Youth unemployment in Europe: persistence and macroeconomic determinants.
Caporale, Guglielmo Maria ; Gil-Alana, Luis
INTRODUCTION
Youth unemployment has attracted significant attention in recent
years, especially in Europe, where it is particularly high relative to
adult unemployment (see, eg, Perugini and Signorelli, 2010), and has
been affected even more than the latter by financial crises (see
Choudhry et al, 2012). Some key factors driving it that have been
identified include the relatively low human capital of young people (see
OECD, 2005), the 'youth experience gap' (see Caroleo and
Pastore, 2007) and the mismatch between the skills acquired through
education and those required by employers (see, eg, Quintini et al.,
2007). Policy recommendations have been put forward both in the academic
literature (see, eg, Brunello et al., 2007) and by the European
Commission (2008).
This paper investigates the main statistical features and the
macroeconomic determinants of youth unemployment in a number of European
countries. It is well-known that an important feature of unemployment in
Europe is its relatively high degree of persistence, which suggests that
a hysteresis model (Blanchard and Summers, 1986; Gordon, 1988) might be
appropriate. In fact, many empirical papers have found evidence
consistent with this hypothesis, including Alogoskoufis and Manning
(1988), Graafland (1991), Lopez et al. (1996), Wilkinson (1997) and so
on using standard unit root methods, and Caporale and Gil-Alana (2008)
and Cuestas et al. (2011) and others applying fractional integration
methods. High persistence appears to be a feature also of European youth
unemployment (see, eg, Heckman and Borjas, 1980; Ryan, 2001; Caporale
and Gil-Alana, 2013). Therefore, first of all we examine the degree of
persistence of the series, which sheds light on whether appropriate
policy actions are required in case of high persistence, by estimating
both autoregressive AR(1) processes and long memory (fractional
integration) models. Second, we investigate the main macroeconomic
determinants of youth unemployment in Europe by means of a fractional
cointegration model that includes variables such as GDP and inflation as
explanatory variables. The organization of the paper is as follows. The
next section outlines the econometric framework. The penultimate section
presents the data and the empirical results. The final section offers
some concluding remarks.
THE ECONOMETRIC FRAMEWORK
As mentioned in the introduction, our main analysis is based on the
concept of fractional integration, which allows the differencing
parameter d making a series stationary 1(0) to be a fraction as well as
an integer. Therefore, the series of interest can be represented as
[(1 - L).sup.d] [x.sub.t] = [u.sub.t], t = 0, [+ or -] 1, ... (1)
where [u.sub.t] is assumed to be an 7(0) process, defined as a
covariance stationary process with a bounded positive spectral density
function. Note that this approach includes the unit root case as a
particular case when d = 1.
Given the above parameterization, one can consider different cases
depending on the value of d. Specifically, if d = 0 and [x.sub.t] =
[u.sub.t], [x.sub.t] is said to be a 'short memory' or I(0)
process, and in the case of autocorrelated (AR) disturbances the
autocorrelation is 'weak', that is, the autocorrelation
function decays at an exponential rate; if d>0, xt is said to be a
'long memory' process, so called because of the strong
association between observations far apart in time. In this case, if d
belongs to the interval (0,0.5), x, is still covariance stationary,
while d>0.5 implies non-stationarity. Finally, if d<1, the series
is mean-reverting, with the effects of shocks disappearing in the long
run, in contrast to the case with d>l where these persist forever.
Two methods of estimation of the fractional differencing parameter
are employed here: one is a Whittle parametric approach in the frequency
domain (Dahlhaus, 1989), while the other is a semiparametric
'local' Whittle method (Robinson, 1995; Abadir et al, 2007).
In addition, a simple AR(1) model is also considered as an alternative
to measure persistence as the autoregressive coefficient. Other more
general AR(p) processes could be considered, with persistence than being
defined as the sum of the AR coefficients. However, given the relatively
small sample size in our case, a simple AR(1) specification is adequate
to describe the short-run dynamics of the series.
The fractional integration framework can be extended to the
multivariate case by estimating a fractional cointegration model.
Specifically, we follow the approach developed in Gil-Alana (2003),
which is a natural generalization of Engle and Granger's (1987)
procedure allowing for fractional parameters. In particular, we estimate
a linear regression of youth unemployment against its macroeconomic
determinants and check the significance of the estimated coefficients as
well as the order of integration of the residuals; if this is smaller
than for the individual series, then cointegration holds and there
exists a long-run equilibrium relationship between the variables that
can be interpreted as the steady state in economic terms. In addition, a
Hausman test for the null of no cointegration against the alternative of
fractional cointegration, as suggested by Marinucci and Robinson (2001),
is also carried out.
EMPIRICAL RESULTS
The data used include the total youth unemployment rate in 15
countries, Austria, Belgium, Denmark, Finland, France, Greece, Ireland,
Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden and
the United Kingdom. This variable is defined as the number of unemployed
in the 15-24 years age group divided by the labor force for that group,
obtained from the International Labor Organisation. For GDP, inflation,
output and consumer prices, data from the World Development Indicators
are used. All series are annual and span the period from 1980 to 2005.
As a preliminary step we estimate a simple AR(1) process to measure
the persistence of the series as its AR(1) coefficient. The results for
the three series are displayed in Table 1.
It can be seen that the autoregressive coefficients are much higher
for youth unemployment and inflation compared with GDP. In the case of
youth unemployment, the highest values are found for the peripheral
(Northern and Southern) countries: Ireland (0.94), Finland (0.92), the
Netherlands (0.89), Spain (0.89), Norway (0.88), Sweden (0.88), Italy
(0.87) and Greece (0.86). This high level of persistence is consistent
with the empirical evidence on total unemployment in most European
countries, suggesting the relevance of hysteresis models in the European
case (see, eg, Gordon, 1989; Graafland, 1991; Lopez et al., 1996).
Next, we estimate the fractional differencing parameter d and the
corresponding 95% intervals for each of the three series, youth
unemployment, inflation and GDP, in each country using the parametric
approach based on the Whittle function in the frequency domain. In all
cases, an intercept is included in the model and the d-differenced
process is assumed to be a white noise process. We report in bold in
Table 2 the cases where the unit root null hypothesis, d = 1, cannot be
rejected.
This happens in five countries, the United Kingdom, Italy, Norway,
Sweden and Ireland, for all three series. In the case of youth
unemployment, rejections of the null hypothesis in favor of higher
degrees of integration only occur for Finland, the Netherlands, Portugal
and Spain, the latter two countries
having some of the highest youth unemployment rates in the sample.
For inflation, the unit root null cannot be rejected in any case. For
GDP, this hypothesis is rejected in favor of explosive behavior (d>1)
in Finland, the Netherlands, Portugal and Spain, evidence of
mean-reversion (d<1) is found for Austria, Belgium, Denmark, France,
Greece and Luxembourg.
Table 3 focuses on the semiparametric results using three different
bandwidth parameters. For each series there is at least one case when
the unit root null hypothesis cannot be rejected. Given the evidence of
non-stationarity, the estimation was carried out using first
differences, then adding 1 to the estimated values to obtain the
integration orders. Overall, this evidence suggests non-stationarity and
the presence of a unit root in all three series in all countries
examined.
The step is the estimation of a multivariate cointegration model.
We started by including the same set of variables as in previous studies
by Jacobsen (1999), Blanchflower and Freeman (2000), Choudhry et al.
(2012). In particular, there is a large literature emphasizing the
impact of output and its growth on unemployment, the so-called
Okun's law (see, eg, Lee, 2000; Solow, 2000). Moreover, it appears
that youth unemployment is even more sensitive to macroeconomic and
labor market conditions than is total unemployment (see Choudhry et al.,
2013). However, since regressors such as FDI and openness were found not
to be significant, the results reported below are those obtained from a
model including GDP and inflation only as the macroeconomic determinants
of youth unemployment, namely
[y.sub.t] = [alpha] + [beta][x.sub.1t] + [x.sub.2t] + [x.sub.t];
[(1 - L).sup.d][x.sub.t] = [u.sub.t], t = 1,2, ... (2)
where [y.sub.t] stands for the youth unemployment rate, [x.sub.1t]
for inflation and [x.sub.2t] for GDP. The error term [u.sub.t] is
assumed to be a white noise or have an autocorrelated structure in
Tables 4 and 5, respectively.
Table 4 shows that for six countries, Italy, Belgium, Denmark,
France, Greece and Luxembourg, the estimated value of d is smaller than
1; however, in all these cases the confidence intervals are so wide that
the unit root null hypothesis cannot be rejected. In fact, the only
rejections of the unit root null occur in the cases of Finland, the
Netherlands, Portugal and Spain, but always in favor of higher orders of
integration. (1) Therefore, there is no evidence of cointegration of any
degree under the assumption of uncorrelated errors. As for the estimated
coefficients, they are all negative and more significant for inflation
than GDP.
Next, we analyze the case with autocorrelated disturbances.
Specifically, we consider a simple AR(1) process, the reason being that,
given the small number of observations, higher orders would lead to
overparameterized models. In this case all the estimated values of d are
below 1 and close to 0 in many cases, implying mean-reversion and
therefore cointegration. The low fractional differencing parameter is
now combined with a very large AR coefficient, implying that the errors
are still very persistent. Only for Finland is d significantly above 0.
As for the estimated coefficients, the inflation coefficient is
significant and negative in all countries except Spain, while the GDP
coefficient is significant in half of the cases. Given the differences
in the results depending on the specification of the error term, we also
estimated d in equation (2) using a log-periodogram semiparametric
estimator. These additional results, not reported, suggest that the
differencing parameter is very sensitive to the bandwidth parameter,
although most cases lie in the interval between 0.5 and 1, implying
fractional integration, non-stationarity and mean- reverting behavior.
Finally, we perform the Hausman test proposed by Marinucci and
Robinson (2001). This is specified as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
where i = x, y and z stand for each of the series under
examination, youth unemployment, inflation and GDP, in turn, s is the
bandwidth parameter (we set s=[(T).sup.0.5]), [[??].sub.i], are the
univariate estimates of the parent series and [[??].sup.*] is a
restricted estimate obtained in the multivariate representation under
the assumption that [d.sub.x] = [d.sub.y] = [d.sub.z]. The results using
this approach are displayed in Table 6.
The test statistics indicate the presence of fractional
cointegration in seven out of the fifteen countries examined, with
statistical significance for youth unemployment and inflation in the
majority of cases. It is also noteworthy that the estimated order of
integration in the cointegrating regression is in the interval (0.5, 1)
in all cases, implying non-stationary mean-reverting behavior. The
highest degree of cointegration is found in the case of Italy and
Portugal, where the estimated d is equal to 0.576 and 0.577,
respectively, followed by the United Kingdom (0.634), Luxembourg
(0.646), the Netherlands (0.746), Ireland (0.771) and Sweden (0.810).
For the remaining countries, this approach provides no evidence of
cointegration.
CONCLUSIONS
Both academics and policymakers have recently focused on the
challenge represented by European youth unemployment, which has become
even higher relative to adult unemployment following the recent
financial crisis and appears to be very persistent. This paper has
investigated its stochastic properties as well as its macroeconomic
determinants by using annual data on total youth unemployment in 15
countries and estimating autoregressive and long memory (fractionally
integrated) models as well as fractional cointegration ones. The
evidence confirms that youth unemployment is highly persistent in all
European countries examined, which suggests the relevance of hysteresis
models (Blanchard and Summers, 1986; Gordon, 1988) in a European context
and the need for active labor market policies aimed at preventing
short-term unemployment from becoming structural or long term. These
could include better school-to-work transition institutions as well as
educational, placement and training schemes (see Choudhry et al, 2012).
As for the macroeconomic factors driving European youth
unemployment, the fractional cointegration results are rather sensitive
to the method applied. Specifically, when following the approach of
Gil-Alana (2003), the findings are different depending on the underlying
assumptions about the error term: if the errors are assumed to be
uncorrelated, no evidence of cointegration is found in any case; by
contrast, under the assumption of autocorrelated errors, cointegration
appears to hold in all cases. When using the semiparametric method of
Marinucci and Robinson (2001) some evidence of (fractional)
cointegration is obtained in some cases with its estimated order in the
interval (0.5,1). A plausible explanation for the sensitivity of the
results to the method employed is the relatively small size of the
sample used. Nevertheless, the analysis provides some useful evidence on
the existence of long-run relationships between youth unemployment in
Europe and two key macroeconomic determinants, GDP and inflation. It
confirms in particular the importance of the linkage between output and
unemployment and the sensitivity of youth unemployment to overall
macroeconomic conditions (see Choudhry et al, 2013). Of course, a key
role is also played by macroeconomic and labor market policies and
institutions, as, for instance, stressed by the OECD (2006), but
recommending the specific actions required to address the so-called
'Euro-sclerosis' or poor employment performance of most
European countries is an issue beyond the scope of the present study,
whose aim is simply to offer some evidence on the persistence of youth
unemployment in Europe and its relationship to output and inflation.
Acknowledgements
We are grateful to MisbahTanveer Choudhry, Enrico Marelli and
Marcello Signorelli for kindly supplying the data set used in this
paper. Comments from the Editor and an anonymous referee are also
gratefully acknowledged. The first-named author gratefully acknowledges
financial support from a Marie Curie International Research Staff
Exchange Scheme Fellowship within the 7th European Community Framework
Programme under the project IRSES GA-2010-269134, and the second-named
author from the Ministry of Economy of Spain (ECO2011-2014 ECON Y
FINANZAS, Spain).
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(1) These countries also display orders of integration above 1 in
the univariate analysis.
GUGLIELMO MARIA CAPORALE [1, 2] & LUIS GIL-ALANA [3]
[1] Department of Economics and Finance, Brunei University,
Uxbridge, London, UB8 3PH, UK.
E-mail: Guglielmo-Maria.Caporale@brunel.ac.uk
[2] CESifo and DIW Berlin, Germany.
[3] School of Economics, University of Navarra, Pamplona, Spain.
E-mail: alana@unav.es
Table 1: Estimated AR coefficients for each series in each country
Country Youth unemployment Inflation GDP
The United Kingdom 0.838 0.683 0.586
Italy 0.872 0.978 0.443
Austria 0.848 0.607 0.194
Belgium 0.715 0.765 0.061
Denmark 0.605 0.876 0.173
Finland 0.925 0.935 0.608
France 0.763 0.969 0.345
Greece 0.866 0.937 0.488
Ireland 0.940 0.764 0.567
Luxembourg 0.795 0.697 0.112
The Netherlands 0.893 0.791 0.648
Norway 0.888 0.908 0.487
Portugal 0.839 0.929 0.639
Spain 0.892 0.963 0.626
Sweden 0.885 0.849 0.434
Table 2: Estimates of d and 95% confidence intervals for the
individual series
Country Youth unemployment Inflation
The United Kingdom 1.37 (0.31, 2.10)# 0.53 (0.31, 1.35)#
Italy 1.15 (0.94, 1.45)# 1.43 (0.47, 1.83)#
Austria 1.09 (0.71, 1.50)# 0.44 (0.12, 1.02)#
Belgium 0.81 (0.31, 1.31)# 0.97 (0.01, 1.54)#
Denmark 0.59 (0.27, 1.35) 0.25 (-0.08, 1.12)#
Finland 1.96 (1.31, 2.72) 1.02 (0.49, 1.58)#
France 1.09 (0.44, 1.61)# 1.33 (1.00, 1.67)#
Greece 1.01 (0.42, 1.52)# 0.72 (0.55, 1.27)#
Ireland 1.29 (0.92, 1.84)# 0.97 (0.10, 1.47)#
Luxembourg 1.16 (0.28, 1.76)# 1.26 (-0.14, 1.88)#
The Netherlands 1.76 (1.31, 2.25) 1.08 (0.42, 1.60)#
Norway 1.41 (0.78, 2.16)# 0.72 (0.49, 1.29)#
Portugal 1.69 (1.10, 2.32) 1.31 (0.77, 2.14)#
Spain 1.62 (1.19, 2.14) 0.99 (0.65, 1.37)#
Sweden 1.33 (0.91, 1.92)# 0.51 (0.33, 1.06)#
Country GDP
The United Kingdom 0.72 (0.02, 1.61)#
Italy 0.29 (-0.07, 1.10)#
Austria 0.08 (-0.30, 0.57)
Belgium -0.15 (-0.62,0.39)
Denmark 0.05 (-0.34,0.55)
Finland 0.72 (0.19, 1.46)#
France 0.23 (-0.24, 0.80)
Greece 0.26 (0.04, 0.53)
Ireland 0.47 (0.24, 1.05)#
Luxembourg 0.05 (-0.34,0.47)
The Netherlands 0.91 (0.42, 1.68)#
Norway 0.41 (-0.11, 1.84)#
Portugal 0.81 (0.24, 1.46)#
Spain 0.78 (0.34, 1.37)#
Sweden 0.33 (-0.04, 1.04)#
Note: In bold, evidence of unit roots (d = 1) at the 5% level.
Note: Evidence of unit roots (d = 1) at the 5% level is
indicated with #.
Table 3: Estimates of d based on a local Whittle semiparametric
method
Youth unemployment
Country 4 5 6
UK 0.701# 1.169# 1.453
Italy 1.386# 1,500 1.363
Austria 0.932# 0.965# 1.220#
Belgium 0.926# 0.955# 1.171#
Denmark 0.901# 1.208# 0.806#
Finland 1.095# 1.388 1.500
France 1.408# 1.149# 1.393
Greece 0.500 0.605 0.878#
Ireland 1.174# 1.335# 1.500
Luxembourg 1.163# 1.294# 1.261#
The Netherlands 1.222# 1.500 1.500
Norway 0.582 0.655# 0.996#
Portugal 0.592# 1.159# 1.455
Spain 0.507 1.189# 1.500
Sweden 0.637# 1.199# 1.421
Lower I(1) interval 0.588 0.632 0.664
Upper I(1) interval 1.411 1.367 1.335
Inflation
Country 4 5 6
UK 0.762# 1.004# 0.770#
Italy 1.423 1.500 1.500
Austria 1.078# 0.669# 0.645
Belgium 0.719# 0.925# 1.052#
Denmark 0.899# 0.881# 1.077#
Finland 0.838# 1.198# 1.084#
France 1.220# 1.500 1.500
Greece 0.500 0.517 0.730#
Ireland 1.500 1.455 1.194#
Luxembourg 0.915# 1.131# 1.256#
The Netherlands 1.430 1.500 1.178#
Norway 0.500 0.774# 0.785#
Portugal 0.678# 0.907# 1.141#
Spain 1.487 1.019# 1.188#
Sweden 0.748# 0.802# 0.777#
Lower I(1) interval 0.588 0.632 0.664
Upper I(1) interval 1.411 1.367 1.335
GDP
Country 4 5 6
UK 0.733# 0.889# 1.166#
Italy 1.137# 0.511 0.572
Austria 0.500 0.521 0.668#
Belgium 0.588# 0.664# 0.563
Denmark 0.598# 0.534 0.710#
Finland 0.500 0.782# 1.008#
France 0.500 0.882# 0.524
Greece 0.500 0.701# 0.500
Ireland 0.725# 0.958# 0.569
Luxembourg 0.500 0.934# 1.100#
The Netherlands 0.664# 0.682# 0.928#
Norway 0.505 0.5 0.788#
Portugal 0.765# 0.994# 1.238#
Spain 0.500 0.999# 0.864#
Sweden 0.612# 0.641# 0.507
Lower I(1) interval 0.588 0.632 0.664
Upper I(1) interval 1.411 1.367 1.335
Note: In bold, estimated value of d in the cases when cointegration
holds.
Note: Estimated value of d in the cases when cointegration
holds is indicated with #.
Table 4: Parameter estimates in the cointegrating relationship with
uncorrelated errors
d a
The United Kingdom 1.25 (0.47, 1.89) 23.233 (27.93)#
Italy 0.89 (0.73, 1.19) 32.965 (9.04)#
Austria 1.09 (0.71, 1.52) 5.285 (3.68)#
Belgium 0.81 (0.29, 1.31) 23.813 (5.76)#
Denmark 0.89 (0.16, 1.46) 14.436 (3.71)#
Finland 1.98 (1.28, 2.91) 9.732 (2.45)#
France 0.91 (0.43, 1.55) 25.247 (4.86)#
Greece 0.91 (0.54, 1.38) 23.435 (6.32)#
Ireland 1.08 (0.82, 1.81) 26.755 (7.42)#
Luxembourg 0.15 (0.18, 1.80) 7.926 (2.14)#
The Netherlands 1.78 (1.30, 2.30) 10.004 (3.20)#
Norway 1.34 (0.59, 2.16) 9.742 (4.04)#
Portugal 2.02 (1.29, 2.90) 21.066 (9.50)#
Spain 1.63 (1.14, 2.18) 35.311 (5.12)#
Sweden 1.29 (0.82, 2,03) 10.011 (2.31)#
[[beta].sub.1] [[beta].sub.2]
The United Kingdom -0.610 (-4.44)# -0.018 (-0.16)
Italy -0.434 (-2.64)# -0.452 (-2.08)#
Austria -0.026 (-0.14) 0.013 (0.09)
Belgium -0.056 (-0.12) -0.042 (-0.11)
Denmark -0.738 (-1.43)# -0.707 (-3.13)#
Finland -0.263 (-0.80) 0.227 (1.51)
France -0.702 (-1.99)# -0.249 (-0.74)
Greece -0.358 (-2.55)# -0.069 (-0.38)
Ireland -0.649 (-2.29)# -0.330 (-2.36)#
Luxembourg -0.093 (-0.28) -0.058 (-0.52)
The Netherlands -0.496 (-1.42) 0.243 (0.82)
Norway -0.410 (-2.62)# -0.194 (-1.38)
Portugal -0.159 (-1.74)# -0.358 (-3.10)#
Spain -0.664 (-1.66)# -0.603 (-1.75)#
Sweden -0.239 (-1.02) -0.353 (-1.73)#
Note: In bold, significant coefficients at the 5% level.
Note: Significant coefficients at the 5% level is
indicated with #.
Table 5: Parameter estimates in the cointegrating relationship with
autocorrelated errors
d a
UK 0.11 (-0.24, 0.38) 44.244 (42.89)#
Italy 0.02 (-0.26, 0.43) -54.025 (-64.11)#
Austria -0.07 (-0.37, 0.29) 42.765 (35.134)#
Belgium 0.01 (-0.36, 0.33) 65.367 (4.17)#
Denmark 0.07 (-0.36, 0.29) 34.287 (32709)#
Finland 0.58 (0.14, 0.89) 28.789 (8.74)#
France 0.10 (-0.29, 0.47) 7.693 (6.74)#
Greece 0.01 (-0.37, 0.39) -254.69 (-167.89)#
Ireland 0.04 (-0.34, 0.45) 122.00 (50.82)#
Luxembourg -0.04 (-0.57, 0.18) 43.189 (30.14)#
The Netherlands 0.14 (-0.23, 0.37) 39.544 (18.41)#
Norway 0.05 (-0.28, 0.39) 22.147 (35.38)#
Portugal 0.21 (-0.07, 0.44) 1.772 (1.41)#
Spain 0.16 (-0.14, 0.47) -1.679 (-0.46)#
Sweden -0.11 (-0.22, 0.41) 15.842 (12.34)#
[[beta].sub.1] [[beta].sub.2] AR
UK -0.174 (-1.88)# 0.319 (1.49) 0.742
Italy -0.143 (-1.80)# 1.496 (4.69)# 0.810
Austria -0.413 (-1.85)# -0.516 (-1.96)# 0.895
Belgium -0.612 (-1.82)# 0.014 (0.03) 0.664
Denmark -0.984 (-3.75)# -0.299 (-1.97)# 0.655
Finland -1.272 (-4.26)# -0.015 (-0.07) 0.710
France -0.551 (-4.50)# -0.312 (-0.85) 0.744
Greece -0.387 (-4.71)# -0.077 (-0.28) 0.863
Ireland -0.723 (-2.04)# -1.220 (-4.98)# 0.708
Luxembourg -0.370 (-2.28)# -0.470 (-2.39)# 0.499
The Netherlands -0.516 (-1.94)# -0.134 (-0.28) 0.735
Norway -0.665 (-9.68)# -0.258 (-1.88)# 0.712
Portugal -0145 (-1.99)# -0.214 (-1.85)# 0.792
Spain 0.081 (-0.27)# -0.649 (-0.96) 0.931
Sweden -1.196 (-8.26)# -1.060 (-2.90)# 0.736
Note: In bold, significant coefficients at the 5% level.
Note: Significant coefficients at the 5% level is
indicated with #.
Table 6: Testing the null of no cointegration with the Hausman test
of Marinucci and Robinson (2001)
The United Kingdom
[H.sub.xs] = 11.449 (a)
[H.sub.xs] = 5.475 (a)
[H.sub.xs] = 2.601
d = 0.634#
Belgium
[H.sub.xs] = 0.625
[H.sub.xs] = 0.361
[H.sub.xs] = 1.102
d= 0.830
France
[H.sub.xs] = 0.134
[H.sub.xs] = 0.665
[H.sub.xs] = 0.275
d = 1.091
Luxembourg
[H.sub.xs] = 16.796 (a)
[H.sub.xs] = 9.409 (a)
[H.sub.xs] = 3.317
d = 0.646#
Portugal
[H.sub.xs] = 13.548 (a)
[H.sub.xs] = 4.355 (a)
[H.sub.xs] = 6.955 (a)
d = 0.577#
Italy
[H.sub.xs] = 23.104 (a)
[H.sub.xs] = 28.696 (a)
[H.sub.xs] = 0.064
d = 0.576#
Denmark
[H.sub.xs] = 3.387
[H.sub.xs] = 0.051
[H.sub.xs] = 1-714
d = 0.917
Greece
[H.sub.xs] = 0.784
[H.sub.xs] = 3.317
[H.sub.xs] = 3.019
d = 1.018
The Netherlands
[H.sub.xs] = 9.063 (a)
[H.sub.xs] = 7.464 (a)
[H.sub.xs] = 1.324
d = 0.746#
Spain
[H.sub.xs] = 0.0144
[H.sub.xs] = 3.193
[H.sub.xs] = 1.747
d = 1.208
Austria
[H.sub.xs] = 0.025
[H.sub.xs] = 0.585
[H.sub.xs] = 2.140
d = 0.957
Finland
[H.sub.xs] = 0.064
[H.sub.xs] = 0.392
[H.sub.xs] = 0.331
d = 1.099
Ireland
[H.sub.xs] = 12.678 (a)
[H.sub.xs] = 7.7157 (a)
[H.sub.xs] = 1.398
d = 0.771#
Norway
[H.sub.xs] = 0.108
[H.sub.xs] = 2.766
[H.sub.xs] = 2.704
d = 1.048
Sweden
[H.sub.xs] = 12.144 (a)
[H.sub.xs] = 14.161 (a)
[H.sub.xs] = 12.144 (a)
d = 0.816#
Note: In bold, estimated value of d in the cases when cointegration
holds.
(a) Statistical evidence of cointegration at the 5% level.
Note: Estimated value of d in the cases when cointegration
holds is indicated with #.
