DEVELOPMENT ECONOMICS

DEVELOPMENT ECONOMICS

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics,

Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department of Economics, Eötvös Loránd University Budapest

Institute of Economics, Hungarian Academy of Sciences Balassi Kiadó, Budapest

2

Author: Katalin Szilágyi Supervised by Katalin Szilágyi

January 2011

Week 4

Growth empirics

From theory to empirics

• Growth models have testable implications on convergence/divergence

• Solow: (conditional) convergence due to diminishing marginal returns

• Models of endogenous growth: no convergence implied

Outline

• Growth accounting

• Growth regressions and speed of convergence

• Barro, Barro – Sala-i-Martin

• ”Taking Solow seriously”

• Mankiw-Romer-Weil

3

1. Growth accounting Growth accounting

• Contributions to overall growth from different sources

• Production function: Y (t) = F [K (t), L (t), A (t)]

• Effect of technology (TFP):

• Growth accounting:

• Solow (1957): growth in the USA mainly from TFP

• Young (1993): East Asian ”growth miracle” is largely from extensive sources

• Abramowitz (1956): TFP is the ”measure of our ignorance”

2. Growth regressions Growth regressions

• Barro (1991), Barro–Sala-i-Martin (2004)

• Cobb–Douglas production function:

A A Y

A x  F

^

L L K

K

g g

g ^  ^  x 



 

 ( ) ( ) ( ) ¹ )

( t A t K t L t

Y

4

• Balanced growth path:

• Sources of growth:

• Technology

• Convergence

• Convergence: rate of growth depends on initial position (distance from steady state)

• Poor countries should grow faster, ceteris paribus

Calibrated speed of convergence

• With typical values for developed countries:

• Calibrated half-life of initial income disparities is ~10 years

• Very optimistic compared to real-world experiences

Growth regressions

• Unconditional (or absolute) convergence (Barro, 1991):

)) ( log ) ( )(log )(

1 ) (

( )

( g g n y t y t

t y

t

y ^        

. 1 so , 1 about is

income national

in capital of

Share

on.

depreciati year

per 5%

about for

0.05

and growth population

1%

ely approximat for

0.01 n

growth, capita

per output year

per 2%

ely approximat for

0.02 g

/3

/3 











t i, 1

t i, 1

0 1

t t,

i,

b b y ε

g

  log



5

• all country-specific features are in the residual

• Results:

• OECD countries: b1 is significant and negative

• All countries: b1 is not significant (positive)

• Conditional convergence: if country characteristics differ in the steady state

• Regression of conditional convergence:

Where b0 is country-specific and contains all the country characteristics relevant for growth performance

• Barro (1991) and Barro–Sala-i-Martin (2004): b0 depends on

• School attendance, population growth, investment rate, ration of government consumption to GDP, inflation rate, openness, quality of institutions (rule of law, democracy)

• Estimated equation:

Conditional convergence

• The estimated coefficient b1 in the equation is significant and negative, but much lower than in the calibration excercise

• Regressions not just about convergence, but on the factors of growth in general (Barro, 2005, Sala-i-Martin, 1997)

• I just ran two million regressions

t i t

i i

t t

i

b b y

g _{, ,}

₁  ⁰  ¹ log _,

₁   _,

t i t

i t

i t

t

i

x b y

g _{, ,}

₁  ^' _,   ¹ log _,

₁   _,

6

3. Solow model with human capital

Solow model with human capital

• Assumption: human capital is a flexible (endogenous) factor of production

• Can be accumulated and is depreciated

• Production function:

• Accumulation of capital:

• Mankiw–Romer–Weil (1992): estimating the balanced growth path of the Solow model augmented with human capital

• Assumption:

• Estimated equation:







  

 ( ) ( ) ( ( ) ( ))

)

( t K t H t A t L t Y

1 and

1 0

, 1

0          

) (t)

k

n)h(t g

(δ )) f(k(t),h(t s

h(t)

n)k(t), g

(δ t)) f(k(t) ,h(

s

h h

k k















 

) exp(

)

( t

gt

j

A

A 

δ ) g n In s ) 1

( 1 In

In ) ( In

h j

hj







 







 



  (















k j

kj j

j n g

gt s A y t

7

MRW, 1992

• Accumulation rates:

• Average investment rate

• Secondary school enrollment

• Assumptions:

• Critical assumption: technology is ortogonal

• Initial level of technology is independent of any other factor of growth

• Estimated equation:

05 .

 0







g

k

 



j h j

hj

k j

kj j

g n s

g n s

y



 











 















 

 



 



 

 



 





) (

1 In ) ( 1 In

) (

1 In ) ( 1 In

cst

In

8 Good: support for the Solow model

• Endogenity bias?

• Problem: implied coefficients of the production function are not really plausible