endogenous growth lecture

7/29/2019 Endogenous Growth Lecture

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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

))()(/()()(()()()(

)()()(

)()()(

)()()(

)]()([)()()(1

tLtAtXtxthgnysth

tkgnystk

tHtYstH

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

ygn

hygnkygnyy

hygnhh

kygngnkyK

Y

s

gnK

YsgnKKkk

hhkkyy

yyvyy

gnKYs

HHhKKkYYy

LR

LR

K

K

LRLRK

LRLRLR

)1)((

))(())((/

))((/Similarly,

)

)(()()

1(

)()(//

///

/;ln

./havemustOne

/;/;/


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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

endogenous growth lecture

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