In a semi-parametric spatial vector autoregressive setting this paper investigates the role of age-structured human capital on output comovements in Europe. Using the proportion of age-structured human capital growth and its degree of appropriations in output production as twin measures of distance, we find significant positive spatial growth volatility/persistence.Spatial growth volatility, Non-linear growth, Age-structured human capital, Semi-parametric VAR.

Mamata Parhi

Tapas Mishra

English

Research Papers in Economics

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« Spatial Growth Volatility and Age-structured 
Human Capital Dynamics in Europe » 
 
 
Auteurs 
 
Mamata Parhi, Tapas Mishra 
 
 
 
Document de Travail n° 2008 - 4 
 
 
Février 2008 
 
 
 
 Spatial Growth Volatility and Age-structured Human
Capital Dynamics in Europe
Mamata Parhia and Tapas Mishrab∗
a BETA, Universit´ e Louis Pasteur,
61 avenue de la Forˆ et Noire, F-67085 Strasbourg, France
b International Institute for Applied Systems Analysis (IIASA)
A-2361 Laxenburg, Austria
Abstract
In a semi-parametric spatial vector autoregressive setting this paper investigates the role
of age-structured human capital on output comovements in Europe. Using the proportion of
age-structured human capital growth and its degree of appropriations in output production
as twin measures of distance, we ﬁnd signiﬁcant positive spatial growth volatility/persistence.
JEL Classiﬁcation: C14, C31, E61, J11, O47
Key words: Spatial growth volatility, Non-linear growth, Age-structured human capital,
Semi-parametric VAR.
∗Corresponding author: T. Mishra. Tel: (43) 2236 807 303 Fax: (43) 2236 71313. E-mail: mishra@iiasa.ac.at
11 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, among others) literature. Taking
cues from the theories of new economic geography, it has been widely established that spatial
factor mobility and knowledge spillovers can potentially propel growth synergies/volatility to
migrate from one economy to another (at least in the neighbourhood and albeit with a lag).
Put simply, cross-country economic growth can be correlated. Latest empirical dissections (viz.,
Ertur and Koch, 2007) have rightly supported this claim by building empirically testable spatial
growth models where interdependence among countries could be modeled via technological and
human capital growth. An imposing feature of locational growth interdependence is that it
could trigger high degree of persistence in international output (e.g., Durlauf, 1989; Raj, 1993;
Levy and Dezhbakhsh, 2003; Mello and Guimaraes-Filho, 2007). Despite some contradictions,
the literature points to the possible coordination failure in economic activities among diﬀerent
countries as major source of persistence. At international level, the evidence of varying degrees
of persistence with some commonality in the degree of shock convergence in output (Mello and
Guimaraes-Filho, 2007) further conﬁrms that output shocks are correlated in space governed by
a complex feedback mechanism and thus volatility (occurring due to either exogenous and/or
endogenous shocks) in one economy would migrate to another. This in turn would induce high
degree of non-linearity in growth across space.
While some recent research (viz., Ertur and Koch, 2007) have explicitly built empirical
spatial growth models, very little has been researched on the nature and source of possible per-
sistence in spatial output volatility and complementarity in growth and their implications for
countries’ policies at individual and collective level. 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 pertinent in Europe where many economies are experiencing faster ageing, thus
exerting enormous impact on their prospective human capital generation and long-run economic
growth. Since many European countries share common socio-economic and demographic dy-
namics, it is pertinent to ask: Are European countries complementary in growth (at least in
the neighborhood) with respect to levels of demographic change and (hence) human capital
accumulation? Is the possible comovement caused by a common aggregate shock? Moreover,
can a demography-based distance measure, viz., age-structured human capital appropriations in
production explain the possible positive spatial correlation and non-linearity in spatial growth?
If so, what lessons can we learn about policies promoting/optimising individual and collective
economic welfare? In the framework of semi-parametric spatial Vector Autoregressive (VAR)
setting (Chen and Conley, 2001), this paper attempts to answer these questions by examining a
sample of 20 countries in Europe for the 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 = A(Dt)Zt + εt+1, εt+1 = Q(Dt)ut+1 (1)
2where Zt = (Y1,t,Y2,t,    ,YN,t)′ ∈ RN is a vector stacking {Yi,t}N
i=1 with Yt = (X1,t,    ,XN,t)′ ∈
RN. {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}. Dt in the Eq. 1 is a stacked vector of
distances (represented by a set of locations in Rk for country i at time t located at point si,t)
between the {si,t}N
i=1 deﬁned for two points i and j as Dt(i,j) =  si,t,sj,t  with  .  denoting
the Euclidean norm. 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 as in Chen and Conley (2001) which designs the
evolution of Zt according to Eq. 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 E(ut+1) = 0 and V(ut+1) = IN. It follows that the conditional covariance
matrix of εt+1 is E(εt+1ε′
t+1) = Q(Dt)Q(Dt)′ := Ω(Dt), which is also function of distances. In
the speciﬁcation (Eq. 1), the conditional mean A(Dt) and the conditional covariance Ω(Dt)
need to be estimated which have the following structure.
1. Conditional means
From (1), the conditional mean of Yi,t+1 given {Zt−l,Dt−l,l ≥ 0} is modelled as
E[Yi,t+1|{Zt−l,Dt−l,l ≥ 0] = αiYi,t +
N  
j =i
fi(Dt(i,j))Yj,t (2)
where the fi are continuous functions mapping from (0,∞) to Rl. It follows that the
conditional mean of Zt+1 given {Zt−l,Dt−l,l ≥ 0} is A(Dt)Zt, where
A(Dt) =

 
 

α1 f1(Dt(1,2))     f1(Dt(1,N))
f2(Dt(2,1)) α2     f2(Dt(2,N))
. . .
. . .
. . .
. . .
fN(Dt(N,1)) fN(Dt(N,2))     αN

 
 

(3)
2. Conditional covariances
The conditional covariance of Zt+1 given {Zt−l,Dt−l,l ≥ 0} is modelled as
Ω(Dt) =

 
 

σ2
1 + γ(0) γ(Dt(1,2))     γ(Dt(1,N))
γ(Dt(2,1)) σ2
2 + γ(0)     γ(Dt(2,N))
. . .
. . .
. . .
. . .
γ(Dt(N,1)) γ(Dt(N,2))     σ2
N + γ(0)

 
 

(4)
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 σ2
i ≥ 0. Our interest lies in the shape of functions fi
and γ. The model is estimated with fi speciﬁed to be common across countries, using
least squares. We approximate f as a linear combination of eight third order spline scaled
to be evenly spaced over the support of the distance distribution (See Chen and Conley,
2001 for details). An important and desirable feature of Eq. 1 is that it does not assume a
priori parametric speciﬁcation of neighborhood structure as is usually done in parametric
spatial models.
1Isotropy means that the stationary random ﬁeld (with indexes in R
k) that generates the process is directional
invariant.
33 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 IIASA/VID data base2 we construct the distance measure based on age-
structured human capital. Secondary educational attainment data for population age groups:
15-29, 30-49, 50-64 is utilized to construct two economic distance measures: (i) the proportion
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 30 years. 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 used for the measure of D2. Country locations si,t are then
identiﬁed with D1 and D2. Thus, two countries are close in the sense of D1 if the proportion
of human capital in the age-structured population for two countries is same, distant, otherwise.
Similarly, two countries are close in the sense of D2 if they utilize approximately same quantity of
human capital in production. While the former induces productivity eﬀects as the stock of human
capital at each demographic level exerts varying productivity eﬀects across country locations, the
latter induces a scale eﬀect in the economies (aﬀecting production through knowledge creation).
Time non-varying distance is assumed for simplicity, which could be reasonable, given the slow
paced demographic changes.
4 Empirical results
Based on the model and data speciﬁcations described above, we explicate here the shapes of f
(estimating the output comovements) and γ (indicating residual covariance comovements) with
respect to the two distance metrics (in Figures 1 and 2). The solid line is our point estimate of
f, plotted against the distances (in the X-axis). The crosses represent 95% bootstrap conﬁdence
interval. Using the age-structured human capital distance, D1 as in Fig. 1, we notice that the
point estimates are large compared to Fig. 2 which uses 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. 2) 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. 2) induces high degree of non-linearity in spatial growth
(f function) for which growths are even found to be correlated at high distances. This could
partially be 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 demographic-change-induced human capital accumulation on the economy. But this is
clearly taken care of by D1 where distance is constructed for each age-structured human capital
2The International Institute for Applied Systems Analysis and Vienna Institute of Demography data base is
a unique and argued to be better than competing databases on educational attainment levels by age and sex for
120 countries in the period 1970-2000. See http://www.iiasa.ac.at/Admin/PUB/Documents/IR-07-011.pdf for
details.
4accumulation thus outlining distinct and expected pattern in cross-country output comovement
at varying distances.
Putting together, this conﬁrms that countries’ growth processes are complementary and
can be explained by the demography-led human capital accumulation, indicating the centrality
of the latter in the generation of spatial growth volatility. Since non-linear positive spatial
correlation is observed for both distance metrics, we conjecture that both scale and productivity
eﬀects arising from the embedding of D1 and D2 in the regression (assuming feedback eﬀect
from demography to economic growth via human capital accumulation) could be behind the
non-linearity.
The estimates of γ (indicating covariances of residuals) divided by the country variance
estimates are presented in right panels of Fig. 1 and 2. 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. 2) and then remains at zero level (after fast decay) for higher distances
(Fig. 1). 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 countries sets in a similar vein. Based
on the evidence, it might be imperative to devise collective European policies to successfully
check spatial growth volatility. A long term policy planning based on a greater co-ordination
among individual countries with a common demographic/human capital management agenda
could be useful in enhancing individual and collective social welfare.
0 1 2 3 4 5 6 7 8
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
f−Function with 8 splines for the gamma−function
Estimate
Sym LB
Sym UB
0 1 2 3 4 5 6 7 8
−0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
gamma−function 8 Splines
Estimate
Sym LB
Sym UB
Figure 1: Conditional mean ( ˆ f [left]) and covariance (ˆ γ [right]) functions based on age-structured
human capital proportion, D1.
50 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
f−Function with 8 splines for the gamma−function
Estimate
Sym LB
Sym UB
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
−1
−0.5
0
0.5
1
1.5
2
2.5
3
x 10
−4 gamma−function 8 Splines
Estimate
Sym LB
Sym UB
Figure 2: Conditional mean ( ˆ f [left]) and covariance (ˆ γ [right]) functions based on elasticity of
human capital input, D2.
References
Boucekkine, R., D. de la Croix, and O. Licandro, 2002, Vintage Human Capital, Demographic
Trends, and Endogenous Growth, Journal of Economic Theory, 104, 340-375.
Chen, X. and T.G. Conley, 2001, A New Semiparametric Spatial Model for Panel Time Series,”
Journal of Econometrics, 105, 59–83.
Conley, T.G. and B. Dupor, 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. and W. Koch, 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. and W. Koch, 2007, Growth, Technological Interdependence and Spatial Externalities:
Theory and Evidence, forthcoming in Journal of Applied Econometrics.
Fujita, M. and J.F. Thisse, 2002, Economics of agglomeration (Cambridge University Press).
Levy, D. and H. Dezhbakhsh, 2003, International evidence on output ﬂuctuation and shock
persistence, Journal of Monetary Economics, 50, 1499-1530.
Mello, M. and R. Guimaraes-Filho, 2007, A note on fractional stochastic convergence, Economics
Bulletin, 3(16), 1-14.
6Raj, B., 1993, An international study of persistence in output: Parametric estimates using the
data dependent systems approach, Empirical Economics, 18(1), 173-195.
7

A New Semiparametric Spatial Model for Panel Time Series,”

A note on fractional stochastic convergence,

A Spatial Analysis of Sectoral Complementarity,

An international study of persistence in output: Parametric estimates using the data dependent systems approach,

Economics of agglomeration (Cambridge

Growth, Technological Interdependence and Spatial Externalities: Theory and Evidence, forthcoming in

International evidence on output ﬂuctuation and shock persistence,

Output Persistence, Economic Structure and the Choice of Stabilization Policy,

Regional Disparities in the European Union and the Enlargement Process: An Exploratory Spatial Data Analysis,

Vintage Human Capital, Demographic Trends, and Endogenous Growth,

Spatial Growth Volatility and Age-structured Human Capital Dynamics in Europe.

http://www.beta-umr7522.fr/productions/publications/2008/2008-04.pdf

Spatial Growth Volatility and Age-structured Human Capital Dynamics in Europe.

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