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-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:


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:


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:


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:


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:


YL LnLnHL

YLnHL

YLnHLtYLn 3210

)0()0()(

gLnsLn 54 )0(10 ALnetg t

te 11

1112

te

113

te

114

te

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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


)(

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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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


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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

45


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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


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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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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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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.


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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

A Romerian Contribution to the Empirics of Economic Growth Bahar Bayraktar-Sağlam

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