TESTING FOR SPATIAL DEPENDENCE IN THE REGIONAL UNEMPLOYMENT IN EUROPE1

André M. Marques2

Gilberto Tadeu Lima3

This version: October 7, 2015

This is a preliminary version solely for discussion purposes. Please do not cite it.

Abstract: One major concern regarding the recent crisis is whether the resulting rise in unemployment in

several OECD countries is short-lived or rather reflect changes in structural conditions and may become

persistent or even permanent. Europe, in particular, has been suffering a prolonged slump with high levels of

unemployment posing a threat to political and social stability of the European Union. In this context, this paper

contributes to the literature on such concerns by testing for spatial dependence in the regional unemployment in

Europe. We employ cross section data which include two unemployment measures (current unemployment rate

and long-term unemployment rate) for 272 regions at NUTS 2 level across 28 European countries from 2007 to

2013. We suggest a theoretical argument which requires a Spatial Durbin Model for such European regions to

control for omitted variables, time-dependence and spatial autocorrelation. We have also checked the robustness

of our results by using two different weight matrices, and relied upon Monte Carlo simulations to compute the

significance and magnitude of direct and spillovers effects on the two unemployment measures of changes in

variables usually assumed to affect them. We have found strong evidence of spatial dependence and spillover

effects and have identified potential channels which can possibly guide policy measures at the level of regional

labor markets in European countries. Key words: Regional unemployment; spatial dependence; spatial Durbin model.

JEL Classification Codes: R23; J640; C150.

1 This paper will be presented at 19

th Conference of the Research Network Macroeconomics and Macroeconomic Policies, “The

Spectre of Stagnation? Europe in The World Economy”, to be held in Berlim, Germany, on 22 – 24 October 2015. 22

Federal University of Paraíba, Brazil. E-mail: 00094751@ufrgs.br 3 University of São Paulo, Brazil. E-mail: giltadeu@usp.br

1

1. Introduction

One major concern regarding the recent financial crisis is that it may have worsened the pattern

persistence of unemployment in OECD countries where various unemployment measures have remained above

pre–crisis levels. This concern regards whether the rise in these unemployment measures in these countries is

short-lived or rather reflect changes in structural conditions and, therefore, may become persistent or even

permanent. In fact, the two most recent editions of the OECD Employment Outlook, launched in mid-2014 and

mid-2015, recognize that the persistence of high levels of unemployment appears to have been translated into a

rise in structural unemployment in some countries, which may not be automatically reversed by a recovery of

economic growth.

Europe, for instance, has been suffering a prolonged slump with high levels of unemployment posing a

threat to political and social stability of the European Union. In this context, it is worth exploring the extent to

which the structural conditions which determine unemployment levels have a spatial dimension to them, so that

regional structural differences would have to be taken into account in explorations of the stagnant behavior of

employment in European countries. In fact, while the structural differences among European regions are often

considerable, these regions are nonetheless interconnected (and often significantly so) especially by migration,

commuting and interregional trade. Therefore, given the existing patterns of spatial interaction among regional

labor markets in Europe, it is worth exploring the spatial structure of unemployment disparities across European

regions.

More precisely, this paper contributes to the existing literature on structural unemployment by testing

for spatial dependence in the regional unemployment in Europe. Conceptually speaking, a significant spatial

interaction between neighboring labor markets implies that cross sectional data is characterized by a positive

spatial autocorrelation. As a result, similar unemployment levels, either high or low, are more spatially clustered

than could be caused by chance. Our investigated cross section includes two unemployment measures (current

unemployment rate and long-term unemployment rate) for 272 regions at NUTS 2 level across 28 European

countries in a period of economic slowdown and sometimes recession (2007-2013). We present a theoretical

argument which requires a Spatial Durbin Model for these European regions to control for omitted variables,

time-dependence and spatial autocorrelation. We have checked the robustness of our results using two different

weight matrices, whereas Monte Carlo simulations have allowed us to compute the magnitude and significance

of direct and spillovers effects on those two measures of unemployment of changes in variables which typically

determine them. Several control variables were considered, including sectoral specialization, population

density, and labor force educational attainment. Strong evidence of spatial dependence and spillover effects

2

were found and we have identified potential channels which can possibly guide policy measures at the level of

regional labor markets in European countries.

These are timely issues bearing relevant policy implications. In fact, some direct effects of policies at the

regional level may not result in a desirable policy outcome at the national level. For instance, a wage restraint at

the regional level may produce a gain in competitiveness to the region itself, but may negatively affect other

regions through trade and sectoral linkages by producing a lower employment level on neighboring regions.

Therefore, policy evaluation exercises should rely on total (or aggregated) effects instead of partial (or isolated)

ones, as regions may exhibit temporal and spatial dependence.

Meanwhile, not considering the possibility of spatial interaction (through trade or migration of labor and

capital, for instance) between different regions is likely to yield biased estimates of the Okun’ coefficient when

there is spatial dependence which is not controlled for. In fact, standard estimates of the Okun’s coefficient

which ignore spatial dependence and interactions find that it is required an output growth of around 4% to get a

reduction of 1% in unemployment per year. Therefore, one timely issue worth exploring is whether taking into

account the possibility of spatial dependence in the regional unemployment in Europe yields different estimates

of the Okun’s coefficient for individual European countries and hence the corresponding growth performance

required to reduce aggregate unemployment. In fact, one of the main contributions of this paper is to carry out

such exploration of the presence of spatial dependence in the regional unemployment in Europe by controlling

for individual regional characteristics such as human capital (as measured by educational attainment) and unit

cost of labor. Our conjecture is that the interregional linkages operating through markets for goods, services and

factors of production (especially labor and capital) are likely to give rise to circular and cumulative causation

processes. Therefore, estimates of the Okun’s coefficient which control for the possibility of spatial dependence

in the regional unemployment in Europe may imply lower required rates of growth than those obtained in the

standard estimates of the Okun’s coefficient which ignore spatial dependence and interactions.

There are some studies which investigate unemployment behavior following a spatial approach. Niebuhr

(2003) studies the regional unemployment in Europe using data for the 1986-2000 period. The author uses as

control only the share of manufacturing and services in overall employment and population density, and find a

significant spatial dependence, with unemployment rates forming regional clusters. Blackley (1991) estimates

the Okun’ coefficient for the 26 largest US states and finds that for each 1% point decrease in unemployment

output has to growth by 2% to 3%. Similar results were found for Canada (Adanu, 2005) and Spain (Villaverde

and Maza, 2009). The latter found that the regional response of unemployment to output growth in Spain in the

1980-2004 period varied with values ranging from a minimum of 0.32 to a maximum of 1.55, which are higher

3

than values found in other studies. The authors suggest that these differences are explained by differences in

productivity: all other things held constant, there is a positive relationship between the evolution of productivity

and the Okun’s coefficient. Meanwhile, Kuscevic (2014) uses panel data analysis with a Spatial Durbin Model

to estimate the Okun’s coefficient for 358 US Metropolitan Statistical Areas for the 2002-2010 period (without

controlling for specific characteristics of those areas) and find that if a given state increases its GDP by roughly

2.2%, a decrease in the unemployment rate of 1% will take place.

This paper contributes to further the understanding of the behavior of the regional unemployment in

Europe in several ways. By following a spatial approach, the paper uses information gathered from regional

accounts at NUTS 2 level to incorporate several factors which affect the state of the labor market, such as

output growth, health conditions, the extent of the market, educational attainment, the share of agriculture and

industry in output, regional competitiveness and unit labor cost. The purpose is to test for spatial dependence

and then detect channels which are likely to determine the state of unemployment for 272 regions at NUTS 2

level across 28 European countries during a period of economic slowdown and recession.

We first test for the presence of spatial dependence in the compiled regional unemployment data. We

then generalize the argument suggested in LeSage and Pace (2009) to show theoretically the importance of also

controlling for ‘time-dependence’ in addition to controlling for the spatial dependence and omitted variable

problems, which we carry out by specifying a Spatial Durbin Model (SDM). This model implies that the current

and long-term regional unemployment rate levels depend on the region’s own and neighboring characteristics,

the spatial connectivity structure and the strength of spatial dependence. The results can be interpreted as a

steady state equilibrium where the region i decides in period t about unemployment level based on the decision

of region j at period t-1. The robustness of our results and the best selected models were checked by using two

types of distance matrix. Finally, through Monte Carlo simulation, we can infer the significance and magnitude

of the direct, indirect (spillovers) and overall effects of the potential spatial channels which affect the current

and long-term unemployment rates.

In summary, the paper derives two main results. First, estimates of the Okun’s coefficient which control

for the possibility of spatial dependence in the regional unemployment in Europe imply lower required output

growth rates than those obtained in the standard, purely aggregate estimates of the Okun’s coefficient. Second,

the two main channels of negative influence were identified as the unit cost of labor and the competitiveness

measure given by the cost of factors weighted by the labor supply, which have produced a substantial reduction

in the growth of employment at regional level.

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The remainder of the paper is organized as follows. Section 2 describes the data and the model used in

the empirical estimations. Section 3 presents and discusses the main empirical results, especially in terms of the

summary scalar measures of direct, indirect (spillover) and total effects. Finally, Section 4 summarizes the main

conclusions derived along the way and offers some closing comments.

2. The data and model specification

2.1 Data description

Our sample is composed of 272 regions at NUTS 2 level. NUTS (Nomenclature of Territorial Units for

Statistics) is the spatial classification established by Eurostat on the basis of national administrative units. All

regional information datasets for NUTS 2 regions across 28 countries of Europe were obtained in regional

accounts tables on the Eurostat.4 The description of the variables is in Table 1. The details about the data and

regions studied are described in the Appendix. One difficult question is how to choose the variables which

affect unemployment of labor, given their limited availability on regional accounts.

Unemployment may have a lot of causes, so is not an easy task to isolate them in a simple model, but

surely the output growth and the growth of supply and demand for labor are natural candidates to explain its

behavior. Since output is defined as the employment level multiplied by the average productivity of labor, there

is a definite relation (in growth terms) between output growth, employment growth and productivity growth.

However, there is not available data at the regional disaggregated level to include the technological progress

and income distribution in the analysis of (un)employment determination.

In addition to output growth, we use the growth of labor supply as a source of variation in regional

unemployment in Europe. Following Kuscevic (2014), we assume that when economic conditions improve in a

given region, the available labor force in such region increases (in-migration), and, when economic conditions

improve in that region’s neighboring regions, the available labor force in that region may decrease (out-

migration). This process is likely to affect both the current and the long-term unemployment rate. Another

variable which is commonly used to account for the demand for labor is the capital stock or some measure of it

(Arelano and Bond, 1998). Unfortunately, this information is not available for all regions we are studying.

In a regional context, we have to consider some specific variables which shape the regional labor and

product markets. In this respect, we follow LeSage and Fischer (2008) by adopting some specific variables such

as: the regional competitiveness which is measured by gross value added at basic prices weighted by economic

active population (supply of labor), the employment composition in agriculture and industry, and the extent of

4 http://ec.europa.eu/eurostat/web/nuts/overview

5

the market (Dall’Erba et. al., 2008) which may help to explain regional unemployment as well. We assume that

the economic activity density can be approximated by population density.

Moreover, some traditional variables which affect the demand for labor were introduced based on Barro

(1991) and Barro and Lee (1994), such as educational attainment (primary, secondary and tertiary education)

and health conditions measured by life expectancy. In addition to the competitiveness measure given by gross

value added at basic prices as a proportion of the labor force, we use the unit cost of labor to control for cost and

demand relations in a Keynesian perspective. The basic idea is to capture the double character of the real wage

as a cost for a region, but as demand for its own production and the production of its neighbors. All variables

are described in Table 1 below along with the signs we expect theoretically for the estimated coefficients.

Table 1

Description of the variables and coefficient’s expected signs

Variable Description Expected

sign

1. Current

unemployment rate

Log of average current unemployment rate, 2007-2013, % active population. ---------

2. Long-term

unemployment

Log of average of long-term unemployment rate (12 months and more), 2010-

2013, % active population. ---------

3. Output growth Log of average of regional gross domestic product (million PPS) - 2007-2011. - 4. Expect Life expectancy, less than 1 year in 2009. + 5. Density Log of population density in 2009, (people/km

2). -

6. Education Less than primary, primary and lower secondary education (levels 0-2), %,

from 15 to 64 years. -

7. Share of agriculture Share of employment in agriculture in 2009 to total employment in 2010, %. - 8. Share of industry Share of employment in industry in 2009 to total employment in 2010, %. + 9. Human resources in

science and

technology

Workers with tertiary education (ISCED) and/or employed in science and

technology (thousand). ?

10. Unit cost of labor Log of the ratio between compensation of employees (million euro) and gross

value added at basic prices (million euro). +

11. gva_eap Ratio between gross value added at basic prices (million euro) and

economically active population (thousand), from 15 to 64 years. -

Source: authors’ elaboration.

2.2 Model specification and interpretation

The choice of model specification to analyze unemployment in 272 regions of Europe was based on four

main reasons. First, the likely presence of spatial dependence due to the institutional effort undertaken in these

countries to adapt their legislation and regional labor, goods and services markets to agreements in the

European Union in the search for greater interdependence and integration (capital and labor mobility, and intra-

regional trade), subjecting them to common external shocks.

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Second, as demonstrated by LeSage and Fischer (2008), the omission of relevant variables correlated

with some variable included in the model, such as the reservation wage and the capital stock (or equipments

used in production), can generate biased coefficients if the specification adopted do not control for that effect.

In the labor market, the intensity of labor’ use in a particular region may depend on the degree of

substitution (or complementarity) between capital and labor in the industrial sectors, however, it is difficult to

obtain reliable values of capital stock at the regional level. Labor tax and the reservation wage have also been

identified as important factors to explain unemployment in the European labor market (Planas et. al., 2007),

however, there is no information available in the region accounts for these variables. Therefore, the choice of

the Spatial Durbin Model specification explicitly controls for the omission of these variables by the inclusion of

spatial lagged dependent variable.5 Third, the introduction of spatial lags for the vector of individual

characteristics of the regions was intended to control for the positive and negative externalities of the nearest

neighbors. Finally, the ‘time dependence’ is another feature that may be present in the data and should be

suitably controlled for by the introduction of the lagged spatially dependent variable, as will be shown below.

It is possible to generalize the theoretical argument suggested in LeSage and Pace (2009) for the case

where the characteristics of the neighbors are also spatially lagged, showing that the agents make decisions in

period t that are dependent on decisions made by other agents or regions in t-1. For example, tax incentives or

relief of the payroll (or the opposite) granted in the region i in t-1 can be imitated or disseminated by region j in

period t affecting their performance as well as the region i itself through nearest neighbors. In this case, the data

will show a pattern of spatial dependence and the indirect and total effects will take account of this circularity

(feedback effects). The Spatial Durbin Model can be written as:

y Wy X WX (1)

where the dependent variable y represents an 1N vector of observed measure of unemployment and the

N k matrix X contains k explanatory variables excluding the intercept vector represented by . The matrix W

is an N N non-stochastic, non-negative spatial weight matrix whose elements are used to specify the spatial

dependence structure between the regions. We have 0ijW if the region i is related to region j, and 0ijW

otherwise. The diagonal elements iiW are set to zero as normalization and also normalized to have row-sums of

unity. Therefore, the spatial lag vector Wy captures the spatial dependence in y , while the spatial lag vector

5 Planas et. al. (2007) conclude that, for the 1970-2004 period with annual data and a reliable estimate for the Euro Area, the rise in

labor taxes since 1970 could have accounted for 40% of the rise in long-term unemployment, and a 1% point decrease in long-term

unemployment could be achieved by decreasing labor taxes by roughly 3% to 4%.

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WX captures the spatial dependence between specific characteristics of the regions, controlling for positive and

negative externalities derived from it.

LeSage and Pace (2009) derive a theoretical ‘time-dependence’ motivation for a SAR (Spatial

Autorregressive Model), in which the spatial lag vector WX is absent. However, this theoretical motivation can

be extended to the case where the specific characteristics of the regions are explicitly considered in the analysis.

Following the procedure in LeSage and Pace (2009), the ‘time-dependence’ can be introduced in a Spatial

Durbin Model by assuming that:

1t t ty Wy X WX (2)

Then, following LeSage and Pace (2009) to omit the constant (without loss of generality), we can specify the

behavior in the previous period as:

1 2 1t t ty Wy X WX (3)

After two successive substitutions, we obtain:

3 3 2 2 2 3 2 2 2

3 2 1t t t t ty W y W X W X W WX W X W X WX

(4)

Generalizing the expression (4) for q tending to become larger, after regrouping the terms, we obtain:

2 2 1 1 2 2 1 1... ...q q q q q q

t t q n ny W y I W W W X I W W W WX u

(5)

where 1

11

2

22

1 ...

qt

qq

ttt WWWu .

The expression (5) can be simplified by observing that 0rtE , 1,...,0 qr implies that 0uE .

Additionally, the magnitude of qt

qq yW becomes small for large values of q, and under the assumption that

1 and also by assuming that W is row-stochastic (W matrix has a principal eigenvalue of 1), the long-run

equilibrium or steady state equilibrium is given by:

1 1

lim t n nE y I W X I W WX

q

(6)

Therefore, in the cross-section SDM model, the decisions of economic agents located at various points

in space depend upon the decisions made by neighbors in previous periods of time as well, conditioned by

positive or negative externalities.

8

To determine the best distance matrix for the estimation of the SDM two types of matrices were

considered. The matrix of contiguity Queen was used by Kuscevic (2014) to study the spatial dependence in

unemployment rates in the metropolitan areas of the United States. And, the distance matrix with k nearest

neighbors was chosen based on the result of the work LeSage and Fisher (2008) 255 European regions (NUTS

2).

The results of the linear regression techniques have a simple interpretation relative to its parameters as

the partial derivatives of the dependent variable with respect to the independent variables. This is so due to

independence hypothesis of individuals and the absence of interaction between them. In the models containing

spatial lags of dependent and independent variables the interpretation requires a step further. A change in a

single explanatory variable in the region i have a ‘direct impact’ on region i itself as well as an ‘indirect impact’

up on other regions ij . LeSage and Pace (2009) provide the means of calculating scalar summary measures

of the two types of impacts and its total from changes in the independent variables of the SDM model.

Thus, the Spatial Durbin Model extends the information set to include information from neighboring

regions. However, in addition to the magnitude of these effects we need to verify whether they are statistically

significant, via Monte Carlo simulation. We can express the SDM model given in (1) as:

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1

WIWIxWSy nnnr

p

r

r (7)

1

r n n r rS I W I W

(8)

where the index pr ,...,1 , so that rx is the rth independent variable (rth column of 0X ) and there are

12 pk explanatory variables in the model. The p by 1 vector contains the regression parameters

associated with the explanatory variables in0X , and the p by 1 vector contains the regression parameters

associated with the spatially lagged explanatory variables 0WX . Following LeSage and Pace (2008), by using

(7) they establish that changes in the rth explanatory variable in a spatial regression model have a partial

derivative impact on yi given by (9), where rS ij refers to the ijth element of the N N matrix rS :

ir

jr

yS ij

x

(9)

where the ‘direct effect’ is measured by the i, ith element ofrS . This includes feedback influences that emerge

as a result of impacts passing through neighbors, and back to the region i itself. The ‘indirect’ or spillover effect

arises from changes in all observations 1,...,j n of an explanatory variable jrx , and it is obtained as the sum

9

of the off-diagonal elements of the rows i from the matrix rS , for each observation i. As it turns out, direct plus

indirect effects result in the total effects from changes in the independent variable r. It should be noted that

these summary measures of the impacts arising from changes in the explanatory variables of the model average

over all regions in the sample, as it is typical in regression model interpretation.

2.3 Model comparison

LeSage and Pace (2009) have shown that estimation of spatial models with least squares can lead to

inconsistent estimates of the regression parameters for models with spatially lagged dependent variables,

inconsistent estimation of the spatial parameters, and inconsistent estimation of standard errors. In contrast,

maximum likelihood is consistent for these models (Lee, 2004). However, some issues regarding the true data-

generating process come about at this stage.

LeSage and Pace (2009) argue that the Spatial Durbin Model is the best point of departure, however, Florax

et. al. (2003) have found that the expansion of a linear regression equation with spatially lagged variables,

conditioned by misspecification tests, is the best choice to find the true data-generating process for this class of

spatial models. The same procedure was also emphasized by Helhorst (2010).

First, we have estimated the OLS model and tested whether the spatial lag (SAR) or the spatial error model

(SEM) is more appropriate to describe the data by using the robust LM-tests proposed by Anselin et. al. (1996).

If the OLS model is rejected in favor of the spatial lag, the spatial error or both, then the Spatial Durbin model

should be estimated. In this first step, two situations are possible: a) strong significance for both tests; b) strong

significance for one kind combined with weak or non-significance for the other.

Since these models can be estimated by maximum likelihood, a likelihood ratio (LR) test can therefore be

subsequently applied to test the hypotheses 0:0 H and 0:0 H , and if both hypotheses are rejected,

the Spatial Durbin Model can best describe the data. The first restriction tests whether the Spatial Durbin can be

simplified as a spatial lag, and the second examines whether the Spatial Durbin can be simplified to the spatial

error model. Both tests follow a chi-squared distribution with one degree of freedom. As indicated in Table 2,

the preferred specification was the Spatial Durbin Model.

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Table 2: Summary of comparison models.

Hypotheses Test statistic for UR and SUR Decision

0:

0:::

0

0*

H

HLM 2.0958 0.0011

No rejection of the null.

0:

0:::

0

0*

H

HLM 49.4910

a 20.0890

a Rejection of the null at

0.01 and 0.05 levels.

0:

0:

1

0

H

H 80.6698

a 47.2166

a Rejection of null at 0.01

and 0.05 levels.

0:

0:

1

0

H

H 28.2970

a 21.7146

a Rejection of null at 0.01

and 0.05 levels.

Note: (a) Significant at 0.01 probability; (b) significant at 0.05 probability; (c) significant at 0.10 probability.

Following Anselin et. al. (1996), all tests were performed using a queen matrix.

Source: authors’ elaboration.

3. General results and discussion

Before testing for the absence of spatial dependence based on the OLS residuals, we have tested for

spatial autocorrelation by performing two tests for the absence of global spatial dependence. The last column in

Table 3 shows that in both cases (the current and long-term unemployment rates) these tests reject the null of

absence of spatial autocorrelation at the 0.05 level. Given that the actual value of Moran’s I exceeds its expected

value and that Geary’s c is less than unity for both unemployment measures, there is indication of the presence

of positive spatial autocorrelation, so that regions with similar (either high or low) unemployment rates tended

to cluster.

Table 3

Tests for global spatially autocorrelated current unemployment and long-term unemployment

Variable Type of test Coefficient Expected value Variance P-value

Current

unemployment

Moran’s I 0.450424528 -0.0039841 0.002046130 0.0000

Geary’s c 0.522163820 1.0000 0.002546782 0.0000

Long-term

unemployment

Moran’s I 0.391041002 -0.0039841 0.002044907 0.0000

Geary’s c 0.562197331 1.0000 0.002546782 0.0000

Note: All tests are two-tailed. Following common practice, the inference for both tests is based on randomization.

Alternatives approaches that could have been adopted are the normal assumption and the permutation approaches.

A visual impression of this spatial clustering for both unemployment measures can be acquired by using

a Moran scatterplot, as depicted in Figure 1. In the bottom left-hand corner of both panels we have regions,

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represented by the points, that had both low unemployment rates and low spatially lagged unemployment rates.6

Therefore, these regions are members of a low-unemployment cluster. In contrast, in the top right-hand corner

we have regions that had both high unemployment rates and spatially lagged unemployment rates. Therefore,

these regions are members of a high-unemployment cluster. In fact, both quadrants are characterized by positive

local spatial autocorrelation, so that regions with similar unemployment rates tended to cluster. As expected

from the global spatial autocorrelation statistics, most of the regions appear in these two quadrants. Meanwhile,

several regions were part of the cluster of high current unemployment rates and the cluster if of high long-term

unemployment rates (for instance, as numbered in the sample and in both panels in Figure 1, 100: Comunidad

de Madrid; 98: La Rioja; 94: Principado de Asturias; 95: Cantabria; 102: Castilla-la Mancha; 101: Castilla y

León; and 74: Hovedstaden).

Figure 1: Moran scatterplot for the average current (2007-2013) and average long-term (2010-2013) unemployment rates.

6 A region’s spatially lagged unemployment rate is a weighted average of the unemployment rate of neighbouring regions, which

means that a region i’s spatially lagged unemployment is given by j jij yw where jy is the unemployment rate of region j and ijw

is the weight.

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The results of the test for the absence of spatial dependence based on Moran's I test for residual spatial

autocorrelation are presented in Table 4.

Table 4 Test for spatial dependence – OLS residuals – best distance matrix selection - results.

Distance matrix /dependent

variable UR SUR

Log-likelihood function

values/UR

Log-likelihood function

values/SUR

k = 3 7.5430

a

(0.0000)

6.2532a

(0.0000) -110.0612 -218.7854

k = 4 8.3326

a

(0.0000)

6.6068a

(0.0000) -108.0154 -218.7436

k =5 9.5302

a

(0.0000)

7.4946a

(0.0000) -106.0795 -217.6840

k = 6 9.8797

a

(0.0000)

7.9675a

(0.0000) -107.6120 -218.4391

k = 7 10.3910

a

(0.0000)

8.4158a

(0.0000) -106.6113 -217.1912

k = 8 10.443

a

(0.0000)

8.3736a

(0.0000) -106.7754 -217.5553

k = 9 10.2740

a

(0.0000)

8.0089a

(0.000) -111.2553 -221.0521

Queen matrix 7.1708

a

(0.0000)

6.5174a

(0.0000) -101.2561 -211.5791

Note: The p-values associated with the estimates are between brackets. (a) Significant at 1% probability; (b) significant at 5%

probability; (c) significant at 10% probability.

Source: authors’ elaboration.

Table 4 also shows the log-likelihood function values associated with various models based on nearest-

neighbor weight matrices with kmin = 3,…, kmax = 9 and a spatial Queen contiguity matrix. From these results

we conclude that the best distance matrix to be used in the estimations is the Queen contiguity matrix, which is

the same used by Kusevic (2014) to analyze the labor market of metropolitan areas in the United States.

In all cases, as we expected, the null of absence of spatial dependence can be rejected at the 1 % level of

significance. Table 5 below presents the results of the estimation of the Spatial Durbin Model presented in

Section 2.2. The two columns of Table 5 show the results from the estimated SDM for the two variables of

interest: the current and long-term unemployment rates.

The estimated coefficients for output growth are quite low relatively to the existing empirical evidence

reported earlier. However, the interpretation of these coefficients should be carried out based on summary

measures of impacts via Monte Carlo simulation, not from these isolated coefficients (without interactions), as

observed before (and displayed in Table 6).

Based on the first column in Table 5 we find all the theoretically expected signs indicated in Table 1.

Except for the share of employment in industry, all the estimated coefficients are statistically significant at

conventional levels of probability. Therefore, all selected variables have some influence on the regional

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unemployment in Europe Union. The average influence of the neighbors, measured by the ‘spatial lag vector’

WX which measures positive and negative externalities, appears significant only for output growth, the share of

employment in industry and labor employment in science and technology.

The second column in Table 5, whose results refer to long-term unemployment, yields similar

conclusions. All estimated coefficients have the theoretically expected signs. Yet health conditions, educational

attainment and the share of employment in industry and agriculture do not seem to affect significantly long-term

unemployment, and the main (and positive) influence on the latter is exerted by the unit labor cost. However,

results in Table 3 still do not consider the possibility of existence of spatial dependence (interactions) between

regions. When this possibility is taken into account, the significance and magnitude of the results is obtained by

calculating scalar summary measures of direct, indirect and total effects, which depend on the strength of the

corresponding spatial interactions, as measured by the coefficient. In fact, for both unemployment measures

this coefficient is positive and statistically significant at a 1% probability level. Moreover, in both cases no

evidence was found of residual autocorrelation and heteroskedasticity. Along with the LM test for absence of

autocorrelation, we have performed the Breush-Pagan test for the absence of heteroskedasticity on fitted spatial

models taking the spatial coefficient into account.

From these results we can conclude that the estimated Spatial Durbin Model accommodates very well

the structure of dependence and heterogeneity across the European regions studied in this paper, as confirmed

by the non-rejection of the null hypothesis of both the LM and Breush-Pagan tests for autocorrelation and

heteroskedasticity. Given these robustness checks of the estimated models, we proceed to the analysis of the

scalar summary measures of direct, indirect and total effects for each independent variable, whose values were

obtained through Monte Carlo simulation. As discussed earlier, the results of a Spatial Durbin Model cannot be

interpreted as in a standard multiple linear regression model, since there is a lot of information and circular

effects of interactions between regions. The scalar summary measures of direct, spillover (indirect) and total

effects are presented in Table 5. The magnitude of each effect was calculated for each independent variable and

its significance was established by 15,000 draws from Monte Carlo simulations, assuming a multivariate normal

distribution.

14

Table 5

Estimation of Spatial Durbin Model – Results Coefficients Current unemployment rate Long-term unemployment rate

constant 3.3992

a

(0.00525)

3.4814c

(0.0560)

loggdp -0.0870

b

(0.0401)

-0.1838a

(0.0039)

expect 0.0232

c

(0.0864)

0.0333

(0.1012)

logdens -0.0641

a

(0.0023)

-0.0778b

(0.0137)

educ -0.0063

b

(0.0455)

-0.0067

(0.1611)

logshag -0.0462

c

(0.0931)

-0.0436

(0.2924)

logshind 0.0290

(0.6121)

0.0667

(0.4376)

hrst 0.0002

a

(0.0142)

0.0003b

(0.0197)

logucl 0.4733

a

(0.0019)

0.5802b

(0.0113)

loggva_eap -0.3347

a

(0.0000)

-0.4380a

(0.0000)

W.loggdp -0.1961

a

(0.0048)

-0.1704

(0.1047)

W.expect -0.0022

(0.8316)

-0.0081

(0.5830)

W.logdens 0.0050

(0.8825)

-0.0038

(0.9394)

W.educ 0.0029

(0.4822)

0.0042

(0.5067)

W.logshag 0.0738

c

(0.0863)

0.0801

(0.2160)

W.logshind -0.0453

(0.6716)

-0.1737

(0.2803)

W.hrst 0.0003

c

(0.0670)

0.0003

(0.2375)

W.logucl -0.2256

(0.3811)

-0.5409

(0.1616)

W.loggva_eap 0.1560

c

(0.0868)

0.1786

(0.1901)

0.4660

a

(0.0000)

0.4459a

(0.0000)

Log-likelihood -101.2561 -211.5791

Wald statistic 52.675

a

(0.0000)

45.5430a

(0.0000)

AIC 244.51 465.16

Breusch-Pagan test for

heteroskedasticity

20.0820

(0.3282)

22.0900

(0.2280)

LM test for residual

autocorrelation

0.7989

(0.3714)

1.4986

(0.2209)

Number of observations 272 272

Note: The p-values associated with the estimates are between brackets. (a) Significant at 1% probability; (b) significant at 5%

probability; (c) significant at 10% probability.

Source: authors’ elaboration.

15

Table 6

Direct, indirect and total effects: magnitude and significance – Results. Variables Current unemployment rate Long-term unemployment rate

Direct Indirect Total Direct Indirect Total

loggdp -0.1184

b

(0.0116)

-0.4117a

(0.0022)

-0.5302a

(0.0013)

-0.2153a

(0.0022)

-0.4239b

(0.0261)

-0.6392a

(0.0067)

expect 0.0244

c

(0.0843)

0.0150

(0.3807)

0.0394

(0.1338) 0.0341

c

(0.1030)

0.0113

(0.6328)

0.0455

(0.2210)

logdens -0.0674

a

(0.0025)

-0.0434

(0.4638)

-0.1108

(0.1201) -0.0826

b

(0.0133)

-0.0647

(0.4533)

-0.1473

(0.1564)

educ -0.0063

b

(0.0320)

0.0000

(0.9991)

-0.0063

(0.2351)

-0.0065

(0.1451)

0.0020

(0.8104)

-0.0045

(0.5532)

logshag -0.0393

(0.1568)

0.0909

(0.2033)

0.0516

(0.5220)

-0.0360

(0.3788)

0.1019

(0.3225)

0.0658

(0.5713)

logshind 0.0248

(0.6563)

-0.0553

(0.7483)

-0.0306

(0.8652)

0.0488

(0.5551)

-0.2418

(0.3281)

-0.1930

(0.4506)

hrst 0.0003

a

(0.0053)

0.0007b

(0.0209)

0.0010a

(0.0070)

0.0004b

(0.0124)

0.0008c

(0.0925)

0.0012b

(0.0338)

logucl 0.4726

a

(0.0018)

-0.0088

(0.9865)

0.4638

(0.3064) 0.5450

b

(0.0158)

-0.4742

(0.4379)

0.0708

(0.9105)

gva_eap -0.3346

a

(0.0000)

0.0000

(0.9987) -0.3346

b

(0.0275)

-0.4400a

(0.0000)

-0.0280

(0.8873) -0.4680

b

(0.0348)

Note: The p-values associated with the estimates are between brackets. (a) Significant at 1% probability; (b) significant at 5%

probability; (c) significant at 10% probability.

Source: authors’ elaboration.

The main conclusions which can be drawn the results in Table 6 are the following. First, as expected, the

health conditions and the extent of the market have significant direct positive and negative effects, respectively,

on the current and long-term unemployment rates. In both cases, the direct effect is larger for the long-term

unemployment rate than the current unemployment rate. As regards educational attainment, the larger the

number of people with tertiary education, the higher the current and long-term unemployment rates, in terms of

both direct and indirect effects, which contributes to a significant total positive effect on both unemployment

measures. Meanwhile, when only less than primary, primary and lower secondary education is considered, the

direct effect on the two unemployment rates is negative and statistically significant. In this case, we find that an

increased 1% in the proportion of people with less than primary, primary and lower secondary education is

associated with a decrease of about 0.6% in both unemployment measures. This result is in accordance with the

traditional results obtained by Barro (1991) and Barro and Lee (1994).

Second, in terms of magnitude of the effects, three determinants stand out: output growth, unit labor

costs and the measure of competitiveness in relation to the supply of labor. Moreover, the indirect effect is

larger than the direct effect for both unemployment measures, indicating high interdependence between regions.

For instance, an 1% increase in output growth in region i will lower the own region’s current unemployment

rate in 0.12% and its neighbors’ current unemployment rate in 0.41%, which amounts to a cumulative total

16

effect of 0.53% decrease in the current unemployment rate. As a rule of thumb, therefore, a 1% decrease in the

average current unemployment rate across the sample regions requires an 1.89% increase in the average

regional growth rate of around 1.9%, which is about one-half of the estimates of the Okun’s coefficient when

the possibility of spatial dependence is not formally taken into account. In fact, this magnitude is similar to the

one found for US metropolitan areas in Kuscevic (2014), who found that an 1% increase in output growth is

associated with an 0.45% reduction in the unemployment rate (but without any control for individual

characteristics of those regions).

Meanwhile, the higher the unit cost of labor in a given region i, the lower the currrent unemployment

rate in its neighbors, probably due to demand leakages, but the higher the current unemployment rate in the

region i itself, probably due to cost pressures (see first and fourth colunms in table 6). An increased 1% in a

region’s unit labor cost is associated with an 0.47% direct increase in the own region’s current unemployment

rate and an 0.54% direct increase in the own region’s long-term unemployment rate. In the case of the current

unemployment rate, therefore, the magnitude of the corresponding direct effect is almost enough to offset the

total effect of the output growth.

As regards the competitiveness measure given by the gross value added (at basic prices) as a proportion

of the economically active population (or labor force), the coefficients are statistically significant, have the

expected sign and are large in magnitude. In fact, an increased 1% in a region’s such competitiveness measure

is associated with an 0.33% both direct and total decrease in the own region’s current unemployment rate and

an 0.44% direct and 0.47% total decrease in the own region’s long-term unemployment rate. Therefore, the

short-run unemployment-reducing direct and total effects of a rise in the gross value added (at basic prices) as a

proportion of the labor force is larger for the long-term unemployment rate than the current unemployment rate.

Meanwhile, given the gross value added (at basic prices), a higher labor supply or availablee labor force (due,

for instance, to a rise in migration), is associated with higher rates of current and long-term unemployment in

the short run, a result also found in Kuscevic (2014). This result is also consistent with the finding from a panel

data study for Canada that, in the short run, immigration raises the unemployment rate (Latif, 2015).

4. Conclusions

The magnitude of the recent crisis has raised the concern that the resulting increase in unemployment in

several European countries may reflect changes in structural conditions and, therefore, may become persistent

or even permanent. This paper contributes to the literature on this timely issue by testing for spatial dependence

in the regional unemployment in Europe.

17

One finding is that an estimate of the Okun’s coefficient which control for the possibility of spatial

dependence in the regional unemployment in Europe imply lower required output growth rates than those

obtained in a standard, purely aggregate estimate of the Okun’s coefficient. Before testing for the absence of

local spatial dependence, we have tested for spatial autocorrelation by performing two tests for the absence of

global spatial dependence. For both the current and the long-term unemployment rate, we could reject the null

of absence of global spatial autocorrelation at a hight level of signifcance. We found evidence of positive global

spatial autocorrelation, so that regions with similar (either high or low) unemployment rates tended to cluster.

Having controlled for the possibility of existence of spatial dependence between regions, we obtained

the scalar summary measures of direct, indirect and total effects for each independent variable affecting the

rates of current and long-term unemployment. Expectedly, health conditions and the extent of the market have

significant direct positive and negative effects, respectively, on the current and long-term unemployment rates.

In both cases, the direct effect is larger for the long-term unemployment rate than the current one. As regards

educational attainment, the proportion of the labor force with tertiary education has positive direct and indirect

effects on the two unemployment measures. Meanwhile, when we considered only less than primary, primary

and lower secondary education, the direct effect on the two unemployment measures is negative and statistically

significant.

Overall, three determinants of the unemployment rate stand out: output growth, unit labor costs and a

measure of competitiveness as a proportion of the labor force. Moreover, in all these cases the indirect effect is

larger than the direct effect for both unemployment measures, which indicates high interdependence between

regions. In fact, the higher the unit cost of labor in a given region, the lower the currrent unemployment rate in

its neighbors, probably due to demand leakages, but the higher the current unemployment rate in the region

itself, probably due to cost pressures. As regards the competitiveness measure given by the gross value added as

a proportion of the labor force, the coefficients are statistically significant, have the expected sign and are large

in magnitude. Moreover, the short-run unemployment-reducing direct and total effects of an increase in the

gross value added as a proportion of the labor force is larger for the long-term unemployment rate than the

current one. Meanwhile, given the gross value added (at basic prices), a higher available labor force (due, for

instance, to a rise in migration) is associated with higher rates of current and long-term unemployment in the

short run.

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20

Appendix

Figure 1a: Natural neighbors of average current unemployment rate (%), 2007-2013.

Figure 1b: Natural neighbors of average long-term unemployment rate (%), 2010-2013.

21

The Data

The raw data used in this paper is described in Table 1, and the choice of the periods is due to availability.

There were some missing values in the raw dataset. All these cases with missing values are described below. To

complete these cases we followed the same procedure adopted in Hassler and Wolters (1995), which use the

average of neighboring values for all computations. We expect to complete these values in the next versions of

this paper as the required information becomes available.

Table 7

Missing values in isolated periods

Variable Region

Human resources in science and technology FR93:Guyane

Education HR04; FI1B; FI1C; CH01; CH07; FR91:Guadeloupe; FR92: Martinique; FR93: Guyane; FR94: Réunion;

Long-term unemployment

UKM6: Highlands and Islands; 2. UKM5: North

Eastern Scotland; 3. FI20: Åland; 4. RO32: Bucuresti -

Ilfov; 5. PT20: Região Autónoma dos Açores (PT); 6.

AT32: Salzburg; 7. AT33: Tirol; 8. AT34: Vorarlberg;

9. AT21: Kärnten; AT11: Burgenland (AT); 11.

NL34:Zeeland; 12. ITH1: Provincia Autonoma di

Bolzano/Bozen ITH1; 13. ITC2: Valle d'Aosta/Vallée

d'Aoste;14. FR83: Corse;

Life expectancy DED4 - Chemnitz e DED5 – Leipzig; FR91 –

Guadeloupe; FR93 - Guyane

Share of industry FR91: Guadeloupe; FR92: Martinique; FR93: Guyane;

FR94: Réunion

Share of agriculture FR91: Guadeloupe; FR92: Martinique; FR93: Guyane;

FR94: Réunion. Note: author’s elaboration.

The current NUTS 2013 classification is valid from 1 January 2015 and lists 98 regions at NUTS 1, 276 regions

at NUTS 2 and 1342 regions at NUTS 3 level. For a more detailed description, see

http://ec.europa.eu/eurostat/web/nuts/overview. NUTS is an acronym of the French for ‘the nomenclature of

territorial units for statistics’, which is a hierarchical system of regions used by the statistics office of the

European Community for the production of regional statistics. At the top of the hierarchy are NUTS 0 regions

(countries), below which are NUTS 1 regions and then NUTS 2 regions. Although varying considerably in size,

the NUTS 2 region is widely viewed as the most appropriate unit for modelling and analysis purposes (see, for

example, LeSage and Fischer, 2008). Therefore, we include the following NUTS 2 regions:

Belgium: Région de Bruxelles-Capitale; Prov. Antwerpen; Prov. Limburg (BE); Prov. Oost-Vlaanderen; Prov.

Vlaams-Brabant; Prov. West-Vlaanderen; Prov. Brabant Wallon; Prov. Hainaut; Prov. Liège; Prov.

Luxembourg (BE); Prov. Namur.

Bulgaria: Severozapaden; Severen tsentralen; Severoiztochen; Yugoiztochen; Yugozapaden; Yuzhen tsentralen.

Czech Republic: Praha; Strední Cechy; Jihozápad; Severozápad; Severovýchod; Jihovýchod; Strední Morava;

Moravskoslezsko.

Denmark: Hovedstaden; Sjælland; Syddanmark; Midtjylland; Nordjylland.

22

Germany: Stuttgart; Karlsruhe; Freiburg; Tübingen; Oberbayern; Niederbayern; Oberpfalz; Oberfranken;

Mittelfranken; Unterfranken; Schwaben; Berlin; Brandenburg; Bremen; Hamburg; Darmstadt; Gießen; Kassel;

Mecklenburg-Vorpommern; Braunschweig; Hannover; Lüneburg; Weser-Ems; Düsseldorf; Köln; Münster;

Detmold; Arnsberg; Koblenz; Trier; Rheinhessen-Pfalz; Saarland; Dresden; Chemnitz; Leipzig; Sachsen-

Anhalt; Schleswig-Holstein; Thüringen.

Estonia: Eesti.

Ireland: Border, Midland and Western; Southern and Eastern.

Greece: Anatoliki Makedonia, Thraki; Kentriki Makedonia; Dytiki Makedonia; Thessalia; Ipeiros; Ionia Nisia;

Dytiki Ellada; Sterea Ellada; Peloponnisos; Attiki; Voreio Aigaio; Notio Aigaio; Kriti.

Spain: Galicia; Principado de Asturias; Cantabria; País Vasco; Comunidad Foral de Navarra; La Rioja; Aragón;

Comunidad de Madrid; Castilla y León; Castilla-la Mancha; Extremadura; Cataluña; Comunidad Valenciana;

Illes Balears; Andalucía; Región de Murcia; Ciudad Autónoma de Ceuta (ES); Ciudad Autónoma de Melilla

(ES); Canarias (ES).

France: Île de France; Champagne-Ardenne; Picardie; Haute-Normandie; Centre (FR); Basse-Normandie;

Bourgogne; Nord-Pas-de-Calais; Lorraine; Alsace; Franche-Comté; Pays de la Loire; Bretagne; Poitou-

Charentes; Aquitaine; Midi-Pyrénées; Limousin; Rhône-Alpes; Auvergne; Languedoc-Roussillon; Provence-

Alpes-Côte d'Azur; Corse; Guadeloupe; Martinique; Guyane; Réunion.

Croatia: Jadranska Hrvatska; Kontinentalna Hrvatska.

Italy: Piemonte; Valle d'Aosta; Liguria; Lombardia; Abruzzo; Molise; Campania; Puglia; Basilicata; Calabria;

Sicilia; Sardegna; Provincia Autonoma di Bolzano; Provincia Autonoma di Trento; Veneto; Friuli-Venezia

Giulia; Emilia-Romagna; Toscana; Umbria; Marche; Lazio.

Cyprus: Kypros.

Latvia: Latvija.

Lithuania: Lietuva.

Luxembourg: Luxembourg.

Hungary: Közép-Magyarország; Közép-Dunántúl; Nyugat-Dunántúl; Dél-Dunántúl; Észak-Magyarország;

Észak-Alföld; Dél-Alföld.

Malta: Malta.

Netherlands: Groningen; Friesland (NL); Drenthe; Overijssel; Gelderland; Flevoland; Utrecht; Noord-Holland;

Zuid-Holland; Zeeland; Noord-Brabant; Limburg (NL).

Austria: Burgenland (AT); Niederösterreich; Wien; Kärnten; Steiermark; Oberösterreich; Salzburg; Tirol;

Vorarlberg.

Poland: Lódzkie; Mazowieckie; Malopolskie; Slaskie; Lubelskie; Podkarpackie; Swietokrzyskie; Podlaskie;

Wielkopolskie; Zachodniopomorskie; Lubuskie; Dolnoslaskie; Opolskie; Kujawsko-Pomorskie; Warminsko-

Mazurskie; PL63:Pomorskie.

Portugal: Norte; Algarve; Centro (PT); Área Metropolitana de Lisboa; Alentejo; Região Autónoma dos Açores

(PT); Região Autónoma da Madeira (PT).

Romania: Nord-Vest; Centru; Nord-Est; Sud-Est; Sud – Muntenia; Bucuresti – Ilfov; Sud-Vest Oltenia; Vest.

Slovenia: Vzhodna Slovenija; Zahodna Slovenija.

Slovakia: Bratislavský kraj; Západné Slovensko; Stredné Slovensko; Východné Slovensko.

23

Finland: Länsi-Suomi; Helsinki-Uusimaa; Etelä-Suomi; Pohjois- ja Itä-Suomi; Åland.

Sweden: Stockholm; Östra Mellansverige; Småland med öarna; Sydsverige; Västsverige; Norra Mellansverige;

Mellersta Norrland; Övre Norrland.

United Kingdom: Tees Valley and Durham; Northumberland and Tyne and Wear; Cumbria; Greater

Manchester; Lancashire; Cheshire; Merseyside; East Yorkshire and Northern Lincolnshire; North Yorkshire;

South Yorkshire; West Yorkshire; Derbyshire and Nottinghamshire; Leicestershire, Rutland and

Northamptonshire; Lincolnshire; Herefordshire, Worcestershire and Warwickshire; Shropshire and

Staffordshire; West Midlands; East Anglia; Bedfordshire and Hertfordshire; Essex; Inner London; Outer

London; Berkshire, Buckinghamshire and Oxfordshire; Surrey, East and West Sussex; Hampshire and Isle of

Wight; Kent; Gloucestershire, Wiltshire and Bristol/Bath area; Dorset and Somerset; Cornwall and Isles of

Scilly; Devon; West Wales and The Valleys; East Wales; Eastern Scotland; South Western Scotland; North

Eastern Scotland; Highlands and Islands; Northern Ireland (UK).

There are twenty regions which have no neighbors, but we have not excluded them from the sample when

carrying out the estimates reported in the paper.

The 20 regions which have no links are the following:

27 85 90 91 92 106 109 110 111 116 138 139 140 141 142 164 165 178 212 213.

Following LeSage and Fischer (2008) and then excluding the islands of our dataset, the following results were

obtained:

Excluded regions: 27 – CY00; 85 – EL62; 90 – EL41; 91 - EL42; 92- EL43; 106 – ES53; 109 – ES63; 110 –

ES64; 111 – ES70; 116 – FI20; 138 – FR83; 139 – FRA1; 140 – FRA2; 141 – FRA3; 142 – FRA4; 164 – ITG1;

165 – ITG2; 178 – MT00; 212 – PT20; 213 – PT30.

As a result of excluding these regions, we have found that:

a) The magnitude of Moran’s I coefficient becomes larger and the corresponding scatterplot is shown below.

b) The results for the Spatial Durbin Model are reported in Table 8 below, while the direct, indirect and total

effects are shown in Table 9.

The results obtained in the paper without excluding the above regions remained very much intact, whereas the

new estimated model is better adjusted to the dataset, as revealed by the value of the log-likelihood function

(see Table 8 below). The residual analysis does not show any substantial change.

The following new results were obtained from the adjusted dataset and the corresponding direct, indirect and

total effects:

# The extent of the market, in addition to the significant negative direct effect found previously, also exerts a

significant total negative effect on the rates of current and long-term unemployment;

# The output growth produces a larger significant negative total effect on the rates of current and long-term

unemployment;

# The unit cost of labor has a marginallly significant larger positive direct and total effect on the unemployment

rate.

24

25

Table 8

Estimation of Spatial Durbin Model – Results Coefficients Current unemployment rate Long-term unemployment rate

constant 3.3992

a

(0.0052)

5.7648a

(0.0001)

3.4814c

(0.0560)

7.0213a

(0.0014)

loggdp -0.0870

b

(0.0401)

-0.0956b

(0.0263)

-0.1838a

(0.0039)

-0.2047a

(0.0012)

expect 0.0232

c

(0.0864)

0.0636a

(0.0049)

0.0333

(0.1012) 0.0916

a

(0.0061)

logdens -0.0641

a

(0.0023)

-0.0730a

(0.0009)

-0.0778b

(0.0137)

-0.0834b

(0.0105)

educ -0.0063

b

(0.0455)

0.00034

(0.9330)

-0.0067

(0.1611)

0.0031

(0.6097)

logshag -0.0462

c

(0.0931)

-0.0632b

(0.0252)

-0.0436

(0.2924)

-0.0633

(0.1293)

logshind 0.0290

(0.6121)

-0.0864

(0.3172)

0.0667

(0.4376)

-0.1629

(0.2018)

hrst 0.0002

a

(0.0142)

0.0002a

(0.0088)

0.0003b

(0.0197)

0.0004a

(0.0091)

logucl 0.4733

a

(0.0019)

0.5621a

(0.0004)

0.5802b

(0.0113)

0.6576a

(0.0049)

loggva_eap -0.3347

a

(0.0000)

-0.3465a

(0.0000)

-0.4380a

(0.0000)

-0.4430a

(0.0000)

W.loggdp -0.1961

a

(0.0048)

-0.2498a

(0.0007)

-0.1704

(0.1047) -0.2459

b

(0.0242)

W.expect -0.0022

(0.8316) -0.0641

b

(0.0169)

-0.0081

(0.5830) -0.0992

b

(0.0124)

W.logdens 0.0050

(0.8825)

-0.0006

(0.9861)

-0.0038

(0.9394)

-0.0158

(0.7436)

W.educ 0.0029

(0.4822)

-0.00196

(0.6728)

0.0042

(0.5067)

-0.0028

(0.6816)

W.logshag 0.0738

c

(0.0863)

0.06093

(0.1558)

0.0801

(0.2160)

0.0573

(0.3669)

W.logshind -0.0453

(0.6716)

0.0977

(0.4357)

-0.1737

(0.2803)

0.0937

(0.6136)

W.hrst 0.0003

c

(0.0670)

0.0005a

(0.0045)

0.0003

(0.2375) 0.0005

b

(0.0377)

W.logucl -0.2256

(0.3811)

-0.1643

(0.5320)

-0.5409

(0.1616)

-0.3778

(0.3286)

W.loggva_eap 0.1560

c

(0.0868)

0.1669c

(0.0663)

0.1786

(0.1901)

0.1955

(0.1432)

0.4660

a

(0.0000)

0.46154a

(0.0000)

0.4459a

(0.0000)

0.4518a

(0.0000)

Log-likelihood -101.2561 -87.52184 -211.5791 -185.6741

Wald statistic 52.675

a

(0.0000)

51.106a

(0.0000)

45.5430a

(0.0000)

47.3690a

(0.0000)

AIC 244.51 217.04 465.16 413.35

Breusch-Pagan test for

heteroskedasticity

20.0820

(0.3282)

21.074

(0.2757)

22.0900

(0.2280)

20.074

(0.3287)

LM test for residual

autocorrelation

0.7989

(0.3714)

0.93245

(0.33423)

1.4986

(0.2209)

0.0376

(0.8462)

Number of

observations 272 252 272 252

Note: The p-values associated with the estimates are between brackets. (a) Significant at 1% probability; (b) significant at 5%

probability; (c) significant at 10% probability.

Source: authors’ elaboration.

26

Table 9

Direct, indirect and total effects: magnitude and significance – Results. Variables Current unemployment rate Long-term unemployment rate

Direct Indirect Total Direct Indirect Total

loggdp -0.1184b/-0.1371

a

(0.0116)/(0.0041)

-0.4117a/-0.5044

a

(0.0022)/(0.0002)

-0.5302a/-0.6416

a

(0.0013)/(0.0001)

-0.2153a/-0.2511

a

(0.0022)/(0.0003)

-0.4239b/-0.5709

a

(0.0261)/(0.0037)

-0.6392a/-0.8219

a

(0.0067)/(0.0006)

expect 0.0244c/0.0587

a

(0.0843)/(0.0052)

0.0150/-0.0597c

(0.3807)/(0.0737)

0.0394/-0.0010

(0.1338)/(0.9609)

0.0341c/0.0837

a

(0.1030)/(0.0076)

0.0113/0.0975

(0.6328)/(0.0444)

0.0455/ -0.0138

(0.2210)/(0.7371)

logdens -0.0674a/-0.0778

a

(0.0025)/(0.0010)

-0.0434/-0.0588

(0.4638)/(0.3096) -0.1108/-0.1367

b

(0.1201)/(0.0544)

-0.0826b/-0.0907

(0.0133)/(0.0090)

-0.0647/-0.0902

(0.4533)/(0.2726)

-0.1473/-0.1809b

(0.1564)/(0.0743)

educ -0.0063b/0.0000

(0.0320)/(0.9889)

0.0000/-0.0031

(0.9991)/(0.6018)

-0.0063/-0.0030

(0.2351)/(0.5733)

-0.0065/0.0029

(0.1451)/(0.6044)

0.0020/-0.0024

(0.8104)/(0.7747)

-0.0045/0.0004

(0.5532)/(0.9496)

logshag -0.0393/-0.0587

b

(0.1568)/(0.0392)

0.0909/0.0545

(0.2033)/(0.4475)

0.0516/-0.0041

(0.5220)/(0.9502)

-0.0360/-0.0593

(0.3788)/(0.1537)

0.1019/0.0484

(0.3225)/(0.6390)

0.0658/-0.0109

(0.5713)/(0.9185)

logshind 0.0248/-0.0782

(0.6563)/(0.3346) -0.0553/0.0992

(0.7483)/(0.5812) -0.0306/0.0210

(0.8652)/(0.9062)

0.0488/-0.1602

(0.5551)/(0.1890)

-0.2418/0.0338

(0.3281)/(0.9056)

-0.1930/-0.1264 (0.4506)/(0.6328)

hrst 0.0003a/0.0003

a

(0.0053)/(0.0014)

0.0007b/0.0011

a

(0.0209)/(0.0010)

0.0010a/0.0014

a

(0.0070)/(0.0003)

0.0004b/0.0005

a

(0.0124)/(0.0029)

0.0008c/0.0012

a

(0.0925)/(0.0100)

0.0012b/0.0017

a

(0.0338)/(0.0030)

logucl 0.4726a/0.5756

a

(0.0018)/(0.0002)

-0.0088/0.1632 (0.9865)/(0.6839)

0.4638/0.7387c

(0.3064)/(0.1008)

0.5450b/0.6466

a

(0.0158)/(0.0055)

-0.4742/-0.1361

(0.4379)/(0.8215)

0.0708/0.5105

(0.9105)/(0.4422)

loggva -0.3346a/-0.3455

a

(0.0000)/(0.0000)

0.0000/0.0119 (0.9987)/(0.9311)

-0.3346b/-0.3336b (0.0275)/(0.0271)

-0.4400a/-0.4437

a

(0.0000)/(0.0000)

-0.0280/-0.0080

(0.8873)/(0.9741)

-0.4680b/-0.4516

b

(0.0348)/(0.0414)

Note: The p-values associated with the estimates are between brackets. (a) Significant at 1% probability; (b) significant at 5%

probability; (c) significant at 10% probability.

Source: authors’ elaboration.