Specification and Testing of Markov Chain Models: An Application to Convergence in the European Union

Published date01 August 1997
Date01 August 1997
DOIhttp://doi.org/10.1111/1468-0084.00072
AuthorBernard Fingleton
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 59, 3 (1997)
0305-9049
SPECIFICATION AND TESTING OF MARKOV
CHAIN MODELS: AN APPLICATION TO
CONVERGENCE IN THE EUROPEAN UNION
Bernard Fingleton*
I. INTRODUCTION
The analysis of regional economic growth within the European Union has
been stimulated by recent policy changes following the 1987 Single
European Act which have lowered barriers to trade and heralded the
implementation of the internal market programme. According to the
standard neo-classical growth model, increased mobility of capital and
labour, lower transport costs, and easier access to markets should ultima-
tely result in the disappearance of the marked differences in per capita
incomes which now exist. However, there have also been fears, reflected
in the strengthening of EU regional policy, that the consequence of closer
economic integration will be widening per capita income differences. This
paper looks at the evidence for ‘convergence’ and the nature of that
convergence. The paper shows that the steady-state to which the regions
appear to be converging may not be the one predicted by basic neo-
classical theory, but a state of permanent inequality. Moreover, and more
controversially, the paper argues that the current distribution may
actually be the steady-state, in which about 20 percent of regions have per
capita income levels only 75 percent of the EU mean.
The approach adopted in this paper is to use Markov chains, following
the work of Quah (1993a) who initially applied this methodology as an
alternative to regression-based cross-sectional analyses. The emphasis in
this paper is on the estimation and diagnostic testing of such models, on
alternative models for the Markov transition matrix, and on the conclu-
sions that can be realistically drawn from the data available. In addition
to the arguments employed by Quah (1993a), that the standard regression
analysis lacks the richness and flexibility of the Markov approach, an
additional motive for adopting Markov chains in the regional context is
that the measurement error associated with cross-national regional
*I wish to thank the referees, and particularly Andrew Scott for his help and encourage-
ment in developing this paper. I am of course responsible for any errors it may contain.
385
© Blackwell Publishers Ltd, 1997. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF, UK & 350 Main Street, Malden, MA 02148, USA.
economic data is undoubtedly greater than for national series. In order to
produce consistent regional series, it is necessary to apply national defla-
tors, since regional deflators are on the whole unavailable. Reducing each
region’s per capita income series to a series of wealth indicators, with
categories, ‘rich’, ‘above average’, through to ‘poor’, helps to allay some
of the problems inherent in this approach. However, with such data, one
enters what for many economists is the relatively unfamiliar realm of
categorical data analysis. The purpose of this paper is to illustrate the
methods available and to highlight some of the difficulties associated with
this approach.
II. ECONOMIC ISSUES
There is at the outset a need to define convergence and equilibrium. The
natural starting point is the neoclassical model since this provides an
explicit definition of what is meant by equilibrium and a direct measure
of a rate of convergence, so-called bconvergence.
1. The Neo-Classical Growth Model
We take the basic neo-classical model to be defined by a production
function characterized by diminishing marginal returns to capital. The
implication of this is that each country’s growth path eventually follows a
steady-state with K/Yconstant across countries. This has the corollary that
countries with low initial capital relative to Ygrow faster than other
countries, and countries with high initial capital grow comparatively
slowly.
Linearizing the dynamics around the steady-state leads to a convenient
reduced form with growth dependent on start-of-period output per capita.
This is the basis of much empirical analysis of convergence due to the
negative relationship between growth and initial level suggested by
theory. Regression analysis provides an estimate of b, the annual converg-
ence rate towards the steady-state,1with the restriction that there are no
interregional differences in steady-state output per capita.
More recent work based on the neo-classical model (see Barro and
Sala-i-Martin, 1995) has generalized the reduced form by allowing the
steady-state to vary across countries due to differences in institutional and
socio-political structures. However, note that these variables do not affect
the long-run growth rate of output per capita, which is determined by the
exogenous technical progress rate. The model with the additional vari-
ables retains the fundamental convergence process at its heart, even
1Cheshire and Carbonaro (1995) argue that bconvergence is the weakest possible test of
the neo-classical model, since it is also consistent with other possible mechanisms.
© Blackwell Publishers 1997
386 BULLETIN

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT