Embed Size (px)
Citation preview
European Regional Science Association36th European CongressETH Zurich, Switzerland
26-30 August 1996
Enrique López-BazoThe European Institute, London School of Economics
London, UKDpt of Econometrics, Statistics and Spanish Econ., U. of Barcelona
Barcelona, [email protected]
Esther VayaAntonio J. MoraJordi Suriñach
Dpt of Econometrics, Statistics and Spanish Econ., U. of BarcelonaBarcelona, Spain
Fax: ++343 402 18 21
REGIONAL ECONOMIC DYNAMICS ANDCONVERGENCE IN SPAIN AND EUROPE
ABSTRACT:
Several studies about regional convergence have appeared in recent years. Most of themapplying the well known concepts ofβ and σ convergence. However, our belief is that bymeans of this approach is not possible to obtain evidence of interesting issues related to thedynamics of the whole regional income distribution. For this reason, this paper uses differenttools to get more information about those dynamics in the UE. We also consider the likelypresence of spatial effects (dependence and heterogeneity) within the UE and theconsequences of not including them on theβ convergence equation. On the other hand, thisstudy allows us to know the spatial distribution of these variables and test the degree of aCore-Periphery scheme in the EU. These tools are applied to per capita GDP and labourproductivity to the EU regions (at NUTSII desaggregation level) through the eighties.
From the results we conclude on the presence of important differences in the convergenceprocess of both variables (persistence of inequalities in per capita GDP yet convergence inproductivity) and the different role of the richest and poorest regions to explain them.Moreover, we detect an important spatial instability in the UE and some stronginterdependences among neighbour European regions.
1. Introduction
Several studies of the regional convergence topic have appeared in recent years. Most of them
applying the well known concepts ofβ and σ convergence as proposed in Baumol (1986),
Barro and Sala-i-Martin (1991), etc. Following that approach, Doladoet al (1994) obtain
evidence of unconditional convergence at a low rate for the Spanish provincies (NUTSIII
regional level), increasing the rate when conditioning variables are considered. Similar results
were obtained in Maset al (1995) for the same case, pointing out also the temporal instability
of the convergence process and the lower convergence rate that it results when analysing a
higher spatial desaggregation level (NUTSIII versus NUTSII). For the European Union
regional case there is a general consensus in the existence of a decrease in regional
inequalities (ie convergence) from the fifties to the seventies and a relative stagnation
afterwards (see Armstrong 1995 among others). Neven and Gouyette (1994) show the
insignificance of theσ convergence process since 1980, in spite of a slight decrease in
disparities since 1984. Their work shows that homogeneity is higher among the Northern
region of the EU than among the Southern ones and the possibility of different patterns in the
evolution of the disparities in both groups.
Other analysis have focused on the economic effects of integration in regional economic
disparities in Europe. In that way, Leonardi (1995) defends the conexion between integration,
cohesion and convergence, while Molle and Boeckhout (1995) and Abraham and Van
Rompuy (1995) are good examples of the analysis of expected differences in regional
responses to the Single European Market and the European Monetary Union, that is, a
deepening in the integration process.
The decrease in regional disparities in Europe, and by extension within most of the member
states, should not hide the remaining level of inequality. In fact, regional inequality in Europe
is far above that existing in the United States or Canada (Esteban, 1994). Moreover, we think
that the most significant convergence processes in the EU were observed after important
changes in economic and social structure. The main one in the postwar period covering the
rebuilding of the European economy and the first steps of the integration process. The other
one, after the turbulent period caused by the oil shocks in the seventies and first part of the
eighties. The latter was also a starting point for important changes in the economic structure
of periferal economies, Spain being the paradigmatic case. The widening and deepening of
integration could reinforce that process, even though it seems too soon to believe that it was
the main reason. Moreover, there is one particulary significant fact: the increase in regional
dispersion observed since 1986 within Southern Europe while the Northern group became
more homogeneous (Neven and Gouyette, 1994). These features highlight the asymmetric
impact of shocks in core and peripheral regions and also the differences in regional responses
within peripheral countries. In this sense, the ability of lagged regions to converge to higher
income levels depends on their specific characteristics and conditions: productive
specialization, location, social and political structures, etc.
Our belief is that by means of the traditionalβ andσ convergence approach it is not possible
to obtain evidence of interesting issues related to the dynamics of the whole regional income
distribution. For instance, whether convergence has existed, what regions have been the main
contributors to that process, are thereconvergence clubs? have the economies changed their
position in the ranking of income or does a strong persistence dominate the process?... To
answer these questions we need more information than the one supplied by the dynamic
behaviour of an average economy (implicit in the traditional approach). This paper uses
different tools (dispersion, inequality and polarization indexs, density functions, expanded
rank-size functions and Markov chains) to get more information about the regional income
distribution dynamics as well as to consider spatial effects as another important criticism to
the convergence Barro and Sala-i-Martin kind of equation (in the sense pointing out by
Armstrong, 1995). In this sense the detection ofhot spotsboth in levels and growth, and their
spatial dynamics, becomes another important question to be considered.
On the other hand, growth models predicts (if some) convergence in the output-labor force
ratio that is supposed to translate into output per capita. In fact, much of the empirical work
has tested the hypothesis in the latter variable due to the availability of data. However, the
existence of important differences in the spatial distribution of the employment-population rate
advice of a differenciated study of both magnitudes. In fact, regional diferences in the activity
rate and, mainly, in the unemployment rate are rather high and showed an increasing trend
during the eighties in the EU (CEC, 1994). Ana priori assumption is that the integration
process (factor mobility, trade integration, tecnological diffusion, etc) and measures adopted
to improve economic performance of lagged regions (infrastructure investments, human capital
formation, etc) may favour the increase in productivity levels of poor regions but not
automatically per capita income levels. This means a convergence process in labour
productivity but not in terms of per capita, the desequilibrium in labour market being the one
which reflects the regional structural inequalities in the short-medium term.
Therefore our analysis focuses on disparities and convergence on both GDP per worker (as
a measure of labor productivity) and per capita in the European Union. In the former case our
sample includes 129 regions (at NUSTII level: Belgium (9), Germany (31), Greece (2)1,
Spain (17), France (21), Italy (20), Netherlands (10) and Portugal (5); at NUTSI level: UK
(11) plus Denmark, Ireland and Luxembourg) for 1981 and from 1983 to 1992. In the case
of per capita GDP we consider 143 regions (at NUTSII level: Belgium (9), Denmark (3),
Germany (31), Greece (13), Spain (18), France (21), Italy (20), Netherlands (10) and Portugal
(5); at NUTSI level: UK (11) plus Ireland and Luxembourg) for the whole 1980-1992 period.
Data source is REGIO database, even though additional information on employed population
for some countries has been used due to a lack of it from that particulary source. We have
preferred to work with a shorter dataset but considering most of periferal regions due to the
belief that convergence must be viewed as poor regions catching up on rich ones. Discarding
those regions will lead to an incomplete picture of the phenomena. Per worker GDP is
measured in ECU in order to take into account differences in the capacity to produce goods
while per capita GDP is in PPS to consider the regional ability to purchase goods and so
achieve different levels of well-being. Results for the EU will be related to the ones obtained
for the Spanish provincies (50) for a longer period (1955-1993).
2. Spatial inequality distribution in the EU
Deepening in the integration process (removal of barriers, factor mobility enhacement, trade
flows increase,...) as well as implementation of EMU are supposed to lead to a high level of
relationship among EU regions. Nevertheless, regional specific shocks will spread to each
other regions depending on real links among them. Several hypothesis have been formulated
about the effects of integration in regional links and in the transmision of region-specific
shocks. But it is also interesting to know how these relationships could have influenced the
regional convergence process. In this way, this section analyses whether the distribution of
both per capita GDP and productivity is spatially random or it follows any pattern of spatial
autocorrelation or dependence. Existence of a global process of (positive) spatial correlation
would be signal of large territorial integration and somewhat symetric economic evolution.
On the other hand, local spatial association (hot spotsof high/low levels of production or
fast/slow growth) would reflect either disparities in structural conditions and different shocks
responses.
We apply recent spatial econometric tools to test global spatial correlation (Moran’s I, Geary’s
C, Getis’ G(d)) as well as local spatial correlation (LISA’s, Anselin, 1995). Comparison of
these statistics in different time periods will show some trends in spatial concentration or
spread of economic activity. Furthermore, existence of clusters of high or low values in the
territory may lead to reject homogeneity and stability in the regional sample and thus to
invalidate following convergence analysis for the whole set of regions. The results obtained
in global autocorrelation spatial statistics applied to per capita GDP and productivity and their
growth rates are shown in Table 1. Large significant and positives (negatives) values of
Moran’s I (Geary’s C) mean the presence of spatial association of similar values among
neighbour european regions along the period. Results for growth rates are not conclusive due
to the negative value of Gettis’ G(d). In any case, it is likely to exist evidence of strong
interdependence among EU regions.
It is worth pointing out that this result should put one in guard about the presence of spatial
autocorrelation omitted in an incorrect way in the growth rates versus initial levels classical
convergence equation. In this sense, the detected spatial dependence might be translated to
perturbance term and then affect efficiency of estimation, or might require the inclusion of
spatial lags of endogenous/exogenous variables to pick up influence of regions in each others,
discarded in the initial equation. The latter would affect the bias and consistency of ordinary
estimation. The results for sustantive and nuisance spatial autocorrelation tests in
unconditional convergence equation for EU regions are summarized in Table 2. The presence
of significant spatial dependence is derived in the equations and thus someone should consider
this fact in an explicit way. These results run parallel to those obtained by Armstrong (1995)
for a different subset of EU regions and time periods from 1950 to 1992.
Furthermore, the omision of spatial dependence in that equation is not the only source of
erroneous specification. Existence of significative spatial heterogeneity, and so regional
differentiation, could lead to unrepresentative estimation results for the whole sample. Early
cited LISA test, jointly with Moran scatterplot localization criteria, allow us to check for
spatial clusters of high/low values of both variables and their growth rates. In this way we
link heterogenity in our sample to the dimension where the phenomenon is observed, the
territorial space. In per capita GDP, the presence of associations in some regions of a few
countries is appreciated, specially in Germany, Italy, Spain, Portugal and Greece. In concrete,
we detect a concentration of high values in Southern Germany (Stuttgard and Karlsruhe,
spreading to Oberbayern, Mittelfranken and Darmstadt in first nineties) and Northern Italy
(Piamonte, Lombardia and Emilia-Rogmana, extending to Trentino-Alto Adige and Veneto
in last eighties). Geographical proximity of both clusters would be reflecting the positive
effect of economic externalities to density and aglomeration economies. In the other hand,
association of low values in per capita GDP is located in poorest regions of the EU: South
of Spain (Galicia, Asturias, Castilla-León, Castilla-La Mancha, Andalucía, Extremadura and
Murcia), all Portuguese and Greek regions. In eighties also appears a cluster of low values
in the South of Italy (Basilicata and Calabria) even though it seems to disappear at the
beginning of nineties. A similar pattern is detected in productivity. Clusters of low values are
concentrated in Southern Spain, Portugal and South of Italy, appearing also a cluster of low
values in UK at the end of the eighties. On the contrary, we have not detected significant
clusters of high values in this case, beeing Ille de France and Liguria the remarkable
exceptions. It is interesting to point the disappearance of an association of high values in the
Netherlands (Groningen, Friesland and Drenthe) in the second half of eighties. Evolution of
gas prices is the well known decisive of this feature.
When spatial association in growth rates were analysed, two facts were outstanding. First the
existence of a larger number of significative clusters in productivity than in per capita GDP,
and second, clusters of high growth rates in productivity in those regions that concentrated
low values through the eighties (Galicia, Castilla-León, Castilla-La Mancha, Andalucía,
Extremadura, Portugal and Italy except the regions of North West, North East, Lombardia and
Emilia-Romagna). We also detected clusters of low growth rates in productivity in regions
that started with high levels (basically The Netherlands and UK).
Two conclusions could be drawn from the above results. First, no evidence of important
movements in the composition of the detectedhot spotsalong the period would lead to think
in regions having difficulties to leave their cluster of high/low values. That is to say, high
persistence in spatial characterization seems to exist. Secondly, the detection of two
significant concentrations, one of high values in the North and another of low values in the
South. This fact is obvious in per capita GDP yet less clear in productivity. It would arise the
idea of a spatial differentiation in the distribution of this variables among the European
regions. In that sense, QAP test (Anselin, 1986) and the estimation of a Spatial Anova
(Griffith, 1992) enhance the existence of structural inestability within the EU and a Core-
Periphery scheme. As point above, these results should advice of an erroneous specification
in the clasical convergence equation for the whole sample. Even though the conditional
approach mightmitigate the problem, our believe is that hardly it can consider the whole set
of factors and regional links neccesary to get a correct specification.
When the equation was respecified in two regimes in order to introduce this inestability,
results were qualitatively similar to those obtained by Neven and Gouyette (1994):
convergence among poor regions of the South during the first half of the decade and
convergence among Northern rich ones during the second half. Further, in productivity can
be observed convergence to a higher speed all along the period in regions showing larger
levels of productivity. This would mean that best placed regions in South could perform better
than their poorest neighbours, reflecting an important heterogeneity in peripheral areas and
some risk of polarization inside these national economies.
3. Description of regional inequality and its evolution.
When considering the standard deviation of (log) relative per capita GDP (usual measure of
σ convergence) in our sample, the results are well known. Figure 1 shows its stagnation
throughout the period. Other inequality indexs show almost the same, as we can see in the
case of the Atkinson index when we don’t show specific aversion to poverty situations (A0.5).
When we do, however, the results are rather different. The Atkinson index with relative
poverty aversion (A20) shows an increase in the inequality mainly due to the behaviour since
1986. In other words, in spite of a global stagnation, poorest regions would have worsened
their relative situation. In per worker GDP things are not much the same (Figure 2). In this
case all indexs (including A20) show an important and general decrease in the inequalities.
In 1992 the level is around 25% less than in 1981. However the process is not linear during
the period. Until mid-eighties the decrease is not significant, while in the second part of the
decade starts a really impressive reduction.
These results show important differences in convergence process in both variables, and agree
with our hypothesis that the mechanism of integration causes convergence in productivity
levels but not in per capita levels (at least in short and medium term). Another important
feature is that an adjustment mechanism seems to exist in less favoured regions, due to the
fact that they tend to improve their productivity levels, and catch up the medium ones, but
at a cost of less employment and so without improving their per capita levels.
Another important issue is the possible occurrence of a polarization process. This means an
increase in the homogeneity within groups of economies but an increase also in the distance
between groups. Clearly this is a concept related tolocal convergenceor convergence clubs
(see for instance Ben-David, 1994; Chatterji, 1992). The polarization index proposed in
Esteban and Ray (1994) summarizes this process and for our variables it is also plotted in
Figures 1 and 2. In both cases a slight increase in polarization is observed although at the end
of the period we note similar initial levels. The characteristics of this index don’t allow us
to evaluate the absolute level of polarization, thus other tools should be used to detect
convergence clubs in both variables. In any case the index shows no evidence of a deepening
in that process.
A useful technique for analysing the existence of convergence clubs is the estimation of the
density function of the regional distribution of per capita and per worker GDP and the
analysis of its multimodality. Quah (1996a) and Bianchi (1995) show the bimodality of
international income distribution whereas Quah (1996b) obtains no insights of it for a
subsample of regions in the EU in terms of per capita GDP. Figures 3 and 4 plot the
estimated density functions for our variables. The densities were obtained using a gaussian
kernel with bandwidth (hopt) selected by means of (Silverman, 1986: formulae 3.28):
hopt= 1.06σ n-1/5
whereσ is the standard deviation andn the sample size. The distribution of (log) per capita
GDP relative to average EU shows a very similar shape for all years. It is highly concentrated
closed to the average value, even though an important mass of probability is observed at the
right (poor regions). Taking into account that this way of selecting hopt may oversmooth
somewhat if the real distribution is multimodal, we estimated the density with a bandwidth
given by the expression 3.31 in Silverman (1986):
hopt= 0.9 A n-1/5
where A=min(σ, interquartile range/1.34). In this case the bimodality is more evident,
reflecting an important group of regions with levels of per capita GDP below the average and
with a trend, in some way, to converge at a lower level than the rest of the economies2. This
result contradicts the ones in Quah (1996), but it is important to note that our sample
considers relatively poor regions of Portugal and Greece, not considered in that work.
On the other hand, neither are there any significant changes in the external shape of the
distribution in per worker GDP along the period. And, in this case, unimodality seems the
likely assumption. Only a long left tail sheds light on the existence of a small subset of
economies with a level of productivity far below the average (mainly Portuguese and Greek
regions), even thougth their dispersion prevents them from being considered as a club.
In the Spanish provincial case, someone observes similar features for a longer period. In per
capita GVA there are shorter tails in both sides but there also exists some trend to a certain
bimodality. Nevertheless both modes are closer than in the European case, that is to say, the
distance between groups is lower. It should also be noted that a significant probability mass
in the left tail of the distribution vanishs through the period. In labor productivity bimodality
is less likely (specially in most recent years) but again a long left tail is evidence of an
inability to catch up by a small number of low productivity regions.
To that point we have derived the possible existence of bimodality in regional distribution of
per capita GDP in the EU, while unimodality of per worker GDP, in a static way and inside
considered sample. The dynamic consideration of these features and an out-sample
extrapolation (as proposed in Quah, 1996a) will be exposed in the next sections.
4. Which regions are the main actors of inequality and its evolution? The application of
the expanded rank-size function to the convergence analysis.
Any index which summarizes the level of dispersion or inequality in a single figure can not
explain all the characteristics of the analysed distribution. Moreover index time evolution is
not able to show important information about the evolving distribution. In this way, Quah
(1996a) and Leung and Quah (1996) show how any value of the parameter in traditional
convergence regression can be consistent with both cross-section distribution expanding or
collapsing to a point. That means the dynamics of a "representative economy" give no guide
of that to the whole distribution.
On the contrary, the rank-size function (a function which relates the level of the variable in
each region and its position in the ranking) allows us to have a vision of the inequalities
through the whole cross-section. Moreover, the comparison in different time points sheds light
on its evolution. The rank-size function is defined as double-logarithmic (1)lny a bln r
wherey is the variable in descending order andr is the rank assigned to each region in that
order. The presence of a high slope,b in the equation, shows a large gap between two regions
in consecutive ranks, then a high level of inequality. From results in Table 3 two conclusions
may be derived. First, a different behaviour during the eighties: there is a continous decrease
of inequality in productivity meanwhile inequality remains almost constant in per capita GDP.
Secondly, global inequality in first half of eighties was higher in productivity than in per
capita GDP, but since 1987 the order is inversed. Unlike this result confirms the convergence
process in productivity, estimation of global inequality from rank-size function is higher in
the case of productivity during a long period in the sample. However, indexs in section two
showed the contrary. In our opinion this is an example of the sensitivity and inconsistency
of sytemicindexs. In fact, rank-size function for both variables shows highly different levels
of inequality for different kind of regions. In concrete it shows how larger inequality in
productivity was the result of important differences in regions with very low levels,
meanwhile other regions shown closer levels. This facts raise some questions: Can linearity
hypothesis be hold? or Is it possible to accept homogeneity in the slope regardless of the
rank?
Figures 5 and 6 show that in spite of the existence of a linear behaviour at medium ranks, the
slope increases quickly with rank when arriving to higher ranks, mainly in productivity.
Moreover, in some years the slope seems to be bigger in lowest ranks (highest incomes) than
the one in medium ranks. Therefore, it seems necessary to consider this non homogeneous
behaviour of the slope3. An easy and direct way is by means of Casetti’s (1972) expansion
method. That method shows how starting from an initial model like (1), it is possible to
endogenize the slope as a function of other variables, picking up the hop in the slope
depending on the ranks. A direct way of doing this is taking the slope as a function ofr. In
our case, and considering a cubic function ofr for the slope expansion, we obtain:
lny a b0lnr b1r lnr b2r 2lnr b3r 3lnr
Moreover, to take into account temporal evolution of inequality, each parameterbi has been
expanded as a function of a time trend,t. A cubic temporal expansion was selected for per
capita GDP while a quadratic was enough for productivity. For instance, in the former the
final estimated expression was:
In this way, it has been possible to conclude about the contribution of particular ranks (types
lnGDP pc a [3
i 0
bi 0t i3
i 0
bi 1t i r3
i 0
bi 2t i r 23
i 0
bi3 t i r 3] lnr
of regions) to global inequality as well as to its evolution. Results are summarized in Figures
7 to 10, where selected ranks or periods are fixed to observe evolution of inequality along
time or ranks. Regarding to per capita GDP, it can be observed the evolution described in
section 2 for all ranks. In spite of this, it is also clear the larger increase in inequality of
richest regions in the first half of the eighties and their larger decrease in the second half. In
the productivity case, all types of regions contribute to continous convergence, even though
low ranks seems to decrease more their inequality again. On the other hand, differences in
inequality among regions with medium-high levels and lowest levels are extremes.
Same analysis for Spanish regions and a longer time period reveals that regions with high
levels of per capita production had a more important role in the period of convergence until
first eighties and also in the period of stagnation afterwards. In productivity, more productive
regions played also the main role, basically at the beginning of the period.
4. Mobility in regional GDP distribution and convergence.
Whether there is intra-distribution mobility or not is an outstanding fact when we are dealing
with levels of inequality and its dynamics (ie convergence). The conclusions, and political
decisions, should be different depending on whether or not individuals exchange their
positions. In the former case amobility situation exists, and decisions to change structural
economic conditions would not be required (only those that soften cyclical responses would
be). Otherwisepersistencecharacterizes the distribution and those decisions might be justified.
By means of the rank-size function we shed light on the contribution to global inequality of
each region, statically as well as dynamically. Nevertheless, when sorting the regions in each
one of the years the movements in the ranking of each economy have not been taken into
account. That is, we may obtain the same value for the slope (b) in the rank-size function for
different years and the conclusions be different in the case that regions don’t exchange their
position (rank) or in the case they do. For instance, with only two economies, A and B, let’s
suppose that in period t: xAt=100 and xBt=200, and in t+1: xAt+1=200 and xBt+1=100. In both
time periods the inequality parameter in the rank-size function would be the same (as would
any dispersion or inequality measure), but perfect mobility would exists. Circumstances would
be rather different if none exchange were observed (persistence). Therefore, the sort procedure
in the rank-size function inequality analysishidesmovements within the distribution.
The analysis of the rank-size function for each period, but keeping fixed the ranking at the
initial is a way of improving the analysis considering mobility. Figures 11 and 12 show those
functions for selected years in per capita and per worker GDP. In addition to the evolution
of inequality levels exposed above, movements (peaks) in productivity are more outstanding
than in per capita GDP. In the former, they seem to be more important since 1985,
strengthenig the convergence process in this magnitude. In order to have an index of the
amount of movements in the distribution for the whole time period, we compute a mobility
measure from the difference between the rank-size function in last year with the ranking of
that year and the same function but keeping the ranking of the initial year:
wherey0T is the distribution in period T keeping the ranking in period 0,yT
T is the distribution
mi | y T0 y T
T | µ T Mi
mi
pi
pn
in period T with ranking in same period, µT is the value of the variable in the whole of the
economic system (set of EU regions considered) and pi / pn is the relative population in region
i. Figures 13 and 14 plot both functions. The value of this index for per capita GDP is
0.05627, clearly lower than the one for labor productivity (0.1189). Moreover some richest
regions show the most significant movements while in the other side of the distribution,
poorer regions show almost perfect persistence. Movements in productivity, besides being
bigger, contributed to convergence basically due to the behaviour of some high-productivity
regions that decreased their relative levels towards the average and some low-productivity
ones (but not the lowest) that increased their position in the ranking. It is worth insisting in
the high persistence of the small subset of regions with the lowest levels of productivity. In
addition to their contribution to global inequality, they were not able no permute positions
with other regions. This means that if we consider them as alow productivity clubno region
was able to surpass its gravity attraction4.
This graphical mobility analysis may be improved and formalized by means of an
econometric model capable of considering the intra-distribution dynamics (Quah 1993, 1996a,
1996c, 1996d). Amodel of explicit distribution dynamics(medd) has been used in the current
convergence literature. In brief, following for instance Quah (1996a), let Ft be the distribution
across the economies for the analysed variable in time t andλt a probability measure
associated with each Ft. The probability measureλt is defined as
The simplest probability model describing distribution dynamics, considering discrete time,
∀ y∈ ℜ : λt ( ( ∞ ,y] ) Ft (y)
is a first order dependence specification
where ut is a secuence of disturbances and T* is an operator that maps probability measures
(1)λt T (λt 1,ut )
in t-1 and disturbances int to probability measures int. In such a model, the operator T*
collects the richness of the distribution dynamics, thus an estimation of it allow us to quantify
such dynamics. Moreover, setting null values to disturbances and iterating in (1) we obtain
how distribution will evolve in future
and therefore the characteristics of the variable distribution in following periods. Taking
(2)λt k (T T ... T ) λt T s λt
expression (2) to the limit as k→∞ provides the long-run distribution of the analysed cross-
section (given the case that an unique steady state solution does really exist). From this long-
run solution derived from in-sample dynamics someone can infer the characteristics of out-
sample (forecasting) convergence/divergence process. Convergence in our variable involves
a long-run distribution collapsing into a degenerate point mass while dispersion inλt+k (k→∞)
should be view as divergence. Interesting conclusions might be drawn from particular non-
convergence solutions. For instance, multimodal limit distribution should be interpreted as
tendency to stratification in differentconvergence clubs(see Quah’s cited works).
An easy way of working with this model is to makeλt discrete, thus becoming a temporal
sequence of vectors summarizing the probability of belonging to each one of the defined
states. Then T* just become a transition probability matrix, traditional in Markov chains type
of analysis5.
Following this approach, Quah (1996b) derives an unimodal ergodic solution about the mean
in per capita GDP, using a reduced sample of 78 regions that doesn’t include, for instance,
Greeke or Portuguese regions, from 1980 to 1989. Different conclusions are drawn in Larch
(1994) for the longer period 1970-1990 and the EU-9. His results show that high degree of
persistence characterizes the upper (richer) and lower (poorer) intervals and mobility in the
eighties even decreased compared to the seventies. Neven and Gouyette (1994) reach similar
results for the same period and a richer NUTSII sample.
Our previous results showed large differences in the convergence process in terms of per
capita GDP and productivity, including the possibility of twin-peakness in the distribution of
the former. Therefore, we continue with a parallel analysis for both magnitudes, considering
five states6 as the result of the discretization process. In per capita GDP the grid points that
define the states were 75%, 90%, 100% and 115% (in percentatge of average EU value). We
took into account either initially the states included similar number of individuals as they had
similar width (in bounded ones). Table 4 summarizes the results. It is really outstanding the
high persistence of lower state (poorest regions). The probability that a region inside that
group left is insignificant. That fact involves apoverty trapand corroborate our previous
results. Persistence is also evident in the other states, being also important for richest regions.
In fact the movements average the 10% and second eigenvalue of the transition matrix (a
measure of mobility) is fairly closed to unity (0.9796). The ergodic distribution reflects the
poverty trapshowing a high mass in lower state while some convergence to the average is
observe on the part of the rest, mainly due to the loss of probability in highest state in the
long-run solution. This result should confirm the idea of a slow convergence mainly due to
the behaviour of regions with per capita GDP levels not far behind the average and above the
average, but lack of convergence to that levels of the group of poorest regions.
When productivity was considered, grid points were stablished at 75%, 90%, 105% and 120%,
maintaining the same criteria as in per capita case. The results show lower persistence than
in per capita case, although the low-productivity state shows the lowest mobility. The second
eigenvalue equals 0.9222, as a result of lower values in each one of the entries in matrix main
diagonal. An interesting feature deduced from the transition matrix is that once a low-
productivity region had left that level, the probability of going on to higher levels is larger
than the probability of returning to the lower one. This was also the case in per capita GDP
but then, the probability of leaving the less favoured state was so small that the effect
vanished. As a result, the ergodic solution for productivity forecasts probability concentration
in average values. In such a process, dynamics of both low and high productivity regions are
outstanding.
In short, dynamics of the whole distribution displays lower mobility in per capita than in per
worker GDP, and a trend to evolve to bimodality in the former, even though aglobal
convergence process is expected to continue in the later.
Due to the inestability in relative regional growth process in the EU, detected in previous
sections and considered in other works, we repeated the previous analysis for subperiods
1980(1)-1985 and 1985-1992. In per capita GDP similar behaviour is observed for low
income regions in both subperiods while in the upper tail of the distribution the convergence
behaviour showed by above average regions in the early eighties vanished in the second
subperiod. This result agrees with the ones obtained in previous sections, confirming that rich
regions were the mainactors of convergence process during the eighties. In productivity,
again things are rather different. Between 1981 and 1985, low-productivity regions showed
high relative persistence due to higher mobility of about and above average regions. However,
the fact that once a region left the lowest state never returned to it causes that state
desapeared in the long-run solution. In following years, the role of about and above regions
slightly decreased while regions under average level increased their movements. Nevertheless
this fact didn’t imply a strenghten in convergence process observed previously due to the
wrong direction of some of those movements.
When we considered Spanish provincies in isolation for the longer period 1955-1993,
differences in per capita GVA and productivity are also clear. In this case we only defined
three states due the lower number of individuals, with bounds in 75% and 100% of Spanish
average values. In this case persistence is in general lower in both per capita and per worker.
Measured by second eigenvalue, mobility scores 0.8776 and 0.8525 in per capita and per
worker variables. Moreover less favoured regions show higher mobility than others. As a
result ergodic distribution in per capita GVA forecasts higher probability in central state than
in lowest one, but also an important mass in above average state. That is, some tendency to
bimodality even though the distance between eachclub doesn’t seem to be large enough to
worried about a break in future regional production distribution. In productivity, clearest trend
to convergence to unimodality distribution exists.
5. Final remarks and Conclusions
It seems quite clear that production is not randomlly distributed in the EU space yet important
concentrations of high/low relative levels are present. The scheme is highly associated with
the classical Core-Periphery division of the EU. Moreover, no significant changes were
observed in this configuration along the analysed period. However, two facts must be
highlighted. First, this pattern is not so clear in the productivity case, where only spatial
clusters of low productivity levels are detected, but not of significant high ones. In second
place, hot spots of high values in growth rates does not follow the pattern of a North-South
or Core-Periphery of the EU but a somewhatmosaictype of regional growth model. This
spatial analysis also advices of two important facts: significant differences might exist
between inequality and convergence process in per capita GDP and in productivity, and tests
of convergence hypothesis based on growth-initial levels equation that doesn’t consider spatial
dependence and heterogeneity could lead to inconsistent results.
On the other hand our analysis has beneficied from an alternative and richer approach,
recently developed in the literature with the aim to study the dynamics of the whole regional
distribution. In this sense some interesting facts have been looked out. For instance,
significant differences in the degree of inequality seems to exist for different type of regions.
Moreover, their contribution to global dynamics is also different. Related to the existence of
convergence clubs at a regional EU level, there could be some signal of two clubs in per
capita GDP even though high heterogeneity within poor regions seems to be the main factor
that would lead to reject such hypothesis. Further statistical analysis will be required to
confirm that fact. Nevertheless, clear sign of apoverty traphas been detected. That means
the existence of a group of really poor and low productivity regions with a small probability
of leaving that situation. Duality in the behaviour of peripheral regions is another possibility
derived from the results. Some clusters of high growth has been observed in some less
developed areas of the EU, but this process is far from beeing the case in all peripheral
regions.
The analysis of both per capita and per worker GDP has allowed us to detect important
differences in their convergence process. The fast and continous convergence observed in
productivity has not equivalence in living standards measured by per capita GDP. The process
of economic integration in the EU would have provoked an equalization of productivity
among firms and, at an aggregate level among regions, as a result of the need to achieve a
common standards of competitiveness. However, in a framework of liberarization and free
trade, firms that were not able to achieve those standards were expulsed from the market. As
a result, weak economies of poor regions would have suffered higher desequilibria in their
labour markets. Whether regional availability of attracting and holding new activities did not
equilibrate that fact, it can be view as a possible explanation of the observed convergence in
productivity but not in living standards. It is also important to note that regional policy at an
EU level (projects of infrastructure dotation, human capital investment, ...) might have a direct
effect over productivity of labour but unless they really improved attractiveness of less
developed regions to economic activity, its effects over per inhabitant GDP are less obvious,
mainly in short-medium term. On the other hand, we must keep in mind that large
interregional migration flows are neither expected nor politically promoted. Moreover,
changes in EU labour markets might favour skilled labour movements that in a long-term
view could have undesirables consequences on convergence. In this sense, movements of
firms to poor regions could offer an alternative to migration as a way to improve their relative
situation (Begg 1995). In this sense, several studies reveals that in spite of Objective 1 regions
beeing net inflows of foreign direct investments, little evidence exists that this investment is
deterred by higher labour costs in Northern regions. Furthermore, it is important to keep in
mind that foreign direct investments tend to concentrate in most favoured regions of poor
countries or areas (as for instance in Catalonia or Madrid in the Spanish case).
It is important to note that regional productivity was not ajusted by partial time employment,
thus differencies in the ratio full-partial employment among regions would have effect on
disparities in that magnitude. Results might also change ifblack economywas in any way
considered as well as changes in the official definition of regions through the analysed period.
Moreover, some possibilities demand a deeper study. For example, García-Milà and Marimon
(1995) conclude that convergence in productivity is only observed among Spanish regions in
semi-public sectors, while non significant convergence is observe in productivity for private
sectors. Thus direct effect of, for instance, regional policy might becontaminingaggregate
results. In any case, an obvious conclusion is that regional convergence is not a simple
process and if someone tries to aproximate the phenomena by means of only a magnitude, a
deformedand uncomplete picture can be obtained. The simultaneous analysis of different
magnitudes seems to be the logical approach.
Acknowledgements
E. López-Bazo gratefully acknowledges finantial support by Commission of the European
Communities, research training grant TMR ERB4001GT951646, while working as a research
fellow at the European Institute, London School of Economics. Authors like to thanks usefull
comments by Prof. R. Leonardi and computational help from Ernest Pons.
Notes
1. Lack of employed population for most Greek regions made not possible consider them inthe analysis in term of GDP per worker.
2. It would be interesting to perform multimodality tests as suggested by Bianchi (1995) toset the likelihood of bimodality in our distribution.
3. It should be note that the shape of the function may shed light on the presence ofconvergence clubs. For example, a S-shape function would be due to low inequality amongrich regions and among poor regions yet large inequality between each group. Obviously, alinear function should be interpreted as no evidence of groups of regions homogeneousenough to become a club.
4. In fact this circumstance belongs to the definition ofconvergence club.
5. Discretization involves loss of information in some degree and innapropiate intervals mightlead to a process with no Markov property. Nevertheless, one suppose this will not hide therelevant features for our analysis, as point out in Quah (1996d)
6. Due to the fact that results might be sensitive to the discretization process (ie number ofstates) we also performed the analysis with a higher and lower number of states. Althoughthe figures obviously changed, main results were quiet robust.
References
Abraham F, Van Rompuy P (1995) Regional convergence in the European Monetary Union
Papers in Regional Science74 2 125-142
Anselin L (1995) Local indicators of spatial association-LISAGeographical Analysis27 (2)
93-115
Armstrong H W (1995) Cross-sectional analysis of the regional growth process In Armstrong
and Vickerman (eds)Convergence and Divergence among European RegionsPion Ltd
London
Baumol W J (1986) Productivity growth, convergence and welfare: what the long run data
showAmerican Economic Review76 1075-1085
Barro R J, Sala-i-Martin, X (1991) Convergence across states and regionsBrookings Papers
on Economic Activity1 107-182
Begg I (1995) Factor mobility and regional disparities in the European UnionOxford Review
of Economic Policy11 (2) 96-112
Ben-David, D (1994) Convergence clubs and diverging economiesCEPR Discussion Paper
Series922 London
Bianchi M (1995) Testing for convergence: evidence from nonparametric multimodality tests
Working Paper Bank of England
Casetti E (1972) Generating models by the expansion method: applications to geographical
researchGeographical Analisys4
CEC (1994)Competitiveness and Cohesion: Trends in the Regions. Fifth Periodic Report on
the Social and Economic Situation and Development of the Regions in the Community
Luxembourg
Dolado J J, Gonzalez-Paramo J M, Roldan J M (1994) Convergencia economica entre las
provincias espanyolas: evidencia empirica (1955-1989)Moneda y Credito198 81-119
Esteban J (1994) La desigualdad interregional en Europa y en Espana: descripcion y analisis
In Crecimiento y Convergencia Regional en Espana y Europavol. 2 IAE Barcelona
García-Milà T, Marimon R (1995) Integración regional e inversión pública en España In
Marimon R (ed)La Economía Española: una visión diferenteA. Bosch Barcelona
Larch M (1994) Regional cross-section growth dynamics in the European Community
European Institute Working PaperLSE London
Leonardi R (1995)Convergence, Cohesion and Integration in the European UnionMacMillan
Press Ltd London
Leung Ch L, Quah D T (1996) Convergence, endogenous growth and productivity
disturbancesCEP Discussion Paper290 April
Mas M, Perez F, Uriel E, Maudos, J (1995) Growth and convergence in the Spanish
provincies In Armstrong and Vickerman (eds)Convergence and Divergence among European
RegionsPion Limited London
Molle W, Boeckhout S (1995) Economic disparity under conditions of integration-A long term
view of the European casePapers in Regional Science74 2 105-123
Neven D J, Gouyette C (1994) Regional convergence in the European CommunityCEPR
Discussion Paper Series914 London
Quah D T (1996a) Convergence as distribution dynamics (with or without growth)LSE
Economics DepartmentApril
Quah D T (1996b) Regional convergence clusters across EuropeEuropean Economic Review
40 forthcoming
Quah D T (1996c) Convergence empirics across economies with (some) capital mobility
Journal of Economic Growth1 95-124
Quah D T (1996d) Empirics for economic growth and convergenceEuropean Economic
Review40 forthcoming
Quah D T (1993) Empirical cross-section dynamics in economic growthEuropean Economic
Review37 2/3 426-434
Silverman B W (1986)Density Estimation for Statistics and Data AnalysisChapman & Hall
London
Figure 1 σ-convergence, Atkinson with low (0.5)and high (20) poverty aversion and Polarizationindexs for per capita GDP. (% of initial year)
Figure 2 σ-convergence, Atkinson with low (0.5)and high (20) poverty aversion and Polarizationindexs for per worker GDP. (% of initial year)
Figure 3 Estimated density function, pc GDP. Figure 4 Estimated density function, pw GDP.
Figure 5 Rank-size function, pc GDP Figure 6 Rank-size function, productivity
Figure 7 Inequality at selected ranks, pc GDP Figure 8 Inequality at selected years, pc GDP
Figure 9 Inequality at selected ranks, productivity Figure 10 Inequality at selected years, productivity
Figure 11 Rank-Size functions with fixed rankingat initial year, pc GDP. Advancing upwards 1980,1985, 1992
Figure 12 Rank-Size functions with fixed rankingat initial year, pw GDP. Advancing upwards 1981,1985, 1992
Figure 13 Mobility in pc GDP distribution, 1980-92
Figure 14 Mobility in pw GDP distribution, 1981-92
Table 1. Global autocorrelation spatial statistics
Per capita GDP Productivity
1981 1985 1992 1981-92 1981 1985 1992 1981-92
Moran’s I
Geary’s C
Getis’ G
7.45
-6.69
3.00
6.98
-6.20
2.62
8.40
-7.74
3.26
3.16
-3.80
-0.12*
7.87
-5.72
2.71
6.74
-4.90
2.06
7.77
-7.09
2.66
11.01
-10.61
0.72*
Note: * non significant at 5%
Table 2. Results of the spatial dependence tests applied to the unconditional convergence equation
(1) Per Capita GDP (2) Productivity
Constant 0.1226 (p:0.000000) 0.1650 (p:0.000000)
β -0.0064 (p:0.010135) -0.0341 (p:0.000000)
Moran’s I (error) 3.7055 (p:0.000211) 9.8473 (p:0.000000)
Lagrange Multiplier (error) 11.7976 (p:0.000593) 88.0376 (p:0.000000)
Robust LM (error) 5.0820 (p:0.024174) 15.9664 (p:0.000064)
Kelejian-Robinson (error) 8.2582 (p:0.016097) 71.2202 (p:0.000000)
Lagrange Multiplier (lag) 9.6403 (p:0.001904) 73.8671 (p:0.000000)
Robust LM (lag) 2.9247 (p:0.087231) 1.7960 (p:0.180188)
Lagrange Multiplier (SARMA) 14.7223 (p:0.000635) 89.83337 (p:0.000000)
Note: Probability in parentheses.
Table 3. Levels of inequality from the rank-size function
GDP pc GDP pw
1981 -0.2766 -0.2935
1985 -0.2791 -0.2822
1987 -0.2645 -0.2704
1989 -0.2558 -0.2395
1992 -0.2638 -0.2293
Table 4. Results of distribution dynamics (markov chains approach).
Per Capita GDP Per Worker GDP
1980-1992
grid: (0, 75%, 90%, 100%, 115%, ∞)
initial: (0.223 0.167 0.188 0.195 0.223)
ergodic: (0.305 0.187 0.222 0.176 0.108)
0.980 0.019 0 0 00.032 0.862 0.105 0 00 0.086 0.856 0.056 00 0 0.069 0.877 0.0530 0.003 0 0.083 0.913
2on eigenvalue: 0.9796
1981-1992
grid: (0, 75%, 90%, 105%, 120%,∞)
initial: (0.201 0.155 0.224 0.255 0.162)
ergodic: (0.097 0.188 0.321 0.273 0.119)
0.839 0.160 0 0 00.082 0.760 0.157 0 00 0.089 0.804 0.103 0.0020 0.002 0.120 0.794 0.0820 0 0.005 0.189 0.804
2on eigenvalue: 0.9222
1980-1985
ergodic: (0.363 0.183 0.247 0.134 0.070)
0.981 0.018 0 0 00.036 0.845 0.118 0 00 0.087 0.851 0.060 00 0 0.111 0.828 0.0590 0 0 0.112 0.887
2on eigenvalue: 0.9777
1981-1985
ergodic: (0 0.242 0.355 0.292 0.026)
0.863 0.136 0 0 00 0.828 0.171 0 00 0.117 0.723 0.148 0.0100 0 0.193 0.724 0.0810 0 0 0.254 0.745
2on eigenvalue: 0.8693
1985-1992
ergodic: (0.247 0.172 0.181 0.227 0.171)
0.978 0.021 0 0 00.030 0.873 0.096 0 00 0.085 0.859 0.054 00 0 0.038 0.912 0.0480 0.005 0 0.058 0.935
2on eigenvalue: 0.9816
1985-1992
ergodic: (0.113 0.169 0.309 0.272 0.134)
0.826 0.173 0 0 00.116 0.732 0.151 0 00 0.079 0.833 0.086 00 0.004 0.090 0.823 0.0820 0 0.008 0.158 0.833
2on eigenvalue: 0.9344
