Structural Adjustment and Unemployment Persistence (With an Application to France and Spain)

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EUI Working Paper R S C No. 98/47

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Sneessens/Fonseca/Maillard: Structural Adjustment and

Unemployment Persistence (With an Application to France and Spain) © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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EU R O PEA N UNIVERSITY IN ST ITU TE, FLO R ENC E ROBERT SCHUMAN CENTRE

Structural Adjustm ent and Unem ploym ent Persistence (With an Application to France and Spain)

HENRI SNEESSENS*- RAQUEL FONSECA* and

B. MAILLARD**

‘ 1RES. Université Catholique de Louvain “ Université Catholique de Lille

EUI Working Paper RSC No. 98/47 BADIA FIESO LANA , SAN D O M EN IC O (FI)

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Abstract’

This paper aims at contributing to a better understanding of structural problems and their impact on aggregate equilibrium unemployment, both on the methodological and the empirical sides. On the methodological side, we aim at developing a model that can take simultaneously into account several structural dimensions (frictions, skill mismatch and regional mismatch) and encompasses earlier modelling approaches as special cases. On the empirical side, we use panel data from France and Spain to evaluate the importance of (skill+regional) structural problems in these two countries. France and Spain are two countries of special interest because skill and regional mismatch may have contributed differently to the persistence of high unemployment rates. This provides a way to check the capability and the robustness of our modelling approach.

' The authors gratefully acknowledge financial support from the Direction de la Prévision, Paris, the EC-TMR programma and the Belgiam Program on Interuniversity Poles of Attraction. Comments addressed to: fonseca@ires.ucl.ac.be. The scientific responsibility is assumed by authors. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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1. Introduction

Most European economies have been characterized since 1975 by the persistence of relatively high unemployment rates. The magnitude of the change may however vary significantly from one country to the other (see Figure 1). Another characteristic of these economies is the deterioration of the unemployment-vacancy relationship (the so-called Beveridge curve), as shown in Figure 2. Several explanations can be thought of to explain these changes. Although skill mismatch is likely to have played a role, there is much disagreement about its importance, relative to other factors like regional mismatch, disenfranchisement, etc... From an empirical point of view, it appears extremely difficult to disentangle the many factors and mechanisms that may come into play (see Bean, 1994, for a survey of the available evidence). If anything, it seems wise to conclude that there is no simple and single cause at work, and that the weight to be given to each explanation may vary from country to country.

The focus of this paper will be on the role played by structural adjustment problems, more precisely frictions, skill mismatch and regional mismatch. This remains a much debated issue. In her introduction to the volume of proceedings of an international conference on Mismatch and Labour Mobility, F. Padoa- Schioppa stresses that “the major result of this volume, in my opinion, consists in highlighting the looseness of the ‘mismatch’ concept -even though the term is frequently used both by experts and laymen- which explains why different mismatch definitions lead to such widely varying judgements on the same observable facts” (Padoa-Schioppa, 1991, p. 2). Entorf (1995) argues that in situations where the evolution of unemployment rates is determined by non- stationary stochastic processes, mismatch measures based on the variance of relative unemployment rates may be severely biased towards zero. The lack of adequate data (especially concerning skills) also explains the difference between the various measures found in the literature.

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Figure 1: Unemployment rates in EU countries and the USA

Source: European Economy

Figure 2: Beveridge curves, in EU countries and the USA

Source: European Economy and Bean (1994).

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Against this background, the objective of the paper will be both methodological and empirical. We start in section 2 with a reexamination of the relationship between structural changes and aggregate equilibrium unemployment (the NA1RU). We come to the conclusion that there is no straightforward and universal way of measuring the impact of structural disturbances on equilibrium unemployment. A less ambitious but more realistic approach is however available.evaluate the extent to which the shifts observed in aggregate Beveridge curves can be traced back to structural problems. Section 3 is devoted to the specification of Beveridge curves that take simultaneously into account the regional and the skill dimensions. The Beveridge curves are obtained by explicit aggregation over heterogeneous agents facing quantity constraints, as in Lambert (1988) and Sneessens-Drèze (1986). This setup is next used in section 4 to construct mismatch indicators; usual formulations based on Cobb-Douglas specifications are obtained as special cases. Section 5 applies this methodology to French and Spanish data and provides measures of the importance of frictions, regional mismatch and skill mismatch in these two countries. France and Spain are two countries of special interest. Some work has already been done on the role of skill mismatch in France (see for instance Sneessens and Shadman-Mehta, 1995; Goux, 1996; Cotis-Germain-Quinet, 1996; Laffargue, 1997, as well as the papers published in the special issue of the Revue économique, 1997, and of Economie et Statistique, 1997). Spain is of special interest too, because both skill and regional mismatch are usually mentioned as factors that may have contributed to the persistence of exceptionally high (even by European standards; see Figure 1) unemployment rates in that country (see for instance Bentolila-Blanchard, 1990, Blanchard et al., 1995, Jimeno-Bentolila, 1995, Dolado-Jimeno, 1997, Jimeno and Bentolila, 1990, Bentolila and Dolado, 1994, de la Fuente, 1997). Our main conclusions are summarized in section 6.

2. S tructural Changes and Equilibrium Unemployment

The interactions between structural and macroeconomic phenomena remain poorly understood. Interactions probably work in both directions. Macroeconomic disturbances may have structural implications, and conversely. Our objective in this section is obviously not to provide a comprehensive and definite framework for such an analysis. The objective is rather to put the analysis that will be developed in the next sections in a proper perspective. We want in particular to emphasize the limits as well as the advantages of the proposed methodology, and explain our motivation.

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We start with a brief description of a log-linear mode! of equilibrium

unemployment with structural features. The model is based on Layard ef a’, (1991, section 6.3), expanded to include other models (for instance Sneessens and Shadman-Mehta, 1995, Sneessens, 1994) as particular cases. In this setup, we show that there exists no simple universal indicator that would provide a robust and reliable measure of the contribution of structural problems to equilibrium unemployment.

We assume that all firms have access to the same technologies. The set of available technologies is represented by a Cobb-Douglas function of capital and an aggregate labour index. Let (3 be the Cobb-Douglas coefficient associated to labour. The aggregate labour index is a CES function with n types of labour indexed by i. Let us use parameter K to measure the effect of (unbiased) technical progress and capital accumulation, and y, to denote biased technical progress. The production function is then written in the following compact form:

where a is the elasticity of substitution between the different types of labour. If we furthemore assume monopolistically competitive price-setting on the goods market (with constant markup rate p), the optimal price-setting rule implies the following real wage frontier :

Setup

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where w stands for the real wage. Log-linearisation yields:

(3) £ « ’ k>g a„ , v „°' i~o and S a* =1 . 2, «, Wj i © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Parameter ciq incorporates all the effects of capital accumulation and (biased + unbiased) technical progress. In the case of a pure Cobb-Douglas production technology, the weight given to each wage rate remains constant over time ( a* = ai for a = 1).

We also assume imperfect competition on the labour market. In general, the real wage prevailing on a segment of the labour market will depend on the unemployment rate U and on the tensions (measured by the vacancy rate V ) observed on that segment.1 It is also likely to depend on the real wages prevailing on other segments. Such spill-over effects may be the consequence of so-called envy effects and of strategic interactions; it may also be the result of asymmetric technical progress when the real wage of a given category of workers is indexed on total average productivity rather than marginal productivity. We thus write the wage equation for workers on a segment i as the following log-linear equation :

(4) logWj = w i + l ° g wj + r, lo gVj - d j logU( , Vi . j*‘

a) measures the effects of "wage-push" variables including labour taxes,

unemployment benefits, market power, etc.... Solving this system of wage equations gives a semi-reduced form equation where each wage rate is a function of all unemployment and vacancy rates :

(5 ) logWj = CO, + £ rij log Vj - X<5y logU j , Mi .

J J

For later use, we rearrange this equation by expressing the unemployment and vacancy rates on each segment as a proportion of the corresponding aggregate rates. We obtain :

(6) logW; = c t ) ; + r , l o g V - 5 , l o g ( / + | x r , ; l o g ^ - S ^ y l o g ^ - j , V i ,

l J j J

where r, = Y.J,j and 5,. (similarly defined) measure the sensitivity of wj to its own vacancy and unemployment rates.

1 Vacancies (in as much as they represent labour shortages) may also affect the firm's price setting behaviour (see Sneessens, 1987). Introducing this additional channel would not change the qualitative properties of the model.

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Finally, we represent the relationship between unemployment and vacancies on a given segment of the labour market by the following log-linear (Cobb- Douglas) Beveridge curve:

(7) <t>u log Ui + <t>v logV) = /„,

where parameter f 0 measures the efficieny of the matching process (frictions).

Equilibrium unemployment

A convenient way of examining the determinants of equilibrium unemployment is by summarizing the information contained in equations (3), (6) and (7) in the UV space (see Figure 3).

The aggregate Beveridge curve is obtained by rearranging equation (7) to obtain the unemployment and vacancy rates on each segment as a proportion of the corresponding aggregate rates, and next taking the weighted sum over i :

(8) 0U log U + b, log V = f„ - X, (a, log )+b, X,(«, log-^Jj

The position of the aggregate Beveridge curve depends on the dispersion of relative unemployment and vacancy rates across segments, as well as on the value of the efficiency parameter / „ ; an increased dispersion shifts the aggregate Beveridge curve outwards, as represented in .

The implications of price and wage setting behaviours are represented in Figure by the WPS schedule. It is obtained by using equation (6) to eliminate the wj’s in equation (3), and shows all the combinations of U and V that are compatible with aggregate wage and price stability :

(9) S \o o U - t \ogV = w0 - a0 - I'Z a .S ij \og^f - | ,

l ij V J

where w0 = a * <w, 8 - X, «* <5, and similarly for x. It is worth stressing that the

position of the WPS schedule depends on structural as well as on aggregate variables2. Increased structural problems (reflected in the increased dispersion

2 Gregg and Manning (1997) develop a similar point of view. See also Agenor and Aizenman, 1997, who show that skill mismatch due a wage rigidity on the low-skill segment of the labour market may induce less employment on the high-skill segment as well, due to efficiency wage considerations.

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of the unemployment and vacancy rates) will in general shift both the Beveridge curve and the WPS schedule (as illustrated in Figure 3), while macroeconomic disturbances (changes in a„ and w0) will shift the WPS curve only.

Figure 3: Determination of the equilibrium unemployment and vacancy rates

The intersection of the WPS schedule with the Beveridge curve determines the equilibrium unemployment and vacancy rates. The contribution of structural problems to equilibrium unemployment can be examined more formally by solving equations (8) and (9). This yields after a few rearrangements :

where v = <j>J(<pvS + 0„r) and U* stands for the aggregate equilibrium unemployment rate. The impact of structural factors on equilibrium unemployment is measured by a weighted sum of the logarithms of the relative unemployment and vacancy rates. The weights are however a function of the structural parameters of the model measuring the sensitivity of prices and wages to excess demands and supplies. To get more insights, we have to be more informative about these parameter values. We illustrate these issues by briefly considering specific cases.

Illustrative cases

The conventional model is a simplified version of (10) obtained by suppressing all tension and spill-over effects; more formally,

V © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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x = xij = 0, V i,j, and &ij = 0 for j t i , = 8/ for i=j.

It is worth noting that with this simplification the WPS schedule in Figure 3 is vertical. Equation (10) becomes :

log U* = v (m'0 - a0) - v X,- a ’ 8, log jj- ,

which, by using a Taylor expansion’, can be recast as:

(11) log U* = v(wB- a 0)+ v £.<** .

The structural effect is decomposed into two components. Each component is equal to a weighted sum of the discrepancies between relative unemployment rates and their mean. In the fisrt component, the sum is over level differences; in the second, it is over squared differences. The weights given to each term of the sum depends on the sensitivity of the corresponding wage rate to its unemployment rate (as measured by parameter 8/). The importance of each component in measuring the impact of structural disturbances depends on the value of these sensitivity parameters.

To illustrate this point, it may be useful to distinguish two extreme cases. If all wages are equally sensitive to their own unemployment rate (i.e., 8/ = 8, V i) and if the weights a ■ are equal to shares of the labour force3 4, the first component cancels while the second becomes equal to the variance of relative unemployment rates; equation (11) then simplifies into :

log U* = u (w0 —a0)+~ v.8 var((/, /{/).

This the motivation for using the variance of relative unemployment rates as an indicator of structural problems; it is the case much emphasised by Layard et al. (1991, ch. 6).

3 _{The approximation is based on the Taylor expansion: logX = (X- 1) - 0,5(X- 1) calculated}7

around X = l.

4 That is, or; =N? I N s . A weaker condition is that the discrepancy between the two be independent of relative unemployment rates (see Layard et a!., 1991).

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The assumption that all wages are equally sensitive to their own unemployment rates need not of course be very realistic. It is particularly unsuitable when the focus is on the effect of downward wage rigidities at the low end of the wage spectrum (least-skilled workers). To simplify, let us assume that there are two groups of workers only, so that u= a‘u, + u-a')U ;. Equation (11) now becom es:

log U*= v(w0 - a 0)+v a * ( l- a * )|( 5 2 -(Sl > ^ + ^ l +a'(<S:

where AU = Uj - U2 is the difference between the two unemployment rates. The second term between the curly brackets correspond to the variance of relative unemployment rates; it is proportional to the square of the difference. If the two wage rates are equally sensitive to unemployment (87 = 62), the difference between the two unemployment rates plays no role; only the variance of relative unemployment rate matters. If one of the two wages is rigid however (87 =0, for instance), the variance term will clearly be dominated by the difference one. In this case, the contribution of structural disturbances to the change (in percentage points) in the equilibrium unemployment rate U should be measured by the change in the discrepancy between the unemployment rates of each category of workers AU, rather than by the change in the variance of relative unemployment rates5.

A less ambitious but more realistic objective

The two cases we considered are of course extreme ones, even for someone willing to accept all the simplifications used in deriving equation (10) (Cobb- Douglas-CES production function, one single type of firms, log-linear forms, etc...). The conclusion of this simple exercice should clearly be that there is no straightforward and universal way of measuring the impact of structural disturbances on the aggregate equilibrium unemployment rate. The measure to

5 It is worth noting in this context that the choice of the optimal production technology implies a relationship between AU and the logarithm of relative wages. Let nj and n, stand for the rate of growth of the number of workers in each group. With a CES production frontier, the first-order optimality condition can then be recast as :

A U = est + [(nt - r^) + (l-o) - Y2)] . trend + o (log Wj - log w 2 ) .

An asymmetric technical progress not matched by changes either in the composition of the labour force or in relative wages will produce structural unemployment and the latter will show up as an increased difference between the two unemployment rates. This reinforces the previous argument. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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be used will depend on the type of disaggregation considered (simplifications that are acceptable along the sectoral or regional dimension need not be acceptable for a disaggregation by skills, e.g.) and on key wage and price equation parameter estimates. The latter are notoriously difficult to estimate, and usually very sensitive to the chosen specification. These difficulties probably explain why so little is known about the interactions between structural and macroeconomic phenomena

There is of course a less ambitious but workable and useful alternative. Instead of focusing on wage and price equations, on could rely on the information contained in unemployment-vacancy data. Structural disturbances show up as shifts in the aggregate Beveridge curves. Measuring the contribution of structural variables to observed shifts in the Beveridge curve gives valuable information about how structural difficulties have changed over time, even though it is not a precise measure of their contribution to total equilibrium unemployment changes. The objective of the next sections is to derive such mismatch indicators based on the observed UV relationship, in a model where labour market segmentation takes two dimensions, regions and skills.

3. Beveridge Curves and Labour Market Segmentation

In line with the conclusions of the previous section, we focus here on the determinants of Beveridge curve shifts. The Beveridge curve is obtained by explicit aggregation in a model with heterogeneous firms and workers. The heterogeneity is two-dimensional and distinguishes different levels of skills and different regions. We thus obtain a single, unifying framework wherein we can evaluate and compare the relative importance of frictions, regional mismatch and skill mismatch.

The starting point is a model with quantity constraints and micromarkets, similar to the one used EUP models (see Dreze-Bean et al., 1990). The context is the same as in the previous section: monopolistic competition on the goods market, imperfect competition on the labour market. In line with the previous discussion though, we shall not focus here on wage-price formation, but rather on the derivation of the regional and economy-wide Beveridge curves. The analysis is admittedly partial; as suggested before, it still provides a valuable and probably more robust information on the importance of structural disturbances. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Employment at the firm level

Let us assume that there is a large number of monopolistically competitive firms, indexed by /. We assume that all firms have access to the same technologies. We also assume that adjustment costs prevent the firm from changing its production technology in response to transitory input shortages, so that the technical input-output coefficients are not affected by purely cyclical phenomena and are determined by relative cost considerations. To keep things as simple as possible, we shall not discuss the determination of the input-output ratios, and will not represent explicitly the effects of capacity constraints and labour hoarding (although we will take it into account on estimation).6 This simplification is unconsequential as long as we focus on long run phenomena (like unemployment persistence) and Beveridge curve shifts (which are not affected by capacity shortages). We do of course allow for labour shortages, i.e., vacancies. Each firm may be subject to idiosynchratic shocks. Wages and prices are assumed to be preset.7

Skills and regions will be indexed by i and k respectively. To keep the presentation as simple as possible, we assume for the moment that there are only two types of skills (high- and low-skilled labour).

High- and low-skilled employment

In this setup, the optimal price level does not necessarily imply full-capacity utilization, i.e., firms may be sales-constrained or may face labour shortages (Sneessens, 1987). At given input-output ratios, low-skilled employment is proportional to high-skilled employment. In the case of a sales constraint, the firm will hire as much low- and high-skilled labour as needed to produce the quantity demanded at the announced price. When there are labour shortages, high-skilled employment is either determined by its own supply (when it is binding) or by the supply of low-skilled labour (when the latter is binding). Let v represent the value of the low- to-high-skilled employment ratio at a given moment of time; subscripts h and / will be used to denote high- and low-skilled labour respectively. The optimal low-skilled employment level in a firm / located in region k must then satisfy the following expression:

6 The importance of labour hoarding over the cycle may differ for low- and high-skilled labour. High-skilled employment is less sensitive to cyclical fluctuations (see for instance Dormont, 1995).

7 We could do without the price pre-setting assumption. Provided there are technological adjustment costs, we would keep the same qualitative features: possibility of sales constraints or input shortages (see Fagnart et al., 1997).

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(12) Nlkj = Min-^V^, N iy , v . N j j j J ,

where denotes the demand-determined low-skilled employment level, and

N*y the supply of labour of type i (with i=h or /) available to firm /in region k

A similar relationship holds, mutatis mutandis, for high-skilled employment. Total employment at the firm level can then be written as:

(13) Nkf = Nlkf +Nhkf

,

= (! + *) Nhkf,

= M i n { < , ( l + V ^ . d + v ) ^ } ,

where Nkf stands for the total (low + high skilled) demand-determined employment level.

Expected output and employment levels

At the time prices and wages are set, the actual values of the demand for goods and the supplies of labour remain uncertain. Provided their joint distribution is log-normally distributed (with some restrictions on the variance-covariance matrix), the expected value of employment can be recast as a (two-stage) CES function of the expected value of its determinants. More precisely, at given optimal input-output ratios, expected total employment can be written as :

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- U p

\

J

where the values of parameters p and \(/ are non-negative and related to the characteristics of the variance-covariance matrix of the joint distribution (see Bierings-Muysken, 1988, and Entorf-Sneessens, 1996). Intuitively, the inverse of p and \jl provide a measure of the dispersion of the idiosynchratic shocks. For instance, when goes to infinity, the second term between the curly brackets corresponds to the minimum of the two labour supplies (low- and high-skilled, weighted by the technological coefficients), so that one type of labour shortage only can be observed.

Regional Employment and Beveridge curves

The setup developed so far allows for firm heterogeneity, at least in terms of sales and supply constraints. This enables us to derive, by explicit aggregation,

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Beveridge curves that are directly connected to the analysis of the determinants of the employment level. We start with employment and next discuss the link with Beveridge curves.

Regional Em ploym ent

Provided all firms face the same uncertainty, cross-sectional differences will have the same joint distribution as individual stochastic disturbances. The aggregate relationship will take the form of CES function similar to (14). More formally, in a given region k, total employment is given by :

where N ^f is given by (13). By using the same procedure as in the previous section (except that we now aggregate over individual firms in a given region k rather than compute individual expectations), we obtain after some rearrangements :

The values of parameters p and \|/ are non-negative and related to the characteristics of the distribution of demands and supplies across firms. In a given region k, p is a weighted average of the p 's , which can be interpreted as measures of the skill composition of the total labour force relative to the skill composition of total employment. Let alk represent the proportion of workers of type i in the labour force of region k (i.e.,aik = N[k \N sk), it is easily checked that the definitions of the p's must satisfy the following constraint:

This in turn implies that the unweighted sum of the (inverse of the) p's will not in general be equal to 1, except if they both have the same value. Moreover, when the two values are not equal, one will be larger than 1 and the other smaller than 1. If there are structural imbalances (p lk * nhk), one of the two terms within the curly brackets in equation (17) will be smaller than 1, and the (15) Nk = Z f Nkf

,

(i6) ^ = { ( < y p + ( ^ y p } UP

where p^ is defined as follows :

0 ' / O = l • © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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other larger; with \)/ large enough (values around 60 or more are not exceptional), the value of pk will be close to the minimum of (Pik.Pilk) and smaller than 1.

Regional Beveridge Curves

Simply rearranging the terms of equation (16) allows one to recast the (regional) employment function as a (regional) Beveridge curve :

(18) l i - v J + i u n J i i - u J } ' 1’ =1

where vk and u k stand respectively for the vacancy and the unemployment rate in region k. Equation (18) shows that the position o f the regional Beveridge

curve depends on the two parameters p and p p The inverse o f pk measures the importance o f skill mismatch; the inverse o f p measures the importance o f structural imbalances between goods demand and the availability o f labour;

These two values may of course change over time. A decrease in the value of pk implies an outward shift of the Beveridge curve; similarly for p, at least as long asp k is not too small and p not too large.

Aggregate Beveridgecurve

Different regions may be characterized by different equilibrium levels of unemployment and vacancy rates (different positions along a given UV curve), as well as by different degrees of skill mismatch (different positions of the UV curve itself, reflecting different values of the skill mismatch indicator pk)- The position of the economy-wide UV relationship and the aggregate performance of the economy will depend on both kinds of structural differences.

By taking the weighted sum over all regions (with weights determined by the share of region k in the total labour force: a, = N't / N ') of equation (18) suitably transformed,' one obtains the following aggregate (economy-wide) Beveridge curve;

(19) ^ . r a - v r + g j o / p n i - i / r } 1' ^ ! . 8

8 The two sides of equation (18) must be raised to the -p . One next introduces (T V) an d (1- U ) /p in the first and second left-hand side terms repectively, and takes the weighted sum over all regions.

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where p is the aggregate equivalent of p£ (equ. (17)), defined as :

(20) \ l y _Hi A’! NS ■ u

N J N f 1 -U: = 1 +U: - U

When \|/ goes to infinity, only one type of labour can be binding and the value of p is then equal to the minimum of the p ('s. and are two shift variables related to cross-regional disparities (regional mismatch) defined by :

(21) i ip Zu = \ 2 t a k (1 ~Uk)lHic)f ,l/p H I * (1 -U) / H ) j { Il H

J

V l - u

J

I

In other words, measures cross-regional differences in vacancy rates, while measures cross-regional differences in unemployment rates corrected for skill mismatch. Altogether, and <^u measure two things: first, cross-regional differences in the unemployment and vacancy rates at given, identical regional UV curves; second, cross-regional skill mismatch differences leading to different positions of the regional UV curves.’

4. Mismatch Indicators

Beveridge curves provide a most natural starting point to construct mismatch indicators. We first discuss the mismatch indicators that can be derived in our framework and next compare them to alternative measures that have been proposed. It will be shown that the latter can be interpreted, under some conditions, as coming from a Cobb-Douglas approximation to the CES-type Beveridge curve obtained in the previous section.

The components o f structural unemployment

’ It is worth pointing out that one can recast the aggregate Beveridge curve in terms of an

aggregate employment function. One obtains for the whole economy : H ( ^ ( " T + ( m ^ ) T ' /p

which generalizes the aggregate employment function used in the EUP programme (Drèze- Bean et al., 1990). © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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There axe, in our setup, only two sources of mismatch at the regions! level. As shown by equation (18), the relationship between unemployment and vacancies at the regional level will change if and only if there are more frictions (measured by 1/p) or more skill mismatch (measured by (1/p^-)). At the aggregate level, regional differences can be a third source of mismatch and produce a change in the aggregate relationship between aggregate unemployment and aggregate vacancies.

Let us define the structural unemployment rate at equality (SURE) as^the aggregate unemployment rate that would be obtained on the diagonal U=V. From (19) we obtain:

(22) sure = i - 1£. y + (s„ y (i/My } ',p.

This structural unemployment rate measures the position o f the aggregate Beveridge curve; its value depends both on frictions and on (skill or regional) mismatch effects. We may evaluate the respective role o f each component by using the following decomposition :

Frictional unemployment (which we shall denote by FURE, "frictional unemployment rate at equality”) measures the contribution o f 1/p; it is defined by equation (22) when the effects o f regional and skill mismatch are eliminated (i.e., \ u =£v = p = 1); this yields :

(23) FU RE= 1 - 2 ' 1/? ;

FURE goes to zero when p goes to infinity.

Total mismatch (TMM) is then defined as the difference between the structural and the frictional unemployment rates at equality (U=V):

(24) TMM = SURE - FURE = -■—— - -1 , 1 -SURE „ -11/ p r o ^ r j _ j

When parameter p goes to infinity, FURE goes to zero, and TMM is equal to the maximum of and CI( !\x.

- . f f e r + e .

1

2

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Regional mismatch (rmm) can be defined as the value that TMM would take if there were no aggregate skill mismatch (p = l), i.e. :

(25) RMM = [( g j + e . r

i

2

i /p - 1.

When p goes to infinity, RMM becomes equal to Max(^v, t,u) minus 1.

RMM is thus, ceteris paribus, increasing in p.

Skill mismatch (SMM) is finally defined as the contribution of skill composition effects to total mismatch; this contribution will be measured by total mismatch less regional mismatch, which is approximately :

1+TMM (26) SMM = TMM - RMM = ---1

1 + RMM

- {, + (1 - rvi l l p ) P f ’ - 1, where rv = •

When 1/p is larger than 1 and p sufficiently large, the weight rv has a négligeable impact, and the previous expression can be approximated by :

(27) SMM 3 - 1

With this latter approximation, skill mismatch (SMM) is defined as the value that

TMM would take if all unemployment and vacancy rates were equal across regions (i.e., = £v = l). It is positively related to the inverse of p. When p goes to infinity, smmbecomes equal to M ax(0,(l/p)-l). Ceteris paribus, smm is

thus (as rmm is) increasing in p. It can also be seen from the definition of p (eq.(20)) that the skill mismatch indicator SMM is based on unemployment rate differences.

Cross-effects

This way of decomposing total structural unemployment into its various components seems fairly natural and has the advantage of being approximately additive (SURE=FURE+RMM+SMM). It is clear however that there are "cross effects". We already pointed out that an increase in p (decrease in FURE)

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increases, ceteris paribus (i.e., at given discrepancies in regional and skill

unemployment rates), the values of both RMM and SMM. This is because a change in the value of p implies a change in the curvature of the regional Beveridge curves: the larger the value of p. the more pronounced the curvature of the UV relationship. At given discrepancies between regional unemployment rates, the Beveridge curve obtained by aggregation over regions moves

outwards.

There are also cross-effects between skill and regional mismatch. Neglecting skill mismatch may affect the estimate of regional mismatch. This comes from

the fact that the regional mismatch indicator takes into account the effect of

cross-regional skill-mismatch differences. If there were no such differences

(i.e., with for all k's), the regional mismatch indicator would simplify

in to :

(28) RMM = f e ) p + & y ]

U p

-1 , where ft, *

i/p

is obtained by setting B£=p for all k's in (see equ. (21). It is readily

shown that the difference between the two mismatch indicators is given by :

(29) RMM’-RMM 1 +RMM 1 + RMM f . . r = 1 - ( rv + (l- r v)| where rv ( U p (Sv)P + ( £ ) P and a k = M i - u t )p l<*k (i ~ u k )p

. The weight a ’ given to each

relative skill mismatch term decreases when the regional unemployment rate is

above average. If there are no skill-mismatch differences across regions, the

difference between the two regional-mismatch measures (RMM and RMM') is of

course nil. The difference may otherwise be positive or negative. It is likely to be positive when larger unemployment rates are associated to larger mismatch values, as one would expect10. In other words, the failure to take simultaneaously into account the skill and the regional dimensions will in

10 This would certainly be the case if the aggregate skill mismatch indicator ( l / p y were a simple average of corresponding regional values.

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general lead to biased regional mismatch indicators; the bias is likely to be positive.

Cobb-Douglas approximations

The Beveridge curve is often specified as a Cobb-Douglas function of the vacancy and the unemployment rates, as we did in section 2, equation (7). This specification is of course not valid for extreme values of the variables (U or V going to 1 or zero), and should thus be seen as a useful approximation of the true relationship around actual values of the vacancy and the unemployment rates. Our objective here is to check the implications of such an approximation for the computation of mismatch indicators.

Regionalbeveridgecurves

We look at Cobb-Douglas approximations to (18) obtained by taking Taylor expansions around the logarithm of the variables. For the original variables (1-

V), (l-£/) and (1/p.), one obtains:

(30) (l-tp) log (1-V* ) + tp log (1 -Uk ) + cp log (1/n* ) = /0 ,

where cp = [(l-U)//c]p/ |l - v )p +[(l-U)//i]‘’} is positive and smaller than one. Log-linearising around V and U yields the more familiar approximation :

(31) [V/(l-V )] (l-cp) log V *+ [t//(l-Z /)]cplog f/jt-<P log (1/Wfc) =- f o 

il should be emphasized that the value of the cp coefficients depends on the

values around which the approximation is made, as well as on the value of parameter p. The value of cp may thus change over time when there is a systematic drift in the observed unemployment rate or a change in the curvature of the true UV-relationship.

Aggregate Beveridgecurves

By taking the weighted sum of all regional Beveridge curves suitably transformed (as in section 2), one obtains from equation (30) the following aggregate relationship :

(32) (l-cp) log (1-V) + cp log (1-t/) + cp log (1/jj.)

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=/o -(!-«>)£* »* 'ogl - n_{1- V} - v i t a k log-1 - ^_{1 - U . - v i t} a k !°g1Uh 1

i//ì T

Similarly, from (31) one obtains :

(33) [V/(l-V )](l-tp) log V+ [U/(1-U )] <p log U -<p log (1/n)

=~fo -(y/d-V)](l-<P)X*{«* lo g-^}- [f7/(l-Z7)>x* {«* log^-}

+ v l k a t logEHl\ l/H 1

MISMATCH INDICATORS

In order to obtain measures of the Beveridge curve shifts that are consistent with those of the original CES formulation, one has to follow the same procedure and measure the shifts in terms of changes in the unemployment rate along the diagonal U=V. Under these restrictions, we obtain from (32)-(33) the following two Cobb-Douglas approximations of the value of the structural unemployment rate at equality (s u r e) :

(34) SURE = cst-Hjud —{/)log(l/^) + (l-ip )(l loS■ - y* 1-V +<o(i-£/Æt i« t 10S T ^ + < p (y - u )lt a k logi z a

1 !»

(35) SURE = est +<p(l-f/) lo g ( l/^ ) —(1 — <jo) U

log-^-- < P U 2 k \ a klog^-} + (l-£ /)ç )S t {at l o g - ^ } ,

where cp is now defined by tp = (l//r)p/[l +(l//t)p] and U is the unemployment rate (on the diagonal) around which the approximation is computed. The second term on the right-hand side measures aggregate skill mismatch (SMM), while the last three ones measure regional mismatch (RMM). The three components of RMM correspond of course to t,v and the two components of \ u .

It is worth noting that the Cobb-Douglas approximation written in terms of the unemployment and vacancy rates does not yield quite the same mismatch

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indicators as those usually mentioned in the literature (see Layard et al., 1991, e.g.) and suggested when discussing equation (8) in section 2. We note in particular that the mismatch indicators are quite different for skill mismatch and regional mismatch. Furthemore, there are interactions between the two phenomena. The mismatch indicator that we obtain is similar to the traditional measure (variance of relative unemployment and vacancy rates) only for the case of regional mismatch, if and only if there is no skill mismatch and the scaling parameters can safely be ignored (that is, when the value of the approximation coefficient cp remains constant and there is no systematic drift in unemployment). It is also worth noting that once 1 /pi is larger than 1, tp goes to 1 for large values of p . It is important to take this into account, especially when 1/p is changing over time. A fair conclusion seems to be that one should be extremeley careful when using Cobb-Douglas approximations to compute mismatch indicators.

5. Empirical Estimates

The objective of this section is to examine to what extent the persistence of unemployment in France and Spain can be related to the type of structural problems discussed so far (frictions, regional mismatch, skill mismatch). Our data set contains observations on the unemployment and vacancy rates region by region in each country, over a period extending approximately from the mid 70's till the mid 90's. We also have information about unemployment rates by skill group in each region". We shall rely on the methodology developed in the previous sections to evaluate the role that increased frictions, regional and skill mismatch may have had in the observed deterioration of the relationship between unemployment and vacancies (Beveridge curve shifts). This exercice provides also an opportunity to check the reliability of the mismatch indicators that we constructed, and compare them to alternative measures of mismatch proposed in the literature.

The framework developed in the previous sections gives us the means to obtain more reliable estimates and a better chance to disentangle structural and non- structural influences by exploiting in a rigorous way the information contained in the unemployment and vacancy data, across regions and skill groups. Our framework also generalizes previous analyses by taking simultaneously into account both the regional and the skill dimension. For estimation purposes, equations (17) and (18) will be recast as :

ii_{We are grateful to Juan F. Jimeno for providing the data on Spain.}

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(22) {i - vh T + (im S 0 - u b T } 'A = 1 + TJo + r;, + + ekl ,

(23) Hh = fe ifa ib Y * ' J V'. w‘th rtt, =77“ ’

where tp and r|£ represent a time-specific and a regional-specific residual respectively, whose sum over time or regions is normalized to zero. Three skill categories will be distinguished in each country.

The first step in the estimation process will to check for the constancy of p over time. We know from the discussion of the previous section that changes in the value of parameter p may affect the estimated value of the mismatch indicators. With panel data and the assumption that p has the same value in all regions of a given country at a given moment of time, we can estimate a value of p for each period. If the values so obtained are not characterized by a systematic drift, we then impose p to remain constant over the whole sample period and estimate the other parameters under this constraint. We do this to avoid capturing purely cyclical effects by variations in the value of a structural parameter. It is well- known that labour hoarding phenomena and differences in the speed of adjustment of unemployment and vacancies over the cycle may generate loops around the long run Beveridge curve. These dynamic features are not accounted for in our theoretical setup and should preferably not be measured by variations in the value of p. In order to catch up this type of dynamic cyclical effects, we may either introduce a time-specific disturbance term rp ., or try to correct the observed vacancy and unemployment rates for the effect of labour hoarding. This alternative procedure is preferable, because it simultaneously purges the estimated values of the mismatch indicators from purely cyclical effects when labour hoarding behaviours are different for different types of labour, as one may expect (see foonote 6). We thus define, for each type of labour, the "efficient" level of employment as a function of actual employment and a cyclical variable:

Ali S [1-A( C , ] ^ , A, > o,

where X[ is a labour hoarding coefficient and Q a cyclical variable defined over the interval [0,1], so that Xj gives the maximum amount of labour hoarding (in percentage points) observed over the sample period. Q is constructed as a moving average of current and past growth rates of GDP (denoted by g and meant to measure the position in the cycle), as follows :

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where the parameters a()t a j a2 are chosen so as to obtain the desired normalization. We discuss successively the results obtained on French and Spanish data.

4.1 France

We have annual data on employment, unemployment and vacancies for 21 regions and three levels of skill, defined by occupation, over the period 1970- 1980. Detailed information on the unemployment rates by skill category at the regional level is however not available for the first part of the sample period, running from 1970 till 1979. We thus assumed that skill mismatch was the same in each region over that sub-period. To avoid any bias that could result from this approximation, the parameter estimation will be based on the 1980-1993 sub-sample. As we shall see, because regional mismatch remains relatively unimportant, these data constraints imply only a small loss of information (for our purposes).

The changes in the unemployment rates across regions and skill groups are shown in Figure 4, left and right panels respectively. The left panel of Figure 5 shows how the ratios between the minimum and the maximum values (across regions) of respectively the unemployment and the vacancy rate have changed over time. All unemployment rates start rising in 1974-75; the ratio of maximum to minimum values of the unemployment and vacancy rates drops sharply before 1975, and remains fairly stable afterwards. A similar picture is obtained with the variance of relative rates (right panel of Figure 5).

a, + a. g,

Figure 4 : Average unemployment rate (thick line) across regions (left panel) and skill groups (right panel), compared to the corresponding maximum and minimum values.

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Figure 5 : Max-Min ratios (left panel) and variance (right panel) of relative regional unemployment and vacancy rates.

The values of the main parameter estimates obtained by minimizing the sum of the squared residuals efa are reported in Table 1. There is no systematic drift in the estimated value of p (Model 1). We thus impose it to be constant and introduce instead a labour hoarding effect (Model 2). The restriction that labour hoarding is négligeable for the least-skilled workers is accepted by a likelihood ratio test at the 5% level (Model 3). Labour hoarding is significantly different from zero for skilled workers. The value of À2 and ÀJ imply that the rate of the hoarding of skilled labour fluctuated from 1980 till 1993 between the extreme values of 0% (in 1990) and 1.18% (in 1993). Finally, the restriction that V|/ is equal to p is also accepted (Model 4); their value is quite high, implying a frictional unemployment rate of only 0,62%.

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Model 1 (variable p) Model 2 ( c o n s t a n t p ) Model 3 ( r e s t r . X / ) Model 4 (restr. v ) n o -.0018 (.00014) n o -.0018 (.000095) -.0019 (.000087) -.0019 (.00008) p 1980 100.10 (3.99) \1 -0.052 (.0254) = 0 = 0 p 1993 95.32 (13.88) *■2 0.013 (.0023) 0.0118 (.0022) 0.0118 (.0022) p max 149.43 _~'K2 _~K2 =X2 p mean 112.17 _P 112.06 (8.40) 110.57 (7.87) 112.08 (2.93) V 206.92 (68.76) V 106.74 (24.21) 117.92 (31.09) =P L O G - L IK . 1862.58 L O G - L IK . 1813.73 1812.09 1812.06 S E R .046% SER .053% .053% .053%

Table 1: Estimation results (standard errors between parentheses; sample period: 1980- 1993)

Structuralvsactualunemployment

The implications of these parameter estimates are illustrated in Figure 6 to Figure 8. Figure 6 shows the evolution of structural unemployment over the entire period, in comparison to actual unemployment. The increase in the structural unemployment rate (see left panel) measures the outward shift of the Beveridge curve, while the difference between the actual and the structural unemployment rates measures the shift down the Beveridge curve. The structural unemployment rate increases steadily from 1975 till 1987, where it reaches a maximum value of 8%; it then decreases slightly and stabilizes around 6.8%. There is a moderate (1.5 percentage points) but permanent movement down the Beveridge curve in the mid-seventies; a much larger movement (3 percentage points) is observed in the early nineties. There is thus a sharp contrast between the periods before and after 1987. The rise in unemployment after 1990 does not seem to be of the same nature as the one observed in the late seventies and early eighties (see L'Horty and Saint-Martin, 1996). The movement down the Beveridge curve observed during the seventies could itself be due to structural problems and their impact on aggregate

wage-© The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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price relationships (see discussion of Figure 3, section 2); it cannot be the case in the nineties. The right panel of Figure 6 shows the changes in the ratio of structural to actual unemployment. The ratio remains most of the time around 75%. It drops to 60% in the 1975 recession, next returns progressively to its initial value, and falls again to 60% during the first half of the nineties.

Figure 6: Actual vs structural unemployment: levels and difference (left panel) and ratio (right panel)

Mismatch Indicators

Figure 7 reproduces the value of the skill mismatch indicators obtained from the "true" model (the CES formulation) and from the two Cobb-Douglas approximations (the latter two are identical in the case of skill mismatch). The figure shows that most of the increase ip the structural unemployment rate is actually associated to skill mismatch. Skill mismatch reaches a peak of 7.7% in 1987, and next decreases continuously but slowly to reach a value of 5.9% in 1993'2. These findings are similar to those previously obtained by Sneessens and Shadman-Mehta (1995). The Cobb-Douglas approximation is quite good (provided the changes in the approximation coefficients is taken into account), much better than the variance of relative unemployment rates. 12

12 This may be the result of genuine structural changes on the labour market (the relative cost of less-skilled workers has decreased since 1986). It might also be an artefact related to the effect of labour market policies on relative unemployment rates (early retirement schemes, training programmes, part-time work, etc...). This remains to be checked!

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r 0.06

Figure 7 : True (CES) and approximated (Cobb-Douglas) SMM indicators (left-hand scale), compared to the variance of relative unemployment rates (right-hand scale).

The role of regional mismatch is illustrated in Figure 8. The indicator computed from the "true" model (CES formulation; see thick line on left pane* o f the

figure) suggests that regional mismatch has been almost continuously

increasing since 1975, although it contributes to the 1993 total structural unemployment rate by much less than one percentage point. Approximations based on Cobb-Douglas specifications of the Beveridge curve yield more or less similar results provided again that one takes into account the changes in

the approximation coefficients related to trend changes in the unemployment rate (see earlier discussion, section 4). The variance of relative unemployment

rates (dotted line, left panel) fails to take these changes into account and for this reason yields totally misleading indicators, as was suggested by Entorf(1995). The right panel of Figure 8 compares the regional mismatch indicators obtained from the "true" model when skill mismatch is or is not accounted for. As suggested in section 4, neglecting skill mismatch may bias the estimate of regional mismatch. In this case, neglecting skill mismatch leads to a 100% overestimation of regional mismatch.

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Figure 8 : Regional mismatch indicators. Left panel: true (CES) vs approximated (Cobb-Douglas) indicators and variance of relative unemployment rates (right-hand scale); right panel: upward bias (r m m'>r m m) due to neglect of skill mismatch.

5.2 Spain

We again distinguish three levels of skill, defined in this case by the educational attainment (rather than occupation): pre-primary and primary, upper-secondary, higher education. There are 17 regions. For each region and skill level, we have data running from 1977 till 1994. Figure 9 illustrates the changes in the average unemployment rate across regions (left panel) and skill groups (right panel), and compare the average value to the maximum and minimum ones. The average unemployment rate increases sharply from 1977 to 1985. During this period, most of the increase in unemployment is associated to a huge employment decline, with only slight labour force increases. The unemployment rate decreases significantly during the recovery of the late eighties, despite sustained labour force increases. After 1991, employment falls again and the unemployment rate reaches a record level (around 25%) despite a moderate labour force increase.

Figure 10 illustrates the changes in the relative values of unemployment and vacancy rates across regions (max/min ratios on the left panel, variance of relative rates on the right panel). Until 1983, vacancy rates seem to vary a lot across regions, much more than in the case of France. Such wide differences are not observed in unemployment rates. This suggest that the quality of the vacancy data may have remained weak until 1983, which could explain why the observed aggregate UV relationship remained flat during that sub-period (concerning the quality of vacancy data, see Antolin, 1994, and Dolado-Gomez,

1996). © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Figure 9: Average unemployment rate (thick line) across regions (left panel) and skill groups (right panel), compared to the corresponding maximum and minimum values.

Figure 10: Max-Min ratios (left panel) and variance (right panel) of relative regional unemployment and vacancy rates.

The estimation results are displayed in Table 2. The estimates reported in the second column (Model 1) suggest that the value of parameter p decreased steadily between 1977 and 1983 and remained stable afterwards (see Figure 11, left scale), implying a significant increase in frictions during the first subperiod (a frictional unemployment rate FURE increasing from about 0.5% in 1977 to about 3% in the mid eighties). Earlier estimates of parameter p obtained on Spanish data led to qualitatively similar results (see Andres et al., 1990). The modelling approach was however quite different, which makes the results not directly comparable. The analysis of structural problems was then made in two steps. The first step was the estimation of an aggregate “EUP-type” model (see Dreze, Bean et al., 1990), without explicit regional and skill dimensions, where parameter p was calculated as a residual and interpreted as a "catch-all" variable accounting for all kinds of frictions and mismatches. The estimates of p so obtained by Molina et al.(1990) are reproduced in Figure 11 (right scale); they imply a structural unemployment rate (calculated in the same way as FURE) rising from 4.2% in 1977 to 6.8% in 1985. The second step aimed at uncovering the causes of structural unemployment by regressing the estimated values p of

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on a set of explanatory variables. Bentolila-Dolado(1991) for example, following Padoa-Schioppa(1990), obtain a significant influence of relative energy prices, long-term unemployment, a turbulence index and measures of regional mismatch and labour mobility. To the extent that it is concentrated among low-skilled workers (see Blanchard et al„ 1995), long term unemployment could be interpreted as a proxy for skill mismatch.

Model 1 Variable p; sample period: 77-94 Model 2 time dummies; sample period: 83-94 Model 3 time dummies; sample period: 83-94 no -0.0025 (.00054) -0.0095 (.00020) -0.0095 (.00019) Pn 141.66 (88.31) Pl% 108.17 (61.51) P 7 9 85.19 (43.04) P 8 0 74.44 (47.89) P81 54.03 (24.94) P 8 2 39.61 (11.13) P 8 3 26.92 (3.04) 78.72 (120.30) 73.99 (22.14) P 8 4 23.01 (1.99) = P 8 3 = P s i P 8 5 17.55 (0.95) = P 8 3 = Ps.3 P86 16.35 (0.76) = P 8 3 — Ps.3 P 8 7 16.85 (0.78) = P 8 3 ~ P « 3 P88 17.30 (0.77) _~P 8 3 = P 8 3 P 8 9 18.46 (0.87) — P 8 3 ~ P 8 3 P 9 0 20.10 (1.11) = P 8 3 = P 8 3 P 91 22.67 (1.50) P 8 3 = P 8 3 Pn 21.51 (1.42) P 8 3 = P 8 3 P 9 3 19.45 (1.23) = P 8 3 — P 8 3 Pm 17.63 (1.19) = P 8 3 = P 8 3 V 54.23 (28.60) 37.89 (190.79) = P 8 3 L O G - 1320.28 945.66 945.59 S E R 0.0034 0.0025 0.0025 sampl 1977-94 1983-94 1983-94

Table 2: Estimation results on Spanish data (standard errors between parentheses)