Trade Growth and Inequality

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Trade Growth and Inequality

• Professor Christopher BlissHilary Term
  2004Fridays 10-11 a.m.

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Why the Poor Stay Poor

• Chapter 3 of the book
• (circulated)

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The Persistence of Poverty

• What are the transmission properties of income at
  t to income at t1?
• Friedman (1992) regression to the mean
• Incomes normally distributed andPositions
  randomPositions fixed

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Are All Agents the Same?

• Herrnstein and Murray (The Bell Curve)
• IncomeF(IQ)
• They claim that technological change has been
  such thatF(IQ))/F(100) has been falling over
  time for values of IQ well below the mean100

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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)

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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)

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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

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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?

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The Stiglitz MASS Model

• Solow-Swan with many agents
• All supply same labour and save the same
  proportion of all income

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Stiglitz Model Result

• Let k satisfy
• s.Fk,1-g.k0
• All agents converge to holding k

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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.

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Convergence and the Discount Rate

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

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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)

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Strotzian Inconsistency
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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).

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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.

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The Elasticity of Inter-temporal Substitution
(EIS)

• ? -c(d2U/dc2)/dU/dc
• If dU/dc u
• ? -c(du/dc)/u

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The Optimal Growth Condition

• -(du/dt)/u F1k,1 d
• ?(dc/dt)/c F1k,1 d
• EISgrowth consumption
• MPK U discount rate

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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

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Diamond Modelkt-1 determines kt

• Max Uct ?Uct1
• Subject to
• ct (1/1rt) ct1 ? kt wt
• wt F2kt-1,1
• 1rt F1kt,1

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Diamond ModelThe fundamental theorem

• Theorem
• kt increases with kt-1
• This makes possible multiple equilibria

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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

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Diamond ModelThe 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

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Diamond ModelMultiple Solution I

• Cobb-Douglas preferences
• Uct,ct1 ct?.ct1 ?-1
• Where ? gt 0.5 gives discounting
• Then kt ?.F2kt-1,1
• In SS k ?.F2k,1
• Both sides increase with k.
• Strict concavity requires F211k,1 lt 0

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The Concavity Conditionwith Cobb-Douglas

• With Cobb-DouglasF2k,1 A(1-a)ka
• F211k,1 -Aa(1-a)2ka-2 lt 0
• So in the Cobb-Douglas case we have uniqueness

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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)

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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.

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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

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Ch. 4 Convergence in Practice and Theory

• Cross-section growth empirics starts with Baumol
  (1986)
• He looks at ß-convergence
• ß-convergence v. s-convergence - Friedman (1992)
• De Long (1988) sampling bias

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Barro and Sala-i-Martin

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

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Table 4.1 Simple regression result N117
F6.245
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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

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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

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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

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Two examples of correlating non-stationary
variables

• The beginning econometrics students consumption
  functionct a ßyt et
• But surely consumption is causally connected to
  income
• ADt a ßTSt etwhere TS teachers
  salaries AD arrests for drunkeness

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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

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Table 4,2 Growth and extra variablesSources
Barro and Sala-i-Martin (1985) Barro-Lee data
set
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Table 4.3 Regression resultN 73 F 8.326
R2 .4308
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Table 4.4 Regression with One Conditioning
Variable
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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.

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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
• vgly0
• where v is the summed products of g and ly

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Inside Growth regressions III

• Thus vgly is N times the co-variance between g
  and ly.
• Now consider the multiple regression
• gßly?ze (3)

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Inside Growth Regressions IV
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Inside Growth Regressions V

• So that
• vglY(ß)(vgg)(?)(vgz) (5)
• Then if vglY0 and vgzgt0, (5) requires
  that either ß or ?, but not both, be negative. If
  vglYgt0 then ß and ? may both be positive, but
  they cannot both be negative. One way of
  explaining that conclusion is to say that a
  finding of ß-convergence with an augmented
  regressions, despite growth and log initial
  income not being negatively correlated, can
  happen because the additional variable (or
  variables on balance) are positively correlated
  with initial income.