Economics Letters 102 (2009) 181–184
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Spatial growth volatility and age-structured human capital dynamics in Europe Mamata Parhi, Tapas Mishra ⁎ School of Business and Economics, University of Wales, Swansea, Singleton Park, Swansea, SA2 8PP, UK
a r t i c l e
i n f o
Article history: Received 31 May 2007 Received in revised form 26 November 2008 Accepted 19 December 2008 Available online 22 January 2009
a b s t r a c t We study dynamic output co-movements in Europe in a spatial setting where proportion of human capital and its appropriation pattern in production define distance among countries. Significant spatial output and shock correlations are found suggesting possible welfare-enhancing cross-country policy coordination. © 2008 Elsevier B.V. All rights reserved.
Keywords: Spatial growth volatility Non-linear growth Age-structured human capital Semi-parametric VAR JEL classifications: C14 C31 E61 J11 O47
1. Introduction The role of ‘space’, though was not central in traditional economic growth framework, has earned increasing prominence in the latest theoretical (e.g., Fujita and Thisse, 2002) and empirical (e.g., Conley and Dupor, 2003; Ertur and Koch, 2006, 2007) literature. Taking cues from the theories of new economic geography, it is now widely recognized that factor mobility and knowledge spillovers in space trigger cross-country migration of growth synergies/volatility, although with a time lag. The dynamic output correlations among countries can arise with countries having (at least) close geographical and/or relational proximities. Recent empirical dissections (viz., Ertur and Koch, 2007) have rightly supported this claim by building testable spatial growth model where interdependence among countries is modeled via technological and human capital growth. An imposing feature of locational growth interdependence is that it can generate high degree of persistence in international output (e.g., Durlauf, 1989; Raj, 1993; Levy and Dezhbakhsh, 2003; Mello and Guimaraes-Filho, 2007). Durlauf (1989) argues that dynamic coordination failure among firms' economic activities is a major source of persistence in output at national level. In a cross-country setting, the literature points to the possible coordination failure in countries' economic activities as major source of international persistence of ⁎ Corresponding author. Tel.: +44 1792 620 2108; fax: +44 1792 295872. E-mail address:
[email protected] (T. Mishra). 0165-1765/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2008.12.014
output. The evidence of varying degrees of persistence with some commonality in the degree of shock convergence in output at international level (Mello and Guimaraes-Filho, 2007) further confirms that output shocks are correlated in space and are driven by a complex feedback mechanism. Thus, it is highly likely that volatility (occurring due to either exogenous and/or endogenous shocks) in one economy would migrate to another with some time lag and induce high degree of non-linearity in spatial economic growth. While some recent researches (viz., Ertur and Koch, 2007) have succeeded in building an empirically testable spatial growth framework, little is known on how output growth across countries could be dynamically correlated when distance among them (in economic or relational sense) varies over time. Could the magnitude of error in spatial output growth possibly recede as a function of the relational distance among them? In a highly internationalized global economic system, dynamic spatial correlation of output is a natural possibility - both theoretically and empirically. We hold that correlation in cross-country growth can be linked to a common source of fluctuation such that possible growth volatility can be explicated by economic theoretic mechanisms viz., human capital and its recent extension — demography led human capital growth (e.g., Boucekkine et al., 2002). The relevance of the latter is quite paramount in Europe where many economies are experiencing faster ageing, thus exerting enormous impact on their prospective human capital generation and long-run economic growth planning. Since many European countries share common socioeconomic and demographic dynamics, it is pertinent to ask: Are
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Fig. 1. Histogram of distances: age structured human capital proportions, D1 (left) and elasticity of human capital, D2 (right).
European countries' output growth spatially correlated? If so, what sort of relational measure(s) might contribute to such correlations? Based on endogenous growth theory's emphasis on human capital accumulation and its demographic extension — age-structured human capital, in this paper, we test whether a demography-based human capital distance measure can explain the possible positive spatial correlation and nonlinearity in spatial output growth. For the purpose, a semi-parametric spatial vector autoregressive (SVAR) method (Chen and Conley, 2001) is employed for a sample of 20 European countries over a three decade period (1970–2000). 2. The model We estimate a fully interconnected model with feedback effects in the semi-parametric SVAR framework of Chen and Conley (2001). The model is described by Zt + 1 = AðDt ÞZt + et + 1 ;
et + 1 = Q ðDt Þut + 1
ð1Þ
where Zt = (Y1,t, Y2,t,⋯, YN,t)′ a N is a vector stacking output, {Yi,t}iN= 1. Yt = (X1,t,⋯, XN,t)′ a N . {Xi,t∶i = 1,⋯, N;t = 1,⋯, T} is described by the sample realizations of N countries' variables at locations {si,t∶i = 1,⋯, N; t = 1,⋯, T} with s a k . Dt in (1) is a stacked vector of distances between locations si,t and sj,t such that Dt = ∥si,t – sj,t∥ where ∥·∥ denotes the Euclidean norm. The distances are such that Dt(i, j) = 0 if and only if i = j. This imposes a limit on the level of disaggregation as the location sit must characterize each country in an unambiguous way. Assuming that the growth of a given country at t + 1 denoted by Yi,t + 1 will depend not only on its own past (home externalities) but also nonparametrically on the performance of its neighbors (spatial spillovers effects), we model the joint process {(Zt, Dt):t = 1,⋯, T} as a first order Markov process which designs the evolution of Zt according to (1) as above. A(Dt) is a N × N matrix whose elements are functions of age-structured human capital distances between countries. We assume that ut + 1 is an i.i.d sequence with (ut + 1) = 0 and (ut + 1) = IN. It follows that the conditional covariance matrix of εt + 1 is (εt + 1ε′t + 1) = Q(Dt)Q(Dt)′: = Ω(D t), which is also a function of distances. The conditional mean and the conditional covariance in (1) need to be estimated. They provide explicit characterization of the slopes of functions corresponding to dynamic interdependence in output growth (viz., the conditional mean specification) and cross country correlation of errors (viz., conditional covariance specification) as functions of age-structured human capital distances among them.
2.1. Conditional means From (1), the conditional mean of Yi, modelled as
t+1
given {Zt – l, Dt – l, l ≥ 0} is
N
½Yi;t + 1 jfZt−l ; Dt−l ; lz0 = α i Yi;t + ∑ fi ðDt ði; jÞÞYj;t
ð2Þ
j≠i
where the fi are continuous functions mapping from (0, ∞) to l . The dynamic spatial output correlations are represented by f functions which are time-invariant functions of the distance between two countries. It follows that the conditional mean of Zt + 1 given {Zt – l, Dt – l, l ≥ 0} is A(Dt)Zt, where 0
α1 B f2 ðDt ð2; 1ÞÞ AðDt Þ = B @ v fN ðDt ðN; 1ÞÞ
f1 ðDt ð1; 2ÞÞ : : : ::: α2 v v fN ðDt ðN; 2ÞÞ : : :
1 f1 ðDt ð1; NÞÞ f2 ðDt ð2; NÞÞ C C A v αN
ð3Þ
and that the spectral radius of A(Dt) is strictly smaller than one. It reflects estimation in a stationary environment. 2.2. Conditional covariances Assuming that the Euclidean distance between two spatial locations is defined by τ = ∥s1 – s2∥ and setting k = 3 in s a k the covariance function can be written following Yaglom (1987): γðτ Þ = 2ðk−2Þ=2 C
k ∞ Jðk−2Þ=2 ðxτ Þ ∫ dW ðxÞ 2 0 ðxτÞðk−2Þ=2
ð4Þ
where Ψ(x) is a bounded nondecreasing function and where J(k − 2)/2 (xτ) is a Bessel function of the first kind (see Yaglom, 1987 for details).
Table 1 ^̂ and σ̂ ^̂ 2 with distance measures D1 and D2 Parameter estimates of α ^̂ α
^σ̂2
Distance measures
Coef.
Std-Dev.
Coef.
Std-Dev.
Obs.
D1 D2
0.226 0.191
0.132 0.115
0.00001 0.0007
0.000 0.0002
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^ [right]) functions based on age-structured human capital proportion distance (D1). Fig. 2. Conditional mean (f^ [left]) and covariance (γ
After some algebra and by explicitly introducing the Bessel function, the covariance function becomes, γ ðτÞ = ∫0∞
sinðxτÞ dΨðxÞ xτ
ð5Þ
In the degenerate case Ψ(x) =x so that the covariance function reduces to single hyperbola. Then for every bounded nondecreasing function Ψ, this implies that the conditional covariance is represented by 0
σ 21 + γ ð0Þ γ ðDt ð1; 2ÞÞ : : : B γ ðDt ð2; 1ÞÞ σ 2 + γ ð0Þ : : : 2 XðDt Þ = B @ v v v γ ðDt ðN; 1ÞÞ γ ðDt ðN; 2ÞÞ : : :
1 γðDt ð1; NÞÞ γðDt ð2; NÞÞ C C A v 2 σ N + γð0Þ
ð6Þ
where γ(.) is assumed to be continuous at zero and is k-dimensional isotropic covariance function.1 The choice of γ ensures that Ω(Dt) is positive definite for any set of interpoint distance Dt and any values of the σ2i ≥ 0. The estimation of f and γ functions proceeds in a semi-parametric environment using a cardinal B-spline polynomial sieve (see Chen and Conley, 2001 for details). In the model, fi is specified to be common across countries where it is approximated as a linear combination of eight third order spline scaled to be evenly spaced over the support of the distance distribution. An important and desirable feature of (1) is that it does not assume a priori parametric specification of neighborhood structure as is usually done in parametric spatial models.
of human capital stock for three age-specific population over 1970–2000 (denoted by D1) and (ii) the input share of human capital in the country's production over the same period (denoted by D2). D1 is constructed by calculating the average of the proportion of people (with secondary education or more) for each age-group over the 30-year period. For D2, a two-sector production function with physical and human capital as inputs has been estimated. Elasticity estimates of human capital for each country are then recovered and are used for the measure of D2. Country locations si,t are identified with D1 and D2. Thus, two countries are close in the sense of D1 if the proportion of human capital in the agestructured population for two countries is the same; distant, otherwise. Similarly, two countries are close in the sense of D2 if they utilize approximately the same quantity of human capital in production. The former induces productivity effects (as the stock of human capital at each demographic level exerts varying productivity effects across country locations) and the latter induces a scale effect within the economies (affecting production through knowledge creation). Time non-varying distance is assumed for simplicity, which is reasonable, given the slow paced demographic changes. The histogram of distances is presented in Fig. 1 (D1 on the left and D2 on the right). As evident, the distances are observed to be skewed and can determine the pattern of f and γ functions, i.e., spatial output and error correlations. In both the cases, it is observed that most of the distances are covered at 75% for D1 measure and at 85% for D2 measure. Bi-modal distribution of distance is observed for D2 which implies that dynamic output correlation can also be found for some countries at higher distances. 4. Empirical results
3. Data and distance measure Per capita real GDP data (from Penn World Table 6.1) with Purchasing Power Parity at 1996 international US$ is used as output measure. Output growth is calculated by their logarithmic differences. Using the newly constructed IIASA/VID data base2, we formulate the distance measure based on age-structured human capital. Secondary educational attainment data for population age groups viz., 15–29, 30–49, 50–64 are utilized to construct two economic distance measures: (i) the proportion 1 Isotropy means that the stationary random field (with indexes in Rk ) that generates the process is directional invariant. 2 The International Institute for Applied Systems Analysis (IIASA) and Vienna Institute of Demography (VID) human capital data base is a unique and argued to be better than similar competing databases on educational attainment levels (see for instance, Lutz et al., 2008).
The coefficient estimates for α and σ2 based on the two measures of distance are reported in Table 1. Note that α values are the average estimates over countries. The significance of the coefficients can be gauged by calculating the corresponding pooled t-ratio. A statistically significant averaged α indicates the presence of spatial autocorrelation or dynamic output correlations in space. From Table 1, it is evident that although α is not particularly large, they clearly exhibit significant dynamic spatial correlation based on both measures of distance. The averaged conditional variances (σ2) in the Table describe idiosyncratic components (σ2i ) and indicate that the covariance structure of the residuals also significantly depends on the distances. Shapes of f (estimating the output comovements) and γ (indicating residual covariance comovements) with respect to the two distance metrics (Figs. 2 and 3) further confirm our results. The solid line is our
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^ [right]) functions based on elasticity of human capital input distance (D2). Fig. 3. Conditional mean (f^ [left]) and covariance (γ
point estimate of f, plotted against the distances (in the X-axis). The crosses represent 95% bootstrap confidence interval. Using the agestructured human capital distance, D1 as in Fig. 2, we notice that the point estimates are large compared to Fig. 3 which use the elasticity of input measure, D2 (compare the f functions). A significant positive dynamic spatial correlation at most distances is thus observed, which is an important indication of positive growth spill-over effects. Moreover, high degree of non-linear spatial growth comovement is observed for the distance D2 with some degree of non-linearity in D1 as well. Notice that D2 (Fig. 3) induces high degree of non-linearity in growth (f function) due to feedback effects in productivity movement across countries, the impacts of which are felt at varying time lags. Indeed, using D1 we observe high complementarity in growth at lower distances which finds natural explanation in migration of productivity effects across countries as mentioned above. However, D2 (Fig. 3) induces high degree of non-linearity in spatial growth (f function) for which growth processes are found to be correlated even at higher distances. This could be partially due to the measure itself: D2 is constructed from the stock of human capital in total population, which does not in stricto sensu explain the complex interaction effect from different levels of demographicchange-induced human capital accumulation on the economy. But this is clearly taken care of by D1 which is constructed for each age-structured human capital thus eking out distinct and expected pattern in crosscountry output co-movement with varying distances. The results confirm that countries' growth processes are complementary and can be explained by the demography-led human capital accumulation mechanism, explicating the centrality of the latter in the generation of spatial growth volatility. Since non-linear positive spatial correlation is also observed for both distance metrics, we conjecture that both scale and productivity effects arising from the embedding of D1 and D2 in the regression (due to the possible feedback effect from demography to economic growth via human capital accumulation) could be behind this non-linearity. The estimates of γ (indicating covariances of residuals) divided by the country variance estimates are presented in right panels of Figs. 2 and 3. These normalized γ estimate would be the sample spatial correlation if country variances were identical. Notice that γ is quite large for D2 and small but positive-constant for D1. Moreover, γ is found to decline monotonically with distance (in Fig. 3) and then remains at zero level (after fast decay) for higher distances (Fig. 2). Taking together, there is (strong) evidence that shocks in our VAR model are spatially correlated as a function of distance.
To conclude, significant cross-country output comovements within European countries are found suggesting possible stochastic shock movements across them. The evidence of spatial growth complementarity could also be generalized for other sets of countries in similar geographical boundaries. Based on the evidence, it might be imperative to devise collective policies to successfully manage spatial growth volatility. A long term policy planning based on a greater coordination among individual countries with a common demographic/ human capital management agenda could be useful in enhancing individual and collective social welfare. Acknowledgments We sincerely thank the editor and an anonymous referee for very helpful comments which significantly improved the quality and content of the paper. The authors acknowledge the financial support from BETA, Louis Pasteur University, France and the International Institute for Applied Systems Analysis, Austria. We also thank Frédéric Dufourt for helpful comments on an earlier draft of this paper. The usual disclaimer applies. References Boucekkine, R., de la Croix, D., Licandro, O., 2002. Vintage human capital, demographic trends, and endogenous growth. Journal of Economic Theory 104, 340–375. Chen, X., Conley, T.G., 2001. A new semiparametric spatial model for panel time series. Journal of Econometrics 105, 59–83. Conley, T.G., Dupor, B., 2003. A spatial analysis of sectoral complementarity. Journal of Political Economy 111 (2), 311–352. Durlauf, S.N., 1989. Output persistence, economic structure and the choice of stabilization policy. Brookings Papers on Economic Activity 2, 69–116. Ertur, C., Koch, W., 2006. Regional disparities in the European Union and the enlargement process: an exploratory spatial data analysis, 1995–2000. Annals of Regional Science 40 (4), 723–765. Ertur, C., Koch, W., 2007. Growth, technological interdependence and spatial externalities: theory and evidence. Journal of Applied Econometrics 22 (6), 1033–1062. Fujita, M., Thisse, J.F., 2002. Economics of Agglomeration. Cambridge University Press. Levy, D., Dezhbakhsh, H., 2003. International evidence on output fluctuation and shock persistence. Journal of Monetary Economics 50, 1499–1530. Lutz, W., Crespo-Cuaresma, J. and Sanderson, W., 2008, The Demography of Educational Attainment and Economic Growth, Science 22, 319(66), 1047–1048. Mello, M., Guimaraes-Filho, R., 2007. A note on fractional stochastic convergence. Economics Bulletin 3 (16), 1–14. Raj, B., 1993. An international study of persistence in output: parametric estimates using the data dependent systems approach. Empirical Economics 18 (1), 173–195. Yaglom, A.M., 1987. Correlation Theory for Stationary and Related Random Functions, vols. I and II. Springer, New York.