1
GROWTH, HUMAN CAPITAL AND SPILLOVERS IN A MANKIW-ROMER-WEIL MODEL FROM A SPATIAL ECONOMETRICS PERSPECTIVE
UNIVERSITY OF GRONINGEN
FACULTY OF ECONOMICS AND BUSINESS MSc THESIS IN ECONOMICS
G. D. ABATE
s1939017@student.rug.nl SUPERVISOR: Dr. J. P. ELHORST AUGUST 2010
Abstract
This paper presents the spatially augmented MRW model. We formulate five distinct hypotheses to investigate the role of human capital and relative location on economic growth in the lens of spatial econometrics. We consider 193 regions across 15 Western European countries over the period 1977-2002 to empirically test the spatially extended MRW model. Time spans and fixed effects are given a due emphasis in our space-time dynamic model. The spatially augmented Arrelano and Bond (1991) GMM estimator together with Elhorst's (2010) ML estimator is applied to overcome the usual small- sample downward lagged dependent variable bias under the fixed effects space-time dynamic panel data model. We make some improvements in Elhorst et al.'s (2010) set of instruments used in the estimation of the spatially extended MRW model.
Keywords: Economic growth, Spatial MRW model, Human capital, Spatial interactions JEL classification: C23, C21, R11
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Acknowledgements
“…it is an interesting proposal…’’. This was part of an email reply that I got from my supervisor, dr. J. P. Elhorst, for the first time. My stay with him was an interesting too. I would like to acknowledge him for having not only provided me with continuous guidance, invaluable feedback and support but also for having assisted me with the practical MATLAB routine throughout this thesis. I am also grateful to The Netherlands Fellowship Program (NFP) which offered me the financial support to study at the University of Groningen where I got not only academic improvements but also lots of life long learning.
Lastly, I am pleased to express my special thanks to my family and friends for their great encouragement while I was far away from home.
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1. Introduction
The concept of interacting agents and social interaction has sparked and retained the interest of different researchers (Fingleton, 2003; Ertur and Koch, 2006; Fischer and Stirbock, 2006; LeSage and Pace, 2009; Elhorst, 2010). The renowned emphasis in modern economic theory on spatial spillovers, spatial mismatch, interacting markets, social interaction and other concepts that implicitly or explicitly incorporate dependence between observations at different points in time and across space has spawned a growing literature in empirical spatial econometrics (Anselin and Rey, 1997). Various empirical findings vindicate spatial interaction effects among economic agents (Moreno and Trehan, 1997; Ertur and Koch, 2006, 2007; Elhorst and Illy, 2008; Elhorst et al., 2010).
Spatial dependence, or alternatively called spatial autocorrelation, is often present between observations in cross-sectional data sets, while the spatial heterogeneity implies that the functional forms and parameters vary with location and are not homogenous over space (Anselin, 1988).
The emergence of new growth theories in the late 1980s has inspired macroeconomic research in human capital1 accumulation and its role on economic growth. Since the seminal paper of Mankiw, Romer and Weil (1992, henceforth MRW), human capital is commonly introduced as a production factor along with physical capital in growth regressions. In fact, Uzawa's (1965) inclusion of human capital through education was the point of departure in considering human capital as a chief culprit for economic growth
1“Human capital” represents the skills, capacities and abilities possessed by an individual which permit him to earn income” (The Penguin Dictionary of Economics, 1984).
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(Heijdra, 2009). In this framework, economic units are most of the time considered as independent observations with no interactions between them. Growth regressions are then estimated by ordinary least squares (OLS) under the standard assumptions. Spatial effects in the form of spatial dependence and spatial heterogeneity are the basic concepts that traditional econometrics fails to take into account (Anselin, 1988). However, evidence in favor of cross-sectional correlation, i.e. spatial autocorrelation, is now well documented in the empirical literature (Moreno and Trehan 1997; Conley and Ligon, 2002; Fingleton, 2003; Ertur and Koch, 2006; Elhorst, 2010) and can no more be neglected in growth modeling. Economies interact with each other and can not be considered as independent units in growth analysis. A complete and a more satisfactory understanding of economic growth requires an appreciation of the economic interaction between economic units (Fingleton, 2003; Ertur and Koch, 2006; Elhorst et al., 2010).
The MRW growth model which incorporates human capital as a factor of production has received recent attention of researchers in flavor of spatial econometrics (López-Bazo et al., 2004; Ertur and Koch, 2006; Fischer, 2009). Accordingly, although the spatial interaction effects play a significant role in growth analysis, human capital does not influence growth as a simple production factor. In fact, while a strong theoretical support exists for a key role of human capital in the growth process (Uzawa, 1965; Romer, 1986;
Lucas, 1988; MRW, 1992), empirical evidence is not clear-cut. Whereas one strand of literature supports the positive role of human capital (Barro, 1991; Jones, 1997; Murthy and Chien, 1997; Abbas, 2001; Bassini and Scrapetta, 2001; Seren, 2001; Leeuwen and Foldvari, 2007; Piffaut, 2009), another strand has found an insignificant and sometimes
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even negative role of human capital in production (Benhabib and Spiegel, 1994; Islam, 1995; Bils and Klenow, 2000; Pritchett, 2001; Ertur and Koch, 2006; Fischer, 2009). With few exceptions such as Benhabib and Spiegel (1994) and Islam (1995), the focus has been on the use of the school enrollment ratio as a proxy measure of human capital in growth empirics.
However, empirical studies that use school enrollment ratio or literacy do not adequately measure the aggregate stock of human capital available as an input for production (Barro and Lee, 1993, 2000). The use of a stock variable for human capital (average years of schooling) instead of a flow variable (e.g., school enrollment ratio) is consistent with the growth model of MRW. Practical and theoretical reasons suggest the use of a stock variable for human capital for a number of reasons (Bassini and Scrapetta, 2001; Piffaut, 2009 ). First, data on enrollment rates are generally lower quality than years of schooling (education).2 Second, the alternative to using changes in years of education as a proxy for the accumulation of human capital is not suitable, as it refers to a net investment in human capital rather than the required measure of gross investment. Finally, reverse causality problems are less severe when a stock measure is considered (Temple, 2000).
Further, Barro and Lee (1993, 2000) years of schooling approach which enables to directly measure the stock of human capital is considered to be an important progress in solving one of the weak spots of growth empirics (Islam, 1995). As school enrollment ratio and adult literacy rate measures of human capital suffer from major deficiencies, average years of schooling have by now become the most popular and most commonly
2Particularly, in developed countries where literacy rate is close to one, school enrollment ratio (literacy rate) hardly measures cross-country human capital differences (Benhabib and Spiegel, 1991).
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used specification of the stock of human capital in the literature (Benhabib and Spiegel, 1994; Barro and Sala-i-Martin, 1995; Gundlach, 1995; Islam, 1995; O’Neill, 1995; Barro, 1997, 2001; Temple, 1999b).
Benhabib and Spiegel (1994) and Islam (1995) use Barro and Lee (1993) data set and have found that the coefficient of human capital is insignificant. However, their analysis ignores spatial dependence between economic units as the growth regressions in their model are estimated by OLS. In Ertur and Koch (2006), although spatial interactions between economic units are found to be highly positive and significant, human capital specified by enrollment ratio is found to be insignificant when it is considered as a simple factor of production.
The aim of this paper is to investigate the role of human capital in a MRW open economy growth model in the lens of spatial econometrics across 193 European regions. In particular, it models technological progress along the lines suggested by Ertur and Koch (2006), but differs from this work in a number of important points. First, the focus is on a MRW rather than a Solow world of economies in which output is produced from physical capital, human capital and labor. Second, the study shifts from the use of school enrollment ratio as a measure of human capital to the Barro and Lee (1993, 2000) human capital measure.
The empirical analysis in this paper uses years of schooling as a proxy for human capital following Barro and Lee (1993, 2000). This variable is allowed to vary across countries
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but the same across regions within countries. The assumption of homogenous years of schooling across regions of a country is not at odds: educational attainment disparities are significant at the national level rather than at regional level, because the guidelines for education systems and structures are, as a general rule, set nationally (Pose and Tselios, 2007). Particularly, human capital in the form of years of schooling calculated focusing on duration of schooling is not expected to vary much across regions of a country as the guidelines and structure are set at the national level. With the exception of some rural parts in Greece, Italy, Spain and Portugal, educational attainment and hence years of schooling is generally high across the whole regions of a country in Europe (Eurostat, 2009; Pose and Tselios, 2007 ). More explicitly, educational attainment is generally more or less similar across regions of a country with the exceptions of the above mentioned countries.
A common feature of existing growth regressions has been the assumption of identical aggregate production functions for all economies. Although it has been correctly felt that the production function may actually differ across economies, efforts at allowing for such differences have been limited by the fact that most of these studies have been conducted in the framework of single cross-section regressions. In this framework, it is econometrically difficult to allow for such differences in the production function as they are not (easily) measurable (Islam, 1995). The present paper advocates and implements a panel data approach to deal with this issue as in Islam (1995) and Elhorst et al. (2010).
The panel data framework makes it possible to allow for fixed effects and also better suits growth convergence analysis (Islam, 1995; Elhorst et al., 2010).
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In presenting the empirical results, particular attention is devoted to the choice of the time span and the inclusion of fixed effects. The Arrelano and Bond (1991) GMM estimator that applies first-differences so as to wipe out the intercept and the spatial fixed effects using a set of appropriate instruments is used in the estimation of the fixed effects basic MRW model. The spatial MRW model under the TSCS estimation is manipulated using the ML estimator whereas the spatially augmented Arrelano and Bond GMM estimator together with Elhorst's (2010) ML estimator is applied to overcome the usual small- sample downward lagged dependent variable bias under the fixed effects dynamic panel data model. We make some improvements in Elhorst et al.'s (2010) set of instruments in the estimation of the spatially extended MRW model.
The remainder of this paper is organized as follows. The next section presents the MRW model and its spatial extension. This model is used to derive five distinct testable hypotheses wherein the effect of human capital and relative location on economic growth are investigated in an open economy MRW model. Section 3 discusses the empirical literature and some relevant spatial econometric estimation techniques. The empirical results are discussed in section 4, while section 5 concludes the paper.
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2. The MRW model and its spatial extension
How does human capital or the educational attainment of the labor force affect the output and growth rate of an economy? A standard approach is to treat human capital, or the average years of schooling of the labor force, as an ordinary input in the production function as in the MRW model. In endogenous growth theories, human capital is used to model technological progress or growth of total factor productivity (Benhabib and Spiegel, 1994). The presumption is that an educated labor force is better at creating, implementing and adopting new technologies, thereby generating economic growth. An alternative way of characterising the role of human capital is as a facilitating factor in the international transfer of technology as in Romer (1990) from innovating countries to
‘imitating’ countries. A country with more human capital would be more able to adopt technologies that were discovered elsewhere. Thus, the higher the stock of human capital for a follower country, the higher the rate of absorption of the leading technology and hence, the higher the follower country's growth rate. This section presents a spatial extension of the MRW model where human capital explicitly enters the production technology as a separate input.
From a quantitative point of view, the basic Solow-Swan framework is unable to explain adequately many stylized facts observed at the cross-country level. When MRW, for example, examine the textbook Solow model using real world data, although the model appears to fit the data quite well, the estimated capital coefficient appears to be much larger than the expected share of about one third (MRW, 1992; Heijdra, 2009). According
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to MRW, most of the empirical problems of the neoclassical growth model, including a much higher share of capital, could be solved, if the concept of capital is broadened to include both human and physical capital. Consequently, MRW suggest that the basic Solow-Swan model works well if human capital is incorporated in the production function as follows:
Yit = AitKitαHitβLit1−α−β, (1)
where i denotes an economy and t a time period. Y is output, K the level of reproducible physical capital, H the level of reproducible human capital, L the level of raw labor, A the aggregate level of technology, and α and β (α, β>0) are, respectively, the shares of physical and human capital with α+β<1, which implies the existence of growth convergence in neoclassical growth models. This production function has become a graveyard model for a bulk of empirical works under the human capital augmented Solow-Swan model. The aggregate production function exhibits constant returns to scale (α+β+1-α-β=1). The model becomes an endogenous growth model if α+β = 1. The implication of the endogenous growth model is that countries that save more grow faster indefinitely and need not converge in income per capita (MRW, 1992).
All variables are supposed to evolve in continuous time. Each economy invests its physical and human capital stocks at constant investment rates written as :
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, ) (
) (
t t
t H
t t
K t
h g n y s h
k g n y s k
δ δ + +
−
=
+ +
−
=
•
•
(2)
where quantities per effective unit of labor are defined (dropping the i index for simplicity) as yt=Yt/(AtLt), kt=Kt/(AtLt), ht=Ht/(AtLt) , s and K s are investment rates in H
physical and human capital respectively, n is the population growth rate, g is the rate of technological progress and δ is the depreciation rate. The dots over kt and ht represent the rate of change of the two types of capital stocks over time. The implicit assumption in the MRW model or from equation (2) above is that the rate of depreciation for both types of capital is identical and given by the single parameter δ. Heijdra (2009) discusses the general case of MRW model where physical and human capital stocks depreciate at different rates. The commonly used specification in the literature is to assume that the same production function applies to physical capital, human capital and consumption and hence both physical and human capital depreciate at the same rate δ (MRW, 1992;
Benhabib and Spiegel, 1994; Gundlach, 1995; Ertur and Koch, 2006; Fischer, 2009).
The assumption of diminishing marginal returns to capital in the neoclassical growth models leads the growth process within an economy to eventually reach the steady state where per capita output, capital stock, and consumption grow at a common constant rate equaling the exogenously given rate of technological progress. This led to the notion of convergence whereby economies converge toward a common steady state. Equation (2) implies that an economy converges to a steady state defined by:
12 ,
) 1 /(
1 1
) 1 /(
1 1
β α α
α
β β α
β
δ δ
δ δ
−
− −
∗
−
− −
∗
+
+
+
= +
+
+
+
= +
g n
s g
n h s
g n
s g
n k s
H K
H K
( 3)
where all the variables and constants are as defined earlier (see MRW, 1992; Gundlach, 1995; Temple, 1998; Heijdra, 2009). Substituting the values of k and ∗ h obtained in (3) ∗ in the per worker production function and replacing yt by qt for convenience, this model is characterized by the steady state of the form:
)], /(
1 ln[
)]
/(
1 ln[
) ln(
ln δ
β α δ α
β α
β + +
− + −
+
− + + −
+
= A− gT s n g s n g
qt t T H K (4)
where qt is the steady state per capita income at time t, T denotes the time span of the growth period considered, At-T is the state of technology at the beginning of the observation period, α and β, respectively, are the cost shares of physical and human capital in production under a Cobb-Douglas technology, sH and sK are, respectively, the investment rates in human and physical capital, n is the population growth rate, g is the rate of technological progress, and δ is the depreciation rate. This equation reduces to the basic Solow steady state equation when β=0.
A linear approximation to the dynamics around the steady state in equation (4) using a
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Taylor expansion gives the convenient growth-initial income-level regression equation (MRW, 1992; Ertur and Koch, 2006; Fischer, 2009; Elhorst et al., 2010). This gives3
) 5 ( , )]
/(
ln[
)]
/(
ln[
) ln / ln(
3 2
1
0 β β δ β δ ε
β + + + + + + + +
= −
− q s n g s n g
T q q
H K
T t T
t t
whereβ0 =(1−e−λT)[ln(At−T)+gT]/T,β1 =−(1−e−λT)/T, (1 e T)/T
2 1
λ
β α
β α − −
−
= −
and (1 e T)/T
3 1 λ
β α
β β − −
−
= − . The disturbance term which is assumed to be independent and normally distributed is represented by ε as a result of which equation (5) can be estimated by OLS (Elhorst et al., 2010). This model implies that economies tend toward the same equilibrium growth path for capital, and hence output per capita, except for differences in sK, sH, n, g and δ. The annual speed of convergence implied by the parameter estimate of β1 is specified as λ=−ln(1+β1T)/T (Fingleton, 2003; Elhorst et al., 2010). The shares of physical and human capital implied by the parameter estimates of α and β , respectively, are
α =
1 2 3
2
β β β
β
−
+ and
1 2 3
3
β β β β β
−
= + (6)
Nowadays, the hypothesis that the relative location of an economy is a determinant of economic growth and the steady-state position of an economy has been corroborated by economic-theoretical models (López-Bazo et al. 2004; Fingleton and López-Bazo, 2006;
Ertur and Koch, 2006, 2007; Elhorst et al., 2010). In López-Bazo et al. (2004) spatial interdependence modelling, physical and human capital accumulation are assumed to be
3In the present paper , the parameter β specifies the share of human capital whereas the indexed β refer to unknown parameters to be estimated.
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the sources of spatial externalities. On the other hand, Ertur and Koch (2006, 2007) assume that spatial externalities are generated from technological interdependencies.
In a more compact and explicit way, Ertur and Koch (2006) model technology as being dependent on three terms as follows:
,
ij H
K w
jt N
i j it it t
it k h A
A φ φ ∏ γ
≠
Ω
= (7)
where i (=1,…,N) refers to a particular economy. This function describing the level of technology in economy i depends on three terms.
First, as in the basic Solow and MRW models, part of technological progress is assumed to be exogenous and identical to all economies:Ωt =Ω0eµt, where µ is the exogenous technical progress growth rate and Ω0 is its initial level. This term represents the amount of knowledge created anywhere in the world which is immediately available to be used in any economy (Ertur and Koch, 2006; Fischer, 2009).
Second, it is supposed that the technical progress increases with accumulated factors. It increases with per worker physical capital kit=Kit/Lit reflecting the learning by doing process as underlined by Arrow (1962) and Romer (1986) and with per worker human capital hit=Hit/Lit reflecting the effect of human capital externalities as underlined by Lucas (1988). Parameters φK and φH, respectively, reflect the strength of physical and
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human capital externalities. In other words, the parameters φK (0<φK <1) and φH (0<φH <1) denote the spatial connectivity of kit and hit, respectively (Fischer, 2009).
Each unit of investment in physical and human capital not only increases the stock of the corresponding capital but also increases the level of technology for all firms in the economy through knowledge spillovers. Further, there is no clear reason to constrain these externalities to the borders of the economy. In fact, we can suppose that the external effect of knowledge embodied in either physical or human capital in one economy extends across its borders but does so with diminished intensity because of frictions generated by socio-economic and institutional dissimilarities captured by exogenous geographic distance or border effects (Ertur and Koch, 2006).
Finally, as in Ertur and Koch (2006), technical progress of economy i depends positively on technical progress of other economies. The level of technology in economy i is also related to the level of physical and human capital per worker kit and hit in that particular economy, because of knowledge spillovers generated by physical and human capital (Ertur and Koch, 2006; Fischer, 2009). The magnitude of these externalities is measured through the parameters φK for physical capital and φH for human capital. Moreover, it is assumed that these externalities affect neighbouring economies j (=1,…,N) according to some distance-decay function γwij, where γ is an unknown parameter to be estimated and wij is an element of an N×N spatial weights matrix W describing the spatial arrangement of the N economies (Elhorst et al., 2010).
Under the assumption that the speed of convergence is identical for all economies, this
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extension gives the following expression for the steady-state per capita income:4
[ ]
[ ] [ ]
[ /( )], (8)
1 ln
) /(
1 ln ) /(
1 ln
) /(
1 ln )
1 ln(
) 1 1 ln(
ln 1
η δ βγ
η δ δ αγ
η φ β
η δ φ α η
η β γ α
+
− + +
+
− + + +
− + + +
+
− + + +
− +
− +
−
= − −
g n s W
g n s W g
n s
g n s gT
A q
W q
H
K H
H
K K T
t t
t
where1−η =1−α − β −φK −φHand ln(qt), ln(At-T), gT, ln[sK/(n+g+δ)] and ln[sH/(n+g+δ)] now denote N×1 vectors of the corresponding variable in each economy.
This model simplifies to the basic MRW model when γ, φKand φH are zero.
A linear approximation to the dynamics around the steady state in equation (8), using a Taylor expansion, again produces a growth-initial income-level regression equation as follows:
[ ]
[ ] [ ]
[ /( )] , (9)
ln
) /(
ln )
ln(
) /(
ln
) /(
ln )
) ln(
/ ln(
) ln(
2
1 4
3
2 1
0
ε δ θ
δ θ
β δ β
δ β
β β ρ
+ + + +
+ + +
+ + + +
+ + +
+ +
=
−
−
−
−
g n s W
g n s W q
W g
n s
g n s T q
q W q
T q q
H
K T
t H
K T
t T
t t T
t t
where β1 =−(1−e−λT)/T, K (1 e T)/T
2 1
λ
η ϕ
β α − −
−
= + , H (1 e T)/T
3 1
λ
η φ
β β − −
−
= + ,
4See Ertur and Koch (2009) where the speed of convergence is allowed to be heterogeneous in the sample units.
17 T
e T)/ 1
1 ( 1
4
λ
η β γ α
β − −
−
−
= − , (1 e T)/T
1 1
λ
η
θ αγ − −
− −
= , (1 e T)/T
2 1
λ
η
θ βγ − −
− −
=
η β γ α
ρ −
−
= − 1 1
and 1−η =1−α−β −φK −φH
This model is commonly known in the spatial econometrics literature as an unconstrained spatial Durbin model, because of the spatially lagged values of both the dependent variable and the independent variables (Ertur and Koch, 2006; Fischer, 2009; Elhorst et al., 2010). This model simplifies to Elhorst et al. (2010) when β3=θ2=φH=0. Since 0<α<1, 0<β<1 , 0<φK<1 and 0<φH<1, γ and ρ are defined on the same interval (1/ωmin,1/ωmax), where ωmin denotes the smallest and ωmax the largest eigenvalue of W. For row-normalized spatial weights, ωmax=1 (Elhorst et al., 2010). The annual speed of convergence, λ, implied by the parameter estimate of β1 (or β4), is the same as in the classical MRW model. Note that, when there are no physical and human capital externalities, the speed of convergence reduces to that of the MRW model. The growth rate of real income per worker is a negative function of the initial level of income per worker reflecting the convergence process. The unknown values of α, β,φK,φH and ρ implied by the parameter estimates of βi (i=1,...4), θ1 and θ2 are5
4 2 1
1
β θ θ α θ
−
= + ,
4 2 1
2
β θ θ β θ
−
= + ,
4 2 1
2 1
1 2
2
) (
) (
β θ θ
θ θ β
β φ β
− +
− +
= −
K ,
4 2 1
2 1
1 3
3
) (
) (
β θ θ
θ θ β
β φ β
− +
− +
= −
H and 1 ( 1 2)
4 2 1
θ θ β
β θ γ θ
+
−
−
= + (10)
5See appendix I for a mathematical derivation of the implied parameters.
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provided that the restriction β4=- ρβ1 holds; otherwise, these unknown parameters are overdetermined.
The Ertur and Koch's extension of the technology term results in a full spatial Durbin specification of equation (9), whereas the extension of the technology term in López- Bazo et al. (2004) yields spatially lagged values of only the growth and the initial-income variables, and not of ln[sH/(n+g+δ)] and ln[sK/(n+g+δ)] (Fingleton and López-Bazo 2006; Elhorst et al., 2010). The present paper focuses on the assumption that the speed of convergence is identical for all economies.
Finally, the first term on the right hand side of equation (9) represents the rate of growth in the neighboring regions reflecting the spatial autocorrelation process implied by technological interdependence. What role do human capital and the relative location of an economy have on economic growth of a particular economy? We consider the following testable hypotheses to answer this and other related questions:
H1 : The rate of growth of a particular economy is related to that of its neighbours.
H2 : The rate of growth of a particular economy is affected by its own human capital accumulation.
H3 : The rate of growth of a particular economy is affected by the human capital accumulation in its neighbouring economies.
H4 : The rate of growth of a particular economy is affected by sK, n, g and δ in its own
19 economy.
H5 : The rate of growth of a particular economy is affected by sK, n, g and δ in its neighbouring economies.
The first two hypotheses can be tested by verifying whether ρ and β3 in equation (9) are significantly different from zero, respectively. H3 can be tested by verifying whether θ2 is significantly different from zero whereas H4 can be tested by verifying whether β4 is significantly different from zero in equation (9). The last hypothesis can be tested by verifying whether θ1 in equation (9) is significantly different from zero.6
Finally, the unconstrained spatial Durbin model derived in Equation (9) generalizes both the spatial lag model and the spatial error model, two models that have been the main focus of the spatial econometrics literature in growth empirics so far (Elhorst et al., 2010). The spatial lag is obtained when β4=θ1= θ2=0. The spatial error model is obtained when the nonlinear common factor constraints are imposed on the coefficients: β4=- ρβ1,
θ1= -ρβ1 and θ2=-ρβ1. This model is also known as a constrained spatial Durbin model.
6See Elhorst et al., (2010 ) where the relationship between the steady state position of an economy and its own as well as neighboring economies' sK, n, g and δ are discussed extensively.
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3. Empirical literature and estimation techniques
This section discusses some of the relevant empirical findings on the role of human capital in economic growth and some spatial econometric techniques that are used in the estimation of models that include spatial dependence.
3.1 An overview of the empirical literature
A substantial literature, both theoretical and empirical, exists on the role of human capital in economic growth analysis. In fact, while there is a strong theoretical support for a key role of human capital in the growth process (Uzawa, 1965; Romer, 1986; Lucas, 1988;
MRW, 1992), empirical evidence is not clear-cut. Whereas one strand of literature supports the positive role of human capital (Barro, 1991 ; Jones, 1997; Murthy and Chien, 1997; Abbas, 2001; Bassini and Scrapetta, 2001; Seren, 2001; Leeuwen and Foldvari, 2007; Piffaut, 2009), another strand has found an insignificant and sometimes even negative role of human capital in production (Benhabib and Spiegel, 1994; Islam, 1995; Bils and Klenow, 2000; Pritchett, 2001; Ertur and Koch, 2006; Fischer, 2009).
Table 3.1 summarizes some of the relevant empirical findings.
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Table 3.1 Summary of empirical findings on the role of human capital in growth empirics
No: Empirical study Variable as human capital
Empirical finding (result)
Spatial interaction effects
1 Barro (1991) Enrollment ratio Positive and significant
Not considered
2 Benhabib and Spiegel (1994)
Years of schooling and literacy ( Kyriacou)
Insignificant Not considered
3 Islam (1995) Years of schooling Insignificant Not considered 4 Murthy and Chien
(1997)
Enrollment ratio Positive and significant
Not considered
5 Bassini and Scrapetta (2001)
Years of schooling Positive and significant
Not considered
6 Ertur and Koch (2006)
Enrollment ratio Insignificant Considered
7 Fisher (2009) Enrollment ratio/literacy rate
Insignificant Considered
Barro (1991) uses the school enrollment ratio as a proxy for human capital and points out that the growth rate of real per capita GDP is positively related to the initial level of human capital. The neoclassical convergence hypothesis holds given some minimum
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amount of human capital. More explicitly, a poor country tends to grow faster than a rich country, but only for a given quantity of human capital; that is, only if the poor country's human capital exceeds the amount that typically accompanies the low level of per capita GDP. Moreover, countries with higher levels of human capital also have lower fertility rates and higher ratios of physical capital investment to GDP.
Benhabib and Spiegel (1994) use various measures to investigate the role of human capital in cross-country growth modeling. One of the measures they employ is the Barro and Lee (1993) measure of human capital. The other measure used is initially developed by Kyriacou (1991). He first estimates the relationship between the years of schooling and past values of human capital investment such as enrollment in primary, secondary, and tertiary education. He then estimates the following relationship between average years of schooling in the labor force and past enrollment ratios:
H75 =κ1+κ2PRIM60 +κ3SEC70 +κ4HIGH70 (11)
where H represents average years of schooling in the labor force in 1975, 75 κi,i=1,...4 are unknown coefficients to be determined, PRIM60 represents the 1960 primary schooling enrollment ratio, SEC70 represents the 1970 secondary schooling enrollment ratio, and HIGH70 represents the 1970 higher education enrollment ratio. The choice of observation periods is based on the availability of data on education. The estimated coefficients are then used to extrapolate the human capital variable.
Neither the Barro and Lee nor the literacy (Kyriacou) measure of human capital
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significantly enters the equation when explaining per capita income growth in Benhabib and Spiegel (1994). Rather, human capital has a positive influence when explaining total factor productivity. In this case, human capital affects through directly influencing the rate of domestically produced technological innovation Romer (1990).
Islam (1995) considers the convergence equation originally developed by MRW and examines how the results change with the adoption of a panel data approach. Taking average years of schooling from Barro and Lee (1993) in the total population over age 25 as a proxy of the stock level of human capital, he finds that the role of human capital in the growth process is not significant.
On the other hand, Murthy and Chien (1997) demonstrate, using single cross-country regression analysis, that human capital has a direct role in explaining economic growth like that of Barro (1991). They use a comprehensive measure of human capital by taking a weighted average of the population enrolled in higher, secondary and primary education, as proxy for human capital.
Similar to that of Barro (1991) and Murthy and Chien (1997), Bassini and Scrapetta (2001) find that human capital has a significant impact on growth. They use Pooled Mean Group (PMG) estimators to asses the long run relationships between human capital and output growth in an annual sample of OECD countries over 25 years. They argue that the contentious empirical evidence on the role of human capital is highly determined by the econometric approach.
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In their path-breaking contribution to the spatial econometrics literature, Ertur and Koch (2006) develop a growth model that includes physical and human capital externalities together with technological interdependence between economies. Spatial autocorrelation is found to be highly positive and significant showing the importance of technological interdependence from both a theoretical and an empirical perspective. Human capital is measured by enrollment ratio, but not found to be significant when it is considered as a simple factor of production.
Fischer (2009) investigates the role of human capital in an open-economy extension of the MRW model that accounts for technological interdependence among regional economies. He uses the literacy rate of the working age population with higher education.
Using cross-sectional framework, he finds that human capital is insignificant.
3.2 Estimation techniques
The estimation of economic models that include spatial interaction effects is commonly carried out using spatial econometric techniques. However, the large size of many of the data sets has caused significant estimation problems. Various techniques have been developed to overcome these estimation problems, including those that rely on spatially- distributed observations. Until recently, three methods have been developed in the literature to estimate models that include spatial interaction effects (Elhorst, 2010).
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The first is the maximum likelihood (ML) estimation technique. The usual interesting asymptotic properties of this estimator are assumed to apply for models with spatially lagged dependent variables (Anselin, 1988). Recently, a number of studies have been carried out to prove the asymptotic properties of the ML estimator (Lee, 2004; Yu et al., 2008; Lee and Yu, 2010).
Yu et al., (2008) investigate the asymptotic properties of the ML estimator for a spatial dynamic panel data model with fixed effects, when both the number of individuals n and the number of time periods T are large. Accordingly, the asymptotic properties of this estimator hold with a limiting distribution varying between 0 and ∞ as n and T take different values. Similarly, Lee (2004) found that the asymptotic properties of the estimator is influenced by the spatial weights matrix of the model used.
The second estimator is the instrumental variables or generalized method of moments (IV/GMM) estimator. Elhorst (2010) and Verbeek (2004) argue that one of the advantages of these estimators is that they do not rely on the assumption of normality of the disturbances. However, the problem with the IV/GMM estimators is the possibility of ending up with a coefficient estimate for the spatially lagged dependent variable (ρ) or the spatial autocorrelation coefficient in the spatial error model (λ) outside its parameter space (Anselin, 1988; Elhorst, 2010). Theoretically, these coefficients are confined to vary within the interval (1/rmin, 1) where rmin refers the smallest real characteristic root of the spatial weight matrix W by the Jacobian term in the log-likelihood function of ML estimators. The final and the third estimation technique is the Bayesian Markov Chain
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Monte Carlo (MCMC) approach. This approach is extensively presented in LeSage and Pace (2009).
The present paper makes use of a mixture of estimators. The Arrelano and Bond (1991) GMM estimator that applies first-differences so as to wipe out the intercept and the spatial fixed effects using a set of appropriate instruments is used in the estimation of the fixed effects basic MRW model. The spatial MRW model under the TSCS estimation is manipulated using the ML estimator whereas the spatially augmented Arrelano and Bond GMM estimator together with Elhorst's (2010) ML estimator is applied to overcome the usual small-sample downward lagged dependent variable bias under the fixed effects space-time dynamic panel data model.
4. Revealing the empirics
In this section, we present the empirical predictions of the MRW model, which is considered under two cases. First, we test the basic MRW model where there are no spatial interactions, and second, we test the spatially augmented MRW model.
4.1 The basic MRW model and its econometric results
Data for the variables like GDP per capita, savings rate and working age population are interpolated from Elhorst et al. (2010). They have a compiled data set of the stated
