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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
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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
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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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Mankiw, Romer and Weil () ECON435/835 Fall 2012 18 / 24
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
Mankiw, Romer and Weil () ECON435/835 Fall 2012 24 / 24