endogenous growth lecture
TRANSCRIPT
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Endogenous growth theory
II. The empirics of GDP growth
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Questions
What are the variables (institutional,
cultural, demographic) which determine
GDP per capita and/or LT growth
Do we expect poor countries close the gap
with rich countries?
What are the policies/institutions which
allow such convergence to take place
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An industry developed in the 1990s
Take a cross-section of countries
Regress their growth performance over a givenperiod on a set of explanatory variables: Investment
Education Financial development
Corruption
Age
Political variables: coups, etc Then write a World Bank report saying that
variable X is good for growth
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The findings:
A recent paper by Sala-i-Martin et al. runs
a horse-race between a large number of
specifications involving more than 67
variables
They rank variables by robustness using
Bayesian techniques
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A distribution of estimators across
models:
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The most robust variables:
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The shortcomings
Whether we are really talking about growth
depends on the specification
The economic interpretation of these
regressions is not clear
Many variables are not robust
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The initial income problem:
If initial income is not included in theregression, we estimate a permanentsustainable growth rate
If it is and has a negative coefficient, weestimate the long-run output level
It can only grow if
One of the explanatory variables grow (butmost cant)
A growth trend affects all countries
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The interpretation problem
Some variables affect growth because they
proxy for the growth in the inputs of the
production function: education, investment, etc
Others matter because they affect humanbehaviour and therefore how the economy
accumulates these inputs
Finally, whether initial income should enter
depends on how the input contributions are
specified
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Example 1
includedbenotshouldoutputinitialregressor,theis/If
)()()(
KI
KI
AA
YY
tKtAtY
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Example 2
outputinitialincludingbythisteapproximmacanOne
Ylowerthe
larger,istcoefficienitsregressor,theis/If
)()()(
1
YI
AKY
I
A
A
K
Y
Y
I
A
A
Y
Y
tKtAtY
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Example 3
Xofeffectout theI/K wipesIncluding/
)()()(
XKI
KI
AA
YY
tKtAtY
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Convergence in neo-classical
models
Neo-Classical models: each country
converges to its own steady state
All own steady states grow at the same
rate
But the level depend on policies, savings
rates, etc
Similar countries converge to same
GDP per capita
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Convergence in endogenous
growth models
A laggard never closes the gap
Therefore, no convergence in income
levels
This because MPK is no higher for the
laggard
Furthermore, differences in policies affectthe long-run growth rate
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Looking at convergence allows us
to
Test the relevance of endogenous growth
models
Assess the magnitude of the returns to
accumulable factors
)1( gv
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Two approaches
Barro and Sala-i-Martin: take a data set of
similar economic units and look at
convergence between them in pc GDP
Mankiw-Romer-Weil: take a cross-country
regression of growth rates on initial
income controlling for own long-run steady
state
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Barro and Sala-i-Martin
They use a data-base of U.S. states over a
long-run period
They estimate the equivalent of our local speed
of convergence regression:
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The BSM Universal Law of
Convergence:
The speed of convergence is2 % per year
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What do we expect?
The Solow model predicts (+g)(1-
)
A reasonable calibration is =0.06,g=0.02, =0.3
This gives v=5.6 % per year
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How universal is the law?
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Findings:
The more similar the countries, the more it
holds unconditionally
The less similar the countries, the more
likely we find divergence
But the law is restored if controls are
added, controlling for own steady state
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How to eradicate poverty?
1. Adopt the policies and institutions of
advanced countries
2. Wait!
How long? Suppose I am 10 times poorer
than the US. How long does it take to be 2
times poorer?
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0
1
ln
ln
ln
1
)0(ln)0(ln)(ln)(ln
)(
)(ln
)(
)(ln
osolution tfor thelookWe|
t
eYYtYtY
tY
tY
tY
tY
dt
d
t
USUS
USUS
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What do we get?
With v=0.02, 0 = 0.1, 1 = 0.5,
t = 60 years!
With v=0.056, we instead get
t = 21 years
We want to understand why the speed of
convergence is so low
Can policy increase the speed of
convergence?
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Gloom?
In principle, the speed of convergence
only depends on the deep technological
parameters
That it is low tells us that the technology is
not what we thought it was
But it does not tell us we can increase v
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Mankiw-Romer and Weil
National accounts suggest that the
elasticity of capital is 0.3
Speed of convergence is more like
1-v/(g+) = 1-0.02/0.08 = 0.75
To reconcile these two facts, they
introduce another form of capital: Human
capital
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The Augmented Solow model
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)()()(
)()()(
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)]()([)()()(1
tLtAtXtxthgnysth
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tKtYstK
tLtAtHtKtY
tH
tK
H
K
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The balanced-growth path
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Explaining cross-country
differenced in pcGDP:
The preceding equations define own steady
state
They use it to see if it explains cross-country
income differences:
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Measuring sH
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What have we learned?
We have seen that with = 0.3, it isdifficult to explain X-country incomedifferences
But now what matters is + , which actsas
So with + large enough we can explain
cross-country differences. A natural question is: can we also expectslow convergence?
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Recomputing the speed of
convergence
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/;/;/
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Empirical strategy
Investment rates and schooling are kept to
proxy for own steady state
Initial output is added
Coefficient in initial output related to SOV
as in BSM
No other control variable is added in strict
interpretation of Solow model
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Old Solow does not work
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but new does.
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Does it add up?
024.0
06.0
3.0;3.0
v
gn
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Summary
The Solow model predicts too low income
disparities and too quick convergence
The AK model predicts zero convergence
and widening disparities
The Augmented Solow model does well to
predict both the disparities and the speed
of convergence