Regional Unemployment Persistence (Spain, 1976-1994) by Juan F. Jimeno Samuel Bentolila

DOCUMENTO DE TRABAJO 95-09

Mayo, 1995

* Universidad de Alcalá de Henares and FEDEA.

** CEMFI.

Regional Unemployment Persistence (Spain,1976-1994)*

Juan F. Jimeno Universidad de Alcalá de Henares and FEDEA

Samuel Bentolila CEMFI

May 11, 1995

Abstract

This paper examines the degree of persistence of regional relative unemployment. A theoretical model is built to explain the role of migration, labor force participation, and real wage flexibility at the regional level, in determining such persistence. The model is used to account for the observed degree of persistence of regional relative unemployment in Spain, as compared to the US and the European Union, also providing new estimates on real wage flexibility in Spanish regions.

Keywords: Regional labor adjustment, Unemployment persistence. JEL nos.: E24,J61.

* We are grateful to Manuel Arellano, Giuseppe Bertola, Juan Dolado, Francis Kramarz, Jonathan Leonard, Leonor Modesto, Enrique Sentana, and Gerard van den Berg for useful comments. We wish to thank Marisol García de Arce and Coral García Esteban, from the Banco de España, for help with data collection, and Antonio Fatás for allowing us to reproduce his results. We are solely responsible for any errors. Parts of this paper were written while the second author was visiting DELTA (Paris) and IGIER (Milano) whose hospitality is gratefully acknowledged.

Correspondence to: Juan F. Jimeno, FEDEA, Jorge Juan 46, 28001 Madrid (Spain). Tel. (341)4350401. Fax (341)5779575. Email: jimeno@fedea.es.

1 Introduction

High unemployment is very persistent in Europe: without having suffered large new shocks, in the mid-1990's many European Union (EU) countries remain stuck at unemployment rates close to the peaks attained after the supply shocks of the 1970's and the demand shocks of the first half of the 1980's. In contrast, in the United States the unemployment rate is now back to the levels of the 1960's.

The persistence of unemployment is usually related to labor market institutions yielding wage rigidity and employment inertia, and to labor force dynamics. Recently, some efforts have been devoted to estimating the relative importance of these sources of persistence (e.g., Layard et al. (1991), ch. 9). At the same time, other studies have analyzed the geographical dimension, by looking at the persistence of regional relative unemployment rates. Since some sources of persistence can be expected to have different effects at the aggregate and regional levels, it should be possible to learn something about those sources by analyzing regional evolutions.

At first glance, this approach may look unpromising, since regional (absolute) unemployment rate persistence is again high in Europe and low in the US. The first impression is, however, wrong. It turns out that European regional relative unemployment rates -with respect to the average European unemployment rate- are scarcely persistent. So, although Eichengreen (1990) finds that the speed of adjustment of national unemployment in nine EU countries to the average in this area is about 25 per cent lower than in US states, Decressin and Fatás (1994) find that the persistence of regional relative unemployment is actually lower in Europe than in the US. According to Blanchard and Katz (1992), regional persistence is low in the US because workers migrate in response to region-specific shocks. In the European case, the low persistence results, according to Decressin and Fatás (1994), from large movements in and out of the labor force in response to changes in regional fortunes.

Therefore, if we classify areas according to the degrees of persistence of the aggregate and regional relative unemployment rates, we have a case where both are low (the US) and a case where the former is high and the latter is low (the EU). A third case is that of countries where both are high, like Italy (according to Decressin and Fatás) or Spain (to be shown).

In this paper we focus on the high-high persistence case, by studying Spanish regional evolutions. We first document the high regional relative unemployment persistence in Spain, and compare it with other areas. Then we model how the main determinants of regional unemployment persistence-namely migration, labor force participation and wage flexibility- interact to yield different degrees of persistence at the national and regional levels.

We highlight the role of wage rigidity and low migration as the main factors introducing a wedge between persistence at the two levels. Increased wage flexibility will, under some conditions, lead to less unemployment persistence. Since there are reasons to believe that wage flexibility is higher at the national than at the regional level (see below), regional relative unemployment would tend to be more persistent than aggregate unemployment. However, even if wages are rigid, as long as interregional migration is very elastic (as in the US) or regional labor force participation is highly cyclical (as in the EU), the persistence of regional relative unemployment will be low.

Wage flexibility, migration, and participation interact in interesting ways. We can show that the reduction of unemployment persistence due to increased wage flexibility will be higher the higher is the elasticity of either migration or participation to relative wages, but it will be lower the higher is the elasticity of these two variables to relative unemployment. Therefore, establishing which mechanisms induce people to migrate and participate in the labor force is important for the effectiveness of policies aimed at achieving lower regional unemployment persistence through higher wage flexibility.

The last part of the paper is devoted to discussing how the model can help account for the pattern of unemployment persistence found in Spain. In particular, after reviewing previous evidence on migration and labor participation behavior in Spain, we present new estimates of wage flexibility at the regional and sectoral level in this country, finding that it is quite low.

The paper is organized as follows. Section 2 presents some stylized facts about regional unemployment persistence in the US, the EU, and Spain. Section 3 introduces a simple theoretical framework, inspired in Blanchard and Katz (1992), focusing on key mechanisms affecting regional unemployment persistence: migration, labor force participation and wage flexibility. Section 4 provides evidence on the main parameters of the model regarding the Spanish case, showing that they interact to yield extremely high unemployment persistence. Lastly, Section 5 contains our conclusions.

2 Regional evolutions: stylized facts

2.1 Regional unemployment dynamics

In this subsection we estimate the degree of persistence of regional unemployment in Spain and compare our estimates with those for other countries' regions.

We examine four regional variables: employment growth ( , with n being the logarithm of employment), the unemployment (u) and labor participation (pa) rates, and real wage levels (w, the logarithm of the real wage). Homogeneous quarterly data on the first three variables are available in Spain only for 1976:3-1994:4. For wages, we use national accounts-type data at the regional level for the period 1980-89 (annually). Nevertheless, our main results on wage persistence are confirmed by regressions estimated using longer wage series available bi-annually (see Appendix 1 for sources and definitions).

A first impression on the persistence of these variables is provided graphically. Figure 1 presents regional unemployment rates in 1977 and 1994 (annual averages), revealing that relative unemployment rates are very persistent. Figure 2 plots average employment growth by region in 1976:4-1985:4 versus 1986:1-1994:4, suggesting that unemployment persistence is not linked to persistent disparities in job creation across regions. Two other variables that show high persistence are regional participation rates, plotted in Figure 3, and real wages, presented in Figure 4. Discarding outliers (like AND, EXT, and CAN in Figure 1) does not alter qualitatively our conclusions.

The high persistence of regional unemployment in Spain does not crucially hinge on the degree of geographical disaggregation. As seen in Figure A1 in Appendix 2, unemployment rates are as persistent in Spanish provinces as in the regions of which provinces are a subunit.

Given the non-negligible, although decreasing, importance of the agricultural sector in Spain, we also analyzed the evolution of regional non-agricultural employment, obtaining very similar qualitative results (not reported, but available on demand).

To assess formally the degree of persistence of national and regional absolute variables, and of deviations of the latter from the national average, we run unit-root tests using the augmented Dickey-Fuller (ADF) regression:

\[\Delta x _ {i t} = \alpha_ {1 i} + \alpha_ {2 i} (L) \Delta x _ {i t} + \alpha_ {3 i} x _ {i t - 1} + \alpha_ {4 i} t + \eta_ {i t}\]

with x standing, alternatively, for , u, pa, and w. t is a time trend, a disturbance term, and a second-order polynomial in the lag operator, . Subindex i denotes regions and t=1977:3-1994:4. Real wages are computed as the average compensation per employee in the region, divided by the appropriate consumer price index (producer prices being unavailable). For wages, the annualized data are used, for 1962-90. These results, which are not reproduced but available upon request, suggest that unemployment and participation rates, employment and real wages appear to be non-stationary; employment growth to be stationary. This description is valid for both national and regional variables in absolute terms, while in the case of regional relative variables (deviations from the corresponding national value), there are a few exceptions.

A lack of persistence of employment growth was also found for US states by Blanchard and Katz (1992) and for EU regions by Decressin and Fatás (1994). But the persistence of regional unemployment and participation rates observed in Spain is significantly higher than those found elsewhere. For example, on comparable AR(2) regressions on pooled annual data, the former report a long-run persistence coefficient of regional relative unemployment of 0.74 for the US and the latter of 0.49 for the EU, while the estimate for Spain is 0.89.

We first tested for, and were able to reject, the presence of unit roots at the quarterly frequency, using the so-called HEGY regression (Hylleberg, Engle, Granger and Yoo, 1990), and then eliminated deterministic seasonality by working with the residuals from the regression of each variable on a set of quarterly dummies.

This is different from the wage, but payroll tax rates are the same in all regions. Also, although these rates may not apply to the wage itself, because there exist legal minima and maxima for the tax base, the deviations are minor.

There is one exception: employment growth at the national level seems to have a unit root even though regional employment growth rates are stationary. This can happen if some regions' weight in total employment have been nonstationary during the period.

ARA;

For relative variables, we can reject the unit root in unemployment in ARA; in participation in six cases (ARA, CAN, CMA, VAL, EXT, and NAV); in employment in three cases (ARA, MAD, and NAV); and in wages in CAT.

In an integrated economy, we would expect regional unemployment, participation, and wage rates, as deviations from the national mean, to be scarcely persistent. It could be, however, that economic shocks are not common to most regions. To check for this possibility we have estimated, following Blanchard and Katz (1992), how much of regional (absolute, as opposed to relative) employment changes can be attributed to national changes , through the following regression (over 1977:4-1994:4):

\[\Delta N _ {i t} = s d _ {t} + \sum_ {j = 0} ^ {3} \beta_ {i j} \Delta N _ {t - j} + v _ {i t}\]

where N is in logs, sd is a set of seasonal dummies and v a disturbance term. The sum of the resulting estimates of the are almost always significantly different from zero but not from one, and the corresponding range most often between 0.4 and 0.75. This indicates that shocks are largely common to all regions (The same pattern, in a stronger form, was found for non-agricultural employment).

This way of estimating the relative importance of aggregate and regional shocks is, however, valid only under quite restrictive assumptions. Alternatively, Jimeno (1992) suggests identifying specific shocks as those which have no contemporaneous aggregate effects (in high frequency data). So, we have also estimated the proportion of the variance of regional employment growth explained by aggregate shocks, via a region-specific bivariate vector autoregression (VAR) of regional and rest-of-the-country employment growth. The results indicate that, in the medium-run (5 years), approximately 50% of the variance, on average across regions, is explained by aggregate shocks. Hence, it makes sense to analyze regional labor market variables expressed as deviations from the corresponding national means.

2.2 The response to region-specific labor demand shocks

We now estimate the typical dynamic response of the average region to a transitory (one-period) shock in its relative employment growth rate. Following Blanchard and Katz (1992), we can interpret this as a region-specific labor demand shock. Thus, we estimate a VAR with the employment growth, unemployment, and participation rates:

Both sets of estimates of the aggregate components of employment changes are available upon request.

\[X _ {i t} = A _ {i} + B (L) X _ {i t - 1} + \Sigma_ {i t}\]

where (excluding wages due to the lack of quarterly data), with variables again in deviations from the national average, and where is a vector of shocks. Since the statistical tests have not allowed us to reject the existence of unit roots in u and pa, we also estimate the previous VAR in differences, . Note that, although we allow for region-specific constants (fixed-effects), we are imposing the same dynamic response across regions, i.e., we are estimating the dynamic behavior at the "average" region.

The identifying assumption amounts to examining the responses of the three variables to an innovation in the first variable of the Choleski orthogonalization of the VAR, with the ordering of the variables being . This implies that employment only responds contemporaneously to labor demand shocks. Since the VAR for Spain is estimated on quarterly data, this identifying assumption is less controversial than when annual data are used.

The responses of the employment level, and of the unemployment and participation rates are plotted in Figure 5. Additionally, a comparison of these responses with similar ones for US states and EU regions, reproduced from Decressin and Fatás (1994) in Figures 6 to 8, implies that the responses of regional relative unemployment and participation to regional labor demand shocks are more persistent in Spain than elsewhere, while the long-run effects on relative employment levels are lower (slightly below those in the EU, and much smaller than in the US). (When all variables are assumed to be nonstationary, the relative magnitudes of the responses do not suffer significant changes, as seen Figure A2 in Appendix 2).

Let us comment on these numbers. A 1 percent labor demand shock has a long-run effect on the relative regional employment level of about 1.4 percent in the US and about 0.6 per cent in the EU (Decressin and Fatás (1994)), and about 0.4 percent in Spain. Secondly, the effects of this shock on regional relative unemployment and participation rates have vanished after 6 years in both the US and the EU, while in Spain, at that time horizon, about one fourth of the original effect of the shock on these variables still remains.

The Engle and Yoo (1990) test did not allow us to reject that the unemployment and participation rates are cointegrated. So, even if these two variables are really nonstationary, the VAR including their levels is still meaningful.

The impulse responses and the standard deviations associated with them, plotted in Figure 5, are computed from Monte Carlo simulations with 200 iterations (see Doan (1992), example 10.1).

The responses corresponding to Spain in Figures 6 to 8 are from the VAR estimated on quarterly data, aggregated to annual values, and normalized by the accumulated response of employment in the first year.

What do these patterns mean? Suppose there is a positive shock to a region's relative employment level. The workers who fill those jobs may come from three sources: the region's unemployed and previously non-participant workers, and immigrants. Therefore, the behavior of migration is captured by the difference between the change in employment, on the one hand, and those of unemployment and participation, on the other. The main feature in the Spanish pattern is that neither migration nor participation responds much to shocks. As in the case of EU regions, the low response of migration explains the low long-run effect on the employment level mentioned above. Note that if there was no interregional migration, there would be no relative employment effects, while the latter would be large with highly elastic migration flows.

The response of participation, alongside of those of unemployment and migration, in the first three years after a shock, is shown in Table 1. In the European Union three-quarters of the new jobs are accounted for by the increase in participation in the first year, and more than 40 percent in the second. In the US the response of participation is much lower but it is compensated by the large response of migration, which by the third year accounts for 70% of the adjustment. Since neither migration nor participation respond much in Spain, unemployment bears a significant fraction of the adjustment, accounting for about one third of the change in employment after three years.

We have thus shown that relative unemployment is more persistent in Spain than in other areas, and that this results from a low response of both migration and participation to region-specific shocks. In the next section we provide a theoretical framework in order to account for these facts, and we then present some evidence on the parameters in that framework.

Table 1. Decomposition of the response of labor variables to a 1 percentage point increase in employment growth (percentages of the change in the employment level)

EU includes the regions of: Belgium, Denmark, France, Greece, Ireland, Italy, Netherlands, Portugal, Spain, UK, and (West) Germany. Source: Decressin and Fatás (1994) for EU and US. Own calculations for Spain.

3 Regional labor markets: a simple framework

3.1 Aggregate unemployment persistence

In this section we present a theoretical framework for analyzing the persistence of regional relative unemployment rates, highlighting its dependence on labor supply and real wage flexibility. We extend the model of Blanchard and Katz (1992) to include labor participation decisions and different degrees of wage flexibility at the national and regional levels.

The model consists of three equations, for labor demand, wage setting, and the labor force. Labor demand depends negatively on real wages (w), so that, in inverted form and in logs,

\[w _ {i t} = - d \left(n _ {i t} ^ {*} - u _ {i t}\right) + z _ {i t}\tag{1}\]

where subscript i denotes regions, n the labor force, and u the unemployment rate, so that employment is given by . Hereafter all constants are non-negative. Labor demand is hit by random shocks, , which follow an autoregressive process (with being white noise):

\[z _ {i t} = \rho_ {z} z _ {i t - 1} + \varepsilon_ {i t} \quad 0 < \rho_ {z} \leq 1\]

The wage setting equation relates regional wages to national wages, and both regional and national unemployment rates:

\[w _ {i t} = f w _ {t} - c _ {A} u _ {t} - c _ {R} u _ {i t} \quad 0 \leq f < 1\tag{2}\]

so that the response of wages to an increase in unemployment equally distributed across regions is . An increase in regional unemployment, with aggregate unemployment remaining constant, reduces wages by . Thus, is a measure of regional real wage flexibility. Aggregating equation (2) across all regions yields

\[w _ {t} = - c _ {N} u _ {t}\]

where captures wage flexibility at the national level. Thus, the difference between wage flexibility at the two levels is given by the dependence of regional wages on national wages and unemployment. This dependence may arise from an attempt by unions to set similar wages in all regions or out of a geographically decentralized bargaining system where wage relativities matter (see, e.g., Bhaskar (1990)). If, as we have assumed, f is between zero and unity (we provide some supportive empirical evidence below), then real wage flexibility is higher at the national than at the regional level.

As for the labor force, we distinguish between participation and migration decisions. Participation is assumed to depend positively on wage levels and negatively on unemployment rates. The parameter captures the degree of permanence of participation decisions, taking economic variables as given. Migration is assumed to be driven by relative real wages and unemployment rates. Thus,

Note that wages are aggregated with employment weights while unemployment rates with labor force weights . Equation (2) is therefore missing a term in the sum across regions of the product of regional unemployment and the difference between those two weights. But this covariance is largely constant and small (around -0.0002 in Spain).

Burda and Mertens (1994) argue this is the optimal response of workers to purely regional, insurable shocks if labor mobility is low.

\[n _ {i t} ^ {*} = \alpha n _ {i t - 1} ^ {*} + b _ {P} w _ {i t - 1} - g _ {P} u _ {i t - 1} + \nu_ {i t} + b _ {M} (w _ {i t - 1} - w _ {t - 1}) - g _ {M} (u _ {i t - 1} - u _ {t - 1}) + \varphi_ {i t}\tag{3}\]

The first four right-hand-side terms capture participation decisions, while the remaining ones capture migration flows. Shocks to participation, , and to migration flows, , are, without loss of generality, assumed stationary.

Aggregating and combining equations (1) to (3) yields the following univariate process for national unemployment:

\[\begin{array}{r} u _ {t} = \rho_ {N} u _ {t - 1} + \frac {d}{c _ {N} + d} \nu_ {t} - \frac {1}{c _ {N} + d} \frac {1 - \alpha L}{1 - \rho_ {z} L} \varepsilon_ {t} \\ \rho_ {N} = \alpha - \frac {d (c _ {N} b _ {P} + g _ {P})}{c _ {N} + d} \end{array}\tag{4}\]

The coefficient could be positive or negative. Negative unemployment persistence being strongly counterfactual, we will assume that the parameters in the economy are such that is strictly positive, which seems plausible since is likely to be close to unity.

The unemployment rate is stationary only if both and are strictly below unity. About , we shall assume that the parameters ensure that it is below unity. This is without loss of generality: in this model unemployment persistence arises exclusively from labor force dynamics. The justification for this assumption is that we are mostly interested in the relationship between the persistence of national and regional unemployment, and the main difference between these two levels of the labor market comes from migration and participation. Many features that we have excluded, like hysteresis effects on wage setting, or employment inertia due labor adjustment costs, would obviously increase unemployment persistence further.

The discouraged worker effect implies that higher unemployment and lower wages induce people to withdraw from the labor force, due to lower perceived chances of finding a good job. By the added worker effect, they induce people to join the labor force to supplement family income. We are assuming the former effect dominates.

Since we will not estimate empirically the full model, we are not concerned with the identification of each equation. Nevertheless, we may note that identification is achieved by the exclusion of variables in the equations and not by having only lagged terms in equation (3).

Note that, since the are shocks to migration, they are by definition equal to zero once aggregated.

With regard to , a good case can be made for the full persistence of technology shocks, so that, unless , the case of a unit root in the unemployment rate cannot be discarded easily. This would only imply that what we are about to say regarding the persistence of the unemployment rate would apply to the persistence of the first differences of the unemployment rate.

Unemployment persistence is determined by the autoregressive coefficient , so we will focus on this coefficient. Table 2 presents some comparative statics results on the determinants of .

Table 2. Determinants of national unemployment rate persistence

Note: Effect of negative if , positive otherwise.

Most of these effects are standard, so we will only discuss real wage flexibility ( ), which turns out to have an ambiguously signed effect. To see why, let us decompose the relationship between current and past unemployment into two parts. The first part is the effect of the current labor force on current unemployment, which is positive (found by combining aggregated equations (1) and (2)). The second part is the effect of past unemployment on the current labor force, which is negative (found by combining aggregated equations (2) and (3)). Formally,

See Karanassou and Snower (1993) for an analysis of different sources of aggregate unemployment persistence.

A typical measure of persistence is the mean lag. Rewriting the unemployment equation above as: , the mean lag with respect to , say, is: . So, we do not lose any information by studying directly.

ρN

\[\frac {\partial u _ {t}}{\partial u _ {t - 1}} = \frac {\partial u _ {t}}{\partial n _ {t} ^ {*}} \frac {\partial n _ {t} ^ {*}}{\partial u _ {t - 1}} = \frac {d}{c _ {N} + d} (- c _ {N} b _ {P} - g _ {P})\]

It is apparent that affects both relationships. Its effect on the first term can be labeled the flexibility effect: the higher , the less dependent is the unemployment rate on the labor force, since wages adjust more to preclude excess labor supply. The effect on the second term can be labeled the participation effect: the higher , the higher the response of the current labor force to past unemployment, since past wages adjust more to past unemployment. The ambiguity arises because increasing lowers the first term but raises the second one. However, it is not hard to argue for persistence being decreasing in real wage rigidity. First, it is quite plausible that , i.e. that the ratio of the relative responsiveness of participation with respect to unemployment and to wages is not higher than d, the inverse of the elasticity of labor demand respect to real wages. Second, if other sources of persistence, like firing costs, were included in the model, then real wage flexibility would clearly lower the persistence caused by them. Hence, we will take to be decreasing in .

3.2 Sources of persistence in regional relative unemployment

We now analyze the sources of persistence of regional relative unemployment. Let us rewrite equations (1)-(3) in deviations from the corresponding national variables (denoted with a ), as

\[\tilde {w} _ {i t} = - d (\tilde {n} _ {i t} ^ {*} - \tilde {u} _ {i t}) + \tilde {z} _ {i t}\tag{5}\]

(i.e..

d)

This first term helps understand why, according to Table 2, the less elastic is labor demand (i.e., the higher is d), the less persistent is unemployment: the higher is d, the lower will be the effect on employment of a shift in wage setting, itself induced by an increase in the labor force.

d,

Regional relative labor demand also depends on the net inflow of firms. Thus we could add to equation (5), as in Blanchard and Katz (1992), terms in either relative wages or unemployment rates. If firms move to high unemployment regions seeking low wages, this would reduce unemployment differentials. On the contrary, if firms move to high productivity regions, such differentials would be exacerbated.

\[\tilde {w} _ {i t} = - c _ {R} \tilde {u} _ {i t}\tag{6}\]

\[\tilde {n} _ {i t} ^ {*} = \alpha \tilde {n} _ {i t - 1} ^ {*} + (b _ {P} + b _ {M}) \tilde {w} _ {i t - 1} - (g _ {P} + g _ {M}) \tilde {u} _ {i t - 1} + \tilde {\nu} _ {i t} + \tilde {\varphi} _ {i t}\tag{7}\]

Then, regional relative unemployment rates are given by:

\[\begin{array}{r l} \tilde {u} _ {i t} & = \rho_ {R} \tilde {u} _ {i t - 1} + \tilde {\xi} _ {i t} \quad \rho_ {R} = \alpha - d \frac {c _ {R} (b _ {P} + b _ {M}) + g _ {P} + g _ {M}}{c _ {R} + d} \\ \tilde {\xi} _ {i t} & = \frac {1}{c _ {R} + d} \left(d \tilde {\psi} _ {i t} - \frac {1 - \alpha L}{1 - \rho_ {z} L} \tilde {\varepsilon} _ {i t}\right) \end{array}\tag{8}\]

where captures all labor supply shocks. As before, we shall assume that the parameters are such that .

Equation (8) shows that the determinants of the persistence of regional relative unemployment are quite similar to those of aggregate unemployment , in equation (4). The differences arise from regional wage flexibility, , being the relevant parameter now, and from the reduction of persistence due to migration. Formally:

\[\rho_ {R} - \rho_ {N} = d \frac {1}{c _ {R} + d} \left(\frac {(c _ {N} - c _ {R}) (d b _ {P} - g _ {P})}{c _ {N} + d} - (c _ {R} b _ {M} + g _ {M})\right)\tag{9}\]

where the first term in brackets captures the effect of participation and the second term that of migration, while wage flexibility affects both terms.

Like we did for the aggregate in Table 2, we summarize our results on in Table 3, all of which are straightforward from equations (4) and (8).

Table 3. Determinants of regional relative unemployment rate persistence

Note: Effects of . (a) On : Negative if . (b) On : Negative if . (Note that will affect both and .)

Two results are worth commenting on. First, depends on the sum of the elasticities of participation decisions and migration flows with respect to wages and unemployment. In other words, assuming a homogeneous labor force, changes in participation are a substitute for migration flows. This result can account for the low observed in both the US and the EU regions.

The second result refers to the impact of labor supply elasticities on the relative values of and . The table indicates that, as long as wage flexibility is higher at the national than at the regional level, the relative importance of wages and unemployment in driving participation matters. The elasticity of participation to regional unemployment provides a self-correcting device that reduces more than . On the other hand, the elasticity to wages tends to make higher than . So, a very high wage elasticity of participation could conceivably lead to higher than . This possibility disappears if there is no aggregate wage norm affecting regional wage determination (i.e., ), and it would not seem to be very relevant empirically in either the US or the EU, where is quite lower than .

One last implication from the model, not shown in Table 3, refers to the interaction of wage flexibility with labor supply parameters. In our model, the reduction of due to an increase in is increasing in the elasticities of migration and participation with respect to wages, but decreasing in their elasticities with respect to unemployment. Formally:

\[\frac {\partial^ {2} \rho_ {R}}{\partial c _ {R} \partial x} < 0 f o r x = b _ {M}, b _ {P}; \quad \frac {\partial^ {2} \rho_ {R}}{\partial c _ {R} \partial x} > 0 f o r x = g _ {M}, g _ {P}\]

This result indicates that the effects of increased wage flexibility on persistence depend on which variables induce people to migrate and participate. Wage flexibility and the elasticity of migration (say) to wages reinforce each other: if a region experiences a bad shock which raises its relative unemployment rate, and wages fall significantly with respect to other regions, then a high elasticity of migration to this wage differential will clearly reduce . On the other hand, a high elasticity of migration to relative unemployment makes for a lower impact of increased wage flexibility, because the latter tends to reduce the original increase in the region's unemployment differential. So, a country with a high (the US, say) could, ceteris paribus, achieve a greater reduction in from a given increase in wage flexibility than a country with a low (Spain), while the opposite would be true for .

4 Sources of unemployment persistence in Spain

4.1 The behavior of migration and participation

In Section 2 we showed that regional relative unemployment is extremely persistent in Spain. The model in Section 3 indicates that this should be related to migration, labor participation, and wage flexibility. In trying to account for persistence, we will briefly summarize the information on the parameters in the model provided by already existing empirical evidence on interregional migration and labor participation in Spain, and we will then offer some new evidence on regional wage flexibility.

Starting with migration, Bentolila and Dolado (1991) have estimated, with aggregate data for 1964-1986, that a 1 percentage point increase in the relative wage in a region causes, on average, an increase in net migration to that region of 0.002 percent of its population in one year, and of of a one percent in the long run (with the national unemployment rate). A 1 percent point fall in a region's relative unemployment rate causes a 0.006 percent increase of its population in net immigration within the year, and of 0.09 percent in the long run. These estimates indicate that migration responds very little to economic variables, and that the responses take a long time to materialize.

These estimates also indicate that migration flows respond more to unemployment than to wage differentials. There is additional evidence supporting this conclusion. First, when Bentolila and Dolado reestimate their equations for the period 1976-1986, the long-run effect of relative wages disappears, and only unemployment differentials make people move. Second, even the sign of the wage effect is in dispute. Antolín and Bover (1993) find, with individual data for 1987-91, that people outmigrate from high wage regions. While they also find a surprising negative effect on migration of regional relative unemployment, this becomes positive when personal characteristics are interacted with the latter variable.

Interregional migration in Spain was very high up to 1973 and very low afterwards. The above papers suggest a change in the determinants of migration over time, by which the traditional role of wage and unemployment differentials in spurring migration has progressively become less important, and other variables like housing price differentials or unemployment benefits have become more relevant. We do not intend to search for the underlying institutional mechanisms explaining the estimated coefficients. In terms of explaining unemployment persistence, what matters is those coefficients' values. The above estimates provide us with a clearly important source of persistence: the lack of response of migration to regional differentials in economic variables.

As to labor force participation, the nationwide participation rate decreased continuously from the mid-1970's to the mid-1980's, to recover a little in the second half of the 1980's. This evolution masks the opposite behavior of male and female participation rates (up for females, down for males). Given the dates of the Spanish business cycle, it is also suggestive of a procyclical behavior. In fact, Bover and Arellano (1994) have shown, for

This is the conclusion reached by Ródenas (1994), after comparing estimated migration equations for 1973, 1985 and 1989. Also, Gil and Jimeno (1993) find, using microeconomic data, that most migrants move when they have already found a job, rather than moving to look for one.

For more details, see Blanchard, Jimeno, et al. (1995), Annex 1.

Spanish women aged 25-45 over the period 1980-90, that the cyclical component is not very large, though not negligible. For this population group, whose participation decisions are plausibly the most sensitive to labor market conditions, they estimate elasticities of regional labor participation of about 0.05 (non-significant) with respect to regional real wages, and -0.2 with respect to regional unemployment.

The evidence therefore indicates that neither migration nor labor participation is very sensitive to real wages or unemployment. So these are clear determinants for high regional unemployment persistence. Nevertheless, it is still interesting -for example, from a policy point of view- to find out whether the high persistence observed in Spanish regions is the result of these two channels erasing any beneficial effects of a high real wage flexibility or, on the contrary, it is the outcome from their interaction with rigid wages.

4.2 Regional wage flexibility in Spain

We now estimate whether regional real wages respond to local economic conditions. Wages in Spain are set by collective bargaining between employers' and workers' representatives. The bulk of collective bargaining is performed at the sectoral level (only about 10% of employees are covered by firm-level agreements). Furthermore, in most sectors, each province within a given region has its own sectoral collective agreement. Thus, in principle, there is wide scope for geographical wage differentiation. In practice, however, there is very low dispersion in wage growth, although dispersion in wage levels is somewhat higher (see Lorences et. al. (1994)).

We estimate an equation like (2) in Section 3, using National accounts data on total compensation per employee for 17 sectors and 17 regions for 1980-88 (See Appendix 1). By exploiting the sectoral dimension we attempt to minimize the effect on the estimated parameters of employment composition. The estimated equation is:

\[w _ {i j t} = \pi_ {0} + \pi_ {1} w _ {i (- j) t} + \pi_ {2} w _ {j (- i) t} + \pi_ {3} w _ {t} - \pi_ {4} u _ {i t} - \pi_ {5} u _ {t} + \pi_ {6} p d _ {i j t}\tag{10}\]

See Jimeno and Toharia (1994), chapter 3, for more details on the institutional characteristics of wage setting in Spain.

The lag of the dependent variable was introduced to capture wage inertia, but it was insignificant in all regressions performed.

where is the real wage in region i and sector j, the real wage in region i excluding sector j, the real wage in sector j excluding region i, w the average national real wage, the regional unemployment rate, u the national unemployment and pd labor productivity (in real terms). Regional wages and productivity are deflated by regional consumer price indices (sectoral price indices are not available by region), and national wages by the national CPI. The reasons for having three different measures of the alternative wage are explained below.

We estimate the equation using the generalized method of moments (GMM) technique due to Arellano and Bond (1991). The equation is estimated in first differences (to eliminate fixed effects). We instrument regional variables with their own lags from t-2 backwards and using all available orthogonality restrictions. National variables are treated as exogenous.

Estimates for equation (10) are presented in Table 4. In column (1) we take each region as an isolated wage-setting area, so that only regional variables enter the specification (as would be the case with no interregional migration and no effects of the national wage and unemployment rate on the regional wage). Productivity, the alternative wage , and regional unemployment are significant, and their coefficients show the expected signs. Nevertheless, the Sargan test rejects the exogeneity of the instruments, casting doubts on the specification. In column (2) we include both the regional and the national unemployment rates, jointly with the average national wage. We find that the unemployment rate coefficients are similar in both size and (low) significance, while the coefficient of the national wage is insignificant. In columns (3) to (5), we try similar specifications as in column (2) but using a different measure of the national wage: the sectoral wage in the rest of the country . The results in column (3) suggest that this measure is much more relevant and also that its inclusion reduces the coefficient of the regional unemployment rate with respect to column (1). But excluding the national unemployment rate results in a rejection of the Sargan test. Column (4) reveals that when the national unemployment rate is reintroduced, it is more significant than regional unemployment. Lastly, in column (5) we drop regional unemployment while keeping national unemployment as a regressor. This does not change much the other coefficients, but leads to an increase in the coefficient of the aggregate unemployment rate with respect to column (4).

With their DPD program (Arellano and Bond (1988)).

To check the robustness of these results we perform additional regressions, presented in Table 5. We first add a trend in real wages and find that the coefficient of the alternative regional wage, , increases significantly, while the coefficients of both national and regional unemployment rates become smaller (columns (1) and (2)). We then allow for hysteresis effects in wage determination by introducing lags of the unemployment rates (columns (3) and (4)). The first lag of regional unemployment is never significant (and is therefore dropped from the regressions reported in Table 5), while the first lag of the national unemployment rate has a significant t-statistic with a coefficient which is close to that of the contemporaneous national unemployment rate. This suggests not only that the response of regional wages to unemployment is low, but also that there is some evidence of hysteresis effects in wage determination.

We have not estimated the fraction of real wage rigidity coming from nominal wages and that coming from prices, due to the unavailability of sectoral price indices by region. We can however indirectly show that the response of wages to unemployment is lower for nominal than for real wages. In columns (5) and (6) of Table 5, we present the estimates of a nominal wage equation, according to which the semi-elasticity to regional unemployment is -0.28 (t-ratio = 1.7), which is lower than the value -0.43 in Table 3 (col. (3)); and when the national unemployment rate is introduced, this coefficient is roughly zero (-0.01 (t-ratio=0.04)), while the coefficient with respect to national unemployment is -0.42 (t-ratio=1.4)). Therefore, most or all regional real wage flexibility comes from prices and not from wages.

Table 4. Estimates of Regional/Sectoral Wage Equations, I Dependent variable:

Notes: Sample period, 1983-1988. Coefficients are first differences one-step robust estimates. t-statistics and 5% critical values of the Sargan test in parentheses. Regional variables are instrumented with their lags. Whenever national unemployment is excluded as a regressor, it is included in the instrument set.

Table 5. Estimates of Regional/Sectoral Wage Equations, II Dependent variable: Notes: * Wages and productivity in nominal terms. See notes to Table 4.

The main results can be summarized as follows. First, both regional and national variables matter for regional wage determination at the sectoral level. The single most important determinant is nationwide sectoral wages, with a coefficient around 0.6 (which, incidentally, confirms our assumption of f<1 in Section 3). However, there seems to be some influence of wages in other sectors within the same region. Second, the typical inside variable, regional+sectoral productivity, matters, with an insider weight around 0.25.

Third, unemployment rate terms are often scarcely significant, have low coefficients, and are very unstable. For example, from column (3) of Table 4, the implied elasticity of real wages with respect to regional unemployment is -0.08. For comparison, a typical long-run estimate of the elasticity of real wages to unemployment for the aggregate Spanish economy, over our sample period, is -0.2 (see Andrés et al. (1990)). Also, if we run the regressions with the log of the regional unemployment rate instead of the rate itself, we find an elasticity of -0.07, which is lower than the elasticity of around -0.1 found by Blanchflower and Oswald (1995) for the effect of log regional unemployment on log wages in a sample of 12 countries.

These estimates indicate a low responsiveness of wages to regional economic conditions. We believe that this outcome is the result of an explicit effort by Spanish unions in order to reduce wage dispersion across regions. This effort is helped by the law: wage floors set at sectoral wage agreements are legally binding for all firms in the sector throughout the country, and are normally so high that they leave little scope for further bargaining at the province/firm level.

This finding suggests that the observed high persistence of regional relative unemployment in Spain results not only from low migration and participation elasticities to wages and unemployment, but also from high real wage rigidity. This rigidity seems to arise partly from a strong impact of nationwide sectoral wages on regional wages.

This is larger than the typical estimate in sectoral regressions without geographical controls, of around 0.1 (see Andrés and García (1994) and Bentolila and Dolado (1994)).

Although this comparison may not be very relevant, because their estimates come from individual data, allowing for a long list of worker characteristics as control variables.

There are additional implications from putting together these estimates with our model. Given that the estimated elasticities of labor participation and migration to regional wages ( and , respectively) are quite low, and lower than the elasticities to regional unemployment ( and ), it is unlikely that lower regional relative unemployment persistence could be achieved only by taking measures to increase wage flexibility. The condition for the reduction in persistence to happen (see Table 3) and the cross-effects between these parameters and flexibility ( ) suggest that, in order to be effective, the increase in wage flexibility would need to take place simultaneously with an increase of the responsiveness of migration decisions to wages.

The relevance of these results is not necessarily circumscribed to Spain. Other European countries also show low migration and high wage rigidity. The most prominent example is that of Italy, a country which features a low responsiveness of migration to economic variables (Attanasio and Padoa Schioppa (1991)), high regional wage rigidity (Faini (1995)), and a high regional unemployment persistence (Decressin and Fatás (1994) and Bertola and Ichino (1995)).

5 Conclusions

Let us now summarize our results, in order to account for the behavior of regional unemployment persistence in Spain. We have shown that regional wages, and relative unemployment and participation rates, are very persistent in Spain, while employment growth rates are not. Also, the responses of the migration and participation rates to labor demand shocks seem to be significantly lower than in US states and EU regions, while the long-run employment level response is significantly lower.

We have presented a simple theoretical framework showing that low regional unemployment persistence can result from high elasticities of either migration flows or participation decisions to economic variables like wages and unemployment, even if wages are rigid. Reductions in persistence may be achieved by increasing wage flexibility (under certain conditions), and the impact of this change would be heightened by a higher responsiveness of migration and participation to regional wages, though it would be reduced by a higher elasticity of these two channels to regional unemployment.

A review of the existing empirical literature indicates that interregional migration flows and regional labor participation decisions in Spain are scarcely responsive to regional real wages and unemployment, although significantly more to the second than to the first. New empirical evidence provided in this paper suggests that regional real wage flexibility is also low in Spain, resulting partly from the impact of national wages and, to a lower extent, of national unemployment rates, on regional wage determination.

As a result of the low elasticities of labor participation and migration to regional wages in Spain, it is unlikely that lower regional relative unemployment persistence could be achieved only by taking measures to increase wage flexibility. If the persistence of regional relative unemployment rates is seen as an undesirable feature, then the policy recommendations from our analysis are straightforward. Policies to increase the responsiveness of migration and participation to wage rates should be taken at the same time when policies to increase the responsiveness of wages to unemployment are implemented.

Lastly, we believe that the results in this paper could be relevant not just for the Spanish case, but also for other European countries, like Italy, showing low migration, high wage rigidity, and a high persistence of regional relative unemployment.

Appendix 1: Sources and definitions

A1.1. Regions

Andalucía (AND), Aragón (ARA), Asturias (AST), Baleares (BAL), Canarias (CAN), Cantabria (CNT), Castilla-La Mancha (CMA), Castilla-León (CLE), Cataluña (CAT), Comunidad Valenciana (VAL), Extremadura (EXT), Galicia (GAL), Madrid (MAD), Murcia (MUR), Navarra (NAV), País Vasco (PVA) and La Rioja (LRJ).

A1.2. Sources of data

* Participation, employment, and unemployment: Encuesta de Población Activa (Instituto Nacional de Estadística, INE).

* Wages: By regions: Renta Nacional de España y su Distribución Provincial (Banco de Bilbao). By regions and sectors: Contabilidad Regional de España (INE).

* Prices: Indice de Precios al Consumo (INE). For regions, this is the average of the consumer price indices of the capitals of the provinces of the region, weighted by the province's nominal GDP.

Appendix 2: Additional figures (Standard errors in parenthesis)

Figure A2. Responses to region-specific labor demand shocks (VAR: dn, du, dpa) quarters

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Figure 1. Persistence of Regional Unemployment (Standard errors in parenthesis)

Figure 2. Persistence of Regional Employment Growth (Standard errors in parenthesis)

Figure 3. Persistence of Regional Participation Rates (0.11) (0.22) (Standard errors in parenthesis)

\[R ^ {2} = 0. 1 8\]

Figure 4. Wage Compensation per Employee (Deflated by CPI, 1985=100) (Standard errors in parenthesis)

Figure 5. Responses to region-specific labor demand shocks quarters

Figure 6. Responses of relative unemployment rates to region-specific labor demand shocks

Figure 7. Responses of relative participation rates to region-specific labor demand shocks

Figure 8. Responses of relative employment levels to region-specific labor demand shocks

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