Wealth, Growth and Inequality

1. Wealth, Growth and Inequality Public Economics: University of Barcelona Frank Cowell http://darp.lse.ac.uk/ub June 2005

2. Overview... Inequality and Redistribution Introduction The basis for the question Growth models World inequality Inequality in advanced countries

3. Focus of the lecture • Major roles of government • Revenue raising • Efficiency • Redistribution / Equity • Distribution always a big question in public economics • Analysing it has always involved other fields • Macroeconomics • Finance • Development economics • Brief look at what is involved...

4. Basic accounting • Begin with the basics of individual wellbeing • Utility: depends on consumption • Resources: income and wealth • The agent’s income • composed of earnings + interest income + transfers • ignore transfers here • yi = wli + rki • A simple decomposition of inequality? • Components statistically uncorrelated? • Income more widely dispersed than earnings? • Evolution of distribution of k important for distribution of y. • Basis of an income-determining model • Role of factor prices • Role of accumulation

5. Old models, modern themes • Why a focus on these issues now? • Trends in within-country distribution • Debate on globalisation • growing inequality? • ...or convergence? • Improved data availability • within-country: mainly based on individual tax records • across country: improved comparability and repeated observations • Growth theory became fashionable again

6. Background • Build on a connection with standard growth models • Role of capital and labour • Can in fact be made more generally • One accumulated factor • One or more non-accumulated factors • Role of factor prices • focus on w and r • assume competitive markets? • will there be a PE equilibrium?

7. Overview... Inequality and Redistribution Introduction New insights from simple neoclassical models Growth models World inequality Inequality in advanced countries

8. An approach • Stiglitz (Econometrica 1969) • Based on Solow-Swan type of model • Affine (linear) savings function • Focus on both macro and distributional issues: • Accumulation of capital • Distribution of wealth • What does equilibrium look like? • Outline of model • Use modified Stiglitz notation

9. Basic model: overall production • y: output per person • k: capital per person • Aggregate production • Assume Inada conditions • Interest rate • Wage rate

10. Basic model: wealth classes • i: indexes individual wealth classes • ki: capital in per person in group i • yi = wli + rki agent’s income in group i • Same labour endowment in every group i • ai: Proportion of population in group i • ki: capital in group i as proportion of population • Simple aggregation

11. Savings and growth • Affine savings function • Wealth accumulation in class i • Substitute savings in class i • Substitute income in class i • Aggregate growth in capital/labour ratio

12. Equilibrium growth: Solow model y f(k) k k*

13. Stability? • Change in capital-labour ratio • Substitute in for w and r • Simple phase-diagram behaviour

14. Equilibrium growth: extended y f(k) k k** k*

15. Basic results (1) • One or two balanced growth paths • Depends on the shape of the savings function • Lower equilibrium is unstable • On each path : • stability • capital labour ratio constant • factor prices constant • Schlicht (1975)

16. Basic results (2) • Aggregate accumulation does not depend on distribution • Follows directly from the savings assumption • Would also hold if savings had a linear component dependent on wealth • Linearity: a reasonable empirical assumption? • Schmidt-Hebbel and Serven (2000) on cross-section and panel data • Use variety alternative inequality measures • Alternative savings definitions and various econometric specifications • Income inequality does not have systematic effect on aggregate saving

17. Wealth classes and distribution • Now examine what is happening with the individual wealth classes i. • The group in equilibrium at any overall k, given by • Gives critical personal wealth level as function of k

18. The critical wealth levels • Implicitly define k~ • Implicitly define k^ • Key relationships

19. Critical wealth levels y f(k) k ~ k* ^ k k

20. Changes in wealth distribution • Rate of change of wealth in group i • Relative change for two groups • If k1< k2 then … • …get convergence if b+mw > 0 • You have to be to the right of k^ for this

21. Basic results (3) • On the balanced growth path k*: • instability in aggregate • instability in distribution • On the balanced growth path k**: • stability in aggregate • stability in distribution • In range k* to k^ : • Overall capital-labour ratio is increasing • Converges on equilibrium • But wealth inequality becomes more unequal along the way • In range k^ to k**: • Overall capital-labour ratio is increasing • Converges on equilibrium • Wealth inequality becomes more equal along the way

22. Role of taxation • Assume a purely redistributive income tax t • Disposable income is • Relative performance of two wealth classes is now • Critical k value for convergence is now where • The income tax makes a difference

23. Tweaking the model (1) • Nonlinear savings • Equality inevitable? Desirable? • May get multiple equilibria • Equality may be Pareto dominated! • Bourguignon (1981)

24. Tweaking the model (2) • Optimised savings: Based on Ramsey (1928) • Many-agent version • In steady states: a paradox? • Agents discount future utility at different constant rates • All the capital owned by agents with the lowest discount rate. • Outcome depends upon the borrowing constraints • If high discount consumer can borrow against future wage income converge to zero consumption. • No steady state need exist • Becker (1980)

25. Bliss model (1) • Focus on simplified multi-person model. • All agent types have the same tastes. • All supply the same quantity of labour in all periods and earn the same wage. • All have same access to capital market, where they all earn the same rate of return. • All have perfect foresight and there are no stochastic effects in the model to upset convergence.

26. Bliss model (2) • Focus on Koopmans- separable preferences • Let c := (c1, c2, ..., ct, ...) • U(c) = W1( u(c1), (c2, c3, ..., ct+1, ...)) • A generalisation of usual definition of separability • Can be used recursively: • U(c) = Wt( u(c1), u(c2), ..., u(ct), (ct+1, ct+2, ..., ct+t, ...)) • Bliss uses just this weak version of preferences • Takes a multi-agent version of Ramsey • Optimising agents • Infinite lives • Again you get a version of the Ramsey paradox

27. Alternative approaches • Role of technology • Increasing returns • Imperfect capital markets • But rational savings behaviour may be the key

28. Alternative approaches • Human capital in the production function. • By itself this does not make a great difference • human capital accumulated optimally to combine with physical capital. • Suppose accumulation of human capital cannot be financed by borrowing. • Imperfect capital mobility will assist income convergence. • Barro, Mankiw Sala-i-Martin (1995) • Consider convergence in a special case • One small low-wealth country converges to a steady state • …where rest of the world occupies from the start. • Country is borrowing constrained all the way to steady state. • Consider general many-agent equilibrium, • same model with borrowing constraints, • low wealth country having significant weight in the world equilibrium • convergence is not assured

29. Overview... Inequality and Redistribution Introduction Convergence? Growth models World inequality Inequality in advanced countries

30. Applying the growth model • Individual incomes and wealth • Role of savings behaviour • What will happen to individual capitalist countries • Wealth of nations • Convergence? • Is the standard growth model the right one?

31. Questions about inequality • Inequality between countries • Role of globalisation • Role of savings behaviour • Or is inequality increasing? • Inequality within countries • Convergence? • Related to countries economic policies?

32. Kuznets reborn? • Kuznets focused on a statistical curiosity • Suggested a speculative conclusion • Inequality first rises, with industrialisation…? • …then falls, as workers become more productive? • He was working just with cross-section data • Now have repeated data for individual countries • Micro-data for many countries

33. A Pattern of inequality • Bourguignon and Morrisson (2002) investigate the distribution of well being among world citizens in 19th, 20th centuries. • Inequality worsened from the beginning of the 19th century to World War II • Then stabilized or to have grown more slowly. • Composition of inequality changed • In the early 19th century inequality mainly due to differences within countries • Later differences between countries. • Inequality in longevity also increased during the19th century • Trend reversed in the second half of the 20th century

34. How does inequality affect growth? • Traditional literature does something like this • Dollar and Kraay (2002) argue that this produces ambiguous answers • Depends on econometric method • Depends on sample • Use an explicit model of poor incomes

35. Model incomes of the poor • Model incomes of the poor this way • Regression is equivalent to • Interested in two parameters: • a1 effect of overall income • a2effect of other factors

36. Is growth good for the poor? • Dollar-Kraay data set covers period from the 1960s • To take account of data on levels and changes use first differences • Income share of poorest fifth does not change with average income • Does not change with institutions or policies designed to help the poor. • But Ravallion (2001) suggests considerable heterogeneity amongst countries

37. International trends • Sala-i-Martin 2002 • Within-country disparities have increased • not enough to offset reduction in cross-country disparities. • But the particular case effect is important • What drives cross-country reductions in inequality? • Large growth rate of the incomes of the 1.2 billion Chinese

38. Overview... Inequality and Redistribution Introduction Results from data sources Growth models World inequality Inequality in advanced countries

39. Within-country inequality: uS • Top shares of income and wages in US • Piketty-Saez (2003) • Use individual tax returns • Data from 1913 to 1998 • Top income and wages shares • A U-shaped pattern over the century • Why?

40. Top income shares in US

41. Piketty-Saez explanation • Wealth effect • capital owners experienced large shocks that in 1930s and 40s • a permanent effect on top capital incomes? • The wage effect • Top wage shares flat before WW II, • Dropped during the war • did not start to recover before the late 1960s • Now higher than before WW II. • Working rich have replaced the rentiers at the top of the distribution. • The tax effect • steep progressive income and estate taxation • may have prevented large estates from fully recovering

42. Also in a developing economy • Top incomes and wages from 1956 to 2000 using individual tax returns data. • Banerjee and Piketty (2003) • Top shares followed a secular U-shape • top 0.01%, 0.1% 1% in total income • shares shrank until the early to mid 1980s • then rose again, so that today these shares are only slightly below what they were in 1956 • U-shaped pattern consistent with the economic policy : • The period from 1956 to the early to mid 1980s was also the period of “socialist” policies in India, • Subsequent period, starting with the rise of Rajiv Gandhi, saw a gradual shift towards more probusiness policies. • The rich getting richer had a significant impact on the overall income distribution.