Business Cycle Synchronization across regions in the EU12:
a structural-Dynamic Factor Approach
Francesca Marino
University of Bari (Italy)
May 2, 2013
Abstract
This work studies regional cycle synchronization in the EU12 looking at regional Gross
Domestic Product (GDP) and Employment dynamics over the period 1977-95. The econometric
framework is a generalization of the Dynamic Factor Model by Forni and Reichlin (2001), and
each regional variable is decomposed into three orthogonal components, driven by european,
national and local shocks. The contribution of our work is twicefold: on the one hand, we
improve on the original model, introducing a structural analysis and estimating the regional
Impulse Response Functions to the common shocks; on the other hand, respect to the European
literature on regional synchronization, we focus on two key variables at once and keep track of
the identity of each region in the evaluation of synchronization. The main results show greater
synchronization of regions in terms of GDP than in terms of Employment dynamics, and the
possibility of within-country di¤erent behaviors, due also to a general minor role played by
the national-speci…c components. Finally, groups of more and less integrated regions do not
appear as homogeneous blocks, according to general criteria like income, geography or economic
structure; especially for Italy, this evidence seems to con…rm the existence of Many Mezzogiorni
(Viesti, 2000).
1
Introduction
The business cycle literature o¤ers a well developed set of tools, known as Dynamic Stochastic Generalized Equilibrium (DSGE) models, usually exploited in a single-economy framework to
study business cycles. These models have strong microeconomic foundations and are theoretically
motivated using consumers’optimization programs, at the expense of a certain degree of ‡exibility
in the speci…cation, in particular when the number of cross-section units and variables of interest
is high. In this perspective, Structural Dynamic Factor Models (S-DFMs) probably represent the
most popular and successful available alternative. Indeed, these models are able to extrapolate
the common sources of ‡uctuations from a potentially large set of variables of interest, and when
the focus is on many countries (or other geographic units) at once, individual responses to these
common drivers can be used to investigate the issue of business cycle synchronization.
Corresponding author: [email protected]
1
In the light of this premise, this work estimates a S-DFM using regional data on Gross Domestic
Product (GDP) and Employment of 107 European regions, observed at NUTS1 and NUTS2 level
of disaggregation in nine EU12 countries over the period 1977-1995. The econometric framework is
a generalization of the regional DFM proposed by Forni and Reichlin (2001), where each regional
variable can be decomposed into three orthogonal components, respectively driven by a set of
european, national and local shocks. Respect to the original model, here we propose an extension to
the multivariate framework, focusing on two key macroeconomic variables at once, thus enriching
the discussion with a structural analysis of the shocks, as in Forni and Reichlin (1998). This
represents the main methodological innovation of this work. Moreover, the selection of these two
speci…c variables is motivated by the relevance their joint dynamics have for policy evaluations:
indeed, common patterns of GDP growth are as important as employment ones in order to evaluate
and coordinate the European integration programs, as it is clear reading the reports on regional
cohesion, published by the European Commission since 1996.
Our purpose is exploiting the useful properties of this class of models, in particular their ability
to deal with a large cross-section dimension, in order to assess the degree of regional synchronization
in Europe. In respect of this, we propose a measure of synchronization involving two complementary dimensions: the degree of variability each regional variable owes to the european shocks, i.e.
the variance of the european component, and the regional responses to the identi…ed shock, here
selected among the main positive drivers of GDP growth. Indeed, the former is an indicator of the
probability for each region to be a¤ected by the common shocks, i.e. a rough measure of integration
across regions. Provided that this probability is su¢ ciently high, the sign and the intensity of responses, assessed respect to a benchmark like the average european response, give complementary
information on regional comovements. In this fashion, synchronized regions show high variance of
the european component and responses in line with the european average. To some extent, this is
the synthesis between the shock accounting approach (e.g., Clark and Shin, 2000), which measures
synchronization as high variance of common components, and the impulse response function approach, used in S-DFMs to study the interrelations of economic variables in terms of reactions to
common shocks. Indeed, high variance of the common components does not necessarily imply that
the series are comoving, since it may happen that the correlation (i.e., the sign of the response)
between two variables is negative (Forni and Reichlin, 2001).
The measures of synchronization generally exploited to assess the degree of comovements of
cycles are mainly based on correlation measures, including simple (Pearson) correlation coe¢ cients
of the cyclical part of the series, generally obtained using …lters like the Hodrick-Prescott1 (1997),
or more complex measures like dynamic correlation (Croux et al., 2001) and the concordance index (Harding and Pagan, 2002).2 An exhaustive review of all the existing approaches and their
1 The Hodrick-Prescott (HP) …lter separates the cyclical component (c ) of a time series from the trend (g ) in
t
t
the data. In practice, given the decomposition of the logarithm of a variable yt
log (yt ) = gt + ct
the …lter estimates gt and ct minimizing
X
c2t +
Xh
(1
L)2 gt
i2
where is a parameter determining the importance of having a smoothly evolving gt (see, for instance, Dejong and
Dave (2007).
2 The dynamic correlation measure by Croux et al. (2001) is the co-spectrum between two series over the product
of the spectra of each series, de…ned over a certain frequency band. Note that the spectrum is the decomposition of
2
di¤erences is beyond our purposes. However, it worth remarking that here we follow the shock
accounting approach, because it has the advantage of …ltering only the relevant sources of ‡uctuations, i.e. those due to common factors, and netting out the non common components (de Haan et
al., 2005). Moreover, and di¤erently from the correlation measures, shocks and impulse response
functions may have a structural interpretation.
Regional cycle synchronization is a …eld of study where little has been written about Europe,
so far. However, the shortage of empirical works on this topic is not the only reason motivating our
analysis. Indeed, the approach here exploited improves on the existing literature on regional cycle
synchronization along several dimensions.
On the one hand, this literature typically analyses the dynamics of either GDP (Barrios et al.,
2003) or employment (Fatàs, 1997; Belke and Heine, 2006) across the European regions, while only
few works (e.g., De Grauwe and Vanhaverbeke, 1993; Clark and van Wincoop, 2001) deal with both
these two variables at the same time. Moreover, the bulk of the existing approaches are mainly
interested in studying the determinants of higher or lower synchronization: to this purpose, they
regress a measure of synchronization, generally the pairwise correlation coe¢ cients of the …ltered
series with a proxy of the european cycle, on those factors whose sign of impact is to be investigated.
For instance, Barrios et al. (2003) regress the pairwise correlation coe¢ cients between GDP growth
rates in the UK regions and six euro-zone countries on, among others, an indicator of industrial
dissimilarity. Tondl and Traistaru-Siedschlag (2006) investigate the relation between the correlation
of GDP growth with the Euro area and regional trade integration, specialization and exchange
rates. As a result, these approaches tend to neglect other issues, like speci…c cross-country and
within-country patterns of synchronization. Even those works comparing within and cross-country
regional correlation evaluate synchronization using average measures, like the mean of the standard
deviations of the regional growth rates of GDP and employment (De Grauwe and Vahaverbeke,
1993) or the average of the correlation coe¢ cients between regional Gross Value Added and the
Euro area cycle (Montoya and de Haan, 2007).
In our S-DFM, instead, we have decided to keep track of the identity of each region, estimating
the responses to common shocks, region by region, and making direct comparisons among all the
cross section units –both across and within countries –possible. This gives us the chance to observe
if similarities and di¤erences in regional responses and variance decompositions are driven by factors
like geography. For instance, if reactions are more similar for regions belonging to a speci…c group
of countries, one could ideally split Europe into high and low synchronized countries, suggesting
that national dimensions should matter in the European stabilization policy. If marked di¤erences
are observed inside the single countries and for instance a common pattern of synchronization is
observed only for weak or rich regions in each country, this would suggest that regional stabilization
policies are instead needed.
Following the lines of this introduction, this chapter is organized as follows. Paragraph 1.2
reviews the literature in the structural dynamic factor domain, with a focus on the evolution of the
two distinct literatures embodied in it. Paragraph 1.3 describes the methodology for the estimation
of the model. The empirical application and the comments on the results are the object of paragraph
1.4. Paragraph 1.5 provides some …nal remarks and concludes. Graphs and further material not
included in the core of the chapter can be found in Appendix 1.
the variance of a variable by frequency, while the co-spectrum is counterpart of the covariance between two variables,
decomposed by frequencies. The concordance index by Harding and Pagan (2002) is a measure of the percentage of
the time two series are in the same phase of the business cycle, given a binary indicator variable for expansions and
recessions.
3
2
Literature Review
Structural Dynamic Factor Models (S-DFMs) result from a combination of factor analysis and
structural VARs, two independent econometric techniques for almost twenty years.
In standard Factor Analysis, factors (or indexes) are statistical constructs that explain the
variance of the variables in a large dataset with the aim of reducing its cross-section dimension with
as little loss of information as possible. Dynamic Factor Models (DFMs) represent an extension of
this approach to the time series domain, going back to two pioneer works by Geweek (1977) and
Sargent and Sims (1977). The basic intuition is that the movements of a set of observed time series
can be explained by a small number of unobserved common factors. Variables can be accordingly
decomposed into a common component, accounted for by these factors, and an idiosyncratic part,
speci…c for each variable.
When the correlation of the idiosyncratic components across the observations is ruled out,
the corresponding model is said exact; when some form of cross-correlation in the idosyncratic
components is introduced (Stock and Watson, 1998; 2002; Forni et al., 2000), the resulting DFM is
said approximate.3
In the approximate DFM, however, only a limited amount of cross-section correlation among
the idiosyncratic components is admitted in order to preserve the asymptotic properties of the
corresponding estimators (Bai and Ng, 2002). As a consequence, the hypothesis structure of the
approximate DFMs could be too restrictive in some speci…c cases, like regional or sectoral analysis.
For this reason, Forni and Reichlin (2001) introduce a variation on the standard decomposition of
the variables: here, along with the usual common and idiosyncratic components, an intermediate
component is identi…ed as the one common to a subset of observations only.4 This is one of the
earliest examples of what has been recently called hierarchical structure in factor models.5
DFMs have been mainly used for forecast purposes (Stock and Watson, 1998; 2002) and for the
construction of indexes, like the euroCOIN, proposed for the Euro Area by Altissimo et al. (2001).
The main limit of these applications, however, is that they are able to extract only statistical objects
–the common factors –which have no immediate economic interpretation.
The second ingredient of S-DFM is derived from the Structural Vectorial Autoregressions (SVAR)
literature. A SVAR is a structural model – a system of equations describing the behaviour and
interconnections of a set of macroeconomic variables driven by structural shocks 6 –put into a VAR
form. Their usefulness for business cycle analysis and policy implications became clear after Sims’s
contributions (1980; 1986), whose main intuition was recognizing that the e¤ects of interventions,
like policy actions or changes in the economy, could be predicted recovering the structural shocks
out of the residuals of the corresponding reduced-form VAR. In practice, by inverting the VAR representation, one obtains a Moving Average (MA) of the variables in terms of the VAR fundamental
innovations. Since structural shocks are a linear combination of these residuals, economically motivated restrictions are needed in order to identify them and their e¤ects on the objective variables.
3 The
approach by Stock and Watson is based on a variance decomposition technique, known as Principal Component Analysis (PCA), while the one by Forni et al. is based on the Dynamic Principal Component Analysis – an
extension of the standard PCA to the frequency domain due to Brillinger (1981). In practice, while the former does
not properly discriminate between static and dynamic factors, considering the lags of the dynamic factors as further
static ones, the latter keeps them distinguished.
4 More technical details shall be provided in next paragraph.
5 We will return to hierarchical models in the end of the following paragraph. We will also discuss the asymptotic
relation between our three-level factor model and the approximate DFM.
6 In structural models, each variable can be explained by its lags and/or the present and lagged values of the other
variables, and the speci…cation is derived from macroeconomic theory. See Hamilton (1994), chapt.11.
4
Justifying the nature of the restrictions on the VAR residuals is the most controversial7 part of
the SVAR literature.8 The main limit of SVARs, however, concerns the problem of non fundamentalness or non invertibility, highlighted by Lippi and Reichlin (1994), among others. This arises
when the number of variables in the VAR is insu¢ cient in order to recover the structural shocks
out of the VAR residuals.9 This is one reason leading to the succeeding development of S-DFMs.
The structural dynamic factor approach, indeed, relies on the idea that structural analysis
should not be performed on the variables per se, but rather on some synthetic indicator of their
dynamics. In Forni and Reichlin (1998), for instance, these indicators are the cross-section averages
of the variables. They use a large dataset consisting of US sectoral observations on industrial
productivity and output, modelled as a classic DFM, and aggregate these two variables across
sectors. After showing that these aggregates are linear combinations of the common shocks, they
estimate a VAR with the aggregates and a structural analysis is performed on these reduced form
VAR residuals in order to identify the common shocks.10 In other S-DFMs – e.g., Sala (2001),
Giannone et al. (2002), Forni et al. (2003), Eickmeier (2004), Forni et al. (2009) –the estimates of
the common factors are used instead of the original variables. As pointed out by Stock and Watson
(2005), in the context of structural DFMs the number of variables is su¢ ciently large to make non
fundamentalness a generic problem.11
A last thing worth noting here is that most of the structural DFMs focus on US variables, while
European studies are rather rare – Sala or Eickmeier, cited above, are two examples. To the best
of my knowledge, no regional structural analysis for Europe is currently available.
3
Model and Methodology
The model is a generalization to the M variables-M shocks framework of the simple one variable-one
shock dynamic factor model described in Forni and Reichlin (2001). In their paper, a generic zeroj
mean, stationary variable xij
t , observed in region i, country j, time t, for j = 1; :::J; i = 1; :::I ; t =
1; :::T , can be written as function of a European (or common), National (or intermediate) and
Local (or idiosyncratic) shock, respectively denoted by et , njt and ltij , such that
j
ij
ij
ij
ij
xij
t = a (L)et + b (L)nt + c (L)lt
aij (L), bij (L)and cij (L) are rational functions in the lag operator (L), whose order of lags is not
speci…ed. et , njt and ltij are unit-variance white noises, orthogonal at all leads and lags.
Respect to the original model, here we propose to consider M variables xij
mt , observed at time t
for a generic region i in country j, with m = 1; :::M ; j = 1; :::J; i = 1; :::I j ; t = 1; :::T . As before,
each xij
mt is a zero mean, stationary variable, and can be decomposed into a European, National and
Local component. However, now these components are driven respectively by a vector of European,
National and Local factors, and the model can be speci…ed as
7 See,
for instance, Faust and Leeper (1997) and Cooley and Dwyer (1998).
(1986), for instance, recurs to the Wold causal chain identi…cation scheme, known as triangular identi…cation
scheme, which consists of orthogonalizing the residuals and assuming that the coe¢ cient matrix of the time-t variables
is lower triangular; Blanchard and Quah (1989) impose long run neutrality of a demand shock on output growth,
following Fischer’s (1977) nominal wage contracting theory. Blanchard and Diamond (1989; 1990) impose sign
restrictions on the structural parameters.
9 We will return to fundamentalness in paragraph 1.3.6.
1 0 More precise details will be provided in next paragraph.
1 1 See, for instance, Forni et al. (2009) and Alessi et al. (2011).
8 Sims
5
ij
ij
ij
ij
ij
0
0 j
ij
0 ij
xij
mt = ECmt + N Cmt + LCmt = am (L) et + bm (L) nt + cm (L) lt
et , njt
(1)
lij
t
Now,
and
are M 1 vectors of unobserved white noises, with zero mean and identity
ij
ij
covariance matrix, mutually uncorrelated at all leads and lags; similarly, aij
m (L), bm (L) and cm (L)
are M 1 vectors of rational functions in the lag operator (L), here assumed of in…nite order
ij
ij
ij
and square-summable.12 Note that ECmt
, N Cmt
and LCmt
are orthogonal by assumption, since
driven by orthogonal shocks, and the variance of each variable, which is …nite by the stationarity
assumption, can be decomposed into the contribution of the (…nite) variance of each component,
ij
ij
ij
var xij
mt = var ECmt + var N Cmt + var LCmt
Finally, note that the nature of the shocks depends on their e¤ects and not on their origin: for
instance, a shock coming from a speci…c country but having e¤ects on all the regions in Europe
should be interpreted as European, and not as National ; in this, we stick to the original model.
Moreover, the extension to the M -dimension framework does not change the basic ideas behind the
estimation methods described in Forni and Reichlin (2001). However, dealing with more variables
at once enriches the discussion, requiring a structural analysis for the identi…cation of the shocks.
For all these reasons, the description of the methodology follows the main structure of the original
paper. Our contribution consists of adapting Forni and Reichlin’s notation to the multivariate case
and adding the structural analysis (par.1.3.4) and the estimation of the impulse response functions
(par.1.3.5) to the original theoretical structure. The resulting methodology is a combination of
Forni and Reichlin’s (2001) dynamic factor model with Forni and Reichlin’s (1998) S-DFM, which
as we shall see, shares the same intuitions as Forni and Reichlin (2001) to proxy the unobservable
factors.
3.1
Estimation
The …rst stage of the model estimation consists of decomposing the regional variables into the
European, National and Local components. The procedure employed for this purpose is the same
as in Forni and Reichlin’s (2001) work, and is based on the implications of the Weak Law of Large
Numbers (WLLN).13
The general underlying idea is that we need a proxy for the unobserved factors that could be
employed as regressor in equation (1.1). These proxies are the M J national aggregates, obtained by
averaging the M variables xij
mt , m = 1; :::M , across regions for all countries J, and the M European
aggregates, given by the average of the J national aggregates across countries, for each variable.
Indeed, for the WLLN, Forni and Reichlin (1998) show that in these aggregates the non-common
1 2 An
in…nite sequence of constants
h,
h = 1; :::1, is said square-summable if
1
X
(
2
h)
h=0
<1
1 3 In its simplest version, the Weak Law of Large Numbers states that the sample average (X ) of a sequence of
n
independent and identically distributed (i.i.d ) random variables, Xi , i = 1; :::N , with common expected value ( )
converges in probability to this expected value when N ! 1:
p
Xn !
6
components14 asymptotically disappear when J and I j are su¢ ciently large. In this way, since
these aggregates are linear combinations of the underlying common shocks, they can be used as
regressors in (1.1) and the model could be estimated by simple Ordinary Least Squares (OLS),
equation by equation.
The formalization of this intuition and the exact steps in order to obtain the variable decompositions are the object of the two following paragraphs, while the second stage of the model estimation,
i.e. the estimation of the parameters in (1.1), is the object of a separate section after the description
of the structural analysis.
3.2
Optimal aggregation
Aggregation is the starting point of the entire analysis, so let us describe the underlying intuition
more formally. For simplicity, let us consider only one variable observed across regions belonging to
the same generic country j, so we suppress for a while the subsctipt m, and equation (1.1) becomes
ij
ij
ij
ij
ij
xij
t = ECt + N Ct + LCt = CCt + LCt
(2)
CCtij
where
is the component driven by the factors common to all the regions i belonging to the
same nation j. Since determined by orthogonal shocks, CCtij and LCtij are not correlated and it is
easy to show that, averaging across i, the local component disappears when the number of regions
is su¢ ciently large.
More formally, let us consider the simple mean of the variable xij
t across i:
xjt
=
Ij
i
1 X h ij
a (L)0 et + bij (L)0 njt + cij (L)0 lij
=
t
j
I i=1
j
j
aj (L)0 et + b (L)0 njt +
I
1 X ij
j
j
c (L)0 lij
t = CC t + LC t
I j i=1
(3)
For the WLLN, the last term in (1.3), i.e. the simple mean of LCtij , is asymptotically zero,15
and as a consequence, last equation can be rewritten as
xjt
j
aj (L)0 et + b (L)0 njt
implying that each National aggregate is a linear function of the European shocks et and of the
shocks speci…c for that nation, njt .
Similarly, while averaging these J National aggregates across countries for the same variable,
the non-common component asymptotically disappears and the resulting European aggregate can
be expressed as a linear combination of the European shocks only:
xt
a(L)0 et
1 4 i.e.,
the local component in the national aggregates and the national component in the European one.
WLLN applies to the Local Components LCtij , i = 1; :::I j , since they are sequences of independent random
variables across i (since driven by the orthogonal local shocks ) with same (zero) mean and heterogeneous …nite
variances.
1 5 The
7
PJ
PJ
where xt = J 1 j=1 xjt and a(L)0 = J 1 j=1 aj (L)0 .
Exactly the same conclusions can be drawn if we consider a weighted, rather than a simple,
average when aggregating across i (i.e., regions), and then across j (i.e., countries). This means
that we have a potentially in…nite number of aggregates to be used as regressors in (1.1). Among
them, however, Forni and Reichlin (2001) identify the most e¢ cient ones as those minimizing the
share of the total variance of each aggregate explained by the non-common component. These
aggregates – and the corresponding set of weights – are said e¢ cient since for them the speed of
convergence to a zero-ratio of the variance of the non-common component to the variance of the
common one is maximized. Provided that the cross section dimension is usually not high for regional
data and that the estimation procedure is based on the asymptotic results illustrated above, the
problem of …nding these optimal weights is not marginal.
Let us focus again on equation (1.2); for a generic j, let us collect the idiosyncratic components
LCtij and the Common components CCtij in two separate I j 1 vectors, respectively
Ljt = LCt1j ; LCt2j ; ::: LCtI
whose covariance matrix is the I j
I j matrix
j
j
j
0
, and
C jt = CCt1j ; CCt2j ; ::: CCtI
j
j
0
Similarly, the variables observed across regions in nation j are stocked in a I j
2j
I
X jt = x1j
t ; xt ; ::: xt
j
1 vector
0
j
j
with I j I j covariance matrix
.
0
j
j
Let us also de…ne a I
1 vector of weights, wj = w1j ; w2j ; :::wI j , used to compute the
national average,
xjt = wj0 X jt = wj0 C jt + wj0 Ljt
Since common and local components are mutually orthogonal, we can decompose the variance
of this aggregate into the sum of the variance of the Common and the Idiosyncratic components:
var wj0 X jt = var wj0 C jt + var wj0 Ljt
Among all the possible weights, we need to select those that minimize the size of the Local
component respect to that of the Common one, i.e. we need to …nd a vector wj such that the ratio
of the variance of the non-common component to the total one,
var wj0 Ljt
wj0
wj0
var wj0 X jt
j
wj
j j
w
(4)
is minimized. Using logarithms, minimizing (1.4) is equivalent to maximize
log wj0
j
wj
log wj0
respect to wj .
8
j
wj
(5)
The solution of this optimization problem is given by wj satisfying the First Order Condition
(FOC)
Assuming
j
1
1
2 j wj
2
wj0 j wj
wj0 j wj
invertible, the FOC can be written as
j
1
j
wj0
wj0
wj =
j
wj = 0
(6)
j
wj j
w
j j
w
or equivalently,
j
1
j
wj =
j
wj
(7)
where
wj0 j wj
(8)
wj0 j wj
Note that j is a scalar corresponding to the reciprocal of the objective function, i.e. the
ratio of the overall variance of the aggregate to the variance of the local component surviving the
aggregation.
Written in this fashion, the FOC simply states that:
j
=
a. the couple ( j , wj ) satisfying (1.7) is given by a couple eigenvalue-eigenvector obtained from
j 1 j
the eigenvalue-eigenvector decomposition of the matrix
, that is the ratio of the
j
j
covariance matrix of X t to the covariance matrix of Lt ;
b.
j
is constrained to be equal to the reciprocal of the objective function evaluated at the
optimum wj .
This solution is unique and wj is given by the eigenvector corresponding to the maximum
1
1
j
j
eigenvalue of j
, i.e. the principal component of j
. Note also that, from (b), the
j
reciprocal of
estimates the share of the variance of the idiosyncratic component remaining in the
aggregate, i.e. surviving the aggregation, and can be used as a check on the quality of aggregation.
At this point, before moving to the succeeding stage, few …nal remarks are required. First of
all, j is assumed invertible. However, the estimation procedure is based on the idea that the local
shocks are orthogonal across regions, so that the covariance matrix of Ljt is diagonal. It results that
invertibility of j is easy to justify in the light of the hypothesis structure of the model.
Furthermore, if j is diagonal, the FOC has a straightforward interpretation. Indeed, since
j
j
wj = X jt X j0
wj = X jt X j0
= Cov X jt ; xjt
t
t w
then j wj is equal to the covariance of each region in country j (X jt ) with the national
aggregate (xjt ) and the FOC can thus be rewritten as
j
Cov xij
t ; xt
var LCtj
=
j
wij ;
This last implies that:
9
i = 1; ::: I j
(9)
a. the larger is the covariance of a region with the aggregate, the larger is the weight of that
region in the aggregate;
b. the smaller is the variance of the idiosyncratic component for a region, the larger is its weight
in the aggregate.
Note that weights can also be negative. Moreover, once the national aggregates are found,
exactly the same reasoning holds in order to …nd the national optimal weights and the corresponding
European aggregate. Simply, call the covariance matrix of the non-common component contained
in each national aggregate (i.e., the covariance matrix of that part of the national aggregates driven
by the corresponding national shocks njt ) and
the covariance matrix of the national aggregates;
1
thus, …nd the principal component of the matrix
and call it w.16
3.3
European, National and Local components
The decomposition of each regional variable into the three components can be summarized by the
following steps.
ij
the optimal weight given to
In the …rst step, generalizing to the M -variables case, let us call wm
th
region i, country j, for the generic m variable. By de…nition, the national aggregate of the mth
variable in country j is given by
j
xjmt
=
I
X
ajm (L)0 et + bjm (L)0 njt
ij
wm
xij
mt
(10)
i=1
where ajm (L)0 is the 1
M vector given by
j
ajm (L)0
=
I
X
ij
0
wm
aij
m (L)
i=1
and
bjm (L)0
is the 1
M vector given by
j
bjm (L)0 =
I
X
ij
0
wm
bij
m (L)
i=1
xjmt ,
Let us collect the M national aggregates
for m = 1; ::: M –i.e., one for each variable –in
a single M 1 vector for each country j. Note that (1.10) can be written also as
xjt
j
Aj (L)et + B j (L)njt
(11)
j
where A (L) and B (L) are M M matrices of rational functions in the lag operator whose mth
rows are given, respectively, by ajm (L)0 and bjm (L)0 .
The second step consists of aggregating these National aggregates across countries, i.e. for
j
j = 1; ::: J, obtaining one European aggregate, xmt , for each variable. Let us call wm
the optimal
th
weight given to country j in the m national aggregate. By de…nition,
1 6 One computational problem in this procedure comes from the non observability of
overcome this limit is illustrated in Appendix 1.
10
j
and
. One way to
xmt =
J
X
j
wm
xjmt
j=1
Again, since weights are chosen so that they minimize the share of the variance of the non
common component remaining in the aggregate, we can say that
am (L)0 et
xmt
where am (L)0 is the 1
(12)
M vector given by
am (L)0 =
J
X
j
wm
ajm (L)0
j=1
In a more compact fashion, (1.12) becomes
xt
(13)
A(L)et
where xt is the covariance-stationary vector collecting the M European aggregates and A(L) is
a M M matrix of rational functions in the lag operator, whose mth row is given by am (L)0 .
Remind that, by the starting assumption on aij
m (L), A(L) is an in…nite order matrix of squaresummable linear …lters. Thus, assuming equality in (1.13) and invertibility of A(L),17 the vector of
the European shocks results to be a linear combination of the present and the past of the European
aggregates collected in xt and shocks are said fundamental 18 for xt . This means that the European
aggregates could be used in principle as regressors in (1.11).
As a consequence, in the third step we estimate M J regressions
xjmt =
j
0
m (L) xt
j
;
+ Nmt
j = 1; ::: J; m = 1; ::: M
(14)
j
m (L)
is a M 1 vector of parameters estimated by OLS, and the order of the lags is de…ned
where
by some arbitrary criterion (like, for instance, an F-test on the speci…cation). More compactly,
xjt = ALF Aj (L)xt + N jt ;
j = 1; ::: J
j
(15)
th
where ALF A (L) is a M M matrix of rational functions in the lag operator whose m row
j
, m = 1; ::: M .
corresponds to jm (L)0 , and N jt is a M 1 vector collecting the residuals Nmt
ij
Similarly, each regional variable xmt can be written as a function of the M European aggregates
collected in xt and of the M National aggregates corresponding to that country, xjt .
As a result, the fourth step consists of estimating
xij
mt
=
m
=
ij
0
m (L) xt
+
ij
0 j
m (L) xt
ij
+ LCmt
;
1; ::: M ; j = 1; ::: J; i = 1; ::: I j
(16)
by OLS
and all the countries, obtaining M N equations, where
P for all the variables, all the regions
ij
N = j I j . Note that ij
(L)
and
are
M
1 vectors of parameters, estimated by OLS, whose
m
m
order of lags is again de…ned by some arbitrary information criterion.
1 7 A(L)
1 8 See
is not invertible if A(z) = 0 for z = 1.
paragraph 1.3.6.
11
In the last step, we obtain the desired decomposition. Indeed, the residuals of the regressions in
ij
(1.16) are an estimate of the Local component in each regional variable, LCmt
. Substituting (1.15),
i.e. the expression found for the national aggregates, in (1.16), we obtain
h
i
j
ij
ij
j
ij
0
0
(17)
xij
mt = m (L) xt + m (L) ALF A (L)xt + N t + LCmt
ij
From here, the European Component ECmt
is simply obtained collecting all the terms depending
on the European aggregates, i.e.
ij
ECmt
=
ij
0
m (L) xt
ij
j
0
m (L) ALF A (L)xt
+
(18)
while the National Component, due to orthogonality, can be recovered by di¤erence:
ij
N Cmt
= xij
mt
3.4
ij
ECmt
ij
LCmt
(19)
Structural analysis
Following Forni and Reichlin (1998), the intuition behind the structural analysis is that the European aggregates are linear combinations of the European shocks et . Starting from (1.13), the Wold
representation 19 of the covariance stationary process xt is given by
xt = A(L)A(0)
1
(20)
"t
where "t is a M 1 vector of white noises, resulting from the linear combination of the original
shocks, "t = A(0)et .
Inverting (1.20), we obtain the reduced-form VAR representation of the aggregated model, which
can also be written as
xt =
IM
A(0)A(L)
L
1
xt
1
+ "t = A(L)xt
1
+ "t
(21)
where A(L) is a M M polinomial matrix of generic …nite order p. Note that equation (1.21) can
be estimated by OLS, using the European aggregates as regressors, obtaining an estimate of A(L)
and "t . The estimated M M covariance matrix of the VAR innovations be .
From here, the matrix of the unobserved parameters capturing the e¤ects of the European shocks
on the European Aggregates, A(L), could be identi…ed using the information contained in A(L)
and "t , as in the traditional methods employed in the structural VAR literature. In particular, the
only thing we need is identifying A(0), since the structural shocks et and the matrix A(L) can be
1
derived from et = A(0) 1 "t and [I A(L)L] A(0) respectively.20
Starting from imposing orthonormality of the shocks, as required by the assumption that the
structural shocks et have unit variance and zero covariance, (1.20) becomes
xt = A(L)A(0)
1
U U
1
^ et
"t = A(L)^
(22)
where U is the lower-triangular matrix derived from the Cholesky decomposition of
de…nition of the Cholesky decomposition, U U 0 = .
. By the
1 9 Using the Wold’s Representation Theorem, the variables in x can be represented in terms of their fundamental
t
innovations, i.e. as a MA(1).
2 0 This
last one comes from A(L) =
IM
A(0)A(L) 1
L
in (1.21), and so A(L) = [I
12
A(L)L]
1
A(0).
Comparing (1.13) and (1.22), it is clear that A(L) is identi…ed up to a M M orthonormal,
static21 rotation matrix R, such that RR0 = I and et = R0 e
^t . This matrix contains the restrictions
needed in order to identify the structural shocks; since the orthonormality assumption (U 1 "t = e
^t )
entails M (M + 1)=2 restrictions, we need to impose M (M 1)=2 further restrictions in R.
In a simple two-shocks framework (M = 2), like the one we are exploiting in this application,
only one constraint is needed, and the rotation matrix can be easily parameterized as function of a
single rotation angle, . For instance,
sin ( )
cos ( )
R=
cos ( )
sin ( )
;
= [0; [
but other parameterizations so that RR0 = I would be equivalent.22
In the light of this, once R is selected, (1.22) becomes
xt = A(L)A(0)
1
(23)
U R et
and A(0) is identi…ed by U R.
3.5
From the aggregated to the disaggregated model
Matrix R identi…es the common components of the variables and, consequently, also the parameters
in the disaggregated factor model (1.1). Indeed, it holds that
ij
0
ECmt
=a
^ij
^t
m (L) e
0
ij
0 0 23
This means that, once R is
and we have in…nite representations, since a
^ij
m (L) = am (L) R .
identi…ed, the dynamic structural model parameters are identi…ed as well.
In order to estimate the vector aij
m (L), let us go back to equation (1.18), where the common
component of the mth variable, in region i, country j, is recovered from the vector of the European
aggregates, xt . In order to express this common component as function of the common shocks, we
simply replace xt with the equivalent expression estimated in (1.23), so we obtain
0
aij
m (L) =
ij
0
m (L)
ij
j
0
m (L) ALF A (L)
+
[I
A(L)L]
1
UR
From here, the Impulse Response Functions for each variable and region to the European shocks
are given by
2 1 Fundamentalness
2 2 For
of the shocks implies that R is a constant matrix. See Forni et al. (2003).
M = 3, the number of constraints grows to 3, and matrix R could be parameterized as
R
=
0
@
cos ( )
sin ( )
0
sin ( )
cos ( )
0
( ; ; ) 2 [0; 2 [
10
0
0 A@
1
cos ( )
0
sin ( )
0
1
0
10
sin ( )
1
A@ 0
0
cos ( )
0
2 3 Indeed,
ij
ECmt
=
0
0
0
a
^ ij
^t = a
^ ij
^t =
m (L) e
m (L) RR e
=
0
aij
m (L) et
0
0
0
0
0
and aij
^ ij
^ ij
^ ij
m (L) = a
m (L) R or, equivalently, a
m (L) = a
m (L) R .
13
0
cos ( )
sin ( )
1
0
sin ( ) A ;
cos ( )
ij
@ECmt+h
@et
For a focus on the derivation and interpretation of the Impulse Response Functions, see Appendix
1.
3.6
The problem of non fundamentalness
As previously asserted, the vector of the European shocks, et , is said to be fundamental for xt if emt ,
m = 1; ::: M , belong to the linear space spanned by the present and past of xt . Stated di¤erently,
fundamentalness means that the shocks are pure innovations with respect to the variables used in
the estimation (Forni et al., 2003).
The assumption of fundamentalness is of primary importance for any structural analysis. Indeed,
it ensures that only the present and past of the (observed) variables are needed in order to recover the
(unobserved) structural shocks; furthermore, it restricts the possible combinations of the structural
shocks to static rotations only, making identi…cation feasible through a limited set of restrictions
on the parameters.
As remarked by many authors,24 the risk of non fundamentalness is a serious problem for
traditional structural VARs. Indeed, recovering the structural shocks out of the VAR residuals
requires that there is no variable-omission bias, i.e. all the relevant variables have been included
in the analysis, so that the residuals span the same space as the structural shocks. If this doesn’t
happen, the shocks are not identi…able from the VAR residuals. In principle, one could face this
problem augmenting the number of the variables in the analysis. However, the number of VAR
parameters increases with the square of the number of observations, making this solution not
feasible.
Dynamic factor models, like those proposed by Forni et al. (2000) or Stock and Watson (1998),
solve this problem since they …rst (enormously) increase the number of variables, then they reduce
the cross-section dimension identifying the factors common to all the observations, and …nally
perform a structural VAR analysis on these (fewer) factors.
In the structural dynamic factor framework proposed by Forni and Reichlin (1998), the structural
analysis is performed on a number of aggregates at least equal to the structural shocks, where this
number is inferred from a heuristic procedure based on the principal component analysis of the
spectral density of a vector of averages of the variables. However, we could not use this (rather
informal) test, since it is based on the assumption that the non-common components are not
correlated across i, while in the case of regional variables there is a non-negligible component driven
by national shocks, that is common to a subset of regions only. Moreover, other heuristic procedures
or more formal tests have been developed for dynamic factor models where only a limited amount
of idiosyncratic cross-correlation is admitted,25 and so they are inappropriate for this application.
As a result, the number of common shocks is here deterministically assumed equal to M , and
so M aggregates are su¢ cient in order to identify et . In this way, fundamentalness relies on the
assumption of invertibility of A(L).26
2 4 Lippi
and Reichlin (1994), Stock and Watson (2005), among others.
for instance, Bai and Ng (2002), or Forni et al. (2000).
2 6 Note that, as remarked by Forni et al. (2003), invertibility of A(L) implies fundamentalness of e , while the
t
reverse does not hold, since if we only assume fundamentalness of et , A(L) could be in principle not invertible.
2 5 See,
14
3.7
Consistency of the estimates
The estimation procedure described above is based on the assumption that a weighted average of the
variables –across regions …rst, and then across countries –kills the non-common components o¤, so
that we are left with optimal aggregates. These aggregates result to be linear combinations of the
unobserved (and underlying) shocks and thus can be used as proxies for the shocks. However, since
the number of cross-section units is necessarily …nite, these averages still include a measurement
error, and this a¤ects the usual properties of OLS. Thus, one related problem to discuss is what
are the properties of this estimator.
Some theoretical result has been provided by Forni and Reichlin (1998) only for the case of the
simple average estimator. They show that consistency of the parameters is reached only if we let
both T (time dimension) and N (cross-section dimension) go to in…nity; moreover, the relative rate
at which T and N approach in…nity does not matter.
For the weighted-average case, no theoretical results have been provided. However, Forni and
Reichlin (2001) perform a set of Monte Carlo simulations and …nd that the weighted average estimators outperform the simple average ones for all T and N . Moreover, no standard errors or
con…dence bands are available for the estimates and impulse response functions, and this inference
problem has been remarked also by Forni and Reichlin (1998).
In principle, con…dence bands for the IRFs could be derived performing some bootstrap procedure; however replicating the model requires performing a high number of steps – …nd optimal
weights, compute the aggregates, estimate the VAR of the european aggregates, estimate national
and regional regressions –before obtaining an estimate of the IRFs; this would add uncertainty at
each step and is likely to result in very high con…dence bands. For this reason, we do not provide
standard errors or con…dence bands. At the same time, we are aware we need to provide some
indicator for the precision and accuracy of the results: this shall be the focus of our future research
e¤orts.
3.8
A comparison with other approaches
As seen in par.1.2, the bulk of the literature on DFM exploits the approximate DFM approach
to deal with the issue of cross section correlation. Forni and Reichlin’s (2001) work is one early
attempt to explicitly model these cross section correlations, introducing some form of hierarchical
(or block) structure in a DFM. A hierarchical structure is needed when there exists some form of
correlation in the idiosyncratic components across the observations, due to factors that are common
to a block of observations only. The hierarchical structure of the model could be identi…ed through
a set of theoretical restrictions (Hallin et al., 2008) or, more likely, it is implicit in the nature of the
data. In our case, the structure depends on geography, and blocks correspond to di¤erent countries;
in other cases, it may be suggested by the di¤erent time releases of the data or by the economic
phenomena measured by the data (industrial production, prices and so on), like in Ng et al. (2008).
The link between the approximate and the hierarchical DFMs has been recently discussed by
Cicconi (2009). Indeed, a multilevel factor model, like Forni and Reichlin’s (2001) one, is asymptotically equivalent to the approximate counterpart only if the amount of cross-correlation due to the
intermediate factors vanishes when the cross-section dimension grows. This is veri…ed when we let
the number of cross-section units (N) grow, but keep bounded the number of series in each block,
i.e. N ! 1 and I j < 1. For instance, this happens when we add additional blocks of data without
15
modifying the existing ones.27 On the other hand, if we increase the number of series for each block,
keeping …xed the number of blocks, intermediate factors cannot be properly distinguished from the
common ones; it results that the PC estimator of an approximate DFM is inconsistent and the
intermediate factors are said weak (Onatski, 2009). In practice, this is veri…ed when we increase
the level of disaggregation of the variables in each block without increasing the number of blocks.
For the purposes of our application, we have not exploited the approximate DFM approach
for two reasons. First, Forni and Reichlin (2001) performed a set of simulations and found that
their hierarchical structure model provides better results than both Forni et al. (2000) and Stock
and Watson’s (1998) approximate DFMs, at least for T and N similar to those in their (and our)
dataset. Second, our analysis is also aimed at recovering the importance of the National component
across Europe, and the approximate DFM does not provide this output, since the intermediate
factors would be treated like the idiosyncratic ones.
Even when the asymptotic equivalence is veri…ed, Cicconi shows that models where the hierarchical structure is explicit provide more precise estimations of the common factors and ensure
better forecast performances than the approximate DFM, since the former has better small sample
properties.28 For this reason, one could wonder why we have decided to use a relatively old methodology and did not refer to any of these new approaches, based on exactly the same intuition but
more formal from the estimation point of view. Indeed, Cicconi uses an exact maximum likelihood
estimator, while Ng et al. (2008) recur to a state-space representation of the model and a Bayesian
approach to estimate it.
The reason is that the methodology proposed by Ng et al., while computationally cumbersome,
is more indicated for very high dimensional datasets. Moreover, both these models are aimed at
extracting the common factors only, while we are also interested in the identi…cation of these shocks.
From this perspective, the approach by Forni and Reichlin (2001) is more appealing, since it is very
intuitive and provides a natural framework for the structural analysis; indeed, it allows to identify
the European shocks on the aggregated model …rst, and then to recover the local dynamics and
estimate the regional IRFs using the disaggregated model, as described in the previous paragraphs.
4
Empirical analysis
As already stressed, a dynamic factor model has been employed here to study the degree of integration and synchronization of the regions in a subset of countries belonging to the EU12. This
empirical exercise employs data on GDP and employment (M = 2) over the period 1977-1995
(T = 19) referring to nine EU12 countries, namely Belgium (B), Germany (D), Greece (GR), Spain
(E), France (F), Italy (I), the Netherlands (NL), Portugal (P) and the United Kingdom (UK).
Variables are observed at NUTS1 or, where possible, NUTS2 level of disaggregation, to the amount
of N=107 regions. Growth rates are computed as the …rst di¤erence of the logarithmic de-meaned
series.29
While Forni and Reichlin (2001) focus on the dynamics of GDP growth rates only, here we
extend their model to a two variables-two shocks framework, introducing also employment growth.
As already remarked, the choice of moving to a multivariate framework improves on the original
analysis, since we can now identify the European sources of ‡uctuations and give them an economic
2 7 Using
the notation of our model, this means that we are adding new countries.
the presence of cross-correlation in the idiosyncratic components slows down the WLLN (Boivin and Ng,
2 8 Indeed,
2006).
2 9 For details, see Appendix 1.
16
interpretation. Moreover, the selection of these two speci…c variables is motivated by the relevance
their joint dynamics have for policy evaluations, since GDP and employment are the two key
dimensions usually explored by national and european institutions in order to assess and coordinate
the European integration programs. This is clear reading the reports on regional cohesion published
by the European Commission since 1996. Moreover, also the other works on regional synchronization
in Europe, brie‡y reviewed in the introduction, analyse the dynamics of GDP and Employment,
though as seen, rarely considering both these dimensions at once.
In our S-DFM, moreover, we have decided to keep track of the identity of each region, estimating the variance decomposistions and the responses to common shocks, region by region. This
gives us the chance to make direct comparisons among all the cross section units – both across
and within countries –and to deal with one interesting and generally neglected issue, i.e. to what
extent geography matters in Europe. If reactions are more similar for regions belonging to a speci…c
group of countries, one could ideally split Europe into high and low synchronized countries, suggesting for instance that national dimensions should matter in the European stabilization policy; if
marked di¤erences are observed within the single countries, and national dimensions are not easily
recognizable in the observed pattern of synchronization, regional stabilization policies are instead
needed.
In the light of our selected measure of synchronization, we need a preliminary look at the
variance decompositions (par.1.4.1). Indeed, following Forni and Reichlin (2001), a rough indicator
of the degree of integration of regions is given by the share of the overall variance of GDP and
employment regional growth rates actually explained by the common factors. The implications
of this issue for the evaluation of synchronicity are not trivial. Indeed, similarity of responses is
crucial for regions with high EU component shares: since they are more likely to be a¤ected by
common shocks, di¤erent reactions would result in divergent regional patterns. At the same time,
if regions mainly driven by non common components have responses similar to the rest of Europe,
then policies aiming at more integration should, in principle, lead to more cohesion.
The identi…cation of the shocks will be discussed in par. 1.4.2. According to our identi…cation
strategy, here we shall focus on the the main positive driver of GDP growth, de…ned as a prevalently
positive shock, explaining as much as possible of the volatility of the european (aggregate) GDP
growth over a …ve-year forecast horizon. The reason behind this choice is twicefold. On the one
hand, focusing on a shock whose realizations are mainly positive implies that we are identifying
a potential source of aggregate growth or decline, depending on the sign of its overall e¤ects on
GDP growth, captured by the cumulated IRF over the selected forecast horizon. On the other
hand, this source of ‡uctuation is a driver of the European economy – i.e., it contributes to the
observed dynamics of GDP growth – only if it explains a relevant share of the overall volatility of
the aggregate GDP growth. The choice of GDP as a benchmark in the identi…cation procedure
is borrowed from Uhlig’s (2003) work and is justi…ed because its dynamics are a good proxy of
the economic performance of a geographic area. Moreover, as remarked by Uhlig, using a …ve-year
forecast horizon means that we are covering both the very short-run (0-1 years) and the medium
run (3-5 years) GDP movements.
The degree of similarity of regional responses is the object of par. 1.4.3, where we compare the
sign and the magnitude of the regional cumulated IRFs with the cumulated response of the EU
aggregates, which can be interpreted as an average response, behaving as a natural benchmark. By
low and high responses we mean the (cumulated) responses respectively below and above the EU
average, while we denote by countercyclical all the (cumulated) IRFs whose sign over a …ve-year
forecast horizon is opposite to the EU aggregate’s one. Note that, in general, we shall always refer
17
to the cumulated IRFs over a …ve year horizon, since they capture the overall e¤ect of the shock over
the horizon which is relevant according to the identi…cation procedure. Similar responses associated
with high european component variance,30 are our …nal measure of business cycle synchronization.
In paragraph 1.4.3 we will also take a closer look at regional responses within two countries –
speci…cally, Italy and Spain. This will make the analysis more e¤ective for a number of reasons. On
the one hand, while for Spain the period of analysis captures the transition from outsider to member
of the EU, since it joined the EU in 1986, Italy is a pioneer of the European integration process,
so they are a good sample to observe the relation between actual integration and synchronization
of cycles. Moreover, these countries are traditionally characterised by high inner heterogeneity in
terms of economic performances: as it emerges from the First Cohesion and the Sixth Periodic
Reports (1996; 1999), quite a large group of Spanish and Italian regions have been included in the
Objective 1 program of structural funds, allocated by The European Commission in order to reduce
the gap between weak and rich regions in the EU.31 Thus, comparing the predicted responses of
the model and the real behaviour of these regions, and using the existing evidences in the regional
literature on growth, productive specializations and business cycles referring to our selected two
cases, we could infer to what extent the common factors can be said responsible for the patterns of
development of this area.
4.1
Variance decompositions
As explained in paragraph 1.2, the reciprocal of the eigenvalue corresponding to the principal component of each aggregate is an estimate of the residual percentage of the non-common component
remaining in that aggregate. According to our results (see Table A1.1 in the Appendix), for the GDP
national aggregates the highest percentage of non-common component variance is 7% in Greece,
followed by 5% in Belgium, all the others standing below 2% –quite an encouraging result. For the
Employment aggregates, in no national aggregate the 4% threshold is overcome, and the highest
share 3.4% in Belgium.
Some less satisfactory results concern the European aggregates: while the percentage of the non
European variance remaining after aggregation is quite low for GDP (3.9%), for Employment it is
really much higher (11.5%), revealing that the non-common component plays a non negligible role
for the Employment dynamics in Europe.
Table 1.1 shows the variance of GDP and Employment growth explained by the three components. These …gures are the average (across regions in the same nation, over time) of the share of
the variance of these two variables explained by the European, National and Local components.
Intuitively, since the variance of the European component measures to what extent a region is
a¤ected by shocks which are common to all the regions in the sample, it can be interpreted as
the degree of integration of each geographical area to the European Union, in line with Forni and
Reichlin (2001).
Table 1.1: variance decompositions by country and component (% of overall variance)
3 0 Note that the magnitute of the shares of the european component variance shall be assessed both respect to the
national and local ones, and using some absolute threshold; following Forni and Reichlin (2001), a high european
component variance explains more than 70% of the overall variance.
3 1 The threshold for the eligibility during the programming periods 1989-94 and 1995-1999 was regional GDP per
head standing below 75% of the EU average.
18
Country
Germany
UK
France
Italy
Belgium
Netherlands
Greece
Spain
Portugal
ECgdp
NCgdp
LCgdp
ECemp
NCemp
LCemp
65.2
26.4
26.1
44.4
8.7
29.2
39.7
29.2
50.7
27.3
9.6
43.6
64.6
66.8
53.1
58.3
26.8
41.7
11.6
11.2
28.1
29.4
29.0
28.9
23.8
22.0
18.8
12.3
44.2
29.4
36.1
24.4
68.7
17.3
18.9
46.3
21.8
24.3
19.1
78.3
19.9
26.7
42.1
51.3
12.2
3.4
61.1
27.7
15.0
42.8
42.2
4.3
72.1
23.7
Note: average over time and across regions, by country
The …rst impression is that the European component explains the largest share of the variance of
GDP growth in the "old-Europe" countries (Belgium, Germany, France, Italy and the Netherlands).
Among the new member states, Spain looks the most European one, with a share close to 42%,
while the European component is the least important one in Greece, Portugal and the UK. GDP
variability is mainly due to local factors in Greece, while national shocks are the main source of
variation in Portugal and the UK.
These results are in line with Forni and Reichlin’s (2001) …nding that these three countries
are less integrated to the rest of Europe in the period of study. Moreover, for the UK this is not
a completely new …nding; similar evidences come, for instance, from Barrios et al. (2003), who
show that, over the period 1966-97, UK regions are lowly correlated with a sample of European
countries,32 while the correlation within borders is high.33
On the other hand, for Greece and Portugal low shares of the European component variance
may be explained by their "new Member" status: since they are new to the EU, trade, …nancial
and institutional links and interdependeces are not so developed yet, so it is less likely for them to
be a¤ected by these common shocks, as in the rest of the Europe.
To sum up, the degree of implementation of the EU integration process across countries is
important but not su¢ cient to explain the observed di¤erences, since high integration characterizes
a new member like Spain and not an old member one like the UK. For this reason, a contribution is
likely to come from some residual characteristics, e.g. economic, institutional, geographic features
characterizing di¤erent regions and countries in Europe but that we cannot either identify or control
for through our procedure.34
These results are con…rmed when looking at the variance decompositions at the regional level
(Appendix 1, table A1.4). Using the arbitrary 50% threshold to identify regions with high European
components, then GDP growth is mainly driven by common factors in the bulk of the european
regions, excepted all those in Greece, Portugal and the UK. Moreover, highest shares seem to
3 2 Namely,
Germany, France, Italy, Netherlands, Belgium and Ireland.
…nd some weak evidence that the geographic distance explains the observed low correlation with the EU.
3 4 The idea that the degree of integration depends on both the degree of implementation of common policies and
on structural characteristics is somewhat close to the distinction made in the Optimum Currency Area literature
between optimality ex post and ex ante. The OCA literature includes a set of studies that describe the criteria an
economic area should meet in order to become a single currency area. Originally (for instance, Mundell, 1961) the
requisites for an OCA were judged ex-ante, since considered exogenous to the Monetary policy. Furher developments
(Kenen, 1967; Krugman, 1993) focus on the e¤ ects the common policies have on the optimality of the OCA decision.
This stream is also de…ned endogenous and takes the view that common economic (in particular, monetary) policies
a¤ect the degree of integration across countries.
3 3 They
19
be more concentrated in the Old European Members, namely Belgium, without Bruxelles,35 the
Netherlands, Germany, with the exception of Berlin,36 and, to a lesser extent, France and Italy.
However, this national dimension is not recognizable if we use the 70% threshold –the same as
in Forni and Reichlin –to de…ne regions with high european component shares: in this case, Europe
does not seem split into high and low integrated countries, since inner di¤erences are now more
evident also for the old european countries. This con…rms that regional dimensions are important
(Fatàs, 1997, Tondl and Traistaru-Siedschlag, 2006) and suggests that divergences are more likely
to arise within than across countries; moreover, countries like Spain and Italy tend to be more
dichotomous, since regions with european component shares well below 50% cohesist with regions
whose shares are well above 70%. Finally, we do observe that, excluding Portugal and the UK,
in almost all the other regions the national component is overcome by european and local factors
together, meaning that the national dimension is not important in explaining GDP variability and
Europe consists of regional, rather than national economies, in line with what found by Forni and
Reichlin (2001).
A di¤erent picture shows up looking at the variance decompositions of employment growth.
Indeed, the European component is the most relevant one only in Belgium and, to a much lesser
extent, Spain, while for the UK, France, Italy and Greece local factors are mainly responsible for
the variance of this variable. In general, it seems that the main drivers of this variable are of local
and national nature. This is in line with what reported by Marelli (2004): there is a persistent
variety of institutional models and labour policies across the European countries, which may be
responsible of the relative importance of national components. Moreover, the importance of local
factors is con…rmed in his empirical analysis, where more than half of the variation of emploment
growth in the EU12 regions is explained by non common factors.
While in Marelli’s work this fact is explained by the implicit propensity of regions (respect
to countries) towards higher specialization in speci…c activities, so that they are more subject to
sector-speci…c shocks, according to our de…nition of common and local shocks, there are further
explanations for this evidence.
Indeed, the existence of more constraints on labour mobility than on capital and goods makes
it not likely that a shock, whatever its nature or origin is, spreads around and a¤ects employment
in all the EU regions. To some extent, the spill-over e¤ects which may explain the importance of
the EU shocks for GDP growth are partially nulli…ed by the segmentation of labour markets. This
interpretation is consistent with the literature on the structural characteristics of european labour
markets (brie‡y reviewed by Marelli) and with the observation that the main reforms in Europe
towards more ‡exibility and integration of labour markets come after the period here analysed.
Looking again at the variance decompositions at the regional level (Appendix 1, table A1.5), we
con…rm that employment in the european regions is mainly explained by local and national factors.
Interestingly, all the regions containing the most important european capital cities –Bruxelles, Île
de France, London, Antwerp – or international economic poles – Hamburg, Lombardia – do have
high shares (greater than 50%) of employment variance explained by common factors, implying that
internationalization is an important factor pushing integration of regional employment dynamics.37
On the other hand, dichotomies both across and within countries are more likely to arise for regional
3 5 Surprisingly, in the capital-city region of Bruxelles the European Component explains 32% of overall GDP growth
variance.
3 6 Also Montoya and de Haan (2007) …nd that Berlin behaves as an outlier. Probably, this result is explained by
the transition Germany (and Berlin) experienced over this period towards the uni…cation with the Eastern part.
3 7 This is something close to the importance of trade openess and …nancial interrelations for GDP integration.
20
employment than for GDP growth, since its sources of volatility are mainly country and regionspeci…c. This is in line with those studies …nding an increasing polarization of regions in terms of
employment, reviewed in Belke and Heine (2006).
4.2
Identi…cation of the shocks
The aim of the IRF analysis is observing the sign and magnitude of responses at the regional level
and comparing them to the behaviour of the european aggregates. This will give a clue of how
synchronized european regions are, since being a¤ected by common shocks does not authomatically
imply that responses are symmetric.
The …rst stage of the structural analysis is the identi…cation of the shocks. For the purposes of
our application, where M = 2 and the variables of interest are GDP and Employment, we focus
on the e¤ects of the main positive driver of the european economy: this is a prevalently positive
shock, explaining as much as possible of the volatility of the european GDP growth over a …ve-year
forecast horizon. The identi…cation strategy is a combination of two di¤erent approaches, both
atheoretical and already exploited in the literature.38
The …rst one is borrowed from Forni and Reichlin’s (1998) structural dynamic factor model
and identi…es a mainly positive shock selecting the rotations with the lowest absolute sum – i.e.,
the lowest sum of the absolute values – of the negative realizations of that shock.39 Among these
rotations, in the second step we select the one for which the Forecast Error Variance (FEV)40
of GDP explained by that shock over a …ve-year horizon is maximized, following Uhlig’s (2003)
approach. As anticipated, using a …ve-year forecast horizon we cover both the very short-run
(0-1 years) and the medium run (3-5 years) GDP movements. The choice of not including long
run horizons is dictated by our focus on a time span which may be more relevant to assess cycle
‡uctuations; moreover, the limited number of available observations and the annual frequency of
the data implies less precision and higher uncertainty over long forecast horizons.
The selected rotation is given by = 3=5 41 (i.e., = 108 ) and the main positive driver –
PD
–corresponds to the …rst shock in et .42 In what follows, we shall focus on this shock
hence, eM
t
only; indeed, the other shock is not interpretable in the light of our identi…cation strategies, since
PD
it captures the e¤ects of all sources of ‡uctuations di¤erent from eM
.
t
MP D
explains 58.7% of the FEV of the aggregated GDP growth rate
For the selected rotation, et
over a …ve-year forecast horizon, and a substantially lower share of employment growth (17.1%);
PD
is not the main driver of employment. Since the European shocks
according to these …gures, eM
t
are orthogonal by assumption, this results in a low correlation between GDP and employment
growth, in line with a well known stylized fact concerning Europe: in the period 1983-1996, European growth was not employment-intensive, expecially if compared to the US economy, since
3 8 For
technical details on the identi…cation strategy, see Appendix 1.
Forni and Reichlin’s strategy, a mainly positive shock is coincident with a technology shock ; the intuition is that
technology shocks are prevalently positive, excepted for some negative events, like for instance oil shocks. However,
here we prefer to be agnostic about the precise nature of this shock, since we do not have su¢ cient information (like
the impact of this shock on prices), nor we can be sure we are identifying technology vs other events (e.g., positive
shocks to capital accumulation). We thank prof. Hendry for pointing out this issue.
4 0 The s-steps-ahead FEV of x is the error one makes while predicting x over the forecast horizon s.
t
t
4 1 We performed …fteen rotations by twelve degrees (or, equivalently, by =15) over the interval [0; ) and computed
separately the absolute sum of the negative realizations of each shock and the FEV accounted for by each shock in
et . See Table A1.6 in Appendix 1.
4 2 See Table A1.7 in Appendix 1.
3 9 In
21
employment did not grow at the same pace as GDP.43
What emerges from the FEV decompositions is con…rmed by the IRFs of the European aggregates (Appendix 1, …gure A1.1): GDP growth aggregate reacts more than employment. While GDP
immediately increases by 1.6%, employment is almost una¤ected. Five periods after the shock, the
cumulated e¤ect on GDP is 2.6%, while for employment it is less than a half (1.2%).
Note that the main positive driver of Europe is still responsible of some comovement of (aggregated) GDP and employment growth rates: this source of growth, on average, has a positive e¤ect
also on aggregate employment.
4.3
Disaggregated dynamics
Taking one step forward, we now move to the disaggregated model and estimate the IRFs of the two
PD
variables to eM
, region by region. Indeed, we want to observe to what extent regional responses
t
to a common shock are heterogeneous, both across and within countries, and if di¤erences or
similarities in these responses re‡ect any speci…c geographic pattern.
Focusing on GDP …rst, and comparing the IRFs across countries, responses (Appendix 1, …gures
A2-10, solid lines) look quite homogeneous, both in sign and shape. Speci…cally, the long-run
cumulated impact is positive almost everywhere; the only countercyclical response is Anatoliki
Makedonia (Greece), which however results to be low integrated also in terms of variance explained
by the common component (9.6%), thus performing as an outlier. This means that, independently of
the level of integration, GDP across regions comove after a common shock, and fostering integration,
in principle, should lead to more synchronization.44
A second thing worth noting is that some degree of inner homogeneity in terms of intensity
concerns the reponses in Belgium, the Netherlands and Germany. On the one hand, this may depend
on their smaller number of regions, since they are observed at the NUTS1 level of disaggregation.
On the other hand, this is consistent with the traditional absence of inner dichotomies in this part of
Europe.45 Since these countries are also characterized by a prevalent european component respect
to the non common ones, they are also synchronized. However, focusing only on the most integrated
regions according to the stringent criterion of 70%, the most synchronized part of Europe has no
national dimension, but also in the old members we …nd regions more or less synchronized to the
rest of Europe.
The behaviour of employment provides useful complementary information about the degree of
integration of regional economies. As anticipated in the variance decomposition analysis, employment in Europe is more a¤ected by local and national, rather than common, factors, both for the
intrinsic nature of this variable and for the european labour markets characteristics. Moreover, since
the main positive driver of GDP explaines on average only a small share of employment variance
in the medium term horizon, we expect regional IRFs to this common shock to do not be much
representative of actual employment dynamics.
4 3 First
Cohesion Report, European Commission (1996).
is woth noting that in the literature on business cycle synchronization across the European countries, reviewed
by de Haan et al. (2005), more integration does not necessarily imply more synchronization. Indeed, Frankel and
Rose (1998) and Baxter and Kouparitsas (2004) …nd that more integration, in terms of more intense trade relations,
leads to higher synchronization of the cycles of the areas involved. However, trade (Krugman, 1993) or capital
market integration (Kalemli-Ozcan et al., 2001) may stimulate sectoral specialization and thus divergence in the
cycles, since the probability of being a¤ected by local-speci…c shocks increases. De…ning the sign of this correlation
is not straightforward.
4 5 Remind that the eastern regions of Germany are excluded from our analysis.
4 4 It
22
Looking …rst at Employment responses across countries, the impression is that a clear common
pattern of behaviour is di¢ cult to be identi…ed, since both the sign and the intensity of responses
look rather heterogeneous. This is not so surprising, since a potentially large set of factors, like
characteristics of local job markets (more or less ‡exibility of job markets, constraints from both
the demand and supply side...) and institutional factors may a¤ect the dynamics of this variable.
In this perspective, since common shocks are not a source of synchronicity for employment and
regions are driven by heterogeneous forces, we can infer that regions are not cohese in terms of
employment dynamics. This result is consistent with Belke and Heine (2006), who …nd a declining
trend of synchronicity of regional employment cycles for many European region-pairs over the period
1989-1997.
When focusing on the most integrated regions, i.e. those whose european component variance
PD
share is at least 70%, we observe that responses of Employment to eM
are quite similar, but this
t
group of synchronized regions consists of only four regions – Vlaams Gewest (BE), Saarland (D),
Lombardia (I) and London (UK) –so we cannot de…ne any geographic pattern. Quite interestingly,
all these regions but Saarland do include important economic poles,46 with international …rms and
networks which make them well connected and su¢ ciently open to foster integration in employment.
The only small and peripheral region is Saarland in Germany. However, its engagement with
globalisation has been shaped by its industrial base and its border location (DERREG Reports,
2011). Indeed, it is a well connected region, endowed with a high developed transportation network,
resonably thanks to its strategic location – it shares its borders with France, Luxembourg and
Germany –which allows a high degree of accessibility: this is in line with the idea that the degree
of integration in employment can be in‡uenced by factors like trasportation costs (Belke and Heine,
2006).
4.3.1
Case 1: Spain
For Spain, regional variance decompositions of GDP reveal a certain prevalence of the European
component (Table 1.2); in some cases, like Galicia, Asturias and Cantabria, it is comparable with the
other two components, while it is marginal in Canarias and Baleares (12% and 14% respectively).
PD
(Appendix 1, …gure A1.5, solid
Moreover, looking at the IRFs of regional GDP growth rates to eM
t
lines), the group of highly synchronized regions involves Pais Vasco, Cataluña, Madrid, Comunidad
Valenciana, Castilla-la Mancha and Andalucia, while particularly lowly synchronized regions are
Canarias and Baleares. This second group of countries stands out also for the not-synchronized
behaviour of employment, which grows more than GDP over the medium-run horizon.
Evidences of asymmetric cycles in Baleares and Canarias after the accession to the EU are
provided by Villaverde Castro (2000); similarly, Cuñado and Sanchez-Robles (2000) …nd some
evidence of higher vulnerability to asymmetric shocks to productivity in this part of Spain.
The group of more synchronized regions looks heterogenous in terms of regional and geographical
characteristics. Indeed, in this group we …nd industrial regions, like Pais Vasco or Cataluña, highincome ones, like Madrid, and poor regions as well, like those included in the Objective 1 program
of funds47 –Comunidad Valenciana, Castilla-la Mancha and Andalucia. This suggests that several
dimensions (e.g., level of income, industrial structure, labour costs, infrastructures, institutional
support and other structural characteristics) are needer in order to explain the degree of integration
4 6 Antwerp
in Vlaams Gewest, Milan in Lombardia, while the city of London coincides with the region.
Objective 1 program of funds involves all the regions whose GDP per capita is less than 75% of the EU
average. Spanish regions in this program over the period of study are: Galicia, Principado de Asturias, Cantabria,
Castilla y Léon, Castilla-La Mancha, Extremadura, Comunidad Valenciana, Andalucia, Murcia and Canarias.
4 7 The
23
and similarity of responses. This idea is somewhat close to the idea, belonging to the regional
literature on convergence (see for instance, López-Bazo et al., 1999), that a certain diversi…ed
behaviour could be observed also within areas traditionally considered homogeneous, like core and
periphery regions.
The existence of some dynamisms, involving also the regions with low income levels or not developed industrial structures is indirectly con…rmed looking at the data on regional GDP growth
rates provided by the European Commission in the Sixth periodic report: the group of the best
performing regions48 for the decade 1986-96 is quite variegated and includes the rich archipelago
of Baleares, the developed region of Madrid and Cataluña, the industrial pole of Comunidad de
Navarra, but also some Objective 1 regions (Canarias, Extremadura, Andalucia, Castilla-la Mancha and Cantabria49 ), followed by Galicia, Castilla y León, Comunidad Valenciana and Aragón50 .
Among them, there is a cluster of regions –Madrid, Castilla-la Mancha, Cataluña, Comunidad Valenciana, Andalucia –belonging also to the group of synchronized regions, according to our results:
in the light of our model, it is likely that the driver of european growth contributed to their actual
positive growth performances.
In terms of employment, generally speaking, the european component is important and there
is a cluster of regions whose shares are particularly high: Comunidad Valenciana, Comunidad de
Navarra, Andalucia and Cataluña. According to the Sixth Periodic Report, these regions are among
the best-performing Spanish (and European) ones, their employment growing at more than 1% per
year over the period 1986-96;51 looking also at their high IRFs (Appendix 1, …gure A1.5, dotted
lines), it seems that the European component may have contributed to their actual high growth
rates.
Though the european component is generally important in Spain, respect to the other new
member states, revealing a general high degree of integration, in the light of the tougher 70%
threshold, only two developed regions –Madrid and Cataluña –are in the group of highest integrated
ones in terms of GDP, while no region is included when looking at Employment variance shares.
This con…rms a somewhat expected immaturity of Spanish process of integration. In terms of inner
dichotomies, synchronicity seems to do not follow any clear geographic or well de…ned pattern of
behaviour, since both rich and developed regions and low-income and developing ones are included in
the group of high synchronized regions: to some extent, this results in a certain degree of dynamism
within Spanish borders, partially con…rmed by the …gures on GDP and Employment growth rates
by the European Commission.
4 8 By best performing, we mean regions growing at a faster rate than the EU, which for this period is on average
2.1% per year.
4 9 On average, they grew by more than 2.7% per year.
5 0 The average growth rate of this second cluster of regions is between 2.3 and 2.7% per year.
5 1 The average European growth rate over this period is 0.4%. The other regions in this group are Canarias,
Baleares, Murcia and Comunidad de Madrid.
24
Table 1.2: variance decompositions GDP and EMP growth, Spain (% overall variance)
Spain
ECgdp
NCgdp
LCgdp
ECemp
NCemp
LCemp
Canarias
Baleares
12.0
13.6
28.6
34.2
59.4
52.3
36.7
27.3
22.9
11.8
40.4
60.9
Castilla y León
Extremadura
La Rioja
Galicia
Principado de Asturias
Murcia
20.3
25.3
33.7
33.7
38.3
39.3
59.2
30.4
46.1
32.7
30.0
12.9
20.6
44.3
20.1
33.5
31.7
47.8
49.0
48.1
28.6
13.9
35.8
53.1
43.7
38.5
8.6
44.2
26.1
18.7
7.3
13.4
62.8
41.9
38.1
28.2
C. de Navarra
Cantabria
Aragón
C. Valenciana
Pais Vasco
Castilla-la Mancha
39.6
40.6
43.2
52.3
53.2
60.6
16.2
35.4
47.7
17.2
8.00
29.5
44.2
24.1
9.20
30.4
38.8
9.80
61.2
56.9
54.9
59.6
46.2
43.5
25.0
17.4
34.9
25.8
19.9
31.4
13.8
25.7
10.2
14.7
33.9
25.1
Andalucia
C. de Madrid
Cataluña
Total
62.9
69.0
70.9
41.7
19.7
18.2
25.7
28.9
17.4
12.8
3.40
29.4
62.3
43.8
65.9
46.3
34.0
28.2
22.6
26.7
3.8
27.9
11.5
27.0
Note: averages over time
4.3.2
Case 2: Italy
Compared to Spain, as expected, the degree of integration of Italian regions is generally higher
(Table 1.3): the european component is prevalent almost everywhere; however, it explains less than
half of the overall variance in four Southern regions52 –Sardegna, Sicilia, Basilicata and Calabria.
According to the 50% threshold, high shares characterize not only the regions in the North
or Centre, traditionally in line with Europe in terms of economic development and performances
(e.g., income, degree of industrialization and internationalization, and so on), but also part of the
Southern regions –Abruzzo, Molise, Puglia, Campania –belonging to the weakest part of Europe
and recipient of the Community structural funds since the …rst programming period.53 However,
referring to the 70% threshold, Italian traditional dichotomies are better recognizable, since all
Southern regions (but Abruzzo and Molise) are out of the most cohese regions group.
From this preliminary overview, two points can be made. Since the local and national components play a not negligible role in the Southern regions, respect to the rest of Italy – the only
two exceptions being Abruzzo and Molise – the existence of the traditional italian dichotomy is
here con…rmed. However, the South does not appear as a cohese and uniform block, but we do
observe a somehow di¤erentiated behaviour among its regions. As seen, the european component is
5 2 Italy can be divided in four macro-areas, according to the geographical collocation of its regions: North (Piemonte,
Valle d’Aosta, Liguria, Lombardia, Trentino-Alto Adige, Veneto, Friuli-Venezia Giulia, Emilia -Romagna); Centre
(Toscana, Umbria, Marche and Lazio); South, (Abruzzo, Molise, Campania, Puglia, Basilicata, Calabria); Islands
(Sicilia and Sardegna). The latter two cathegories are generally referred to as Mezzogiorno. However, for simplicity,
here we consider South and Mezzogiorno as synonymous.
5 3 The …rst programming period ran from 1989 to 1993. In this period, for Italy, the Objective 1 program involves
all the Southern regions.
25
neatly dominant in Abruzzo and Molise,54 while Puglia and Campania have a degree of european
integration comparable to regions like Toscana and Lazio.
Table 1.3: variance decompositions GDP and EMP growth, Italy (% overall variance)
Italy
ECgdp
NCgdp
LCgdp
ECemp
NCemp
LCemp
Piemonte
Valle d’Aosta
86.8
75.2
6.2
6.8
7.0
18.0
47.8
13.7
18.0
10.8
34.2
75.5
Liguria
Lombardia
Trentino-Alto Adige
Veneto
Friuli-Venezia Giulia
Emilia-Romagna
81.3
85.3
75.1
83.3
87.8
78.9
6.3
8.8
5.4
7.2
9.5
10.5
12.4
5.8
19.5
9.6
2.7
10.6
14.0
71.2
31.6
26.4
50.6
22.5
6.2
19.8
24.4
46.4
21.7
29.6
79.8
9.0
44.0
27.2
27.7
47.9
Toscana
Umbria
Marche
Lazio
Abruzzo
Molise
66.3
72.2
75.6
68.8
87.9
78.4
8.5
6.7
7.8
19.9
8.0
6.9
25.2
21.1
16.6
11.3
4.1
14.6
17.2
1.7
51.3
18.8
22.2
18.6
19.3
49.0
14.4
34.7
8.1
14.6
63.5
49.2
34.3
46.5
69.7
66.8
Campania
Puglia
Basilicata
Calabria
Sicilia
Sardegna
58.9
64.2
28.2
4.3
37.9
39.0
6.5
5.3
2.8
2.9
46.3
41.8
34.6
30.5
69.0
92.8
15.8
19.3
11.0
15.1
8.2
5.6
5.8
34.0
25.1
39.3
10.0
18.3
25.8
50.6
63.9
45.7
81.7
76.1
68.5
15.3
Total
66.8
11.2
22.0
24.4
24.3
51.3
Note: averages over time
The existence of many Mezzogiorni is not a novelty; it is a well accepted idea in a recent specialized Southern literature, when looking at the rising degree of internationalization of these regions
and their increasing exports (Viesti, 2000) or at the ratio export/Mezzogiorno’s trade (Guerrieri
and Iammarino, 2002; 2007). Hints of economic dynamism respect to the rest of the South concern
Abruzzo, Campania and Puglia since 1985, and more evidently during the 1990s, when a local
system of small and medium entreprises (SMEs) has been emerging, reproducing the structure of
the Northern industrial districts (Viesti, 2000). However, while Campania and Puglia have been
reinforcing the traditional made in Italy sectors (clothing, textile, footwear, leather products, furnitures), Abruzzo has been developing a combination of both traditional and high-tech intensive
sectors, like electrical products and Pharmaceuticals (Guerrieri and Iammarino, 2007). Note also
that Molise can be considered as an industry-inclined centre, along with Abruzzo and Basilicata,
its provincial system being characterized by high industrial dynamism (Guerrieri and Iammarino,
2002).55 On the other hand, Calabria, Sicilia and Sardegna have been con…rming the failure of their
sectoral specialization, mainly characterized by a strenghtening of slow-growing, resource-intensive
sectors (Ibidem; Iammarino and Santangelo, 2001).
5 4 Their standing-out behaviour seems to somehow anticipate the exclusion of these two regions from the Objective
1 funds as for the programming period 2000-2006.
5 5 This emerges when looking at their evolution at the NUTS3 (provincial) level, from 1985 to 1998.
26
Looking at regional IRFs of GDP (Appendix 1, …gure A1.7, solid lines), it seems that the
lowest synchronized regions are in the South, and are, namely, Calabria, Sicilia and Sardegna,
followed by Basilicata, whose variance is low but the response is in line with the EU aggregate. The
other Southern regions, Puglia, Campania, Abruzzo and Molise, appear more synchronized to the
European average behaviour.
In this setting, few more words should be spent on the region Basilicata: indeed, though not
highly integrated, the response of this region to the common shock is above the EU average. As
seen in the literature quoted above, Basilicata is portrayed as a high-potential region, expecially
in terms of industry and export internationalization and specialization, ranging from arti…cial and
synthetic …bres to railway vehicles (Guerrieri and Iammarino, 2007); moreover, it is included in the
group of emerging industrial regions over the period 1985-1996, along with Abruzzo, Marche and
Umbria, its local system being in line with the North-Eastern regions. To this extent, we could
intepret its behaviour as typical of an emerging region.
Employment dynamics, as anticipated, are mainly driven by local and national factors. Only
Lombardia shows shares well above 50% for the EU component; this is not surprisingly, given the
international nature of the …rms located in this region: indeed, this is the region accounting for
45% of the national over the cumulated gross FDI in‡ows for the period 1994-2000 (Bronzini, 2004)
and where the greater number of new foreign a¢ liates located in Italy was concentrated over the
period 1991-1999 (Basile et al., 2005).
One interesting regularity comes out when comparing employment in the South respect to the
rest of Italy (Appendix 1, …gure A1.7, dotted lines): here, employment results almost una¤ected
(Puglia, Sicilia, Sardegna) or even declining (Campania, Basilicata, Calabria) after the identi…ed
european shock. This feature reproduces one important aspect of these regional economies, whose
main problem concerns employment: the failure of catching-up of this part of Italy, when focusing
on the decade 1980-90, seems to be due to the decreasing of the share workers per capita (Felice,
2009).
What emerges from the previous discussion is that a somehow variagated picture of the least
developed part of Italy exists and is partially captured by this model. However, since models are
only simpli…ed representation of reality, though the encouraging performances and the documented
evolution of the productive structure of some Southern regions, signi…cant gaps still exist, in terms
of productivity, technology di¤usion and innovation, if compared to the rest of Italy and Europe as
well.56
5
Conclusions
Structural DFMs are useful tools to investigate some interesting issues in the business cycle literature, like cross-country patterns of synchronization. Moreover, in regional analysis they give
detailed insights on both across and within-country paths of developments of the economic areas
involved. In the empirical section of the present work, a two-variables-two shocks DFM is estimated,
and the main positive driver of GDP growth over a …ve-year horizon identi…ed. We do believe that
S-DFMs like this one can improve on the existing European literature on regional synchronization,
since they allow to (i) perform multivariate analysis on more key macroeconomic variables at a time
(ii) identify the sources of common volatility (iii) keep trace of the identity of each observation unit,
estimating variance shares and responses to common shocks, region by region.
5 6 See,
for instance, Iammarino and Santangelo (2001) or Iammarino et al. (2004).
27
The results of our empirical exercise o¤er a quite complex picture of Europe as a whole and of
its regional structure, and can be summarized as follows. First, both variance decompositions and
IRFs show that, in general, regions are more integrated and synchronized in terms of GDP dynamics
than of Employment. This re‡ects, on the one hand, a somewhat successful integration of regional
economies through common trade, monetary and economic policies or …nancial interdependences
and, on the other hand, a much slower integration of labour markets, con…rming the existence of
tighter constaints on the labour mobility side. Moreover, GDP and Employment seem to be driven
by di¤erent forces: while very common and very local factors are prevalent in the former, national
and local-speci…c components dominate in the latter, and the main positive driver of GDP growth
contributes only marginally to the Employment growth dynamics. Since dichotomies both within
and across countries are more likely to arise in terms of Employment, this result highlights the
importance of increasing labour market integration on the one hand, and the need of a special focus
on regional Employment dynamics, carried along with the one on income growth, in order to design
proper policies and achieve more cohesion across di¤erent parts of Europe.
Second, Europe is mainly characterized by regional, rather than national economies, in line with
other empirical evidences: GDP is mainly driven by very common and very speci…c components,
meaning that the national one is generally not prevalent; moreover, the more synchronized regions
are not de…ned by national borders, but almost all countries have more and less integrated regions
within their borders. This highlights the importance of monitoring synchronization at the regional
level, since the evolution towards less synchronized regions would reduce the optimality of extreme
integration policies, like the choice of a common currency. In this perspective, regional cohesion
programs for dichotomous countries, like those realized by the European Commission since 1989,
become crucial.
When looking at Spain and Italy, we …nd that though at di¤erent stages of the integration
process, both these countries are characterized by some extreme polarization of its regions, especially
in terms of the european component variance. Moreover, groups of more and less integrated regions
do not appear as homogeneous blocks: the most integrated regions include also low income and
developing regions in Spain, and similarly for Italy, two Southern regions show high shares of the
European component variance, revealing some dynamism in the process of integration.
Since the e¤ects of integration can be observed only in the long run, it would be interesting to
extend this analysis to a wider sample, including the most recent years and new member states.
This would be much interesting, also in the light of the most recent events a¤ecting the cohesion
of the European Union and its stability.
Finally, since regional analysis have relevant implications for European policies in many domains,
including the renewed debate on the optimality of the single currency area, we hope that the
improvements of structural analysis like the one presented here could …nd a place in the oncoming
European research agenda.
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6
6.A
Appendix 1
Methodological issues
In order to obtain the three components for each variable and estimate equations (1.14) and (1.16),
we need to …nd the optimal weights. One …rst computational problem, however, is that the covariance matrix of the non common components is non observable, so in principle we cannot …nd the
1
1
j
j
principal component of
m.
m
m and ( m )
As suggested by Forni and Reichlin (2001), the estimation procedure could start by assuming
that jm and m are diagonal matrices with the same entries as jm and m respectively, multiplied
by a random scalar between 0 and 1. Stated di¤erently, the procedure is initialized assuming that the
non-common components explain a random percentage of the overall variance of the corresponding
j
variables.
m are then used to …nd the preliminary weights and estimate the models,
m and
running the OLS regressions of equations (1.14) and (1.16).
After this stage, we observe both jm and m , given respectively by the estimated covariance
matrix of the local components in the regional variables –i.e., the residuals in equation (1.16) –and
of the non-common components in the national aggregates, given by the residuals in equation (1.14).
Setting the non diagonal elements of these matrices equal to zero, as required by the orthogonality
assumption, these estimates of jm and m are used to …nd the new optimal aggregates and estimate
again equations (1.14) and (1.16).
The optimal weights of national aggregates, extracted in the last step, and the residual share of
non-common variance in the national and European aggregates are shown in Table A1.1.
Table A1.1: optimal weights by country and non -common component residual share
Country
wGDP
wEMP
emp
Germany
UK
0.12
0.02
0.009
0.018
0.04
0.48
0.003
0.006
France
Italy
Belgium
Netherlands
Greece
Spain
0.36
0.22
0.08
0.08
0.02
0.08
0.012
0.009
0.052
0.012
0.069
0.017
0.10
0.02
0.29
0.01
-0.02
0.08
0.018
0.029
0.034
0.008
0.002
0.010
Portugal
0.01
0.010
0.00
0.018
-
0.039
-
0.115
EU
6.B
gdp
VAR basics
Consider a N 1 vector of zero-mean variables y t , with generic VAR(1) representation,
yt = ' yt
1
+ "t
(A1.1)
where ' is a N N matrix of autoregressive parameters and "t is a vector of white noises, not
correlated at di¤erent times, with zero mean and covariance matrix .
Inverting the initial VAR(1) representation, the corresponding MA( 1) one is given by
y t = "t +
1 "t 1
33
+
2 "t 2
+ :::
1
where the MA coe¢ cient matrices are obtained from [I '(L)] = I + '(L) + '2 (L)2 + :::
From here, since y t i , i 1, is a linear function of "t i , i 1, which are all uncorrelated with
"t , it results that "t is uncorrelated with all the lags of y t , and a linear forecast of y t based on its
past information is given by
y
^t=t
1
= ' yt
(A1.2)
1
while "t can be interpreted as the fundamental innovation for y t , i.e. the error in forecasting y t
based on the information available until (and including) period t 1.
From (A1.1), leading y t s periods ahead and substituting recursively the lags, it results that
y t+s = 's y t +
s 1
X
'i "t+s
i
=
s yt
i=0
Since y
^t+s=t
1
= 's y
^t=t
1,
+
s 1
X
i "t+s i
i=0
the s-step-ahead forecast error for y t+s is given by
y t+s
y
^t+s=t
=
1
s
X
i "t+s i
i=0
where 0 = I.
The variance of the s-step-ahead forecast error, or Mean Squared Error, is given by
M SE y
^t+s=t
1
=
+
0
1
1
+ :::
0
s
s
(A1.3)
Passing from the reduced-form VAR residuals to the structural shocks et , using "t = U Ret ,
with U the lower-triangular matrix from the Cholesky decomposition of and R unitary rotation
matrix, then the s-step-ahead forecast error becomes
y t+s
y
^t+s=t
1
=
s
X
(A1.4)
i U Ret+s i
i=0
Denoting by ur k the kth column of the matrix U R, "t can be written as
"t =
N
X
ur k ekt
k=1
Post-multiplying this one by its transpose and taking expectation, we obtain
= ur 1 ur 01 + ur 2 ur 02 + :::ur N ur 0N =
N
X
ur k ur 0k
k=1
This means that we can decompose the variance of the residuals into the contribution of each
structural shock, which in turn depends on the selected rotation R. Substituting this expression of
into the formula of the MSE in (A1.3), we obtain the decomposition of the forecast error variance
into the contribution of the structural shocks over the forecast horizon s:
M SE y
^t+s=t
1
=
s X
N
X
i=0 k=1
34
0
i ur k ur k
0
i
(A1.5)
When the forecast horizon is su¢ ciently far, MSE converges to the (unconditional) variance of
the variables in y t , provided that the VAR is covariance-stationary. Thus, (A1.5) represents also
the contribution of each shock to the overall variance. The contribution of the kth shock to the
variancePof the nth variables in y t over the forecast horizon s is the (n,n) element of the N N
s
matrix i=0 i ur k ur 0k 0i .
By de…nition, the Impulse Response Function (IRF) of a N 1 vector of variables y t to a N 1
vector of shocks et is a N N matrix collecting the reactions of each variable to each shock as
functions of the period s when we observe these responses. Formally,
IRF (y t ; et ; s) =
@y t+s
=
@e0t
sU R
where the second equality comes from the MA(1) representation of y t+s , with "t = U Ret . Note
that in this N N matrix, the generic (i, j) element refers to the response of the ith variable in y t
to the jth shock in et as function of s, so the IRF of the ith variable in to the jth shock in is a plot
of the (i, j) element in s U R against s.
Note that, since the variables have zero mean and are stationary, in the no-shock case their
value is zero. If s = 0, the contemporaneous reaction of y t is U R; for s > 0, s U R measures the
"residual" e¤ect after s periods, i.e. the variable variation still accounted s periods after the shock.
As a result, the total variation of the ith variable respect to the no-shock case over the de…ned
horizon period s is the cumulative sum of IRF (y t ; et ; i), for i = 1:::s. The result is the matrix of
the cumulative IRF of the variables y t to et .
6.C
Identi…cation strategy
In order to identify a prevalently positive shock, de…ne
e
~t = et +
e~
where e~ is the vector of the means of the common shocks. Similarly, for the vector ot the aggregates,
we have
x
~ t = xt +
where
x
~
x
~
is the vector of the means of the European aggregates. It holds that
x
~t = xt +
x
~
= A(L)~
et = A(1)
e~
+ A(L)et
If det(A(1)) is di¤erent from zero, A(1) is invertible and
e~
= A(1)
1
x
~
Di¤erent rotations identify di¤erent vectors et , that correspond to di¤erent e
~t and e~. Denoting
P
by e~M
the series of the mainly positive shocks, R is selected so that the sum of the absolute values
t
P
of the negative realizations of e~M
is minimized. Alternatively, Forni and Reichlin (1998) show
t
that, assuming normality of the shocks, the sum of the absolute values of the negative realizations
P
is minimized when the mean of e~M
is maximized, since variance is not in‡uenced by the rotations.
t
As a consequence, one could either minimize the absolute sum of negative values or maximize the
shock mean. However, here we follow the former method.
35
In order to identify the main driver of a vector of variables xt over a speci…c forecast horizon
H, we need to derive the share of the overall forecast error variance of xt explained by each shock
over H. Using basic VAR de…nitions, and sticking to the notation used throughout the paper, the
H-step-ahead forecast error for xt is given by
H h
X
[I
A(L)L]
1
h=0
ih
"t+h =
H h
X
[I
A(L)L]
h=0
1
ih
U Ret+h
As seen above, the variance of the H-step-ahed forecast error, also said FEV, can be decomposed
into the contribution of each orthogonal shock (k) to the overall variance:
H_F EV =
M X
H
h
X
[I
1
A(L)L]
k=1 h=0
ih
ur k
h
[I
A(L)L]
1
ih
ur k
0
In order to identify the shocks contributing the most to the variance of GDP growth over the
…ve-year horizon, this formula should be computed for di¤erent rotations R, with H = 5 years, k
corresponding to the shock whose contribution we are computing, and focus on the (m, m).element
of this matrix, where m is the position of GDP growth in the vector collecting the European
aggregates. For instance, in our application, where M = 2 and GDP growth is the …rst variable
(m = 1) in xt , the contribution of shock two (k = 2) to the FEV of this variable over a …ve-year
horizon (H = 5) is the (1,1) element of the 2 2 matrix
5
h
X
h=0
[I
A(L)L]
1
ih
ur 2
where ur 2 is the second column of the matrix U R.
36
h
[I
A(L)L]
1
ih
ur 2
0
6.D
Data
The dataset covers 107 European regions whose GDP and Employment are observed with annual
frequency for the period 1977-1995. The countries involved are Belgium, western Germany, Greece,
Spain, France, Italy, the Netherlands, Portugal and the UK. The level of disaggregation is NUTS2,
according to the European nomenclature, for all countries but Belgium, Germany, the Netherlands
and the UK, whose data are available only at the NUTS1 level for that period. The details on the
geographic area concerned in the analysis are in Table A1.2.
The main source of the data is the CRENoS Data Bank On European Regions, available at
http://www.crenos.unica.it/en/databases.
GDP is Gross Domestic Product in Purchasing Power Standard (PPS) at constant prices, 1990
= 100. EMP is total employment measured as thousands of employed people in the region. For all
the series, natural logarithms have been taken and the …rst di¤erence computed in order to obtain
the growth rate of the variables. Finally, the mean has been subtracted from the resulting series.
In table A1.3, we have listed the codes identifying the regions involved in the analysis. The
sources are the European Commission and EUROSTAT.57
All the results (optimal weights, variance and FEV decompositions, IRFs,...) have been obtained
writing a MATLAB code that reproduces step by step the procedures explained in detail in par.1.3.
For the OLS regressions, we have employed the MATLAB code written by Mario Forni, available
on line at:
http://www.economia.unimore.it/forni_mario/matlab.htm.
For the VAR estimations, we have employed a MATLAB program written by James P. LeSage
(Department of Economics, University of Toledo), available on line at his homepage:
http://www.rri.wvu.edu/WebBook/LeSage/etoolbox/var_bvar/contents.html.
5 7 See
http://epp.eurostat.ec.europa.eu/portal/page/portal/nuts_nomenclature/introduction
37
38
NUTS1
NUTS1
NUTS2
NUTS2
NUTS2
NUTS2
NUTS1
NUTS2
NUTS1
Belgium (B)
Germany (D)
Greece (GR)
Spain (E)
France (F)
Italy (I)
Netherlands (NL)
Portugal (P)
United Kingdom (UK)
12
5
4
20
22
17
13
11
3
N. REGIONS
EXCLUDED
Região Autónoma dos Açores, Região Autónoma da Madeira
Guadeloupe, Martinique, Guyane, Réunion
Ciudad Autónoma de Ceuta, Ciudad Autónoma de Melilla
Eastern Germany
Source: Crenos Data Bank On European Regions
DISAGGREGATION
COUNTRY
Table A1.2: list of the countries included in the analysis
39
Région Bruxelles-capitale
Vlaams Gewest
Région Wallonne
Baden-Württemberg
Bayern
Berlin
Bremen
Hamburg
Hessen
Niedersachsen
Nordrhein-Westfalen
Rheinland-Pfalz
Saarland
Schleswig-Holstein
Anatoliki Makedonia, Thraki
Kentriki Makedonia
Dytiki Makedonia
Thessalia
Ipeiros
Ionia Nisia
Dytiki Ellada
Sterea Ellada
Peloponnisos
Attiki
Voreio Aigaio
Notio Aigaio
Kriti
Galicia
Principado de Asturias
Cantabria
BE1
BE2
BE3
DE1
DE2
DE3
DE5
DE6
DE7
DE9
DEA
DEB
DEC
DEF
GR11
GR12
GR13
GR14
GR21
GR22
GR23
GR24
GR25
GR3
GR41
GR42
GR43
ES11
ES12
ES13
FR61
FR62
FR53
FR52
FR43
FR51
FR42
FR3
FR41
FR26
FR24
FR25
FR23
FR21
FR22
FR1
ES7
ES61
ES62
ES52
ES53
ES51
ES43
ES42
ES41
ES3
ES24
ES22
ES23
ES21
Aquitaine
Midi-Pyrénées
Poitou-Charentes
Bretagne
Franche-Comté
Pays de la Loire
Alsace
Nord-Pas-de-Calais
Lorraine
Bourgogne
Centre
Basse-Normandie
Haute-Normandie
Champagne-Ardenne
Picardie
Île de France
Canarias (ES)
Andalucia
Murcia
Comunidad Valenciana
Baleares
Cataluña
Extremadura
Castilla-la Mancha
Castilla y León
Comunidad de Madrid
Aragón
Comunidad Foral de Navarra
La Rioja
Pais Vasco
CODE DENOMINATION
NL3
NL4
NL2
NL1
ITA
ITB
IT93
IT91
IT92
IT8
IT71
IT72
IT6
IT52
IT53
IT51
IT4
IT32
IT33
IT2
IT31
IT13
IT12
IT11
FR83
FR82
FR81
FR71
FR72
FR63
CODE
West-Nederland
Zuid-Nederland
Oost-Nederland
Noord-Nederland
Sicilia
Sardegna
Calabria
Puglia
Basilicata
Campania
Abruzzo
Molise
Lazio
Umbria
Marche
Toscana
Emilia Romagna
Veneto
Friuli Venezia Giulia
Lombardia
Trentino-Alto Adige
Liguria
Valle d'Aosta
Piemonte
Corse
Provence-Alpes-C. d'Azur
Languedoc-Roussillon
Rhône-Alpes
Auvergne
Limousin
DENOMINATION
UKM
UKN
UKL
UKK
UKI
UKJ
UKG
UKH
UKF
UKE
UKD
UKC
PT15
PT14
PT12
PT13
PT11
CODE
Scotland
Northern Ireland
Wales
South West
London
South East
West Midlands
Eastern
East Midlands
Yorkshire and The Humber
North West (includ. Merseyside)
North East
Algarve
Alentejo
Centro (P)
Lisboa e Vale do Tejo
Norte
DENOMINATION
Source: European Commission and EUROSTAT (http://epp.eurostat.ec.europa.eu/portal/page/portal/nuts_nomenclature/introduction)
DENOMINATION
CODE
Table A1.3: list of the NUTS1-NUTS2 codes according to the standard European nomenclature
40
0,337
0,383
0,406
ES12
ES13
0,324
GR14
0,168
0,371
GR13
ES11
0,096
0,396
GR11
GR12
GR43
0,562
DEF
0,115
0,202
0,755
0,714
DEB
DEC
0,356
0,807
DEA
GR41
GR42
0,679
0,692
DE7
DE9
GR3
0,519
DE6
0,451
0,292
0,797
DE5
0,344
0,034
DE3
GR24
GR25
0,765
DE2
GR23
0,845
DE1
0,146
0,224
0,699
0,570
BE2
BE3
GR21
GR22
0,325
EC
BE1
CODE
0,300
0,354
0,327
0,196
0,038
0,005
0,224
0,443
0,517
0,443
0,243
0,350
0,550
0,023
0,411
0,329
0,311
0,181
0,156
0,173
0,249
0,292
0,443
0,078
0,629
0,217
0,145
0,271
0,273
0,299
NC
GDP
0,317
0,241
0,335
0,636
0,847
0,793
0,420
0,106
0,192
0,213
0,610
0,426
0,126
0,606
0,494
0,275
0,126
0,064
0,130
0,020
0,072
0,016
0,039
0,125
0,337
0,018
0,010
0,030
0,157
0,377
LC
FR61
FR62
FR53
FR52
FR43
FR51
FR42
FR3
FR41
FR26
FR24
FR25
FR23
FR22
FR1
FR21
ES7
ES61
ES62
ES53
ES51
ES52
ES43
ES42
ES41
ES3
ES24
ES22
ES23
ES21
CODE
0,513
0,624
0,701
0,705
0,644
0,755
0,694
0,826
0,860
0,678
0,713
0,620
0,221
0,798
0,530
0,825
0,120
0,629
0,393
0,136
0,709
0,523
0,253
0,606
0,203
0,690
0,432
0,396
0,337
0,532
EC
0,288
0,175
0,082
0,295
0,065
0,068
0,046
0,020
0,005
0,164
0,117
0,159
0,121
0,024
0,110
0,012
0,286
0,197
0,129
0,342
0,257
0,172
0,304
0,295
0,592
0,182
0,477
0,162
0,461
0,080
NC
GDP
0,200
0,201
0,217
0,000
0,291
0,177
0,260
0,154
0,134
0,158
0,170
0,221
0,658
0,179
0,360
0,162
0,594
0,174
0,478
0,523
0,034
0,304
0,443
0,098
0,206
0,128
0,092
0,442
0,201
0,388
LC
NL3
NL4
NL2
NL1
ITA
ITB
IT93
IT91
IT92
IT8
IT71
IT72
IT6
IT53
IT51
IT52
IT4
IT32
IT33
IT31
IT13
IT2
IT12
IT11
FR83
FR82
FR81
FR71
FR72
FR63
CODE
0,430
0,704
0,645
0,551
0,379
0,390
0,043
0,642
0,282
0,589
0,879
0,784
0,688
0,756
0,663
0,722
0,789
0,833
0,878
0,751
0,813
0,853
0,752
0,868
0,347
0,773
0,368
0,866
0,580
0,572
EC
0,180
0,283
0,334
0,380
0,463
0,418
0,029
0,053
0,028
0,065
0,080
0,069
0,199
0,078
0,085
0,067
0,105
0,072
0,095
0,054
0,063
0,088
0,068
0,062
0,301
0,067
0,217
0,070
0,104
0,043
NC
GDP
0,390
0,013
0,021
0,069
0,158
0,193
0,928
0,305
0,690
0,346
0,041
0,146
0,113
0,166
0,252
0,211
0,106
0,096
0,027
0,195
0,124
0,058
0,180
0,070
0,352
0,161
0,415
0,064
0,315
0,385
LC
UKN
UKL
UKM
UKK
UKI
UKJ
UKH
UKF
UKG
UKE
UKD
UKC
PT15
PT14
PT12
PT13
PT11
CODE
0,239
0,275
0,309
0,449
0,131
0,230
0,233
0,312
0,281
0,247
0,239
0,225
0,186
0,107
0,013
0,192
0,254
EC
0,380
0,467
0,485
0,463
0,219
0,178
0,236
0,578
0,661
0,500
0,691
0,471
0,134
0,481
0,528
0,250
0,746
NC
GDP
0,381
0,259
0,206
0,088
0,650
0,591
0,530
0,110
0,058
0,252
0,070
0,304
0,681
0,412
0,459
0,558
0,000
LC
Table A1.4: Variance of GDP growth rates due to European (EC), National (NC) and Local (EC) shocks (shares of total variance)
41
0,603
0,803
0,655
0,412
0,347
0,024
0,366
0,566
0,457
0,340
0,368
0,402
0,730
0,354
0,440
0,143
0,098
0,079
0,036
0,049
0,084
0,044
0,101
0,213
0,323
0,274
0,577
0,139
0,358
0,569
BE2
BE3
DE1
DE2
DE3
DE5
DE6
DE7
DE9
DEA
DEB
DEC
DEF
GR11
GR12
GR13
GR14
GR21
GR22
GR23
GR24
GR25
GR3
GR41
GR42
GR43
ES11
ES12
ES13
EC
BE1
CODE
0,174
0,261
0,442
0,140
0,194
0,056
0,787
0,132
0,007
0,089
0,079
0,307
0,042
0,156
0,310
0,294
0,597
0,513
0,023
0,624
0,533
0,579
0,387
0,586
0,557
0,632
0,546
0,181
0,242
0,150
NC
EMPLOYMENT
0,257
0,381
0,419
0,282
0,482
0,670
0,000
0,824
0,892
0,827
0,884
0,644
0,879
0,746
0,250
0,564
0,049
0,085
0,247
0,009
0,010
0,081
0,047
0,048
0,418
0,022
0,043
0,016
0,103
0,247
LC
FR62
FR61
FR53
FR52
FR43
FR51
FR42
FR3
FR41
FR26
FR24
FR25
FR23
FR22
FR1
FR21
ES7
ES61
ES62
ES53
ES51
ES52
ES43
ES42
ES41
ES3
ES24
ES22
ES23
ES21
CODE
0,527
0,174
0,289
0,503
0,320
0,457
0,526
0,571
0,284
0,293
0,367
0,470
0,091
0,491
0,492
0,573
0,367
0,623
0,531
0,273
0,659
0,596
0,481
0,435
0,490
0,438
0,549
0,612
0,286
0,462
EC
0,046
0,634
0,635
0,012
0,230
0,054
0,018
0,001
0,295
0,315
0,619
0,008
0,319
0,256
0,058
0,041
0,229
0,340
0,187
0,118
0,226
0,258
0,385
0,314
0,437
0,282
0,349
0,250
0,086
0,199
NC
EMPLOYMENT
0,427
0,192
0,077
0,485
0,449
0,490
0,455
0,429
0,421
0,392
0,013
0,522
0,590
0,252
0,450
0,386
0,404
0,038
0,282
0,609
0,115
0,147
0,134
0,251
0,073
0,279
0,102
0,138
0,628
0,339
LC
NL4
NL3
NL2
NL1
ITA
ITB
IT93
IT91
IT92
IT8
IT71
IT72
IT6
IT53
IT51
IT52
IT4
IT32
IT33
IT31
IT13
IT2
IT12
IT11
FR83
FR82
FR81
FR71
FR72
FR63
CODE
0,151
0,169
0,210
0,163
0,058
0,340
0,056
0,151
0,082
0,110
0,222
0,186
0,188
0,513
0,172
0,017
0,225
0,264
0,506
0,316
0,140
0,712
0,137
0,478
0,509
0,511
0,184
0,114
0,017
0,183
EC
0,810
0,778
0,771
0,813
0,258
0,506
0,183
0,393
0,100
0,251
0,081
0,146
0,347
0,144
0,193
0,490
0,296
0,464
0,217
0,244
0,062
0,198
0,108
0,180
0,079
0,019
0,470
0,138
0,492
0,047
NC
EMPLOYMENT
0,039
0,053
0,019
0,024
0,685
0,153
0,761
0,457
0,817
0,639
0,697
0,668
0,465
0,343
0,635
0,492
0,479
0,272
0,277
0,440
0,798
0,090
0,755
0,342
0,412
0,469
0,345
0,748
0,491
0,771
LC
UKN
UKL
UKM
UKK
UKI
UKJ
UKH
UKF
UKG
UKE
UKD
UKC
PT15
PT14
PT12
PT13
PT11
CODE
0,227
0,144
0,014
0,103
0,918
0,054
0,401
0,470
0,104
0,422
0,619
0,026
0,008
0,006
0,038
0,018
0,143
EC
0,220
0,401
0,477
0,401
0,081
0,248
0,266
0,440
0,439
0,197
0,076
0,026
0,847
0,921
0,881
0,804
0,152
NC
EMPLOYMENT
0,554
0,456
0,509
0,496
0,001
0,698
0,333
0,091
0,457
0,381
0,305
0,948
0,145
0,073
0,081
0,179
0,705
LC
Table A1.5: Variance of Employment growth rates due to European (EC), National (NC) and Local (EC) shocks (shares of total variance)
42
9
3,113
6,147
8,654
10,930
11,612
10,158
7,649
6,331
4,163
3,290
3,400
3,053
5,797
8,516
10,705
θ=0
θ=12
θ=24
θ=36
θ=48
θ=60
θ=72
θ=84
θ=96
θ=108
θ=120
θ=132
θ=144
θ=156
θ=168
SHOCK 1
0,771
0,823
0,503
0,179
0,225
0,587
0,849
0,709
0,328
0,145
0,371
0,745
0,837
0,541
0,197
MSE(GDP)
0,426
0,888
0,903
0,454
0,058
0,171
0,663
0,968
0,734
0,231
0,038
0,377
0,858
0,926
0,504
MSE(EMP)
3,312
2,986
3,130
3,849
5,780
7,386
9,521
11,539
11,345
9,172
6,920
3,558
2,967
3,087
3,700
ABS. SUM
9
4
4
6
6
6
10
13
12
11
11
9
5
4
6
e2t < 0
SHOCK 2
e1t < 0, e2t < 0 are the number of negative realizations for shock 1 and 2
12
11
11
8
4
5
6
6
8
11
12
12
10
11
e1t < 0
ABS. SUM
ROTATION
0,229
0,177
0,497
0,821
0,775
0,413
0,151
0,291
0,672
0,855
0,629
0,255
0,163
0,459
0,803
MSE(GDP)
0,574
0,112
0,097
0,546
0,942
0,829
0,337
0,032
0,266
0,769
0,962
0,623
0,142
0,074
0,496
MSE(EMP)
Table A1.6: absolute sum and number of negative realizations, MSE of GDP and EMP growth rates, horizon s=5 years, for di¤erent rotations
43
3.290
3.400
3.053
3.113
Abs. sum
Rotation
shock 1
shock 2
e1t < 0 FEV (%) Abs. sum Rotation e2t < 0 FEV (%)
= 132
8
17.9
2.967
= 24
5
16.3
2.986
= 156
4
17.7
=0
9
19.7
= 108
5
58.7
3.087
= 12
4
45.9
= 120
4
22.5
3.130
= 144
4
49.7
e1t < 0, e2t < 0 are the number of negative realizations for shock 1 and 2
Table A1.7: results from the identi…cation strategy
6.E
6.E.1
Graphs
European aggregates
Figure A1.1: IRFs of GDP (solid line) and EMP (dotted line) European aggregates to eM P D
Left panel: simple IRF; right panel: cumulated IRF
44
45
6.E.2
Regional variables
Figure A1.2: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Belgium
46
Figure A1.3: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Germany
47
Figure A1.3: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Germany
48
Figure A1.4: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Greece
49
Figure A1.4: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Greece
50
Figure A1.5: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Spain
51
Figure A1.5: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Spain
52
Figure A1.6: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
France
53
Figure A1.6: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
France
54
Figure A1.6: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
France
55
Figure A1.7: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Italy
56
Figure A1.7: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Italy
57
Figure A1.7: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Italy
58
Figure A1.8: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
The Netherlands
59
Figure A1.9: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
Portugal
60
Figure A1.10: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
The UK
61
Figure A1.10: IRFs of GDP (solid line) and EMP (dotted line) to eM P D
The UK