Trade Growth and
Inequality
Professor Christopher Bliss
Hilary Term 2004
Fridays 10-11 a.m.
Why the Poor Stay Poor
Chapter 3 of the book
(circulated)
The Persistence of Poverty
 What are the transmission properties of
income at t to income at t+1?
 Friedman (1992) regression to the mean
 Incomes normally distributed and:
Positions random
Positions fixed
Are All Agents the Same?
 Herrnstein and Murray (The Bell Curve)
 Income=F(IQ)
 They claim that technological change has
been such that:
F(IQ))/F(100) has been falling over time
for values of IQ well below the mean=100
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)
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)
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
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?
The Stiglitz MASS
Model
•Solow-Swan with many agents
•All supply same labour and save
the same proportion of all income
Stiglitz Model Result
Let k* satisfy:
s.F[k*,1]-g.k*=0
All agents converge to holding k*
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.
Convergence and the
Discount Rate
• Utility and Consumption Discount Rates
Distinguished
• Endogenous Discount Rates
• Do the poor have high discount rates?
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)
Strotzian Inconsistency
Period
1
2
3
Choice
I
95
20
25
II
95
22
22
III
100
18
18
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).
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.
Period
2
3
Choice
I
20
25
II
22
22
The Elasticity of Intertemporal Substitution
(EIS)
η =-c(d2U/dc2)/dU/dc
If dU/dc = u
η =-c(du/dc)/u
The Optimal Growth
Condition
-(du/dt)/u = F1[k,1] – δ
η(dc/dt)/c = F1[k,1] – δ
EIS*growth consumption
= MPK – U discount rate
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
Diamond Model:
kt-1 determines kt
• Max U[ct] + U[ct+1]
• Subject to:
• ct +(1/1+rt) ct+1  kt +wt
• wt = F2[kt-1,1]
• 1+rt = F1[kt,1]
Diamond Model
The fundamental theorem
• Theorem
• kt increases with kt-1
• This makes possible multiple
equilibria
Diamond Multiplicity
and 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
Diamond Model:
The 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
Diamond Model
Multiple Solution I
• Cobb-Douglas preferences
• U[ct,ct+1] = ctλ.ct+1 λ-1
• Where λ > 0.5 gives discounting
• Then: kt = λ.F2[kt-1,1]
• In SS: k = λ.F2[k,1]
• Both sides increase with k.
• Strict concavity requires F211[k,1] < 0
The Concavity Condition
with Cobb-Douglas
• With Cobb-Douglas
F2[k,1] = A(1-α)kα
• F211[k,1] = -Aα(1-α)2kα-2 < 0
• So in the Cobb-Douglas case we have
uniqueness
Diamond model
and the elasticity of inter-temporal
substitution
• With Cobb-Douglas production and a
constant EIS there is a unique nondegenerate steady state
• With a variable EIS this is no longer the
case (see the next figure)
Which Model
Diamond 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.
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
Ch. 4 Convergence in
Practice and Theory
• Cross-section growth empirics starts with
Baumol (1986)
• He looks at β-convergence
• β-convergence v. σ-convergence Friedman (1992)
• De Long (1988) – sampling bias
Barro and Sala-i-Martin
• World-wide comparative growth
• “Near complete” coverage (Summers-Heston
•
•
•
data) minimizes sampling bias
Straight test of β-convergence
Dependent variable is growth of per-capita
income 1960-85
Correlation coefficient between growth and
lnPCI60 for 117 countries is .227
Table 4.1 Simple regression
result N=117 F=6.245
Variable
Coefficient
t-value
Constant
-.0135
-.998
LnPCI60
.0046
2.50
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
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
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
Two examples of correlating nonstationary variables
• The beginning econometrics student’s
consumption function
ct = α + βyt + εt
• But surely consumption is causally
connected to income
• ADt = α + βTSt + εt
where TS = teachers’ salaries
AD = arrests for drunkeness
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
Table 4,2 Growth and extra
variables
Sources * Barro and Sala-i-Martin (1985)
* Barro-Lee data set
Variable
Definition
Mean
Standard deviation
Growth*
Growth rate per
capita income
1960-85
.0226
.0161
LnPCI60*
Log of PCI 1960
7.5201
,8930
bmp**
Forex black market
premium
.1188
,1675
govsh4**
Gov. con. / GDP
.1571
.0656
geerec**
Public exp. On
Edu./GDP
.0245
,0103
I/Y*
Invest./
GDP ratio
.0968
.1893
pinstab**
Political instability
.1916
,0859
Table 4.3 Regression result
N = 73 F = 8.326 R2 = .4308
Variable
Coefficient
t-value
Partial Rsquared
Constant
.0698
3.83
.1821
LnPCI60
-.01133
-3.89
.1863
Bmp
.0035
.345
.0018
Govsh4
-.0419
-1.66
.0400
Geerec
.4922
2.71
.0999
Pinstab
.0003
.029
.000
I/Y
.1673
6,02
.3545
Table 4.4 Regression with One
Conditioning Variable
Variable
Coefficient
t-value
Partial R2
Constant
.0281
2.17
.0403
LnPCI60
-.0048
-2.33
.0463
I/Y
.1502
7.08
.3092
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.
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:
v{gly}≥0
where v is the summed products of g and ly
Inside Growth regressions III
Thus v{gly} is N times the co-variance
between g and ly.
Now consider the multiple regression:
g=βly+γz+ε
(3)
Inside Growth Regressions IV
Inside Growth Regressions V
So that:
v{glY}=(β)(v{gg})+(γ)(v{gz}) (5)
Then if v{glY}≥0 and v{gz}>0, (5) requires that either β
or γ, but not both, be negative. If v{glY}>0 then β and γ
may both be positive, but they cannot both be negative.
One way of explaining that conclusion is to say that a
finding of β-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.