A Romerian Contribution to the Empirics of
Economic Growth
Bahar Bayraktar-Sağlam
Hacettepe University
Hakan Yetkiner
Izmir University of Economics
Atılım University, Ankara
May 4, 2012
1
PLAN OF PRESENTATION




Motivation
The Model
Empirical Results
Conclusion
2
A Critique of Convergence Literature
The following equation (or its variations) is used in
empirical growth literature in order to designate the
determinants of variations in real income across
countries (cf., Mankiw, Romer and Weil, (1992) :
Ln [ y ss ]  Ln [ A ( 0 )]  g  t 

1
Ln [ s ] 

1
Ln [ g  n   ]
In the equation above,
Ln [ A ( 0 )] : Initial knowledge stock plus all sources of
g:
variations
Exogenous rate of growth/ technological progress
We now know that g is defined by the characteristics
3
of R&D sector, by and large.
A Critique of Convergence Literature
In a similar vein, the following equation (or its
variations) is used in identifying the speed of
convergence, that is, the rate at which poorer
countries tend to grow faster than rich ones and
catch them up: ~
dLn [ y ]
dt
  v   Ln [ ~y ]  Ln [ ~y ss ] 
v  (1   )( n  g   )
Ln [
Y (t )
]  Ln [
L (t )
 (1  e
Y (0)
]  (1  e
 vt
) Ln [ A ( 0 )]  (1  e
 vt
) Ln [Y ( 0 )]  g  t
L (0)
 vt
 
)
1  


 vt 
 Ln [ s ]  (1  e ) 

1  

 Ln [ g    n ]  

4
A Critique of Convergence Literature-I
In almost all empirical studies, the exogenous growth
rate of technology is taken same across countries and
constant in time.
This is understandable, as the Solow framework is a
one-sector simple model and there is no way to
decompose the technological progress into its
components.
However, it is unrealistic (and unacceptable), as it is
the technological progress that determines long-run
economic growth and convergence performance (cf.
5
Howitt, 2000).
A Critique of Convergence Literature-I
Bloom et al. (2002):
Object both the idea of identical rate of technological
progress in every country and the fixed effects
approach adopted by panel data studies, which allow
for TFP differentials across countries that persist
indefinetely.
6
A Critique of Convergence Literature-II
Consider the naivety of adding new components into
these equations across the whole empirical literature.
The current application is merely to add the variable in
question to the growth/ convergence equations. At the
best, researchers follow MRW (1992)-type modeling
approach and add new accumulation functions.
To what extent is this satisfactory? Can we find a more
elegant way of introducing additional elements to study
the determinants of long run GDP per capita and speed
of convergence?
7
A Critique of Convergence Literature-III
How about Robustness of MRW (1992) Model?
Y (t )  K

H
 1   
L
vs.
Y (t )  K

H
1 
K  s I Y   K
K  s I Y   K
H  s H Y   H
H  s H Y   H
Steady state at levels vs.
Endogeneous Growth!
8
A Critique of Convergence Literature-IV
Since 1986, thousands of studies have been done in
endogenous/ new growth theory, showing the role of
endogenous technological change on transtitonal and
long run economic growth.
On the empirical side, however, we still use the Solow
framework and we continue to assume exogenous
technological change and exogenous growth rate.
Is it impossible to endogenize technological change in
such a way that fits ‘empirical world’? Though this is
not achieved in this paper, this work underlines the
9
need in this direction.
Literature (1)
 Romer (1990): Endogenous Technological Change
 Solow (1956): Exogenous Technological Change
 Mankiw, Romer Weil (1992): Solow model is too good to
ignore.
 Islam (1995): Panel data version of MRW (1992)
 Barro, Sala-i-Martin (1992): Convergence in Ramsey
 Jones (2002); Kim (2008, 2011)
 Whelan (2007)
10
Contribution of this paper
This paper develops a Romerian Solow Framework/
Solovian Romer Framework/ semi-endogenous growth
model and tests it, in which it is possible
(i) to decompose the components of exogenous growth
rate
(ii) to work out a richer and more flexible framework
(iii) to extend the framework in several directions
(limited only by imagination)
(iv) introduce human capital in a more elegant way
(v) possibly more robust compared to MRW (1992)
11
General Features of the Model
- Solovian Romer model
- Factors of production: X (intermediate goods) and L
(human capital)
- Exogenous determination of consumption-saving
tradeoff
- Final-goods market is perfectly competitive
- Intermediate goods market is monopolistically
competitive
- R&D sector is perfectly competitive.
12
The model
I. Final-Good Production
A (t )
1

Y  H
 X
Y
i
i 1
0  1
Y: Final Output
Xi: Intermediate Good i (Variety i)
HY: Human Capital allocated to Y
13
The model
II. Human Capital Allocation
H
Y

HY
HR&D
θY
θR&D
Y
H
H
R&D

R&D
H

Y

R&D
1
: Human capital allocated to final-good sector
: Human capital allocated to R&D-sector
: Human capital share of final-good sector
: Human capital share of R&D sector
III. Macroeconomic Budget Constraint:
K  s  Y    K
14
The Model
IV. R&D Sector
A    H R & D  A
A
: Stock of Knowledge
HR&D : Human capital allocated to R&D
Using the share definition:
A     R & D  H  A
15
Solution Procedure
Profit maximization in the final-good market yields:
A(t )
(1   )   Y   x i  w Y

1 
  Y

i 1
 1
 xi
 pi
Profit maximization in the intermediate-good market
yields:
pi  p 
r 

r


r  r  
1
   1 
xi  x   Y 

 r 
2
1   
1 


  r   x  (1   )     Y  x
H
 a 
i
16
Solution Procedure
Final-good and intermediate-good markets’ profit
maximization results imply:
A(t )
K 
K
A(t )
i
i 1
1 
y  Y


A(t )
Xi  X A
i 1

x A
k 
k
A(t )
i
i 1
1 
y  Y

x
i
 xA
i 1

k  A
1 
17
R&D Sector equilibrium process implies:
 R& D  VR& D    H R& D  A  wR& D  H R& D 
VR& D    LR& D  A  wR& D
The value of patents is found as follows:


V R & D ,i ( t )     H  e
t

 r ( s ) ds
t
d   V R & D ,i ( t ) 
H   (t )
r (t )
18
Recall that we assumed  Y and  R & D are constant.
Solving the model under this assumption, we find that

 s  1 
~
y ss   Y  

  g 
g  Aˆ ss     R & D  H
This is very similar to the Solow-result:

 s  1 
~
y ss  

  g 
Evidently, much richer in the sense that it decomposes Aˆ ss
into its components and underlines the role of human
capital in final good production in growth.
19
Empirical Applications:
Long-run determinants of GDP per capita
Solovianized Romer version:
ln y ss  a  gt  ln[  Y ] 

1
ln[ s ] 

1
ln[   g ]
g  Aˆ ss     R & D  H
a  Ln [ A ( 0 )]
Solow version:
ln y ss  a  g  t 
a  Ln [ A ( 0 )]

1
ln[ s ] 

1
ln[   g ]
g  0 . 02
20
Empirical Applications:
Convergence Equation
Solovianized Romer version:
 Y (t ) 
 Y (0) 
 Y (0) 
Ln 

Ln





Ln




   2  Ln  Y
0
1
 H 
 H 
 H 

  3  Ln  s    3  Ln   g 
β0
β1
β2
β3
: Constant term
: Coefficient of initial level of income
: Contribution of human capital
: Contribution of investment rate
 0  g  t  1  e
 1   1  e
 2  1  e
 3  1  e
 t
 t
 t


 t
  Ln  A ( 0 ) 




1   
21
Empirical Applications:
Convergence Equation
Solow version :
 Y (t ) 
 Y (0) 
 Y (0) 
Ln 

Ln





Ln




   3  Ln  s    3  Ln   g 
0
1
 H 
 H 
 H 
β0 : Constant term
β1 : Coefficient of initial level of income
β3 : Contribution of investment rate
Recall that g is not defined in Solow version…
Therefore, it is taken constant in time and identical
across countries.
22
Extensions-1
Generalized Knowledge/ R&D Sector
Suppose that


A    H R & D  A
 : Duplications/
production
elasticity of HR&D
 : Degree of positive externality on
current R&D
 n
ˆ
A ss 
1
One can show that:
1
k ss
0   ,  1

 1 


s

  Y  A ss  
 n 

n 

1





y ss

 1 


s

  Y  A ss  
 n 

n 

1



 23
Extensions-1
Generalized Knowledge/ R&D Sector
Determinants of long-run growth:

 n
y ss   Y  e
ln y ss 

1
1 
t

1
 (1   )     R & D  1


 n


ln[ s ]  ln[  Y ] 
1
1
ln[  ] 

 1 


s



 n 

n 

1 


1
ln[  R & D ] 

where
g 
 n
1
and

1
1
1
ln[ g ]
ln[ g  n   ]  gt
H (0)  1
24
Extensions-1
Generalized Knowledge/ R&D Sector
Convergence:
Under   1    A    H R& D  A 1  and g  Aˆ ss  n
Knowledge accumulation in terms of per human
capital becomes

a     R & D  a
1 
 na
Together with capital accumulation equation
~
~
~
1 
ˆ
k  s   Y  k  ( n    A ( t ))  k
We have a two-equation differential equation system 25
Extensions-1
Generalized Knowledge/ R&D Sector
Convergence:
Solving this system through log-linearization, we get
~
Ln ( k ) 
b1
(1   )( n    g )
 const 1  e
 ( 1  )( n    g ) t

b2
n
(1   )( n    g )   n  b 2
Ln ( a ) 
 const

n
 n
2
 const
e
  nt
2
e



~
Ln ( y )  (1   ) Ln ( Y )   Ln ( k )  Ln ( a )  nt
26
  nt
Extensions-2
Unskilled Labor Next to Skilled Labor
A(t )
Suppose that Y  L 1    H Y   X i di
0
L
: The constant amount of unskilled labor
One can show that:
~
K ss  L
~
Y ss  L
1   

1 
1 
Y
H
1   

1 
1 
Y
H
1
 s  1 


  g 

 s  1 


  g 
27
Extensions-2
Unskilled Labor Next to Skilled Labor
Long-run determinants of economic growth:

 L  1 


L H
L H 
Y ss
Ln  y ss   a  g  t 
1   
 HY 


L H 

1
1 

 s  1 

A

  g 
Ln [ L ] 
1  
1
Ln [ Y ] 

y ss 
Y ss
L H
Ln [ A ( 0 )]  a  

1

1
Ln [ s ]
Ln [  g ]  
g    H R& D  L 
L
L H
28
Extensions-2
Unskilled Labor Next to Skilled Labor
Convergence:
 Y (t ) 
 Y (0) 
 Y (0) 
Ln 

Ln




Ln




   2 Ln  L    3 Ln  Y 
0
1
L H 
L H 
L H 
  4 Ln  s    5 Ln   g 
 t
 0  g  t  1  e Ln  A ( 0 ) 
 1   1  e
 t

1     
 2  1  e 

1




 
 t 
 3  1  e 

1




 t
 4  1  e
5  4
 t
  


1




29
Extensions-3
Endogenous Allocation of Skilled Labor between
Y and R&D
Long-run determinants of Economic Growth:
ln y ss  a  g  t  ln[  Y , SS ] 

1
ln[ s ] 

1
ln[   g ]  
where
 Y , ss 
(  s )      H
(1  s )      H
30
Suitability for Further Extensions-1
Health
1   
Y  NY
A(t )
NL  Xi


i 1
N Y  hY  H Y
ln
Y ss
H L
 a  g t 

N L  hL  L
N R& D  hR& D  H R& D
1  

1
1
ln[ hY ] 
ln[  L ] 

1
1  
1
ln[ s ] 
ln[  Y ] 

1

1
ln[ h L ]
ln[   g ]  
31
Suitability for Further Extensions-2
Defense Spending
I. The Defense Sector
wM  H M  M   M  Y
M: Military Expenditure
τM: tax rate (=share of military expenditure in GDP)
(=research intensity in defense sector)
wM: Real wage rate of human capital in military
sector
32
Suitability for Further Extensions-2
Defense Spending
II. Profit Equation
Y
1 

 H   (1   M )   Y  x i  w Y   Y   p i  x i 


i 1
i 1
A(t )
A(t )
III. Human Capital Allocation
H Y  Y  H
H R& D   R& D  H
H M  M  H
Y   R& D   M  1
33
Suitability for Further Extensions-2
Defense Spending
IV. Macroeconomic Budget Constraint:
K  s  (1   M )  Y    K
V. R&D Sector
A    H R & D  (1   M )  A
34
Suitability for Further Extensions-2
Defense Spending
Long-run determinants of GDP per capita
ln y ss  a  g  t  ln[  Y ] 
Ln [ A ( 0 )]  a  

1
ln[ s ] 

1
ln[ 1   M ] 

1
ln[   g ]  
g     R & D  H  (1   M )
35
Empirical Applications:
Long-run determinants of GDP per capita for
developing Countries (No Spillover Effect)
wM  L  M   M  Y
Balanced Budget
ln y ss  a  g  t  ln[  Y ] 
Ln [ A ( 0 )]  a  

1
ln[ s ] 

1
ln[ 1   M ] 
g    R& D  H

1
ln[   g ]  
Y   R& D  1
36
Suitability for Further Extensions-2
Defense Spending
Convergence Equation
 Y (t ) 
 Y (0) 
 Y (0) 
Ln 

Ln





Ln




   2  Ln  Y    3  Ln  s 
0
1
 H 
 H 
 H 
  4  Ln 1   M    5  Ln   g 
β0
β1
β2
β3
β4
β5
: Constant term
: Coefficient of initial level of income
: Contribution of human capital
: Contribution of investment rate
: Contribution of defense intensity
: Contribution of effective
depreciation rate
 0  g  t  1  e
 1   1  e
 2  1  e
 t
 t
  Ln  A ( 0 ) 


 3   4   1  e
5  4
 t
 t




1




37
TESTING THE MODEL
38
Testing the Model (1)
Following MRW 1992, empirical growth studies have estimated
an augmented Solow model by assuming the (exogenous)
technology growth rate, g, to be a constant value.
Even studies like Nonneman and Vanhoudt (1996), Murthy and
Chien (1997) and Keller and Poutvaara (2005), using the
augmented Solow model to test for the role of technological
know-how on economic growth and convergence, assumed that
the exogenous technology parameter, g, is constant and be 0.02,
as in the vein of the MRW 1992.
One first and foremost empirical contribution of this paper is
dropping this assumption, based on our theoretical results. We
determined g through using the share of R&D personnel in the
labor force/ share of R&D expenditure in GDP.
39
Testing the Model (2)
This paper, to the best of our knowledge, is also the
first which estimates the convergence equation by
defining the technological progress as a function of the
share of R&D personnel in the labor force.
Our first empirical run replaces the constant
technology growth by the share of R&D personnel in
the labor force, which differs across countries and time.
Second empirical run (testing sensitivity of the model)
replaces the constant technology growth by the share of
R&D expenditure in GDP
40
Testing the Model (3)
Variables and sources of data:
Variable
 
Ln y

Ln y t 1

 
Ln s
 
 
R & D 
R & D 
Ln h
1
Ln h
2
Ln
1
Ln
2
Definition
Logarithm of growth in real
GDP per head of population
aged 15-64 years expressed in
2000 purchasing power parities
logarithm of lagged growth in
real GDP per head of population
aged 15-64 years expressed in
2000 purchasing power parities
Gross fixed investment share of
GDP
Secondary school enrollment
rate
The share of final good workers
in the labor force.
Data Source
OECD
Annual
Accounts
The share of R&D in the labor
force
The share of R&D expenditure
on GDP
OECD Main Science and
Technology Indicators database
OECD Main Science and
Technology Indicators database
OECD
Accounts
Annual
National
National
World Development Indicators
Database
Barro-Lee Education Dataset
(2010)
Own
calculations
where
 Y   R& D  1
41
Testing the Model (4)
Basic statistics:
Variables
Mean
Standard
Min
Max
Deviation
Real GDP per capita
21291
8858
5326
62731
Share of Investment in GDP
22.8
3.8
17
37
Secondary Enrollment rates
45.6
13.9
8.2
88
4.9
2.68
0.44
15
R&D
1.56
0.83
0.2
3.9
The population growth rate
0.65
0.68
-0.4
6
The share of R&D personnel
in the labor force
The
share
of
expenditure in GDP
(%)
42
Testing the Model (5)
The equation estimated:
ln y it  ln y it 1   1 ln y it 1   2 ln s it
  3 ln hit   4 ln[ n it  g it   ]
  i   t   it
43
Testing the Model (6)
Methodology: System GMM estimation proposed by
Arellano and Bover (1995) and Blundell and Bond
(1998) (Stata 10 is used for analyses).
Advantages of the System GMM
1. It provides consistent estimates in the presence of
• Measurement error
• Endogenous regressors
2. It is highly recommended for the empirical growth
studies (Bond et al., 2001).
To check for the validity of the instruments, we
carried out Hansen Test and serial correlation
(M2) test and they approve the validity of
44
instruments.
Findings (1): The share of labor devoted to R&D
45
Findings (2): The share of R&D expenditure over GDP
Dependent Variable: log differences in GDP per working person
Constant

Ln yit 1

 
 
Ln s
it
OLS
OLS
Within
Group
2.015***
(0.417)
System GMM
System GMM
-0.084
(0.402)
Within
Group
2.1698***
(0.427)
-0.089
(0.387)
0.299
(0.577)
0.645
(0.542)
-0.023***
(0.038)
-0.032***
(0.042)
-0.2784***
(0.031)
-0.2749***
(0.032)
-0.097***
(0.107)
-0.1539***
(0.064)
0.133**
(0.063)
0.245***
(0.066)
0.243***
(0.067)
0.031
(0023)
-0.040
(0.037)
0.222***
(0.058)
0.005
(0.024)
0.123**
(0.059)
0.030
(0.020)
0.007
(0.025)
0.056
(0.038)*
0.190***
(0.060)
0.085**
(0.032)
0.081*
(0.042)
0.97
0.97
0.94
0.94
0.0008
0.001
0.011
0.011
0.003
0.005
150
150
150
30
150
30
150
30
20
0.10
0.06
0.837
150
30
21
0.15
0.06
46
0.845
Ln h
it
Ln
nit  g it   
2
R
Implied ν
Number of Observations
Number of Groups
Number of Instruments
Hansen test p value
Difference Hansen p value
M2
-0.043
(0.036)
Findings (3)
1. All runs imply a convergence rate lower than that which
is suggested by the literature in general.
2. The investment rate has a positive and statistically
significant contribution to convergence in all runs.
3. The role of human capital on convergence is positive but
statistically insignificant according to the OLS and Within
Group estimators. But, human capital has significant and
positive impact on economic growth once the regressions are
carried out by the system GMM, where the system GMM
estimates are more efficient than the once obtained by the
OLS and Within Group estimators (Bond et al., 2001).
47
Findings (4)
4. The sum of population growth and the technology
growth, which is proxied by the share of R&D workers
in the labor force, and the constant depreciation rate
has a positive and statistically significant impact on
economic growth according to the system GMM
estimation.
48
Findings (5)
To check for the consistency of the results, we also replicate the
basic MRW (1992) model with human capital accumulation . The
estimation of the model, under the assumption of exogenous
growth rate of technology, finds a convergence rate to be 0.02.
But, once the intensity is substituted for the growth rate of
technology, the estimation of the model reveals a lower
convergence rate, namely, 0.01.
g (the growth rate of
technology)
0.02
R&D
intensity
Implied ν
0.02
0.01
49
Conclusion
The Solovian growth framework, which is widely used
in empirical studies has two weaknesses: exogenous
growth rate is undefined and is not suitable for
theoretical extension.
Romerian Solow framework is a good candidate for
overcoming these weaknesses because:
(i) it allows for theory-backed extensions for empirical
work,
(ii) The framework yields conservative convergence
rate results, which is intuitive
(iii) the determinants of the exogenous growth rate is
unveiled.
50
Thanks
51