Transcript No Slide Title

Frank Cowell: UB Public Economics
June 2005
Wealth, Growth and Inequality
Public Economics: University of Barcelona
Frank Cowell
http://darp.lse.ac.uk/ub
Frank Cowell:
Overview...
Inequality and
Redistribution
UB Public Economics
Introduction
The basis for the
question
Growth models
World
inequality
Inequality in
advanced countries
Frank Cowell:
Focus of the lecture
UB Public Economics
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Major roles of government
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Distribution always a big question in public economics
Analysing it has always involved other fields
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Revenue raising
Efficiency
Redistribution / Equity
Macroeconomics
Finance
Development economics
Brief look at what is involved...
Frank Cowell:
Basic accounting
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Begin with the basics of individual wellbeing
UB Public Economics
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The agent’s income
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composed of earnings + interest income + transfers
ignore transfers here
yi = wli + rki
A simple decomposition of inequality?
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Utility: depends on consumption
Resources: income and wealth
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
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Role of factor prices
Role of accumulation
Frank Cowell:
Old models, modern themes
UB Public Economics
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Why a focus on these issues now?
Trends in within-country distribution
Debate on globalisation
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Improved data availability
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growing inequality?
...or convergence?
within-country: mainly based on individual tax records
across country: improved comparability and repeated
observations
Growth theory became fashionable again
Frank Cowell:
Background
UB Public Economics
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Build on a connection with standard growth models
Role of capital and labour
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Can in fact be made more generally
One accumulated factor
One or more non-accumulated factors
Role of factor prices
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focus on w and r
assume competitive markets?
will there be a PE equilibrium?
Frank Cowell:
Overview...
Inequality and
Redistribution
UB Public Economics
Introduction
New insights
from simple
neoclassical
models
Growth models
World
inequality
Inequality in
advanced countries
Frank Cowell:
An approach
UB Public Economics
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Stiglitz (Econometrica 1969)
Based on Solow-Swan type of model
Affine (linear) savings function
Focus on both macro and distributional issues:
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Accumulation of capital
Distribution of wealth
What does equilibrium look like?
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Outline of model
Use modified Stiglitz notation
Frank Cowell:
Basic model: overall production
UB Public Economics
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y: output per person
k: capital per person
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Aggregate production
Assume Inada conditions
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Interest rate
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Wage rate
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Frank Cowell:
Basic model: wealth classes
UB Public Economics
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i: indexes individual wealth classes
ki: capital in per person in group i
yi = wli + rki agent’s income in group i
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Same labour endowment in every group i
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ai: Proportion of population in group i
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ki: capital in group i as proportion of
population
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Simple aggregation
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Frank Cowell:
Savings and growth
UB Public Economics
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Affine savings function
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Wealth accumulation in class i
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Substitute savings in class i
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Substitute income in class i
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Aggregate growth in
capital/labour ratio
Frank Cowell:
Equilibrium growth: Solow model
y
f(k)
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k
k*
Frank Cowell:
Stability?
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Change in capital-labour ratio
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Substitute in for w and r
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Simple phase-diagram behaviour
Frank Cowell:
Equilibrium growth: extended
y
f(k)
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k
k*
k**
Frank Cowell:
Basic results (1)
UB Public Economics
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One or two balanced growth paths
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Depends on the shape of the savings function
Lower equilibrium is unstable
On each path :
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stability
capital labour ratio constant
factor prices constant
Schlicht (1975)
Frank Cowell:
Basic results (2)
UB Public Economics
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Aggregate accumulation does not depend on
distribution
Follows directly from the savings assumption
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Would also hold if savings had a linear component dependent
on wealth
Linearity: a reasonable empirical assumption?
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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
Frank Cowell:
Wealth classes and distribution
UB Public Economics
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Now examine what is happening with the individual wealth classes
i.
The group in equilibrium at any overall k, given by
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Gives critical personal wealth level as function of k
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Frank Cowell:
The critical wealth levels
UB Public Economics
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Implicitly define k~
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Implicitly define k^
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Key relationships
Frank Cowell:
Critical wealth levels
y
f(k)
UB Public Economics
k
k*
^k
~
k
Frank Cowell:
Changes in wealth distribution
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Rate of change of
wealth in group i
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Relative change for
two groups
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If k1 < k2 then …
…get convergence if b+mw > 0
You have to be to the right of k^ for this
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Frank Cowell:
Basic results (3)
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On the balanced growth path k*:
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On the balanced growth path k**:
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stability in aggregate
stability in distribution
In range k* to k^ :
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instability in aggregate
instability in distribution
Overall capital-labour ratio is increasing
Converges on equilibrium
But wealth inequality becomes more unequal along the way
In range k^ to k**:
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Overall capital-labour ratio is increasing
Converges on equilibrium
Wealth inequality becomes more equal along the way
Frank Cowell:
Role of taxation
UB Public Economics
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Assume a purely redistributive income tax t
Disposable income is
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Relative performance of two wealth classes is now
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Critical k value for convergence is now where
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The income tax makes a difference
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Frank Cowell:
Tweaking the model (1)
UB Public Economics
Nonlinear savings
 Equality inevitable? Desirable?
 May get multiple equilibria
 Equality may be Pareto dominated!
 Bourguignon (1981)
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Frank Cowell:
Tweaking the model (2)
UB Public Economics
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Optimised savings: Based on Ramsey (1928)
Many-agent version
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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
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If high discount consumer can borrow against future wage
income converge to zero consumption.
No steady state need exist
Becker (1980)
Frank Cowell:
Bliss model (1)
UB Public Economics
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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.
Frank Cowell:
Bliss model (2)
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UB Public Economics
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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:
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Bliss uses just this weak version of preferences
Takes a multi-agent version of Ramsey
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U(c) = Wt( u(c1), u(c2), ..., u(ct), (ct+1, ct+2, ..., ct+t, ...))
Optimising agents
Infinite lives
Again you get a version of the Ramsey paradox
Frank Cowell:
Alternative approaches
UB Public Economics
Role of technology
 Increasing returns
 Imperfect capital markets
 But rational savings behaviour may be the
key
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Frank Cowell:
Alternative approaches
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Human capital in the production function.
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UB Public Economics
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Suppose accumulation of human capital cannot be financed by
borrowing.
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Imperfect capital mobility will assist income convergence.
Barro, Mankiw Sala-i-Martin (1995)
Consider convergence in a special case
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By itself this does not make a great difference
human capital accumulated optimally to combine with physical capital.
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,
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same model with borrowing constraints,
low wealth country having significant weight in the world equilibrium
convergence is not assured
Frank Cowell:
Overview...
Inequality and
Redistribution
UB Public Economics
Introduction
Convergence?
Growth models
World
inequality
Inequality in
advanced countries
Frank Cowell:
Applying the growth model
UB Public Economics
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Individual incomes and wealth
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Role of savings behaviour
What will happen to individual capitalist countries
Wealth of nations
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Convergence?
Is the standard growth model the right one?
Frank Cowell:
Questions about inequality
UB Public Economics
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Inequality between countries
 Role of globalisation
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Role of savings behaviour
Or is inequality increasing?
Inequality within countries
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Convergence?
Related to countries economic policies?
Frank Cowell:
Kuznets reborn?
UB Public Economics
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Kuznets focused on a statistical curiosity
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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
Frank Cowell:
A Pattern of inequality
UB Public Economics
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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
th
 In the early 19 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
Frank Cowell:
How does inequality affect growth?
UB Public Economics
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Traditional literature does something like this
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Dollar and Kraay (2002) argue that this produces
ambiguous answers
 Depends on econometric method
 Depends on sample
Use an explicit model of poor incomes
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Frank Cowell:
Model incomes of the poor
UB Public Economics
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Model incomes of the poor this way
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Regression is equivalent to
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Interested in two parameters:
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a1 effect of overall income
a2effect of other factors
Frank Cowell:
Is growth good for the poor?
UB Public Economics
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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
Frank Cowell:
International trends
UB Public Economics
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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
Frank Cowell:
Overview...
Inequality and
Redistribution
UB Public Economics
Introduction
Results from
data sources
Growth models
World
inequality
Inequality in
advanced countries
Frank Cowell:
Within-country inequality: uS
UB Public Economics
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Top shares of income and wages in US
Piketty-Saez (2003)
 Use individual tax returns
 Data from 1913 to 1998
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Top income and wages shares
 A U-shaped pattern over the century
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Why?
UB Public Economics
1997
1993
1989
1985
1981
1977
1973
1969
1965
1961
1957
1953
1949
1945
1941
1937
1933
1929
1925
1921
1917
1913
Frank Cowell:
Top income shares in US
50
45
40
P90–100
35
30
25
P99–100
CG excl
20
15
10
P99–100
CG Incl
5
0
Frank Cowell:
Piketty-Saez explanation
UB Public Economics
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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
Frank Cowell:
Also in a developing economy
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UB Public Economics
Top incomes and wages from 1956 to 2000 using individual tax
returns data.
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Top shares followed a secular U-shape
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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 :
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Banerjee and Piketty (2003)
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.