a romerian contribution to the empirics of economic growth bahar bayraktar-sağlam
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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 , 201 2. PLAN OF PRESENTATION. Motivation The Model Empirical Results Conclusion. - PowerPoint PPT PresentationTRANSCRIPT
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A Romerian Contribution to the Empirics of Economic Growth
Bahar Bayraktar-SağlamHacettepe University
Hakan YetkinerIzmir University of Economics
Atılım University, Ankara
May 4, 2012
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· Motivation· The Model· Empirical Results· Conclusion
PLAN OF PRESENTATION
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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) :
][1
][1
)]0([][
ngLnsLntgALnyLn ss
In the equation above,
We now know that is defined by the characteristics of R&D sector, by and large.
:)]0([ALn Initial knowledge stock plus all sources of variations
:g Exogenous rate of growth/ technological progress
g
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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:
tgYLneALneLYLn
tLtYLn vtvt )]0([)1()]0([)1(]
)0()0([]
)()([
][
1)1(][
1)1( ngLnesLne vtvt
]~[]~[]~[ssyLnyLnv
dtydLn
))(1( gnv
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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. Howitt, 2000).
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· 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.
A Critique of Convergence Literature-I
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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?
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A Critique of Convergence Literature-III
How about Robustness of MRW (1992) Model?
1)( LHKtY vs. 1)( HKtYKYsK I
HYsH H
Steady state at levels vs. Endogeneous Growth!
HYsH H KYsK I
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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 need in this direction.
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· 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)
Literature (1)
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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)
Contribution of this paper
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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.
General Features of the Model
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I. Final-Good Production
Y: Final OutputXi: Intermediate Good i (Variety i)HY: Human Capital allocated to Y
The model
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)(
1
1 tA
i iXYHY
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II. Human Capital Allocation
HY : Human capital allocated to final-good sector
HR&D : Human capital allocated to R&D-sectorθY : Human capital share of final-good sectorθR&D : Human capital share of R&D sector
The model
KYsK
III. Macroeconomic Budget Constraint:
HYYH HDRDRH && 1&
DRY
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IV. R&D Sector
The Model
A : Stock of KnowledgeHR&D : Human capital allocated to R&D
Using the share definition:
AHA DR &
AHA DR &
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Profit maximization in the final-good market yields:
Profit maximization in the intermediate-good market yields:
Solution Procedure
Y
tA
iiY wx
)(
1
)1( iiY px 11
rrppi
11
2
rxx Yi
rr
xxraH Y
i
1)1(1
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Final-good and intermediate-good markets’ profit maximization results imply:
Solution Procedure
AXXKKtA
ii
tA
ii
)(
1
)(
1Axxkk
tA
ii
tA
ii
)(
1
)(
1
Axy Y 1 11 Aky Y
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The value of patents is found as follows:
R&D Sector equilibrium process implies:
DRDRDRDRDR HwAHV &&&&&
DRDRDR wALV &&&
)()()()( ,&
)(
,& trtHtVdeHtV iDR
t
dssr
iDRt
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Recall that we assumed and are constant. Solving the model under this assumption, we find that
This is very similar to the Solow-result:
1~
gsy Yss
1~
gsyss
HAg DRss &ˆ
Y DR&
Evidently, much richer in the sense that it decomposes into its components and underlines the role of human capital in final good production in growth.
ssA
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Solovianized Romer version:
Empirical Applications:Long-run determinants of GDP per capita
]ln[1
]ln[1
]ln[ln gsgtay Yss
)]0([ALna
Solow version:
]ln[1
]ln[1
ln gstgayss
)]0([ALna 02.0g
HAg DRss &ˆ
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Solovianized Romer version:
Empirical Applications:Convergence Equation
YLnHYLn
HYLn
HtYLn
210)0()0()(
gLnsLn 33
β0 : Constant termβ1 : Coefficient of initial level of incomeβ2 : Contribution of human capitalβ3 : Contribution of investment rate
)0(10 ALnetg t
te 11
te 12
113
te
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Solow version :
Empirical Applications:Convergence Equation
Recall that g is not defined in Solow version…Therefore, it is taken constant in time and identical across countries.
gLnsLnHYLn
HYLn
HtYLn
3310
)0()0()(
β0 : Constant termβ1 : Coefficient of initial level of incomeβ3 : Contribution of investment rate
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One can show that:
Suppose that
Extensions-1Generalized Knowledge/ R&D Sector
AHA DR &
: Duplications/ production elasticity of HR&D
: Degree of positive externality on current R&D
1,0
1ˆ nAss
11
1nn
sAk ssYss
1
1nn
sAy ssYss
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Determinants of long-run growth:
Extensions-1Generalized Knowledge/ R&D Sector
1
11
&1
1
)1(nn
sn
ey DRtn
Yss
]ln[1
1]ln[1
]ln[1
1]ln[]ln[1
ln & gsy DRYss
gtng
]ln[1
1ngwhere and 1)0( H
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Convergence:
Extensions-1Generalized Knowledge/ R&D Sector
Under
Together with capital accumulation equation
1
Knowledge accumulation in terms of per human capital becomes
anaa DR 1&
nAg ss ˆ 1& AHA DR
and
ktAnksk Y~))(ˆ(~~ 1
We have a two-equation differential equation system
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Convergence:
Extensions-1Generalized Knowledge/ R&D Sector
Solving this system through log-linearization, we get
nttgn econstnbeconst
gnbkLn
2
2))(1(1
1
))(1()~(
nteconstnb
nngnaLn
22))(1()(
ntaLnkLnLnyLn Y )()~()()1()(
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One can show that:
Suppose that
Extensions-2Unskilled Labor Next to Skilled Labor
)(
0
1tA
iY diXHLY
L : The constant amount of unskilled labor
1
1
111~
gsHLK Yss
1
111~
gsHLY Yss
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Long-run determinants of economic growth:
Extensions-2Unskilled Labor Next to Skilled Labor
A
gs
HLH
HLL
HLY Yss
11
11
][1
][1
1][1
sLnLnLntgayLn YLss
][1
gLn
HLYy ss
ss aALn )]0([ DRHg & HL
LL
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Convergence:
Extensions-2Unskilled Labor Next to Skilled Labor
YL LnLnHL
YLnHL
YLnHLtYLn 3210
)0()0()(
gLnsLn 54 )0(10 ALnetg t
te 11
1112
te
113
te
114
te
45
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Long-run determinants of Economic Growth:
Extensions-3Endogenous Allocation of Skilled Labor between
Y and R&D
]ln[1
]ln[1
]ln[ln , gstgay SSYss
HsHs
ssY
)1()(
,
where
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Suitability for Further Extensions-1Health
)(
1
1tA
iiLY XNNY
YYY HhN DRDRDR HhN &&& LhN LL
]ln[1
]ln[1
1]ln[1
1ln LYYss hhtgaLH
Y
]ln[
1]ln[
1]ln[
1gsL
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Suitability for Further Extensions-2Defense Spending
I. The Defense Sector
M: Military ExpenditureτM: tax rate (=share of military expenditure in GDP) (=research intensity in defense sector)wM: Real wage rate of human capital in military
sector
YMHw MMM
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II. Profit Equation
Suitability for Further Extensions-2Defense Spending
)(
1
)(
1
1)1(tA
iiiYY
tA
iiYMY xpwxH
III. Human Capital Allocation
HH YY HH DRDR && HH MM
1& MDRY
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Suitability for Further Extensions-2Defense Spending
IV. Macroeconomic Budget Constraint:
KYsK M )1(
V. R&D Sector
AHA MDR )1(&
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Long-run determinants of GDP per capita
]ln[1
]1ln[1
]ln[1
]ln[ln gstgay MYss
aALn )]0([ )1(& MDR Hg
Suitability for Further Extensions-2Defense Spending
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Balanced Budget
Empirical Applications:Long-run determinants of GDP per capita for developing Countries (No Spillover Effect)
aALn )]0([
YMLw MM
Hg DR & 1& DRY
]ln[1
]1ln[1
]ln[1
]ln[ln gstgay MYss
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Convergence Equation
β0 : Constant termβ1 : Coefficient of initial level of incomeβ2 : Contribution of human capitalβ3 : Contribution of investment rateβ4 : Contribution of defense intensityβ5 : Contribution of effective
depreciation rate
)0(10 ALnetg t
te 11
te 12
1143
te
sLnLnHYLn
HYLn
HtYLn Y
3210)0()0()(
gLnLn M 54 1
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Suitability for Further Extensions-2Defense Spending
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TESTING THE MODEL
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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.
Testing the Model (1)
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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
Testing the Model (2)
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Testing the Model (3)
Variables and sources of data:Variable Definition Data Source
yLn Logarithm of growth in real GDP per head of population aged 15-64 years expressed in 2000 purchasing power parities
OECD Annual National Accounts
1tyLn logarithm of lagged growth in real GDP per head of population aged 15-64 years expressed in 2000 purchasing power parities
OECD Annual National Accounts
sLn Gross fixed investment share of GDP
World Development Indicators Database
1hLn Secondary school enrollment
rate Barro-Lee Education Dataset (2010)
2hLn The share of final good workers
in the labor force. Own calculations where
1& DRY
1
& DRLn The share of R&D in the labor force
OECD Main Science and Technology Indicators database
2
& DRLn The share of R&D expenditure on GDP
OECD Main Science and Technology Indicators database
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Testing the Model (4)
Basic statistics:Variables Mean Standard
Deviation
Min Max
Real GDP per capita 21291 8858 5326 62731Share of Investment in GDP 22.8 3.8 17 37Secondary Enrollment rates 45.6 13.9 8.2 88The share of R&D personnel
in the labor force 4.9 2.68 0.44 15
The share of R&D
expenditure in GDP1.56 0.83 0.2 3.9
The population growth rate
(%)0.65 0.68 -0.4 6
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Testing the Model (5)
The equation estimated:
itti
itititit syyy lnlnlnln 2111
]ln[ln 43 ititit gnh
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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 GMM1. It provides consistent estimates in the presence of • Measurement error• Endogenous regressors2. 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 instruments.
Testing the Model (6)
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Findings (1): The share of labor devoted to R&D
Dependent Variable: log differences in GDP per working person
OLS OLS Within Group
Within Group
System GMM System GMM
Constant -0.089 (0.387)
-0.084 (0.402)
2.1698*** (0.427)
2.015*** (0.417)
0.299 (0.577)
0.645 (0.542)
1ityLn -0.023*** (0.038)
-0.032*** (0.042)
-0.2784*** (0.031)
-0.2749*** (0.032)
-0.097*** (0.107)
-0.1539*** (0.064)
itsLn 0.133**
(0.063) 0.123** (0.059)
0.245*** (0.066)
0.243*** (0.067)
0.222*** (0.058)
0.190*** (0.060)
ithLn 0.030
(0.020)
0.031 (0023)
0.085** (0.032)
itit gnLn 0.005 (0.024)
0.007 (0.025)
-0.043 (0.036)
-0.040 (0.037)
0.056 (0.038)*
0.081* (0.042)
2R 0.97 0.97 0.94 0.94
Implied ν 0.0008 0.001 0.011 0.011 0.003 0.005
Number of Observations 150 150 150 150 150 150 Number of Groups 30 30 30 30
Number of Instruments 20 21 Hansen test p value 0.10 0.15
Difference Hansen p value 0.06 0.06 M2 0.837 0.845 46
Findings (2): The share of R&D expenditure over GDP
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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).
Findings (3)
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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.
Findings (4)
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Findings (5)
g (the growth rate of technology)
0.02 R&D intensity
Implied ν 0.02 0.01
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.
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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.
Conclusion
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Thanks