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Frank Cowell: UB Public Economics Wealth, Growth and Inequality June 2005 Public Economics: University of Barcelona Frank Cowell

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Presentation on theme: "Frank Cowell: UB Public Economics Wealth, Growth and Inequality June 2005 Public Economics: University of Barcelona Frank Cowell"— Presentation transcript:

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

2 Frank Cowell: UB Public Economics Overview... Introduction Growth models World inequality Inequality in advanced countries Inequality and Redistribution The basis for the question

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

4 Frank Cowell: UB Public Economics Basic accounting Begin with the basics of individual wellbeing Begin with the basics of individual wellbeing  Utility: depends on consumption  Resources: income and wealth The agent’s income The agent’s income  composed of earnings + interest income + transfers  ignore transfers here  y i = wl i + rk i A simple decomposition of inequality? 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 Basis of an income-determining model  Role of factor prices  Role of accumulation

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

6 Frank Cowell: UB Public Economics Background Build on a connection with standard growth models Build on a connection with standard growth models Role of capital and labour 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 Role of factor prices  focus on w and r  assume competitive markets?  will there be a PE equilibrium?

7 Frank Cowell: UB Public Economics Overview... Introduction Growth models World inequality Inequality in advanced countries Inequality and Redistribution New insights from simple neoclassical models

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

9 Frank Cowell: UB Public Economics Basic model: overall production Aggregate production Aggregate production Assume Inada conditions Assume Inada conditions Interest rate Interest rate Wage rate Wage rate y: output per person y: output per person k: capital per person k: capital per person

10 Frank Cowell: UB Public Economics Basic model: wealth classes i: indexes individual wealth classes i: indexes individual wealth classes  i : capital in per person in group i  i : capital in per person in group i y i = wl i + r  i agent’s income in group i y i = wl i + r  i agent’s income in group i Same labour endowment in every group i Same labour endowment in every group i a i : Proportion of population in group i a i : Proportion of population in group i k i : capital in group i as proportion of population k i : capital in group i as proportion of population Simple aggregation Simple aggregation

11 Frank Cowell: UB Public Economics Savings and growth Affine savings function Affine savings function Wealth accumulation in class i Wealth accumulation in class i Substitute savings in class i Substitute savings in class i Substitute income in class i Substitute income in class i Aggregate growth in capital/labour ratio Aggregate growth in capital/labour ratio

12 Frank Cowell: UB Public Economics Equilibrium growth: Solow model k y f(k)f(k) k*k*

13 Frank Cowell: UB Public Economics Stability? Change in capital-labour ratio Change in capital-labour ratio Substitute in for w and r Substitute in for w and r Simple phase-diagram behaviour Simple phase-diagram behaviour

14 Frank Cowell: UB Public Economics Equilibrium growth: extended k y f(k)f(k) k*k* k **

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

16 Frank Cowell: UB Public Economics Basic results (2) Aggregate accumulation does not depend on distribution Aggregate accumulation does not depend on distribution Follows directly from the savings assumption Follows directly from the savings assumption  Would also hold if savings had a linear component dependent on wealth Linearity: a reasonable empirical assumption? 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 Frank Cowell: UB Public Economics Wealth classes and distribution Now examine what is happening with the individual wealth classes i. Now examine what is happening with the individual wealth classes i. The group in equilibrium at any overall k, given by The group in equilibrium at any overall k, given by Gives critical personal wealth level as function of k Gives critical personal wealth level as function of k

18 Frank Cowell: UB Public Economics The critical wealth levels Implicitly define k ~ Implicitly define k ~ Implicitly define k ^ Implicitly define k ^ Key relationships Key relationships

19 Frank Cowell: UB Public Economics Critical wealth levels k y f(k)f(k) k*k* k ^ k ~

20 Frank Cowell: UB Public Economics Changes in wealth distribution Rate of change of wealth in group i Rate of change of wealth in group i Relative change for two groups Relative change for two groups If  1 <  2 then … If  1 <  2 then … …get convergence if b+mw > 0 …get convergence if b+mw > 0 You have to be to the right of k ^ for this You have to be to the right of k ^ for this

21 Frank Cowell: UB Public Economics Basic results (3) On the balanced growth path k*: On the balanced growth path k*:  instability in aggregate  instability in distribution On the balanced growth path k**: On the balanced growth path k**:  stability in aggregate  stability in distribution In range k* to k ^ : 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**: In range k ^ to k**:  Overall capital-labour ratio is increasing  Converges on equilibrium  Wealth inequality becomes more equal along the way

22 Frank Cowell: UB Public Economics Role of taxation Assume a purely redistributive income tax  Assume a purely redistributive income tax  Disposable income is Disposable income is Relative performance of two wealth classes is now Relative performance of two wealth classes is now Critical k value for convergence is now where Critical k value for convergence is now where The income tax makes a difference The income tax makes a difference

23 Frank Cowell: UB Public Economics Tweaking the model (1) Nonlinear savings Nonlinear savings Equality inevitable? Desirable? Equality inevitable? Desirable? May get multiple equilibria May get multiple equilibria Equality may be Pareto dominated! Equality may be Pareto dominated!  Bourguignon (1981)

24 Frank Cowell: UB Public Economics Tweaking the model (2) Optimised savings: Based on Ramsey (1928) Optimised savings: Based on Ramsey (1928) Many-agent version 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 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 Frank Cowell: UB Public Economics Bliss model (1) Focus on simplified multi-person model. Focus on simplified multi-person model. All agent types have the same tastes. All agent types have the same tastes. All supply the same quantity of labour in all periods and earn the same wage. 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 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. All have perfect foresight and there are no stochastic effects in the model to upset convergence.

26 Frank Cowell: UB Public Economics Bliss model (2) Focus on Koopmans- separable preferences Focus on Koopmans- separable preferences Let c := (c 1, c 2,..., c t,...) Let c := (c 1, c 2,..., c t,...) U(c) = W 1 ( u(c 1 ), (c 2, c 3,..., c  +1,...)) U(c) = W 1 ( u(c 1 ), (c 2, c 3,..., c  +1,...)) A generalisation of usual definition of separability A generalisation of usual definition of separability Can be used recursively: Can be used recursively:  U(c) = W t ( u(c 1 ), u(c 2 ),..., u(c t ), (c t+1, c t+2,..., c t+ ,...)) Bliss uses just this weak version of preferences Bliss uses just this weak version of preferences Takes a multi-agent version of Ramsey Takes a multi-agent version of Ramsey  Optimising agents  Infinite lives Again you get a version of the Ramsey paradox Again you get a version of the Ramsey paradox

27 Frank Cowell: UB Public Economics Alternative approaches Role of technology Role of technology Increasing returns Increasing returns Imperfect capital markets Imperfect capital markets But rational savings behaviour may be the key But rational savings behaviour may be the key

28 Frank Cowell: UB Public Economics Alternative approaches Human capital in the production function. 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. 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 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, 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 Frank Cowell: UB Public Economics Overview... Introduction Growth models World inequality Inequality in advanced countries Inequality and Redistribution Convergence?

30 Frank Cowell: UB Public Economics Applying the growth model Individual incomes and wealth Individual incomes and wealth  Role of savings behaviour  What will happen to individual capitalist countries Wealth of nations Wealth of nations  Convergence?  Is the standard growth model the right one?

31 Frank Cowell: UB Public Economics Questions about inequality Inequality between countries Inequality between countries  Role of globalisation  Role of savings behaviour  Or is inequality increasing? Inequality within countries Inequality within countries  Convergence?  Related to countries economic policies?

32 Frank Cowell: UB Public Economics Kuznets reborn? Kuznets focused on a statistical curiosity 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 He was working just with cross-section data Now have repeated data for individual countries Now have repeated data for individual countries Micro-data for many countries Micro-data for many countries

33 Frank Cowell: UB Public Economics A Pattern of inequality Bourguignon and Morrisson (2002) investigate the distribution of well being among world citizens in 19 th, 20 th centuries. Bourguignon and Morrisson (2002) investigate the distribution of well being among world citizens in 19 th, 20 th centuries. Inequality worsened from the beginning of the 19th century to World War II Inequality worsened from the beginning of the 19th century to World War II Then stabilized or to have grown more slowly. Then stabilized or to have grown more slowly. Composition of inequality changed Composition of inequality changed  In the early 19 th century inequality mainly due to differences within countries  Later differences between countries.  Inequality in longevity also increased during the19 th century  Trend reversed in the second half of the 20 th century

34 Frank Cowell: UB Public Economics How does inequality affect growth? Traditional literature does something like this Traditional literature does something like this Dollar and Kraay (2002) argue that this produces ambiguous answers Dollar and Kraay (2002) argue that this produces ambiguous answers  Depends on econometric method  Depends on sample Use an explicit model of poor incomes Use an explicit model of poor incomes

35 Frank Cowell: UB Public Economics Model incomes of the poor Model incomes of the poor this way Model incomes of the poor this way Regression is equivalent to Regression is equivalent to Interested in two parameters: Interested in two parameters:   1 effect of overall income   2 effect of other factors

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

37 Frank Cowell: UB Public Economics International trends Sala-i-Martin 2002 Sala-i-Martin 2002 Within-country disparities have increased Within-country disparities have increased not enough to offset reduction in cross-country disparities. not enough to offset reduction in cross-country disparities. But the particular case effect is important 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 Frank Cowell: UB Public Economics Overview... Introduction Growth models World inequality Inequality in advanced countries Inequality and Redistribution Results from data sources

39 Frank Cowell: UB Public Economics Within-country inequality: uS Top shares of income and wages in 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 Top income and wages shares A U-shaped pattern over the century A U-shaped pattern over the century  Why?

40 Frank Cowell: UB Public Economics Top income shares in US

41 Frank Cowell: UB Public Economics Piketty-Saez explanation Wealth effect Wealth effect  capital owners experienced large shocks that in 1930s and 40s  a permanent effect on top capital incomes? The wage effect 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 The tax effect  steep progressive income and estate taxation  may have prevented large estates from fully recovering

42 Frank Cowell: UB Public Economics Also in a developing economy Top incomes and wages from 1956 to 2000 using individual tax returns data. 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 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 : 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. The rich getting richer had a significant impact on the overall income distribution.


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