Trade Growth and Inequality

1
Trade Growth and Inequality

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

2
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

3
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

4
Table 4.1 Simple regression result N117
F6.245
5
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

6
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

7
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

8
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

9
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

10
Table 4,2 Growth and extra variablesSources
Barro and Sala-i-Martin (1985) Barro-Lee data
set
11
Table 4.3 Regression resultN 73 F 8.326
R2 .4308
12
Table 4.4 Regression with One Conditioning
Variable
13
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.

14
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

15
Inside Growth regressions III

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

16
Inside Growth Regressions IV
17
Inside Growth Regressions V

• So that
• vglYßvgg ?vgz (5)
• Then if vglY 0 and vg gt 0, (5) requires
  that either ß or ?, but not both, be negative. If
  vglY gt 0 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
  regression, 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.

18
A Growth Regression with one additional variable
19
Growth Regression with I/Y
20
One additional variable regression

• From (5) and the variance/covariance matrix
  above
• .00384 .82325ß .05216?
• Now if ? is positive, ß must be negative
• This has happened because the added variable is
  positively correlated with g

21
Adding the Mystery Ingredient L

• gßly?Le (7)
• The correlation matrix is

22
Growth Regression with L

23
Correlation and Cause

• The Barro equation is founded in a causal theory
  of growth
• The equation with L cannot have a causal basis
• What is causality anyway?
• Granger-Sims causality tests. Need time series
  data. Shocks to causal variables come first in
  time

24
Causality and Temporal Ordering

• An alarm clock set to ring just before sunrise
  does not cause the sun to rise.
• If it can be shown that random shocks to my alarm
  setting are significantly correlated with the
  time of sunrise, the that is an impressive puzzle
• Cause is a (an optional) theory notion

25
Convergence Theory

• The Solow-Swan Model

26
Solow-Swan Model II

• The model gives convergence in two important
  cases
• Several isolated economies each with the same
  saving share. Only the level of per capita
  capital distinguishes economies
• There is one integrated capital markets economy
  and numerous agents with the same saving rate.
  Only the level of per capita capital attained
  distinguishes one agnet from another.

27
Solow-Swan Model III

• If convergence is conditional on various
  additional variables, how precisely do these
  variables make their effects felt?
• For country I at time t income is
• AiFKi(t),Li(t)
• A measures total factor productivity, so will be
  called TFP

28
(No Transcript)
29
Determinants of the Growth Rate

• The growth rate is larger
• The larger is capitals share
• The larger is the saving share
• The larger is the TFP coefficient
• The smaller is capital per head
• The smaller is the rate of population growth

30
Mankiw, Romer and Weil (1992)

• 80 of cross section differences in growth rates
  can be accounted for via effects 2 and 5 by
  themselves
• The chief problem for growth empirics is to
  disentangle effects 3 and 4

31
Convergence The Ramsey Model

• Ramsey (1928) considered a many-agent version of
  his model (a MARM)
• He looked at steady states and noted the
  paradoxical feature that if agents discount
  utility at different rates, then all capital will
  be owned by agents with the lowest discount rate

32
Two different cases

• Just as with the Solow-Swan model the cases are
• Isolated economies each one a version of the same
  Ramsey model, with the same utility discount
  rate. The level of capital attained at a
  particular time distinguishes one economy from
  another
• One economy with a single unified capital market,
  and each agent has the same utility function. The
  level of capital attained at a particular time
  distinguishes one agent from another

33
Isolated Economies

• Chapter 3 has already made clear that there is no
  general connection between the level of k and
  (1/c)(dc/dt).
• The necessary condition for optimal growth is
• -c(du/dc)/u(1/c)(dc/dt)F1k(t),1-r (
  20)
• Where u is U1c(t)

34
Determinants of the Growth of Consumption

• The necessary condition for optimal growth is
• -c(du/dc)/u(1/c)(dc/dt)F1k(t),1-r When
  k(t) takes a low value the right-hand side of
  (20) is relatively large. If the growth rate of
  consumption is not large, the elasticity of
  marginal utility
• -c(du/dc)/u
• Must be large.
• The idea that ß-convergence follows from optimal
  growth theory is suspect.

35
Growth in the MARM

• With many agents the optimal growth condition
  (20) becomes
• -d(du/dc)/dt/uF1Skii(t)),1-r (23)
• In steady state (23) becomes
• F1Skii(t)),1r
• Note the effect of perturbing one agents capital
  holding

36
A non-convergence result

• In the MARM
• Non-converging steady states are possible
• Strict asymptotic convergence can never occur
• Partial convergence (or divergence) clubs are
  possible depending on the third derivative of the
  utility function

37
What does a MARM maximize?

• Any MARM equlibrium is the solution to a problem
  of the form
• Max SN1?08Uci(t)dt
• Non-convergence is hsown despite the assumptions
  that
• All agents have the same tastes and the same
  utility discount rate
• All supply the same quantity of labour and earn
  the same wage
• All have access to the same capital market where
  they earn the same rate of return
• All have perfect foresight and there are no
  stochastic effects to interfere with convergence

38
Asymptotic and ß-convergence

• For isolated Ramsey economies we have seen that
  we need not have ß-convergence, but we must have
  asymptotic convergence
• On the other hand we may have ß-convergence
  without asymptotic convergence
• lnyI aI - b/t2 lnyII aII - b/t1
• aIlt aII
• Country I has the lower income and is always
  growing faster

39
Strange Accumulation Paths can be Optimal

• In the Mathematical Appendix it is shown that
• Given a standard production function and a
  monotonic time path k(t) such that k goes to k,
  the Ramsey steady state value, and the implied c
  is monotonic, there exists a well-behaved
  utility function such that this path is Ramsey
  optimal

40
Optimal Growth with Random Shocks

• Bliss (2003) discusses the probability density of
  income levels when Ramsey-style accumulation is
  shocked each period with shocks large on absolute
  value
• Two intuitive cases illustrate the type of result
  available
• Low income countries grow slowly, middle income
  countries rapidly and rich countries slowly. If
  shocks are large poverty and high income form
  basins of attraction in which many countries will
  be found. Compare Quah (1997)
• If shocks are highly asymmetric this will affect
  the probability distribution of income levels,
  even if the differential equation for income is
  linear. Earthquake shocks.

41
The BMS Model

• Barro, Mankiw and Sala-i-Martin (1995)
• Human capital added which cannot be used as
  collateral
• One small country converges on a large world in
  steady state (existence is by exhibition).
• A more general case is where many small countries
  have significant weight. Then if they differ some
  may leave the constrained state before others and
  poor countries may not be asymptotically
  identical

42
Concluding Remarks

• There is no simple statistical association
  between initial income and subsequent growth,
  hence no support for ß-convergence from a basic
  two-variable analysis
• With multivariate analysis the hypothesis of a
  causal connection between initial income and
  subsequent growth on an other things equal basis
  is not rejected
• Theoretical models with common technology often
  confirm the ß-convergence hypothesis
• Surprisingly the literature neglects catching-up