A Contribution to the Empirics of Economic Growth

"This paper takes Robert Solow seriously" Mankiw, Romer and Weil(1992)

Fall 2012

Mankiw, Romer and Weil () ECON435/835 Fall 2012 1 / 24

First paper to use data from the Penn World Tables (PPP adjusted)

Estimates steady state and transitional dynamic equations

Develops augmented Solow model

Still underlies most empirical work on growth (despite criticisms)

Mankiw, Romer and Weil () ECON435/835 Fall 2012 2 / 24

Mankiw, Romer and Weil () ECON435/835 Fall 2012 3 / 24

Conditional steady�state analysis

In Cobb�Douglas case

YiLi= Aiyi = Ai

�si

ni + g + δ

� α1�α

Taking logs:

lnYiLi= lnAi +

α

1� α[ln si � ln(ni + g + δ)] .

Mankiw, Romer and Weil (1992) estimate:

lnYiLi= a+ b ln si + c ln(ni + 0.05) + εi

Using OLS imposes the assumption that si and ni are uncorrelatedwith εi

Mankiw, Romer and Weil () ECON435/835 Fall 2012 4 / 24

Mankiw, Romer and Weil () ECON435/835 Fall 2012 5 / 24

Discussion of Results

Accounts for a substantial fraction of varation in per capita income

b > 0 and c < 0 and signi�cant.

BUT implied α is very large (> 0.6)

,! capital shares are typically around 1/3

Restriction that b = �c is rejected

Mankiw, Romer and Weil () ECON435/835 Fall 2012 6 / 24

Conditional Convergence

Previous estimates assume that deviations from a country�s steadystate are random. MRW (1992) also test convergence properties.

Recall the convergence equation:

ln yt = ln y � + e�λt (ln y0 � ln y �)

ln yt � ln y0 = (1� e�λt ) ln y � � (1� e�λt ) ln y0

,! substituting for y �:

ln yt � ln y0 = (1� e�λt )α

1� αln�

sini + g + δ

�� (1� e�λt ) ln y0

Mankiw, Romer and Weil () ECON435/835 Fall 2012 7 / 24

Since yt = Yt/AtLt :

lnYtLt� ln Y0

L0= gt + (1� e�λt )

α

1� αln�

sini + g + δ

��(1� e�λt ) ln

Y0L0+ (1� e�λt ) lnA0

MRW estimate growth equation (with t = 25):

lnYiLi� ln Yi ,0

Li ,0= a+ b ln si + c ln (ni + 0.05) + d ln

Yi ,0Li ,0

+ εi

Mankiw, Romer and Weil () ECON435/835 Fall 2012 8 / 24

Mankiw, Romer and Weil () ECON435/835 Fall 2012 9 / 24

Results

Coe¢ cients have the right sign

Consistent with conditional convergence

BUT estimated rate of convergence, λ, is much slower than modelpredicts

Restriction that b = �c is rejected

Mankiw, Romer and Weil () ECON435/835 Fall 2012 10 / 24

The Augmented Solow Model

Aggregate production function given by

Yt = K αt H

βt (AtLt )

1�α�β

Evolution of physical and human capital

Kt = sKYt � δKtHt = sHYt � δHt

Intensive form:yt = kα

t hβt .

,! dynamics

kt = sK kαt h

βt � (n+ g + δ)kt

ht = sHkαt h

βt � (n+ g + δ)ht

Mankiw, Romer and Weil () ECON435/835 Fall 2012 11 / 24

k

h

(k=0)

(h=0)

k*

h*

.

.

Figure: Phase Diagram for Augmented Solow model

Mankiw, Romer and Weil () ECON435/835 Fall 2012 12 / 24

Stable BGP where kt = ht = 0:

k =

s1�βK sβ

H

n+ g + δ

! 11�α�β

and h =

sαK s

1�αH

n+ g + δ

! 11�α�β

) output per e¤ective worker:

y =

"sαK s

βH

(n+ g + δ)α+β

# 11�α�β

Mankiw, Romer and Weil () ECON435/835 Fall 2012 13 / 24

Empirical Evaluation �Steady-state

In logs we have

lnYL

= lnA+α

1� α� βln sK +

β

1� α� βln sH

+α+ β

1� α� βln(n+ g + δ)

Mankiw, Romer and Weil estimate

lnYiLi= a+ b ln sKi + c ln sHi + d ln(ni + 0.05) + εi

Mankiw, Romer and Weil () ECON435/835 Fall 2012 14 / 24

Mankiw, Romer and Weil () ECON435/835 Fall 2012 15 / 24

Results

Accounts for almost 80% of the variation in per capita GDP

b > 0, c > 0 and d < 0 and signi�cant

Implied values factor shares are α = 0.31 and β = 0.28.

Restriction that b+ c = �d , cannot be rejected at the 5% level.

Mankiw, Romer and Weil () ECON435/835 Fall 2012 16 / 24

Empirical Evaluation �Conditional onvergence

Same idea as for basic Solow model:

Growthi = a+ bK ln sKi + bH ln sHi + c ln (ni + 0.05) + d lnYi ,0Li ,0

+ εi

where according to the theory

bK = (1� e�λt )α

1� α� β

bH = (1� e�λt )β

1� α� β

c = �(1� e�λt )α+ β

1� α� β

d = ��1� e�λt

�

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Results

Explains more of the variation in growth rates than basic model

Estimated rate of convergence, λ, is closer to model prediction

,! estimated λ is higher

,! model prediction is lower

Restriction that bK + bH = �c is not rejected

Mankiw, Romer and Weil () ECON435/835 Fall 2012 19 / 24

Problems with MRW Methodology

Endogeneity bias.

Omitted variable bias

Proxy for sH is arbitrary �Klenow and Rodriguez�Clare (1997)

,! other proxies suggest a large role for residual TFP

TFP growth rates are signi�cantly correlated with savings rates �Bernanke and Gurkaynak (2002)

,! consistent with �endogenous growth�

Mankiw, Romer and Weil () ECON435/835 Fall 2012 20 / 24

Cross�country rates of returnLucas (1990) � why doesn�t capital �ow from rich to poor countries?

y=f(k)

k

y

∆yR

∆yP

∆k=1 ∆k=1

Rich

Poor

∆yP > ∆yR

Figure: Implication of Diminishing ReturnsMankiw, Romer and Weil () ECON435/835 Fall 2012 21 / 24

Example:

rIrUS

=

�kIkUS

�α�1=

�yUSyI

� 1�αα

If α = 0.3:

rIrUS

=

�yUSyI

�2=

�YUS/LUSYI/LI

� AIAUS

�2If AI = AUS , then rI

rUS= 202 = 400

Mankiw, Romer and Weil () ECON435/835 Fall 2012 22 / 24

MRW argue that the augmented model might address this too

y=f(k , hR)

k

y

∆yR

∆yP

∆k=1 ∆k=1

Rich

Poor

∆yP < ∆yR

y=f(k , hP)

Figure: Implication for Rates of Return Conditional on Human Capital

Mankiw, Romer and Weil () ECON435/835 Fall 2012 23 / 24

Other problems with the Augmented Solow model

Predicts that payment to human capital is higher in developingcountries

Does not explain why sK , sH , n and g vary across countries

Does not explain long run di¤erences in growth rates

What are the fundamental determinants of growth and development?

,! geography, history, institutions

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