Wealth, Growth and Inequality

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Wealth, Growth and Inequality

June 2005 June 2005

Public Economics: University of Barcelona Public Economics: University of Barcelona

Frank CowellFrank Cowell

http://darp.lse.ac.uk/ubhttp://darp.lse.ac.uk/ub

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Overview...

Introduction

Growth models

World inequality

Inequality in advanced countries

Inequality and Redistribution

The basis for the question

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Focus of the lecture

Major roles of governmentMajor roles of government Revenue raisingRevenue raising EfficiencyEfficiency Redistribution / EquityRedistribution / Equity

Distribution always a big question in public economicsDistribution always a big question in public economics Analysing it has always involved other fieldsAnalysing it has always involved other fields

MacroeconomicsMacroeconomics FinanceFinance Development economicsDevelopment economics

Brief look at what is involved...Brief look at what is involved...

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Basic accounting Begin with the basics of individual wellbeingBegin with the basics of individual wellbeing

Utility: depends on consumptionUtility: depends on consumption Resources: income and wealthResources: income and wealth

The agent’s incomeThe agent’s income composed of earnings + interest income + transferscomposed of earnings + interest income + transfers ignore transfers hereignore transfers here yyii = = wlwlii + + rkrkii

A simple decomposition of inequality?A simple decomposition of inequality? Components statistically uncorrelated?Components statistically uncorrelated? Income more widely dispersed than earnings?Income more widely dispersed than earnings? Evolution of distribution of Evolution of distribution of kk important for distribution of important for distribution of yy..

Basis of an income-determining modelBasis of an income-determining model Role of factor pricesRole of factor prices Role of accumulationRole of accumulation

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Old models, modern themes

Why a focus on these issues now?Why a focus on these issues now? Trends in within-country distributionTrends in within-country distribution Debate on globalisationDebate on globalisation

growing inequality?growing inequality? ...or convergence?...or convergence?

Improved data availabilityImproved data availability within-country: mainly based on individual tax recordswithin-country: mainly based on individual tax records across country: improved comparability and repeated across country: improved comparability and repeated

observationsobservations

Growth theory became fashionable againGrowth theory became fashionable again

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Background

Build on a connection with standard growth modelsBuild on a connection with standard growth models Role of capital and labourRole of capital and labour

Can in fact be made more generallyCan in fact be made more generally One accumulated factorOne accumulated factor One or more non-accumulated factorsOne or more non-accumulated factors

Role of factor pricesRole of factor prices focus on focus on ww and and rr assume competitive markets?assume competitive markets? will there be a PE equilibrium?will there be a PE equilibrium?

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Overview...

Introduction

Growth models

World inequality

Inequality in advanced countries

Inequality and Redistribution

New insights from simple neoclassical models

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An approach

Stiglitz (Econometrica 1969)Stiglitz (Econometrica 1969) Based on Solow-Swan type of modelBased on Solow-Swan type of model Affine (linear) savings functionAffine (linear) savings function Focus on both macro and distributional issues:Focus on both macro and distributional issues:

Accumulation of capitalAccumulation of capital Distribution of wealthDistribution of wealth

What does equilibrium look like?What does equilibrium look like? Outline of modelOutline of model Use modified Stiglitz notationUse modified Stiglitz notation

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Basic model: overall production

Aggregate productionAggregate production Assume Inada conditionsAssume Inada conditions

Interest rateInterest rate

Wage rateWage rate

yy: output per person : output per person kk: capital per person: capital per person

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Basic model: wealth classes

ii: indexes individual wealth classes: indexes individual wealth classes ii: capital in per person in group : capital in per person in group ii

yyii = = wlwlii + + rri i agent’s income in group agent’s income in group ii

Same labour endowment in every group Same labour endowment in every group ii

aaii: Proportion of population in group : Proportion of population in group ii

kkii: capital in group : capital in group ii as proportion of as proportion of

populationpopulation

Simple aggregationSimple aggregation

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Savings and growth Affine savings functionAffine savings function

Wealth accumulation in class Wealth accumulation in class ii

Substitute savings in class Substitute savings in class ii

Substitute income in class Substitute income in class ii

Aggregate growth in capital/labour ratioAggregate growth in capital/labour ratio

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Equilibrium growth: Solow model

k

y f(k)

k*

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Stability?

Change in capital-labour ratioChange in capital-labour ratio

Substitute in for Substitute in for ww and and rr

Simple phase-diagram behaviourSimple phase-diagram behaviour

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Equilibrium growth: extended

k

y f(k)

k* k**

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Basic results (1)

One or two balanced growth pathsOne or two balanced growth paths Depends on the shape of the savings functionDepends on the shape of the savings function Lower equilibrium is unstableLower equilibrium is unstable

On each path :On each path : stabilitystability capital labour ratio constantcapital labour ratio constant factor prices constantfactor prices constant Schlicht (1975)Schlicht (1975)

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Basic results (2)

Aggregate accumulation does not depend on Aggregate accumulation does not depend on distributiondistribution

Follows directly from the savings assumptionFollows directly from the savings assumption Would also hold if savings had a linear component Would also hold if savings had a linear component

dependent on wealthdependent on wealth Linearity: a reasonable empirical assumption? Linearity: a reasonable empirical assumption?

Schmidt-Hebbel and Serven (2000) on cross-section and Schmidt-Hebbel and Serven (2000) on cross-section and panel datapanel data

Use variety alternative inequality measuresUse variety alternative inequality measures Alternative savings definitions and various econometric Alternative savings definitions and various econometric

specificationsspecifications Income inequality does not have systematic effect on Income inequality does not have systematic effect on

aggregate savingaggregate saving

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Wealth classes and distribution

Now examine what is happening with the individual wealth classes Now examine what is happening with the individual wealth classes ii..

The group in equilibrium at any overall The group in equilibrium at any overall kk, given by, given by

Gives critical personal wealth level as function of Gives critical personal wealth level as function of kk

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The critical wealth levels

Implicitly define Implicitly define kk~~

Implicitly define Implicitly define kk^̂

Key relationshipsKey relationships

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Critical wealth levels

k

y f(k)

k*

k̂ k~

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Changes in wealth distribution

Rate of change of Rate of change of wealth in group wealth in group ii

Relative change for Relative change for two groupstwo groups

If If 11 < < 22 then … then …

……get convergence if get convergence if b+mw b+mw > 0> 0 You have to be to the right of You have to be to the right of kk^̂ for this for this

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Basic results (3)

On the balanced growth path On the balanced growth path kk*:*: instability in aggregateinstability in aggregate instability in distributioninstability in distribution

On the balanced growth path On the balanced growth path kk**:**: stability in aggregatestability in aggregate stability in distributionstability in distribution

In range In range kk* to * to kk^̂ : : Overall capital-labour ratio is increasingOverall capital-labour ratio is increasing Converges on equilibriumConverges on equilibrium But wealth inequality becomes more unequal along the wayBut wealth inequality becomes more unequal along the way

In range In range kk^̂ to to kk**:**: Overall capital-labour ratio is increasingOverall capital-labour ratio is increasing Converges on equilibriumConverges on equilibrium Wealth inequality becomes more equal along the wayWealth inequality becomes more equal along the way

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Role of taxation Assume a purely redistributive income tax Assume a purely redistributive income tax Disposable income isDisposable income is

Relative performance of two wealth classes is nowRelative performance of two wealth classes is now

Critical Critical k k value for convergence is now wherevalue for convergence is now where

The income tax makes a differenceThe income tax makes a difference

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Tweaking the model (1)

Nonlinear savingsNonlinear savings Equality inevitable? Desirable?Equality inevitable? Desirable? May get multiple equilibriaMay get multiple equilibria Equality may be Pareto dominated!Equality may be Pareto dominated!

Bourguignon (1981)Bourguignon (1981)

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Tweaking the model (2)

Optimised savings: Based on Ramsey (1928)Optimised savings: Based on Ramsey (1928) Many-agent versionMany-agent version

In steady states: a paradox?In steady states: a paradox? Agents discount future utility at different constant ratesAgents discount future utility at different constant rates All the capital owned by agents with the lowest discount rate. 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 If high discount consumer can borrow against future wage

income converge to zero consumption. income converge to zero consumption. No steady state need exist No steady state need exist Becker (1980)Becker (1980)

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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 All supply the same quantity of labour in all

periods and earn the same wage.periods and earn the same wage. All have same access to capital market, where All have same access to capital market, where

they all earn the same rate of return.they all earn the same rate of return. All have perfect foresight and there are no All have perfect foresight and there are no

stochastic effects in the model to upset stochastic effects in the model to upset convergence.convergence.

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Bliss model (2) Focus on Koopmans- separable preferencesFocus on Koopmans- separable preferences Let Let cc := ( := (cc11, , cc22, ..., , ..., cctt, ...), ...) UU((cc) = ) = WW11( ( uu((cc11), (), (cc22, , cc33, ..., , ..., cc+1+1, ...)), ...)) A generalisation of usual definition of separabilityA generalisation of usual definition of separability Can be used recursively:Can be used recursively:

UU((cc) = ) = WWtt( ( uu((cc11), ), uu((cc22), ..., ), ..., uu((cctt), (), (cctt+1+1, , cctt+2+2, ..., , ..., cctt++, ...)), ...)) Bliss uses just this weak version of preferencesBliss uses just this weak version of preferences Takes a multi-agent version of RamseyTakes a multi-agent version of Ramsey

Optimising agentsOptimising agents Infinite livesInfinite lives

Again you get a version of the Ramsey paradoxAgain you get a version of the Ramsey paradox

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Alternative approaches

Role of technologyRole of technology Increasing returnsIncreasing returns Imperfect capital marketsImperfect capital markets But rational savings behaviour may be the But rational savings behaviour may be the

keykey

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Alternative approaches Human capital in the production function. Human capital in the production function.

By itself this does not make a great differenceBy itself this does not make a great difference human capital accumulated optimally to combine with physical capital.human capital accumulated optimally to combine with physical capital.

Suppose accumulation of human capital cannot be financed by Suppose accumulation of human capital cannot be financed by borrowing. borrowing.

Imperfect capital mobility will assist income convergence. Imperfect capital mobility will assist income convergence. Barro, Mankiw Sala-i-Martin (1995)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 One small low-wealth country converges to a steady state ……where rest of the world occupies from the start. where rest of the world occupies from the start. Country is borrowing constrained all the way to steady stateCountry is borrowing constrained all the way to steady state. .

Consider general many-agent equilibrium, Consider general many-agent equilibrium, same model with borrowing constraints, same model with borrowing constraints, low wealth country having significant weight in the world equilibriumlow wealth country having significant weight in the world equilibrium convergence is not assuredconvergence is not assured

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Overview...

Introduction

Growth models

World inequality

Inequality in advanced countries

Inequality and Redistribution

Convergence?

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Applying the growth model

Individual incomes and wealthIndividual incomes and wealth Role of savings behaviourRole of savings behaviour What will happen to individual capitalist countriesWhat will happen to individual capitalist countries

Wealth of nationsWealth of nations Convergence?Convergence? Is the standard growth model the right one?Is the standard growth model the right one?

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Questions about inequality

Inequality between countriesInequality between countries Role of Role of globalisationglobalisation Role of savings behaviourRole of savings behaviour Or is inequality increasing?Or is inequality increasing?

Inequality within countriesInequality within countries Convergence?Convergence? Related to countries economic policies?Related to countries economic policies?

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Kuznets reborn?

Kuznets focused on a statistical curiosityKuznets focused on a statistical curiosity Suggested a speculative conclusionSuggested a speculative conclusion Inequality first rises, with industrialisation…?Inequality first rises, with industrialisation…? ……then falls, as workers become more productive?then falls, as workers become more productive?

He was working just with cross-section dataHe was working just with cross-section data Now have repeated data for individual countriesNow have repeated data for individual countries Micro-data for many countriesMicro-data for many countries

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A Pattern of inequality

Bourguignon and Morrisson (2002) investigate the distribution Bourguignon and Morrisson (2002) investigate the distribution of well being among world citizens in 19of well being among world citizens in 19thth, 20, 20thth centuries. centuries.

Inequality worsened from the beginning of the 19th century to Inequality worsened from the beginning of the 19th century to World War IIWorld War II

Then stabilized or to have grown more slowly. Then stabilized or to have grown more slowly. Composition of inequality changedComposition of inequality changed

In the early 19In the early 19thth century inequality mainly due to differences century inequality mainly due to differences within countrieswithin countries

Later differences between countries. Later differences between countries. Inequality in longevity also increased during the19Inequality in longevity also increased during the19thth century century Trend reversed in the second half of the 20Trend reversed in the second half of the 20thth century century

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How does inequality affect growth?

Traditional literature does something like thisTraditional literature does something like this

Dollar and Kraay (2002) argue that this produces Dollar and Kraay (2002) argue that this produces ambiguous answersambiguous answers Depends on econometric methodDepends on econometric method Depends on sampleDepends on sample

Use an explicit model of poor incomesUse an explicit model of poor incomes

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Model incomes of the poor Model incomes of the poor this wayModel incomes of the poor this way

Regression is equivalent toRegression is equivalent to

Interested in two parameters:Interested in two parameters: 11 effect of overall income effect of overall income

22effect of other factorseffect of other factors

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Is growth good for the poor?

Dollar-Kraay data set covers period from the 1960sDollar-Kraay data set covers period from the 1960s To take account of data on levels and changes use first differencesTo take account of data on levels and changes use first differences

Income share of poorest fifth does not change with average incomeIncome share of poorest fifth does not change with average income Does not change with institutions or policies designed to help the Does not change with institutions or policies designed to help the

poor.poor. But Ravallion (2001) suggests considerable heterogeneity amongst But Ravallion (2001) suggests considerable heterogeneity amongst

countriescountries

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International trends

Sala-i-Martin 2002Sala-i-Martin 2002 Within-country disparities have increased Within-country disparities have increased not enough to offset reduction in cross-country not enough to offset reduction in cross-country

disparities. disparities. But the particular case effect is importantBut the particular case effect is important

What drives cross-country reductions in inequality?What drives cross-country reductions in inequality? Large growth rate of the incomes of the 1.2 billion Large growth rate of the incomes of the 1.2 billion

ChineseChinese

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Overview...

Introduction

Growth models

World inequality

Inequality in advanced countries

Inequality and Redistribution

Results from data sources

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Within-country inequality: uS

Top shares of income and wages in US Top shares of income and wages in US Piketty-Saez (2003)Piketty-Saez (2003) Use individual tax returns Use individual tax returns Data from 1913 to 1998Data from 1913 to 1998

Top income and wages sharesTop income and wages shares A U-shaped pattern over the centuryA U-shaped pattern over the century

Why?Why?

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Top income shares in US

0

5

10

15

20

25

30

35

40

45

50

1913

1917

1921

1925

1929

1933

1937

1941

1945

1949

1953

1957

1961

1965

1969

1973

1977

1981

1985

1989

1993

1997

P90–100

P99–100CG excl

P99–100CG Incl

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Piketty-Saez explanation

Wealth effectWealth effect capital owners experienced large shocks that in 1930s and capital owners experienced large shocks that in 1930s and

40s40s a permanent effect on top capital incomes?a permanent effect on top capital incomes?

The wage effectThe wage effect Top wage shares flat before WW II, Top wage shares flat before WW II, Dropped during the warDropped during the war did not start to recover before the late 1960sdid not start to recover before the late 1960s Now higher than before WW II. Now higher than before WW II. Working rich have replaced the rentiers at the top of the Working rich have replaced the rentiers at the top of the

distribution.distribution. The tax effectThe tax effect

steep progressive income and estate taxation steep progressive income and estate taxation may have prevented large estates from fully recovering may have prevented large estates from fully recovering

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Also in a developing economy Top incomes and wages from 1956 to 2000 using individual tax Top incomes and wages from 1956 to 2000 using individual tax

returns data. returns data. Banerjee and Piketty (2003)Banerjee and Piketty (2003)

Top shares followed a secular U-shapeTop shares followed a secular U-shape top 0.01%, 0.1% 1% in total incometop 0.01%, 0.1% 1% in total income shares shrank until the early to mid 1980sshares shrank until the early to mid 1980s then rose again, so that today these shares are only slightly below what then rose again, so that today these shares are only slightly below what

they were in 1956they 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 The period from 1956 to the early to mid 1980s was also the period of “socialist” policies in India, “socialist” policies in India,

Subsequent period, starting with the rise of Rajiv Gandhi, saw a gradual Subsequent period, starting with the rise of Rajiv Gandhi, saw a gradual shift towards more probusiness policies. shift towards more probusiness policies.

The rich getting richer had a significant impact on the overall The rich getting richer had a significant impact on the overall income distribution. income distribution.