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Spatial Spillovers in Regional Labor Markets:
Does Your Neighbor Affect Your Job Prospects?
Solmaria Halleck Vega† (s1944258) Supervisor: J. Paul Elhorst†
Research Master Thesis, August 25, 2011
Abstract
This paper tests for the existence of spatial spillovers in regional labor markets in a cross-country perspective. In order to quantify these spillovers, the point of departure is the Blanchard and Katz (1992) model that accounts for both lagged effects and mutual relations between unemployment, participation, and employment growth at the regional level over time. This model is particularly useful for analyzing labor market adjustment processes after a demand shock. However, a major limitation of the model is that regions are treated as independent entities, whereas in view of the spatial econometrics literature, it is more likely that neighboring regions interact with each other. In order to incorporate these interaction effects, we extend the model using a dynamic spatial panel data approach. Using annual data from 1986-2001 for 112 regions across 8 EU countries, we estimate the model and find empirical evidence that a region-specific shock not only has an impact on the region itself, but also on neighboring regions.
Key words: Regional labor markets, spatial spillover effects, dynamic spatial panels
JEL classification: R23, C31, C33
__________________________________ †
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1. Introduction
Attaining acceptable levels of employment, unemployment, and participation is a top priority of the European Union’s policy agenda, as they are important indicators of economic and social welfare.1 Focusing on these labor market variables at a national level can hide striking differences between regions within countries (see e.g., Elhorst, 2003a; OECD, 2009; Eurostat, 2010). For example, the variation in unemployment rates between regions within countries is even larger than that between countries (OECD, 2009).2 Recent figures from Eurostat on regional labor market disparities across the EU show stark contrasts between regions and due to the recent economic crisis, it is predicted that these disparities will only increase (Eurostat, 2010). This makes it extremely pertinent to understand the impact of shocks on regional labor markets.
The response of regional labor markets to region-specific shocks has gained a vast amount of attention in the literature, especially following the seminal paper of Blanchard and Katz (1992) on demand shocks to regional labor markets in the United States and Decressin and Fatás (1995) on regional labor markets in European countries. The most prominent result from these studies is the dichotomy between the US and Europe. Whereas migration is found to be the major adjustment channel to a demand shock in the US, changes in labor force participation is found to be the major adjustment channel in Europe, suggesting that European workers are less mobile.
The regional labor market model developed by Blanchard and Katz (1992) is a vector autoregression (VAR) model built to simulate a demand shock. In contrast to a single equation approach, one can decompose the response of a regional labor market to a demand shock into changes in regional unemployment, participation, and employment growth over time. To the extent that a demand shock is not reflected in a change of the unemployment or participation rate, it is absorbed by migration (i.e. migration acts as a “residual”). An attractive feature of the model is that it allows for the mutual interaction between these variables. People may not decide to join the labor force because of poor employment prospects. For example, students may decide to stay longer at the university which shows up not as higher unemployment, but rather as lower
1 See for example, the recent Europe 2020 growth strategy. 2
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participation (Blanchard, 2006). Since all these variables are interrelated, the model represents the complexity of labor market interactions well.
Another attractive feature of the model is that it is regional.3 Since the model is regional in nature, Blanchard and Katz (1992), as well as subsequent studies use regional data for their estimations. Most of them confirm the conclusion of Decressin and Fatás (1995) that migration plays a more limited role as an adjustment mechanism to a labor demand shock for European regions (see e.g. Jimeno and Bentolila, 1998; Mäki-Arvela, 2003; Gács and Huber, 2005). However, there have also been studies that find that European workers may not be as immobile (Fredriksson, 1999; Tani, 2003). Other studies provide a more in-depth analysis of within country differences, instead of analyzing average patterns of all regions in several countries. For example, Broersma and van Dijk (2002) find that even within a small country as the Netherlands, there are remarkable differences in labor market adjustment processes between regions. In particular, they find that labor mobility plays a more prominent role in the North than in other Dutch regions, especially during the initial phase of the adjustment process.
Although these studies use regional data for the estimations, thus taking into account regional heterogeneity, a common feature of all studies is that regions are treated as independent entities.4 However, in view of the spatial econometrics literature, it is more likely that neighboring regions interact with each other. A comprehensive analysis of the repercussions of region-specific shocks provides interesting insights for regional policy development within an integrated Europe. Yet, thus far, these repercussions have focused on the impact of a region-specific shock on the region itself. In this paper we will provide insights into what the repercussions of a shock are on other regions as well.
Modeling of these spatial interactions presents many methodological challenges for which we will apply advanced spatial econometric techniques. Specifically, we extend the Blanchard and Katz (1992) model by using a dynamic spatial panel data approach which has recently gained more attention in the spatial econometrics literature (Yu et al., 2008; Lee and Yu, 2010a; Elhorst, 2012) as well as in applications to other fields such as housing prices (Brady, 2009), consumption (Korniotis, 2010), commuting (Parent and LeSage, 2010), and finance
3The model will be described in more detail in Section 2.
4To some extent linkages between regions are taken into account by the migration “residual,” but the models do not
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(Elhorst et al., 2011). Issues such as region-specific and time-specific fixed effects, identification, estimation methods, and specification of the spatial weights matrix will be addressed before estimating the model using annual data from 1986-2001 for 112 regions across 8 EU countries. After specification and estimation of the extended Blanchard and Katz model, we find that spatial spillover effects are significant and thus, analyses of regional labor markets that treat regions as isolated points in space do not capture the full picture of regional labor market dynamics.
The rest of the paper is structured as follows. Section 2 starts with an overview of the Blanchard-Katz model. Then, our methodology to extend the model with spatial interaction effects using a dynamic spatial panel data approach is outlined. Section 3 describes the data that is used for estimating the model. Section 4 presents and discusses the empirical results and Section 5 concludes.
2. Methodology
2.1 Blanchard-Katz model
In order to investigate the response of regional labor markets to demand shocks in the US, Blanchard and Katz (1992) develop a VAR model that describes the interaction between unemployment, participation, and employment growth at the regional level over time. It should be noted that they also study other aspects of the underlying mechanisms of regional slumps and booms and thus, also present other models.5 We focus on the VAR model (from now on referred to as the Blanchard-Katz model) since it is particularly useful for analyzing adjustment processes after a shock. Another important aspect of the model is that it takes into account regional heterogeneity. Since regions produce different bundles of goods and services, they also experience different shocks to labor demand and thus, also experience adjustment mechanisms
5These include: 1) a regression equation for each region to test for unit roots in the log level of employment (e), the
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that differ from those observed at a national level. For example, a region-specific shock could be a technological innovation in the production of the products in which a region specializes and/or an increase in the demand for these products.
In its basic form, the Blanchard-Katz model is expressed as
𝑢 = 𝛽11𝑢[−1] + 𝛽12𝑝[−1] + 𝛽13𝑒[−1] + 𝛽14𝑒 + 𝜀1, (1a)
𝑝 = 𝛽21𝑢[−1] + 𝛽22𝑝[−1] + 𝛽23𝑒[−1] + 𝛽24𝑒 + 𝜀2, (1b)
𝑒 = 𝛽31𝑢[−1] + 𝛽32𝑝[−1] + 𝛽33𝑒[−1] + 𝜀3, (1c)
where the endogenous variables u, p, and e are the unemployment rate, the logarithm of the labor force participation rate, and the employment growth rate, respectively. The model is recursive in nature because both unemployment and participation in period t are explained by employment growth in period t and employment growth in period t-1, whereas employment growth is only explained by participation in period t-1 and unemployment in period t-1. Each endogenous variable is also explained by its lagged value since labor market variables tend to be strongly correlated in time. Note that both unemployment and participation are defined in levels, while employment is defined as a growth variable. This is because unemployment and participation are stationary series (integrated of order 0), whereas employment is non-stationary (integrated of order 1). If non-stationary time series are used in regression analysis, this leads to spurious results (Greene, 2003).6 The problem is solved by using employment growth instead of the employment level.
To analyze the repercussions of a region-specific labor demand shock, the estimated system of equations (1) is used to conduct impulse-response analysis. By extrapolating the model over several time periods, it is possible to observe how the model evolves and to what equilibrium values the endogenous variables converge to. It should be noted that Blanchard and Katz (1992), as well as subsequent studies, associate unexpected changes in regional employment within the year with changes in labor demand. This assumption is plausible if most of the unexpected movements in employment are caused by shifts in labor demand rather than by shifts in labor supply. It then follows that the labor demand shock can be modeled as an innovation to the error term in equation (1c). By calculating the differences in the endogenous variables before and after the shock over time, it is possible to observe the impact of a change in regional labor demand.
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2.2 Extension of Blanchard-Katz model: A dynamic spatial panel data approach
In the Blanchard-Katz model, it is only possible to observe how a region-specific demand shock affects unemployment, participation, and employment growth in the region itself. Neglecting the effects of a region-specific shock on labor market conditions in neighboring regions may result in sub-optimal projections of its true impact. To overcome this limitation, we extend the Blanchard-Katz model to incorporate these spatial spillover effects.
Each equation in model (1) can be rewritten in the form of the following dynamic spatial panel data model
Yt = τYt−1+ δWYt+ ηWYt−1+ Xtβ1 + WXtβ2 + Xt−1β3 + WXt−1β4 + µ + αt0ιN+ εt, (2)
where Yt denotes an Nx1 vector consisting of one observation of the dependent variable for every region (i=1,…,N) in the sample at a particular point in time (t=1,…,T), and Xt is an NxK matrix of explanatory variables. In this case, the explanatory variables are the other labor market variables (e.g., in equation (1a) they are p and e). W is a non-negative NxN matrix of known constants describing the spatial arrangement of the regions in the sample. Its diagonal elements are set to zero by assumption, since no region can be viewed as its own neighbor. A vector or matrix with subscript t-1 denotes its serially lagged value, while a vector or a matrix pre-multiplied by W denotes its spatially lagged value. τ, δ, and η are the response parameters of respectively, the lagged dependent variable Yt-1, the lagged dependent variable in space WYt, and the dependent variable lagged both in space and time WYt-1. δ is called the spatial autoregressive coefficient, while η is referred to as the lagged spatial autoregressive coefficient. β1, β2, β3, and β4 are Kx1 vectors of response parameters of the explanatory variables. εt = (ε1t, … , εNt)T is a vector of independently and identically distributed (i.i.d.) disturbance terms, whose elements have zero mean and finite variance σ2
. µ = (µ1, … , µN)Tis a vector with regional fixed effects μi. αt0 is the coefficient of a time period fixed effect and ⍳Nis an Nx1 vector of ones.
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Table 1. Variables included in extended Blanchard-Katz model
we leave aside even though they are included in the original model (1). Otherwise the full dynamic spatial panel data model would suffer from identification problems. One immediate explanation for why the parameters in the unemployment and participation rate equations are not identified is because they include the variables et and Wet, as well as et-1 and Wet-1. According to Anselin et al. (2008), variables lagged in time should be avoided. One option to deal with this problem would be to not measure employment growth over the last year, but instead over the last two years. However, this implies that the impact of employment growth in years t and t-1 are the same, which is not realistic.
An alternative option would be to drop et-1 and Wet-1 from model (2). An advantage of this option is that the number of observations that we lose due to including lagged variables diminishes from two to one.7 We chose this latter option since it is more plausible than assuming employment growth in the present and previous periods to be the same, and also since the employment growth variable lagged one period in time turned out to be insignificant when we estimated the full model (i.e. including et-1 and Wet-1). Therefore, the final equation can be formulated as
Yt = τYt−1+ δWYt+ ηWYt−1+ Xt/t−1β1 + WXt/t−1β2 + µ + αt0ιN+ εt, (3)
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Note that this holds for the unemployment rate and participation rate equations, not for the employment growth rate equation (see Table 1). The reason that the number of observations that we lose reduces from two to one is because
et is measured as log(Et/Et-1), where E measures the level of employment.
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which takes into account that the explanatory variables are different for different equations in the extended Blanchard-Katz model.8 However, identification issues still remain.9
2.3 Direct effects and indirect (spatial spillover) effects
Many empirical studies use point estimates of one or more spatial regression model specifications to test the hypothesis as to whether or not spatial spillover effects exist. However, LeSage and Pace (2009, p. 74) have recently pointed out that this may lead to erroneous conclusions, and that a partial derivative interpretation of the impact from changes to the variables of different model specifications represents a more valid basis for testing this hypothesis. They also prove this using a static spatial econometric model (ibid, pp. 34-40).
By rewriting equation (3) as
Yt= (I − δW)−1(τI + ηW)Yt−1+ (I − δW)−1(Xtβ1 + WXtβ2 ) + (I − δW)−1(µ + αt0ιN+ εt), (4)
the matrix of partial derivatives of Y with respect to the kth explanatory variable of X in unit 1 up to unit N at a particular point in time can be seen to be
�∂x∂Y 1k… ∂Y ∂xNk�t = ((I − δW) −1[β1kIN+ β2kW] (5)
These partial derivatives denote the effect of a change of a particular explanatory variable in a particular spatial unit on the dependent variable of all other units in the short term. Similarly, the long-term effects can be seen to be
�∂x∂Y 1k… ∂Y ∂xNk� = [(I − τ)I − (δ + η)W] −1[β1kIN+ β2kW] (6) 8The notation X
t/t-1 (and WXt/t-1)is used because for the u and p equations these variables are observed in both time t
(employment growth) and time t-1 (participation and unemployment, respectively). However, in the e equation they are only observed in time t-1 (unemployment and participation).
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The expressions in (5) and (6) show that short-term indirect effects do not occur if both δ=0 and β2k=0, while long-term indirect effects do not occur if both δ=-η and β2k=0. The results of this model can be used to determine short-term and term direct effects, and short-term and long-term indirect (spatial spillover) effects. Even though this makes the model optimal, Anselin et al. (2008) point out that it might suffer from identification problems, which is addressed in the subsequent section.
Since both the direct and indirect effects are different for different regions in the sample, the presentation of both effects is difficult. With N regions and K explanatory variables, it is possible to obtain K different NxN matrices of direct and indirect effects. Even for small values of N and K, it may be challenging to compactly report these results. Therefore, LeSage and Pace (2009) propose to report one direct effect measured by the average of the diagonal elements, and one indirect effect measured by the average of either the row sums or the column sums of the non-diagonal elements of that matrix. Note that even though the average row effect and average column effect quantify different impacts, the numerical magnitudes of their sums are the same and thus, it does not matter which one is used.10 The total effect is the sum of the direct and indirect effects.
2.4 Identification
To avoid identification problems, one of the following four restrictions taken from the spatial econometrics literature on dynamic spatial panel data models might be imposed on the parameters in equation (3).
The first restriction is β2=0, which is the model considered in Yu et al. (2008) and Lee and Yu (2010a). However, the price that needs to be paid for identification is relatively high since the local indirect (spatial spillover) effects are set to zero by construction. As a result, the indirect effects in relation to the direct effects become the same for every explanatory variable, both in the short term and in the long term. If this ratio happens to be p percent for one variable, it is also p percent for any other variable. This is because β1k in the numerator and β1k in the
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denominator of this ratio cancel each other out. For example, the ratio for the kth explanatory variable in the short term takes the form
[(I − δW)−1(β1kIN)]rsum��������/[(I − δW)−1(β1kIN)]d� = [(I − δW)−1]rsum��������/[(I − δW)−1]d�, (7)
which shows that it is independent of β1k and thus the same for every explanatory variable. A similar result is obtained when considering this ratio in the long term. The superscript rsum������� denotes the operator that calculates the mean row sum of the non-diagonal elements and the superscript d� denotes the operator that calculates the mean diagonal element of a matrix.
The second restriction that might be imposed is δ=0, which is the model considered in LeSage and Pace (2009, Ch.7) and Korniotis (2010). The disadvantage of this restriction is that the matrix (I − δW)−1 degenerates to the identity matrix and thus, the global short-term indirect (spatial spillover) effect of every explanatory variable is zero. In other words, this model is less suitable if the analysis focuses on spatial spillover effects in the short term. In our case, this is crucial and it is best not to give up this variable since we are interested in the short-term effects of a shock in employment growth.
The third restriction that might be imposed is η=-τδ, which is presented in Parent and LeSage (2010, 2011). The advantage of this restriction is that the impact of a change in one of the explanatory variables on the dependent variable can be decomposed into a spatial effect and a time effect; the impact over space falls by the factor δW for every higher-order neighbor, and over time by the factor τ for every next time period (see Elhorst 2010a for a mathematical derivation). The disadvantage is that the indirect effects in relation to the direct effects remain constant over time for every explanatory variable. The ratio of the kth explanatory variable takes the form
[(I − δW)−1(β1kIN+ β2kW)]��������rsum/[(I − δW)−1(β1kIN+ β2kW)]d�, (8)
both in the short term and in the long term. In other words, if it is p percent for one variable in the short term, it is also p percent for that variable in the long term.
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and Jacobs et al. (2010). Although this model also limits the flexibility of the ratio between indirect and direct effects, it seems to be the least restrictive model. Below we will further investigate this.
We carried out Wald tests for the four different restrictions since this test may be used to see whether these restrictions are acceptable on the data.11 We fail to reject most of the restrictions, but not for all the equations (e.g., for the employment growth equation two restrictions were not rejected, while the other two were). In principle, for those restrictions that can be rejected, we can impose them on the model without loss of information. However, for the other equations all the restrictions were not rejected. Thus, overall the test results pointed out that if one of these restrictions is not imposed, the parameters are not identified. To demonstrate the identification problem of the full model, we carried out a Monte Carlo simulation experiment based on the full model specified in equation (3). The basic idea is to randomly draw (e.g., 1,000 times) the error terms based on σ2 of the estimated equation to generate data, and then this data is used to re-estimate the model. On average, these results should be similar to those of the “original” parameter estimates. However, the differences came out to be quite substantial. The first column of Table 2 reports the original and the simulated parameter values averaged over 1,000 replications. The results reported in this table show that the parameters are indeed biased, as was expected (see e.g., Anselin et al., 2008).
<< insert Table 2 >>
Therefore, we decided to impose the fourth restriction, i.e. the dependent variable lagged both in space and time WYt-1 is no longer included in each equation of the model. We chose this fourth restriction since it is the one with the least information loss. After imposing the restriction, we again carried out a Monte Carlo simulation in order to check whether the parameters are identified. This time we find that the estimated and simulated parameter estimates are very close in value (see column (2) of Table 2). Therefore, the final model which serves as the basis of our empirical results includes all the variables in Table 1, with the exception of the third column of the explanatory variables.
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The Wald test has a chi-square distribution with R degrees of freedom, where R stands for the number of restrictions. In our case, for the first type of restriction (β2=0), there are K degrees of freedom; the other three
12 2.5 Region-specific and time-specific effects
An important aspect to consider is whether to treat region-specific and time-specific effects as fixed effects or random effects. In the fixed effects model, a dummy variable is introduced for each region. Regional fixed effects control for all region-specific, time-invariant variables whose omission could bias the estimates (Baltagi, 2005). For example, regions can be landlocked or located at the seaside, peripheral or centrally-located, etc. In addition to geographical differences, regions can have different norms and values regarding unemployment, participation, and employment. A limitation of the fixed effects model is that any time-invariant variable is eliminated by the within transformation. In our case, we do not have this problem since we do not have time-invariant variables in the model.
Similarly, time-period fixed effects control for all time-specific, region-invariant variables whose omission could bias the estimates in a typical time-series study (ibid). An example of time-specific effects is that one year can be marked by economic recession, while the other by a boom. Furthermore, legislation or government policy can significantly affect the functioning of the labor market. For example, the signing of the Maastricht Treaty in 1992 led to the creation of the euro and the pillar system of the EU. Additionally, it has been found that if time-period fixed effects are ignored, this leads to stronger evidence in favor of spatial spillovers since the common time effect is not separated from the interaction effect among spatial units (see e.g., Elhorst, 2010b; Lee and Yu, 2010a). Therefore, we also control for time-period fixed effects so that we do not overestimate the spatial interaction effects.
Instead of fixed, μ and α can also be specified as being random. In the random effects model, μi is treated as a random variable that is i.i.d. with zero mean and variance σµ2 and it is assumed that the random variables μi and εit are mutually independent. Furthermore, there is a strong assumption of zero correlation between the random effects μi and the explanatory variables, which is particularly restrictive. However, the choice between a fixed effects and a random effects approach for a given set of adjacent spatial units remains controversial. If the sample happens to be a random draw of the underlying population, unconditional inference about the population necessitates estimation with random effects.12
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In other words, the random effects approach is not conditional upon the individual μis, but integrates them out so
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If, however, the objective is to make conditional inferences about the sample, then fixed effects should be specified. In our case, each region represents itself (i.e. has its own characteristics setting it apart from a larger population) and has not been sampled randomly, so that specific effects should be fixed (Anselin, 1988; Nerlove and Balestra, 1996; Beck, 2001; Beenstock and Felsenstein, 2007). Therefore, in this case a fixed effects model is more appropriate and both region-specific and time dummies are included in each equation.
2.6 Estimation method
Yu et al. (2008) construct a bias corrected estimator for a dynamic model (Yt-1, WYt and WYt-1) with spatial fixed effects. Lee and Yu (2010b) extend this study to include time period fixed effects. They first estimate the model by the ML estimator developed by Elhorst (2003b, 2010b) for the spatial lag model with spatial and time-period fixed effects.13 This estimator is called the least squares dummy variable (LSDV) estimator and is based on the conditional log-likelihood function of the model, i.e., conditional upon the first observation of every spatial unit in the sample due to the regressors Yt-1 and WYt-1.
Then, they provide a rigorous asymptotic theory for the LSDV estimator and their bias corrected LSDV (BCLSDV) estimator when both the number of spatial units (N) and the number of time periods (T) in the sample go to infinity such that the limit between N and T exists and is bounded between 0 and ∞ (0<lim(N/T)<∞). As pointed out by Lee and Yu (2010c), this condition implies that T→∞ where T cannot be too small relative to N. It should be noted that the BCLSDV estimator produces consistent parameter estimates provided that the model is stationary, that is, if τ+δ+η<1.
characteristics (Verbeek, 2008). In contrast, the fixed effects approach considers the distribution of the dependent variable given μi, which is relevant if the units in the sample are unique.
13The estimation of the fixed effects model is based on the demeaning procedure described in Baltagi (2005). The
standard method is to eliminate the regional fixed effects μi from the regression by demeaning the Y and X variables.
That is, the variables for each region are taken in deviations of their average over time (e.g., the dependent variable is defined as 𝑌𝑖𝑡− 𝑌�𝑖., where 𝑌�𝑖.=1
𝑇∑𝑇𝑡=1𝑌𝑖𝑡). However, since the model also contains fixed effects for time periods,
we eliminate the (regional and time-period) fixed effects from the regression equation by double demeaning the Y and X variables. For example, the dependent variable is defined as 𝑌𝑖𝑡− 𝑌�𝑖.− 𝑌�.𝑡+ 𝑌�.., where 𝑌�.𝑡=1
𝑁∑𝑁𝑖=1𝑌𝑖𝑡 (i.e. the
average over all regions at time t), and 𝑌�..= 1
𝑁𝑇∑𝑁𝑖=1∑𝑇𝑡=1𝑌𝑖𝑡 (i.e. the overall average). Instead of estimating the
14 2.7 Specification of spatial weights matrix
One of the most criticized aspects of spatial econometric models is that the spatial weights matrix W cannot be estimated, but needs to be specified in advance. Recently, Corrado and Fingleton (2011) directly confront this issue. Despite the criticism, trying to find alternatives to incorporating spatial spillovers is difficult. They point out that alternatives to W that have been proposed by e.g., Folmer and Oud (2008) and Harris et al. (2010), such as entering variables in the regression model that proxy spillovers, also requires identifying assumptions. In other words, this approach also involves an a priori specification of the spatial relation between units in the sample.
Considering that this is a critical issue in spatial econometric modeling, it is not surprising that there have been many studies that attempt to investigate how robust results are to different specifications of W and which W is to be preferred. For example, in a recent Monte-Carlo study, Stakhovych and Bijmolt (2009) demonstrate that a weights matrix selection procedure that is based on goodness-of-fit criteria increases the probability of finding the true specification. The most widely used criterion is the log-likelihood function value, but this approach has also received criticism because it only finds a local maximum among competing models and it might be the case that the correctly specified W is not included (see e.g., Harris et al., 2010).
LeSage and Pace (2009) propose the Bayesian posterior model probability as an alternative criterion to select models. The basic idea is as follows. Suppose that we are considering S alternative models based on different spatial weights matrices. The other model specification aspects (e.g., the explanatory variables) are held constant. The Bayesian model comparison approach requires setting prior probabilities to each model S. In order to make each model equally likely a priori, the same prior probability 1/S is assigned to each model under consideration. Each model is estimated by Bayesian methods and then posterior probabilities are computed based on the data and the estimation results of the set of S models. The model with the highest Bayesian posterior probability indicates the W that best fits the data.
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alternative spatial weights when estimating the model. The first W matrix is based on the binary contiguity principle of sharing a common border (denoted as W1 in Table 3), where element wij
takes the value one when regions i and j are neighbors, and zero otherwise. The diagonal elements are set to zero since regions are not considered neighbors to themselves. The advantage of this specification is that the information is completely exogenous. It should be noted that we include neighboring regions across national borders as well. This is because it can be the case that regions that are close-by will interact more even if they are located in different countries, than regions in the same country, but located further away. This could especially be the case with increased integration among EU member states.
The second W we use is a binary contiguity matrix based on population sizes (W2 in Table 3), where we take the average population for each region over 16 years.14 Since population size does not change much over this period, W is kept constant over time. We consider this specification because it can be expected that regions with larger populations have a greater influence than those with fewer inhabitants, so that W is no longer symmetric. For example, whereas W1 takes into account that the Community of Madrid borders Castile-La Mancha, W2 also reflects the fact that the Community of Madrid has a much larger population and thus, a shock in this region of Spain will have more of an effect on its neighbors than vice versa.
In order to take into account distance between regions we use a third weights matrix based on inverse travel times (W3 in Table 3).15 Travel times are a better reflection of the true distance between regions since impediments other than just the geographical distance are included. For example, travel time over land takes into account different road types, national car speed limits, and speed constraints in urban and mountainous areas; overseas travel time depends on embarkation waiting time and the travel time by ferry (for more details, refer to Schürmann and Talaat, 2000).16 We invert the travel times since this corrects for the fact that regions that are closer will have a larger weight and those that are further away, a smaller weight. We thought that this specification was particularly relevant since it incorporates the transport infrastructure linking the different regions in our sample. If regions are more accessible to each other (e.g., in
14The data for regional population is taken from Eurostat (see Section 3 for details).
15The data comes from Schürmann and Talaat (2000), which was part of a report compiled for the General
Directorate Regional Policy of the European Commission.
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terms of the effort, time, or cost that is required to reach them), this provides a greater opportunity for interaction between households and firms in different regions. Lower travel times can be beneficial for workers commuting daily from one region to another, or for the unemployed to find a job in another region when the job prospects in their own region are less promising.
The construction of the fourth spatial weights matrix is based on population sizes and inverse travel times (W4 in Table 3). It is therefore a hybrid matrix combining both the size of the regions and also the distance between them. Specifically, we divide the population in region j by the distance from region i to region j. We did not restrict the weights to only contiguous regions since it can be the case that the travel time already takes this into account. However, just in case, we also specified a related spatial weights matrix (W5 in Table 3) that restricts the weights to contiguous neighbors because the population size could overestimate the strength of the connections between regions.
In the sixth spatial weights matrix we use, not only are first-order neighbors considered (e.g., that Madrid is a neighbor of Castile-La Mancha), but also second-order neighbors (e.g., Madrid and Aragón). In our specification of this matrix (denoted W6 in Table 3), no distinction is made between first and second-order neighbors, i.e. they are treated with equal weights. This concept can be thought of in terms of the number of direct and indirect connections a person has in a social network where the first-order identifies friends and the second-order friends of friends (LeSage and Pace, 2009). In our case, it might be commuting (e.g., you can live in one place and commute to another for work and this could take place through various regions). Another example could be that a firm in Madrid requires more inputs from Castile-La Mancha to produce its products due to higher demand. Since the firm in Castile-La Mancha produces more output in order to satisfy increased demand from Madrid, this in turn, could increase their demand for inputs from a firm in e.g., Aragón. To further explore the inclusion of higher-order neighbors, we incorporate third-order neighbors to the previous specification (denoted W7 in Table 3).17
Even though increased integration among EU member states might make national boundaries less relevant, it is still realistic to assume that there are barriers (social, political, cultural, etc.) between neighboring countries. It could also be the case that people are simply not
17
17
willing to move and work in a neighboring region of a different country, even if the region is close-by. It is also relevant to note that the sample spans the period from 1986, which was at the beginnings of the formation of the EU, until 2001. We therefore consider a W matrix based on the binary contiguity principle of sharing a common border, but limit contiguity to within country linkages only (W8 in Table 3).18
Since spatial interaction can also be determined by economic variables rather than on physical features of how units are spaced, we also consider ‘economic distance.’19 For example, Fingleton and Le Gallo (2008) take into account the size of each area’s economy (measured in terms of the total employment level) and argue that it is more realistic to base spatial spillovers relative to economic distance. Therefore, we estimate the model using a binary contiguity matrix based on regional GDP (W9 in Table 3), where we take the average GDP for each region over 16 years.20 It is expected that the impact of regions with greater ‘economic mass’ will be greater than the other way around, so that the spatial weights matrix is asymmetric.
The final spatial weights matrix that we construct is based on a gravity model specification (W10 in Table 3), with typical element w𝑖𝑗 = [GDP𝑖(GDP𝑗)/d𝑖𝑗]. Thus, the interaction is expressed as a ratio of the multiplied economic mass of region i and region j over the distance between regions i and j. This type of model has recently gained even more attention in the social sciences, such as the gravity model of trade in international economics (see e.g., Brakman and Bergeijk, 2010).21 It is expected that the level of flows (trade, migration, commuting, etc.) between regions will depend on both scale and distance impacts. For example, consider regions i, j, and k. Suppose that i and j have similar GDP levels, whereas k has a lower level of GDP. The potential interactions between i and j is expected to be greater than in the case of i and k, which is the multiplicative scale effect. That is, regions with larger economic size tend to generate and attract more activities. Furthermore, if k is farther away from i, it is expected that the flows between them will be smaller due to the negative influence distance has on interaction.
18For Denmark and Luxembourg, we also considered including their closest neighbors, which are
Schleswig-Holstein (Germany) and Luxembourg (Belgium), respectively. However, we find that it did not make a difference in the estimation results and therefore leave them without having shared borders in the W8 specification.
19For a brief overview of the literature on incorporating the notion of economic distance, see Corrado and Fingleton
(2011). They also mention other distances related to e.g., the industrial organization literature (industrial structure space, commercial space, etc.). However, it is often difficult to measure these other distance measures, as in our case at the regional level in a cross-country perspective.
20
The data for regional GDP (expressed in PPPs) is taken from Eurostat.
18
Table 3 reports the performance of our model based on the alternative spatial weights matrices. Taking into consideration the different criteria to determine which W best describes the data, we compare the log-likelihood function values relative to the number of observations. An alternative approach is to compare the Bayesian posterior model probabilities as outlined above. An attractive feature of this latter approach is that it does not require nested models for the comparisons. In contrast, tests for significant differences between log-likelihood function values (such as the likelihood ratio test) can formally not be used if models are non-nested, i.e. for alternative spatial weights. The parameter estimate of the residual variance (σ2
) is similar for all the W specifications and thus is not reported in Table 3.22
<< insert Table 3 >>
At first, the results are surprising since it is expected that taking into account factors such as population size, inverse travel times, and regional GDP would have described the data better. For example, it makes intuitive sense that the more difficult it is to reach a location, the weaker the interactions between regions will be. In addition to distance, it is also intuitively appealing that scale matters in the analysis of spatial spillovers in regional labor markets. Since these results were unanticipated, we wanted to make sure they are robust to other specifications. An issue that has recently drawn more attention in this respect is how the spatial weights matrix is normalized (Kelejian and Prucha, 2010). It should be noted that all the weights matrices we use are row-normalized, so that the entries of each row sum to unity to facilitate interpretation and computation of spatial autocorrelation. Even though this is common practice in the empirical literature, we examine whether the results are sensitive to another type of normalization. Therefore, we re-estimate the model with all the different spatial weights, but instead of normalizing by row, we scale each of the matrices by the maximum eigenvalue.23
22σ2 is 0.0001 for the u equation, 0.0002 for the p equation, and 0.0009 for the e equation for all the alternative Ws.
An exception was for W8, where σ2<0.0001 for the u equation. 23
19
We find that the results are robust to the alternative normalization factor. The spatial weights matrix that best fits both the data and any prior distributions assigned for the parameters is W8 for the unemployment and participation rate equations and W6 for the employment growth equation. Although Kelejian and Prucha (2010) claim that a row-normalized weights matrix will in general lead to a misspecified model (unless this approach is chosen on theoretical grounds), we find that using either approach does not make a difference for the empirical results. The only main difference was for the participation rate equation; the Bayesian posterior model probability for W8 came out to be even larger when we used a single normalization factor approach (see Table 3).
In line with our results, Stakhovych and Bijmolt (2009) find that spatial models estimated using the first-order contiguity weights matrix on average perform better than those using inverse distance weights matrices.24 However, the fact that incorporating geography, population size, and economic measures in the specification of the spatial weights matrix does not improve the performance of the model is counterintuitive. Yet, after more thought the results are explicable. A reason why economic distance does not outperform other specifications is that neighboring regions already share similar labor market characteristics. For example, Overman and Puga (2002) find that regional unemployment has a strong geographical component, i.e. regions have unemployment characteristics similar to surrounding regions. Similarly, Elhorst and Zeilstra (2007) find that regions with high or low values of (male and female) participation rates tend to be surrounded by regions with similar values, provided these regions are located in the same country.
Our results confirm these latter findings since they strongly indicate that it is not necessary to add other kinds of measures to the specification of the spatial weights matrix. In other words, even though Corrado and Fingleton (2011) have a strong argument for incorporating economic distance, simply indicating whether regions share common borders captures the strength of the interactions well since nearby regions tend to share similar economic structures. Nevertheless, one important distinction is the spatial weights matrix that comes to the surface for the employment growth equation and for the unemployment and participation rate equations. In the first case, the best performing matrix is the binary contiguity matrix extending
24
20
across national borders and including higher-order neighbors as well. In the second case, the
binary contiguity matrix limited to within country neighbors turned out to be the best performing weights matrix. This is intuitively appealing since the employment growth equation reflects labor demand. Firms are willing to exploit advantages of location close to borders, such as the ability to use suppliers from different countries (Overman and Puga, 2002). In this way, borders do not matter as much. Furthermore, since higher-order neighbors are also included in W6, this indicates that firms demanding more inputs from a neighboring region also indirectly affect demand for inputs from neighboring regions of their neighbor, i.e. second-order neighbors.
In contrast, the result for the unemployment and participation rate equation reflects the low labor mobility in the EU compared to the US (European Commission, 2010). Even within EU countries, migration across regions also remains small (Puga, 2002). This result is also intuitive since for the unemployment (participation) rate equation, W8 represents the perspective of unemployed people (workers) in a particular region with regard to finding a job (commuting to their job) in another region. Since there are small flows of workers across borders in terms of commuting and permanent moves, the binary contiguity matrix that also includes neighboring regions across national borders does not reflect reality. In fact, there have also been empirical studies that find that the amount of time that commuters travel is on average much less than an hour (see e.g. Elhorst and Oosterhaven, 2006, Table 1, p. 43). This can also explain why the inverse travel time specifications, such as W3 and W4, did not reflect the data better than W6 and W8. At a more spatially disaggregated level, it is more probable that distance measures (such as travel times) would better reflect the interactions between location pairs.
21
market participants do not migrate, it is interesting that our results strongly indicate that the
within country specification better reflects the data for these two equations, especially for the
unemployment rate.25
3. Data
The regional level data on unemployment, participation, and employment is obtained from the Labor Force Survey provided by Eurostat.26 The sample that we use in our empirical analysis includes 112 regions across 8 EU countries covering a period of 16 years, from 1986-2001. Although there is data available from 1983 for most countries in the sample, Spain did not begin data registration until it became a member of the EU in 1986 and to have a balanced panel we start from this latter year.27 The countries included in the analysis are (number of regions within parentheses): Belgium (11), Denmark (1), France (21), West Germany (20), Italy (20), Luxembourg (1), the Netherlands (12), and Spain (16). Even though we also have data available for Greece and Ireland, we decided to not include them since starting with an unbroken study area was necessary to test the different spatial weights matrices.
For the regional unemployment rate, we divide the number of unemployed people by the number of people in the labor force (i.e. economically active population, which consists of the sum of the employed and unemployed). Since unemployment data often suffer variations across countries and time in the definition or measurement of unemployment rates, we use Eurostat's harmonized unemployment rates.28 For the participation rate, we take the logarithm of the ratio of the labor force and the working age population (aged between 15-64 years old). Finally, the employment growth rate is calculated as the logarithm of the number of people employed in period t divided by the number of people employed in period t-1. Recall that we define
25
It will be interesting to observe whether these outcomes change when considering a later period to see if European workers may not be as immobile as in the findings of e.g., Fredriksson (1999) and Tani (2003).
26This data can be found at: http://epp.eurostat.ec.europa.eu/portal/page/portal/region_cities/introduction
Eurostat uses a classification in NUTS 1, NUTS 2, and NUTS 3 level regions. (NUTS is the French acronym for Nomenclature of Territorial Units for Statistics.) Most regional data are available for NUTS 2 level regions, which is what we use in this study. Eurostat (2008) provides a comprehensive overview.
27Additionally, as mentioned in Overman and Puga (2002), regional unemployment data prior to 1986 is limited and
is not mutually consistent creating problems for comparability across countries.
28
22
employment as a growth variable because the employment level is stationary and non-stationary time series cannot be used in regression analysis. Instead of providing summary statistics for each individual region and time period, we facilitate the visualization of our sample by depicting the variables for the most recent year using ArcGIS (see Figs. 1-3).
4. Results
The estimation results are reported in Table 4. We find that using either form of spatial weights normalization results in similar estimates and inferences.29 Since normalizing the spatial weights matrix to have row-sums of unity is most frequently used in the empirical literature, the reported results are based on this approach.30 We also include the LSDV estimator results without any interaction effects in the first column of Table 4. In this way, the spatial model can be compared with that of a traditional non-spatial Blanchard-Katz model. Regarding the computation of the goodness-of-fit measure, in spatial panel data models there is no precise counterpart of the R2. We calculate the squared sample correlation coefficient (corr2) between actual and fitted values since this measure ignores the variation explained by the regional fixed effects, which is reported under the R2 for both models in Table 4.31
<< insert Table 4 >>
4.1 Spatial vs. non-spatial model
The coefficient estimates of the non-spatial variables in both the LSDV model and the extended model with spatial interaction effects are significantly different from zero, mainly at the 1% level. Note that the coefficients of the serially lagged endogenous variables, especially for the unemployment and participation rates, are large and significant. This outcome is in line with previous studies, as labor market variables tend to be strongly correlated over time. The lagged
29This also holds for the short-term and long-term direct, indirect, and total effects presented in Table 5. 30The results based on maximum eigenvalue normalization are available upon request.
31
23
unemployment rate in the employment growth equation is the only non-spatial variable with an insignificant coefficient estimate (t-value = -1.566). However, the latter coefficient appears highly significant in the spatial model (column (2) of Table 4).
We also find that the majority of the estimated coefficients of the spatial variables are highly significant. The only exception is the response parameter of the participation rate lagged both in space and time in the unemployment growth equation (0.01, t-value = 0.521). This result is noteworthy because it indicates that the spatially lagged dependent and explanatory variables should be included in the model. Omission of relevant explanatory variables results in a misspecified model, i.e. the estimated coefficients of the remaining variables will be biased and inconsistent (Greene, 2003). The spatial autoregressive coefficients reflect the fact that labor market variables of a particular region interact with those of its surrounding regions. The latter coefficients in all three equations (u, p, and e) turn out to be positive (0.248, 0.162, and 0.577, respectively) and statistically significant at 1%. The fact that the spatial autocorrelation is positive indicates that e.g., the unemployment rate in neighboring regions varies directly with an increase in the unemployment rate in a particular region.
Because models containing spatial lags of dependent and explanatory variables become more complicated with a greater wealth of information (LeSage and Pace, 2009), due care should be taken when interpreting the coefficient estimates. Whereas these estimates represent the marginal effect of a change in an explanatory variable on the dependent variable in the non-spatial model, this is not the case in the non-spatial model. For this purpose, we use the direct and indirect effect estimates derived from equations (5) and (6). Recall that the direct effect estimates measure the impact of changing an explanatory variable on the dependent variable of a spatial unit. We therefore use the coefficient estimates of the LSDV model (column (1) of Table 4) and the direct effects of the spatial model reported in Table 5 to provide a valid comparison. A comparison of the indirect (spatial spillover) effects is not possible since in the LSDV model, these latter effects are set to zero by construction.
24
model, whereas its counterpart in the LSDV model is -0.023.32 Therefore, the latter effect is underestimated by 46.9%. Since the original and extended Blanchard-Katz model with spatial interaction effects is recursive in nature (i.e. u and p are not observed in time t), the short-term effects of the unemployment and participation rates have a one year time lag. However, note that the short-term direct effect of e.g., -0.103 indicates that an increase in employment growth by one percentage point in region i decreases the unemployment rate in region i by 0.103 percentage points in the same year. As in the u equation, we also find that there are substantial differences when comparing the direct effects of the two models in the other equations. In the p equation, the direct effect of e is underestimated by 1.41%, which is not as large as the other differences. However, the direct effect of u is underestimated by 34.4%. Finally, in the e equation the direct effect of u is underestimated by 71%, and that of p is overestimated by 2.46%.
<< insert Table 5 >>
4.2 Direct and indirect effects vs. coefficient estimates of spatial model
It should be noted that the direct effects measure includes feedback effects that arise as a result of impacts passing through neighboring units (e.g., from region i to j to k) and back to the unit that the change originated from (region i). This is precisely the reason that there are differences between the direct effects of the explanatory variables and their coefficient estimates. In general, the direct effect estimates reported in Table 5 and the coefficients in column 2 of Table 4 are quite similar, so that the feedback effects appear to be relatively small. For example, the direct effect and the coefficient estimate of p in the employment growth equation are -0.818 and -0.518, respectively.33 Its feedback effect therefore amounts to only 2.08%. Other feedback effects range from close to 0% to around 6%. There are also negative values; e.g., of -6.87%
32
The coefficient estimate of -0.015 is divided by the average p in our sample, which is 0.647. We make this adjustment because p is measured in logs, while u and e are both measured in percentage points. For the u equation,
u = ln(p)β, where β is the coefficient estimate. Then, it follows that 𝜕𝑢
𝜕𝑝= 𝜕𝑢 𝑝𝜕𝑙𝑛𝑝=
𝛽
𝑝. The e equation has a similar
expression. In contrast, for the p equation, lnp = uβ and thus, 𝜕𝑝
𝜕𝑢= 𝑝𝜕𝑙𝑛𝑝
𝜕𝑢 = 𝑝̅𝛽. The coefficients in Table 4 are
reported without the adjustment, as we wanted to show the original estimation results. For ease of interpretation, the adjusted coefficient estimates are reported in Table 5.
33
25
because the estimated coefficient of u exceeds its direct effect estimate in the employment growth equation.
In contrast, the discrepancies between the spatial lag coefficients and the indirect effect estimates are quite substantial. Whereas the coefficient of the spatially lagged value of employment growth in the unemployment rate equation is positive (0.023), its indirect (spatial spillover) effect is negative (-0.025). If we were to take the former coefficient of 0.023 as reflecting the indirect effect, this would lead us to conclude that the employment growth rate exerts a positive and significant indirect impact on the unemployment rate. In other words, job growth in region i has adverse effects on the labor market conditions in neighboring regions since the result is higher unemployment rates. Many empirical studies use the point estimates to test for the existence of spatial spillover effects. However, the results from this study illustrate that this may lead to erroneous conclusions.
As indicated above, rather than turning out to be positive, the short-term indirect effect is negative and significant. This indicates that job growth in region i not only decreases the unemployment rate in region i, but also in other regions j. Specifically, we find that if the employment growth rate in region i increases by one percentage point, on average, the unemployment rate in neighboring regions decreases by 0.025 percentage points in the short-term. Therefore, an increase in the economic opportunities available to citizens of a particular region does not appear to worsen the job prospects of citizens living in neighboring regions. In general, we also find substantial differences between the other spatial lag coefficients and indirect effects, indicating that a partial derivative interpretation (as outlined in Section 2.3) provides a more valid basis to test for the existence of spatial spillovers.
4.3 Statistical significance and interpretation of direct, indirect, and total effects
26
Pace (2009, p. 39) suggest simulating the distribution of the direct and indirect effects using the variance-covariance matrix implied by the maximum likelihood estimates.
Therefore, we use the variation of 1,000 simulated parameter combinations drawn from the multivariate normal distribution implied by the ML estimates in order to draw inferences regarding the statistical significance of the effects. Based on the calculated t-statistics, we find that most of the indirect effects differ significantly from zero, providing evidence of the existence of spatial spillovers in regional labor markets. Only the indirect effects in the unemployment rate equation turn out to be largely insignificant; note this also holds for the direct and total effects in this equation, especially in the long-term. In the other two equations (p and e), the majority of the indirect effects are highly significant, except for the long-term indirect effect of the unemployment rate in the participation rate equation (t-value = -1.314).
The short-term direct effect of employment growth on the unemployment rate is highly significant. This result has the expected sign. If a regional economy creates new jobs, this increases the opportunities available for e.g., the currently unemployed population. Specifically, we find that an increase of 1 percentage point in the employment growth rate in a particular region decreases the unemployment rate in its own region by 0.103 percentage points. The expected sign was not as clear for the short-term indirect effect. It may be that growth in an individual region comes at the expense of the performance of the labor market in neighboring regions. However, as was discussed in detail to illustrate how using point estimates may lead to erroneous conclusions, it appears there is not a tradeoff. In other words, job growth in one region does not create more unemployment in other regions, but also lowers it. However, note that the indirect effect is less than the direct effect, which makes sense since the impact of a change will most likely be larger in the place that instigated this change. The short-term total effect is also highly significant and negative as well. The long-term direct effect of employment growth on the unemployment rate is negative and that of the indirect effect and total effect are positive, but they are all insignificant.
The short-term direct effect of p in the u equation is significant (t-value = -3.765) and can be interpreted as follows. If the participation rate increases by one percentage point in region i, the unemployment rate in region i decreases by 0.049 percentage points.34 This indicates that if
34
27
there is a regional policy target to increase labor force participation, this in turn will also contribute to attaining a more acceptable level of unemployment in that region. Our result corroborates the majority of previous empirical studies that find this effect is negative and rejects the accounting identity that states that the effect of the participation rate on the unemployment rate should be positive (i.e. if the participation rate increases, ceteris paribus, the number of unemployed must also increase). Increased participation encourages the growth of more local jobs, i.e. “people cause jobs” (Layard, 1997). Elhorst (2003a) identifies 11 empirical studies with negative and significant effects of (male, female, or total) participation rates, while 3 studies report a positive but insignificant effect and only one study a positive and also significant effect. Therefore, overall, the negative effect dominates. The short-term indirect effect turns out to be positive, which thus suggests a discouragement effect on neighboring regions. However, note that this estimate is insignificant (t-value = 1.126). The short-term total effect is negative, but insignificant, while the long-term effects show up as being both negative and positive, yet also insignificant.
Employment growth in a particular region has a tremendous effect on labor force participation (in the region itself, as well as on its neighbors), especially in the long-term. We find that a one percentage increase in the regional employment growth rate increases the participation rate in the region itself by 0.353 percentage points in the same year. Similarly, such an increase also raises the participation rate in surrounding regions by 0.026 percentage points. Consequently, the short-term total effect is also quite substantial (0.379, t-value = 28.337). Most notable is that the long-term impacts of an increase in job growth are even larger. A one percentage point increase in the employment growth rate raises the participation rate by 1.605 percentage points in the home region. The total effect is 3.606, while the long-term spatial spillover effect is also highly significant. This suggests that policy aiming to increase regional employment growth (or a regional economy that creates and fills new jobs at a faster speed) is extremely beneficial for reaching more acceptable levels of participation across several regions. Additionally, these benefits are observed in the same year, and even more so in future periods.
28
Therefore, fewer jobs encourage less people to enter the labor force (i.e., there is a net discouragement effect over the additional worker affect) in the home region. By contrast, we find a positive and significant short-term spatial spillover effect; and a negative though insignificant spatial spillover effect in the long-term. Both spatial spillover effects are again smaller in magnitude than the direct effects. The first positive spatial spillover effect points out that if the labor market conditions in their home region are less promising compared to other regions, people may change their participation decision and e.g., move to neighboring regions for work, though only in the short-term. The total effects (both short-term and long-term) are both negative and significant. In particular, an increase of one percentage point in the unemployment rate appears to have large and long-lasting effects, reducing the participation rate by 1.337 percentage points economy wide.
The direct, indirect, and total effects of unemployment and participation on employment growth, the last equation of the three equation model, are substantial and highly significant. A rise of one percentage point in the unemployment rate increases the employment growth rate by 0.524 percentage points in the region itself, but decreases the employment growth in neighboring regions by 0.996 percentage points. Similar values can be seen for the long-term effects. Although this result is not anticipated at first, it reflects firms moving to regions where unemployment is high. This result reaffirms the idea of convergence, i.e. lagging regions taking over leading regions. A similar leading-lagging pattern is observed regarding a change in participation on job growth. If the participation rate increases by one percentage point in region i, employment growth decreases significantly by 0.818 percentage points. Conversely, this latter impact significantly increases employment growth in other regions by 0.668 percentage points. Thus, the total effect is negative and also turns out to be significant. The long-term effects show the same pattern as the short-term effects. This result is insightful since it indicates that attaining higher regional participation rates may be detrimental to employment growth in the region where the policy is implemented, but favorable to surrounding (lagging) regions.
4.4 Impulse-response analysis
29
over to other regions. For this purpose, we use the estimated system of equations of the extended Blanchard-Katz model to conduct impulse-response analysis. This type of analysis (as described in Section 2.1) becomes more complicated when using the spatial rather than the non-spatial model because exogenous shocks propagate both over time and across space. In other words, the impulse response functions include temporal dynamic effects as in a standard VAR model, as well as spatial dynamic effects.
Figure 4 depicts the labor market adjustment process in the region itself following an employment growth shock of one percent over a 25-year period.35 It should be stressed that the shock in a particular region is not entirely idiosyncratic; an employment shock is simultaneously accompanied by employment shocks in other regions through the model’s spatial autocorrelation structure. The unemployment rate drops by around 0.12 percentage points at time t = 1, yet this impact dies down quite rapidly in the following years. The participation rate rises by almost 0.4 percentage points in the first year, but the effect diminishes quickly to almost half this value by the second year. After around five to seven years, the effect of the shock on all variables weakens entirely.
Figure 5 illustrates the response of the labor market in neighboring regions.36 We find that a region-specific positive demand shock initially leads to an increase in the participation rate by around 0.18 percentage points and a small decline in the unemployment rate of 0.07 percentage points. The magnitudes are smaller than in Figure 4, which is expected since the impact of a shock is most likely to be felt the most in the region where it occurs. The additional employment growth of 0.48 percentage points in the first year and 0.55 in the following year is due to the highly significant coefficient estimate of the spatially lagged employment growth variable (0.577, t-value = 15.014) in Table 4. However, this effect decreases markedly after the second year.
Besides the magnitudes, there are also other notable differences between Figures 4 and 5. The impact of the shock in neighboring regions is even greater in the second year, suggesting that it takes more time for the shock to propagate across space. Another difference is that the
35Similar to the results of the direct, indirect, and total effects, we present average results for the shock impacts to
facilitate the presentation of the results due to the large amount of regions in our sample.
36We first compute the cumulative difference between the endogenous variables before and after the shock over time
30
effect on the variables after the shock is much more persistent in neighboring regions than in the region itself. However, in both cases the labor market variables eventually settle down to their equilibrium values after approximately 25 years.37 On a final note, we check to see whether there is much variation in the results of the impulse response functions across the sample of 112 regions. The standard deviation is larger for the indirect effects; it appears there are a few regions whose impact on other regions is greater.38 However, the impact of the demand shock on the region itself is similar across all regions in our sample.
5. Conclusions
In this paper we test for the existence of spatial spillovers in regional labor markets in a cross-country perspective. For this purpose, we extend the Blanchard and Katz (1992) model to incorporate interaction effects using a dynamic spatial panel data approach. We find that the spatially lagged dependent and explanatory variables are highly significant. However, our results illustrate that using point estimates to test the hypothesis as to whether or not spatial spillovers exist can lead to erroneous conclusions, as recently pointed out by LeSage and Pace (2009). We therefore calculate direct, indirect, and total effects and find strong evidence for the existence of spatial spillovers; your neighbor affects your job prospects. In general, we find that an improvement in labor market conditions in a particular region also benefits labor market conditions for (potential) workers living in neighboring regions.
From a regional policy perspective, our results provide strong evidence that targeting employment growth is the most effective way to attain more acceptable levels of unemployment, participation, and employment across regions in the EU. An increase in employment growth in an individual region has a tremendous impact on the participation rate in both the region itself and in surrounding regions, especially in the long-term; it also results in lower unemployment rates across regions. On the other hand, directly targeting unemployment and participation has less of an economy-wide effect and even adverse effects on the region where the policy is instigated, which reaffirms the idea of convergence.
37
The exception is e in the region itself, remaining at around 0.22 percentage points higher.
