possible multiple equilibria

28. Diamond Multiplicityand Poverty Traps • This idea is not influential: Why not? • Seldom realised in connection with two popular model features:stability of SS solutions of interestsimple standard functional forms

29. Diamond Model:The Corner Steady State • Are there zero-capital economies?The Empty Quarter of Saudi Arabia? • Any Corner solution can be converted to a positive income SS by allowing production with zero-capital

30. Diamond ModelMultiple Solution I • Cobb-Douglas preferences • U[ct,ct+1] = ctλ.ct+1 λ-1 • Where λ > 0.5 gives discounting • Then: kt = λ.F2[kt-1,1] • In SS: k= λ.F2[k,1] • Both sides increase with k. • Strict concavity requires F211[k,1] < 0

31. The Concavity Conditionwith Cobb-Douglas • With Cobb-DouglasF2[k,1] = A(1-α)kα • F211[k,1] = -Aα(1-α)2kα-2 < 0 • So in the Cobb-Douglas case we have uniqueness

32. Diamond modeland the elasticity of inter-temporal substitution • With Cobb-Douglas production and a constant EIS there is a unique non-degenerate steady state • With a variable EIS this is no longer the case (see the next figure)

34. Which ModelDiamond or Ramsey? • Diamond allows a SS poverty trap, which the one-agent Ramsey model excludes. • Diamond is most clearly appropriate for a rich country with large funded pension schemes. • In poor countries, however, parents invest for their children, by buying education or land.

35. Implications for Policy • Solow style models do not support the Kuznets view of inequality • Non-concave models permit poverty traps • Even when all agents converge inequality may not be monotonic • Convergence is not a justification for inaction

36. 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) • De Long (1988) – sampling bias

37. Barro and Sala-i-Martin • World-wide comparative growth • “Near complete” coverage (Summers-Heston data) minimizes sampling bias • Straight test of β-convergence • Dependent variable is growth of per-capita income 1960-85 • Correlation coefficient between growth and lnPCI60 for 117 countries is .227

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

39. Correlation and Causation • Correlation is no proof of causation • BUT • Absence of correlation is no proof of the absence of causation • Looking inside growth regressions perfectly illustrates this last point

40. The spurious correlation • A spurious correlation arises purely by chance • Assemble 1000 “crazy” ordered data sets • That gives nearly half a million pairs of such variables • Between one such pair there is bound to be a correlation that by itself will seem to be of overwhelming statistical significance

41. Most correlations encountered in practice are not “spurious” • But they may well not be due to a simple causal connection • The variables are each correlated causally with another “missing” variable • As when the variables are non-stationary and the missing variable is time

42. Two examples of correlating non-stationary variables • The beginning econometrics student’s consumption functionct = α + βyt + εt • But surely consumption is causally connected to income • ADt = α + βTSt + εtwhere TS = teachers’ salariesAD = arrests for drunkeness

43. Regression analysis and missing variables • A missing variable plays a part in the DGP and is correlated with included variables • This is never a problem with Classical Regression Analysis • Barro would say that the simple regression of LnPCI60 on per capita growth is biassed by the exclusion of extra “conditioning” variables

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

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

46. Table 4.4 Regression with One Conditioning Variable

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

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

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

50. Inside Growth Regressions IV