CEIS Tor Vergata RESEARCH PAPER SERIES. Vol. 6, Issue 5, No. 119 March Dual Labour Markets and Matching Frictions

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1 CEIS Tor Vergata RESEARCH PAPER SERIES Vol. 6, Issue 5, No. 119 March 2008 Dual Labour Markets and Matching Frictions Dario Sciulli, Antonio Gomes de Menezes and José Cabral Vieira This paper can be downloaded without charge from the Social Science Research Network Electronic Paper Collection: Electronic copy available at:

2 Dual Labour Markets and Matching Frictions Dario Sciulli University of Pescara and CEEAplA António Gomes de Menezes University of the Azores and CEEAplA José Cabral Vieira University of the Azores, CEEAplA and IZA ABSTRACT This paper focuses on friction in the matching process arising in a dual labour market where good and bad jobs coexist. In particular, we present an empirical investigation of the role of strong preferences for permanent contracts to explain job mismatch and longer unemployment duration. To allow for a more flexible matching technology specification and to control for the role of micro level characteristics, we estimate a matching function using different specifications of hazard models for multiple unemployment spells, allowing both random matching and stock-flow matching mechanisms. We find evidence that the determinants of reemployment probabilities differ by gender. We also find a positive effect from having previous job experiences and, according to semi-parametric specifications, undergoing training while unemployed on reemployment probabilities. Overall we find that higher heterogeneity in searched and offered contract types increases frictions in the matching process. Specifically, individuals looking for a permanent contract experience longer unemployment duration, suggesting the existence of congestion problems related to the permanent job labour market segment. Finally, in order to reduce frictions in the matching process, policies aimed to provide training and to increase desirability of temporary contracts should be promoted. JEL classification: J64, C41 Keywords: Hazard Models, Dual Labour Markets, Temporary Contracts, Matching Mechanism. Dario Sciulli, Dipartimento di Metodi Quantitativi e Teoria Economica, Università d Annunzio di Chieti- Pescara, Viale Pindaro n. 42, Pescara (Italia). d.sciulli@unich.it; Antonio Gomes de Menezes, Departamento de Economia e Gestao, Universidade dos Açores, Rua da Mae de Deus, Ponta Delgada (Portogallo). menezesa@notes.uac.pt; Jose Cabral Vieira, Departamento de Economia e Gestao, Universidade dos Açores, Rua da Mae de Deus, Ponta Delgada (Portogallo). josevieira@notes.uac.pt; 1

3 1. Introduction Since the 1990s labour market analysis has extensively used matching functions in search and match frameworks (Mortensen, 1987). Matching functions allow the researchers to investigate frictions on the labour market, that play a crucial role to explain the existence of unemployment and labour market effectiveness in matching unemployed workers to available vacancies. Hence, it comes as no surprise that in recent years there has been a growing if not widespread interest in empirical estimates of matching functions. As highlighted by Petrongolo and Pissarides (2001), frictions derive from various sources. For example, they are caused by imperfect information about potential trading partners, absence of perfect insurance markets, slow mobility, congestion, and so on. Recently, most contributions devoted to estimating matching functions have focused on the role of heterogeneity of job seekers in explaining frictions in the matching process. An important argument put forward by such studies is that failure to take into account the heterogeneity of job seekers may lead to a misspecification of the estimating matching function and, concomitantly, to biased estimates of the estimating parameters and to misleading inferences on search elasticities. van Ours and Ridder (1995), Coles and Smith (1998), Mumford and Smith (1999), Anderson and Burgess (2000) and Burgess and Profit (2001) find evidence of job competition between different skill groups and between employed and unemployed job seekers. Fahr and Sunde (2001) find heterogeneity in matching technologies across members of different age and education groups, indicating the importance to disaggregate the matching function to explain the inner workings of the labour market and to avoid the loss of important information. Hynninen and Lahtonen (2007) find that wider heterogeneity of job seekers in terms of their educational levels increases the importance of frictions in the matching process. However, matching frictions may also due to other sources. Labour market reforms which were widely introduced in Europe since the 80s 1 to reduce labour market rigidity constitute a potential source of matching frictions. A large number of studies 2 highlighted possible negative effects of temporary employment with respect to traditional permanent employment relationships, contributing to rationalize in the economic literature the existence of segmented labour markets divided into primary and secondary sectors and, specifically, a segmentation in good and bad jobs 3. Permanent jobs (that is good jobs) feature better working conditions, employment stability and prospects of career advancement. Temporary jobs (that is bad jobs) are often characterized by lower wages, lower job security and impediments to career developments (Amuedo-Dorantes, 2000). In a dual labour market, where good and bad jobs coexist, it is likely that job seekers have strong preferences for permanent 1 In Portugal, temporary jobs were introduced in 1976 and suffered a major revision in For example, Jimeno and Toharia, 1993, Bertola and Ichino, 1995; Dolado, Garcia-Serrano and Jimeno, 2002; Cahuc and Postal-Vinay, 2002 and Gagliarducci, 2005). 3 See Dolado, Jansen and Jimeno (2005) for a theoretical framework on dual employment protection legislation. 2

4 contracts and firms looking for workers to fill their vacancies prefer to offer, in turn, temporary contracts, since they can use this contractual form to more easily adjust their workforce to business cycle conditions or to reduce expected labour costs. Therefore, a labour market characterized by a quite homogenous supply side, with most unemployed workers searching for a permanent job, and an heterogeneous demand side, where temporary job offers and permanent job offers co-exist, may involve a higher degree of mismatch, and, hence, higher mean unemployment duration. In fact, it is most likely that individuals looking for a permanent job tend to first refuse offers of temporary jobs and only after some time accept those temporary job offers in the event that they do not find a suitable permanent job. Our paper tests the hypothesis of higher mismatch probability, hence higher unemployment duration, due to heterogeneity between searched contracts and offered contracts, estimating a matching function using Portuguese data on individual transitions from unemployment to employment. Before presenting our empirical approach is important to underline that the literature allows two possible approaches in the estimation of matching functions: the random matching models and the stock-flow matching models. Broersma and van Ours (1999) argue that the estimates of the degree of returns to scale in the matching technology depend heavily on the data for active job seekers and posted vacancies used and emphasize the importance of looking at comparable measures for flows and explanatory stocks. Coles and Smith (1998) and Gregg and Petrongolo (2005), among others, argue, in turn, that part of the instability of estimated matching functions derives from problems of misspecification, due to the assumption of random search, rather than a stock-flow matching. As its name suggests, in a random matching set up the unemployed workers randomly routinely select a vacant job from the pool of existing vacancies and apply for it. Under the stock-flow matching technology, at the time an individual becomes unemployed he samples the existing stock of vacancies for a suitable job. If he fails to find a suitable match among the existing stock of vacancies, then he has to wait to eventually be matched with the flow of new vacancies and he does not re-apply to the previously searched stock of old vacancies. Stock-flow matching implies that exit rates are higher when individuals first enter the labour market and drop thereafter as it implies that the unemployed are able to sample all existing offers when they become unemployed, while their probability of finding a job is reduced in the following periods since they can only match then with the inflow of offers (which tends to be smaller than the stock; see Coles and Smith, 1998). However, expected negative duration dependence may be also explained by stigma or loss of skills during unemployment. Hazard models allow us to test these predictions 4. In our case, since we use data from job-centres, the stock-flow approach seems better representing matching mechanism, since the existence of a central matcher (i.e. the job centre) 4 Positive duration dependence is also possible, for example in presence of unemployment benefits exhaustion. 3

5 makes it unlikely that the same job may be re-offered to the same unemployed worker, as allowed by the random matching approach. However, for comparison purposes, we also estimate a matching function based on the random matching mechanism. Our empirical specification analyses a reduced form equation that estimates the factors affecting the product of the two probabilities, i.e. the probability of receiving a job offer and the probability of accepting it, that constitute the components of the matching process (Petrongolo and Pissarides, 2001). The probability of receiving an offer is determined by individual and job related characteristics and labour market conditions. The probability of accepting the job offer is determined by the individual reservation wage, which, in turn, depends on the expected wage distribution, costs of searching, unemployment benefits, individual and family characteristics, and the distribution of the arrival of new job offers. Estimating individual reemployment probabilities allows for rather more flexible specifications of the matching function when compared to estimates of aggregate matching functions, since hazard models allow for a wide range of distributional forms of unemployment durations. In addition, estimating individual reemployment probabilities allows us to control both for observed and unobserved heterogeneity at the individual level, which are only implicitly considered in an aggregate matching function. Despite the obvious aforementioned advantages of using hazard models to estimate matching functions, in the literature only a few studies did use hazard models to estimate matching functions. For example, Lindeboom, van Ours and Renes (1994) investigated the link between matching functions and hazard models to study the relative effectiveness of alternative search channels. Petrongolo (2001) used hazard function specifications to test the empirical relevance of the constant returns to scale hypothesis in the matching technology. Other studies estimated hazard functions to explore the individual determinants of unemployment duration, but they did not investigate the matching technology underlying the matching process (see Devine and Kiefer, 1991, for a review). We estimate three versions of individual hazard functions for multiple spells, namely a Mixed Proportional Hazard (MPH) model with a parametric baseline hazard (see van den Berg, 2001), a Mixed Proportional Hazard model with a non parametric baseline hazard, and, finally, a Cox Proportional Hazard (PH) model. We use a sample drawn from the IEFP (Institute for Employment and Vocational Training) dataset, the public entity responsible for Portuguese public job placement centres, for the period from June 1998 to December This dataset provides information about personal and job related characteristics of all individuals who registered in the Portuguese job centres. Having at our disposal the date of registration and the date of reemployment for each individual, we are able to construct multiple spells of individual unemployment durations. In addition, our dataset allows us to construct stocks and flows of unemployed job seekers and vacancies offered for each month at the job-centre level. The dataset also contains information about vacancies, enabling us to determine the number of 4

6 vacant jobs available for each month at the job centre level. In particular, the IEFP data provide information about the contract type sought by unemployed workers and the contract type offered by firms. Hence, we are able to construct an index of the degree of the heterogeneity found between contracts searched and contracts offered. Quite importantly, this index varies over time and across job centres. We explore this variation in order to learn if a higher degree of heterogeneity between contract type searched contract type offered increases matching frictions in the sense that it leads to longer unemployment durations if everything else is the same. The remainder of the paper is organized as follows. Section 2 presents the econometric specification. Section 3 describes the data. Section 4 presents the results. Finally, Section 5 concludes. 2. Econometric Specification We apply three different hazard models to estimate reemployment probabilities using data on multiple spells of unemployment durations. The probability distribution of durations can be specified by the cumulative distribution function: ( t) ( T t) F = Pr < (1) which denotes the probability that a continuous random variable T is less than some value t (see Kiefer, 1988, and Lancaster, 1979 and 1990). By providing monthly information, the data allow us to analyze a part of the individual s work history, to identify the origin state and, in presence of uncensored spells, the transition to the employment state. Since our data contain information about the destination state (i.e. permanent or temporary job) for only those individuals who got a job through the job centres but not for those individuals who got a job through their own means we are unable to apply a competing risks framework. Therefore, the destination state is simply the employment state. For each individual i it is possible to observe a sequence t i = {t c i } c є{1 Ci} of periods of time (spells) spent in the unemployment state. t indicates the elapsed duration in a particular state and c denotes the (c th ) spell of individual i. In order to allow for the presence of repeated spells, we implement two versions of the MPH model that allow us to control for unobserved heterogeneity at the individual level. We note that unobservable heterogeneity is likely to matter in this context due to differences in tastes, abilities, or other characteristics not reported in the IEFP data but that may condition, say, reservation wages, and, concomitantly, job acceptance rates. The MPH model consists of a specification of the Proportional Hazard model that allows for the presence of unobserved heterogeneity at the individual level. Duration analysis ignoring the presence of unobserved heterogeneity can imply biased estimates 5

7 (Lancaster, 1990). Lancaster (1979) was the first to treat this problem, proposing an estimate of a Proportional Hazard Model with multiplicative unobserved heterogeneity. In our first MPH model, we assume that the baseline hazard follows a Weibull distribution. In our second MPH model we remove the parametric assumption and adopt instead a piece-wise constant baseline hazard. Our third model, in turn, consists in a Cox PH model in which unemployment spells belonging to the same individual are clustered. In fact, since some omitted variables may cause observations within individuals to be correlated over time, the usual standard errors may be incorrect, and we implement the Huber-White estimator to obtain robust standard errors with additional correction for the effects of clustered data. The hazard rate of the MPH model for the individual i reads: λ i c c ' ( ti xi, vi; β ) λ0i ( ti ) exp( x i β ) v i = (2) λ 0i is a baseline hazard and measures the effect of elapsed duration (duration dependence). We allow for two alternatives specifications of the baseline hazard. The first one is a Weibull distribution, with possible monotone time dependence that can be expressed as: 0i c ( t ) c p 1 i λ = pt (3) i with: a. Positive duration dependence for p > 1 b. Negative duration dependence for p < 1 c. No duration dependence for p = 1 The second baseline hazard is assumed to be piece-wise constant, namely, a linear function of elapsed duration with spikes at 6, 12, 24 and 36 months: ( t) + a 2 I ( t > 6) ( ln( t) ln( 6) ) + a3i( t > 12) ( ln( t) ln( 12) ) + ( )( ( ) ( )) ( )( ( ) ( )) I t > 24 ln t ln 24 + a5 I t > 36 ln t ln 36 a1 ln λ 0 ( t c ) = exp (4) i i + a 4 I is an indicator function. This specification allows for possible non monotone evolutions of the exit rates. x i is a vector of no-time varying individual covariates, pertaining to personal and job related characteristics, and includes the (contract) heterogeneity index and tightness variables defined monthly at the job centre level. β 1 is a vector of unknown parameters to be estimated. Finally, v i is a random 6

8 individual effect, that catches the effect of individual heterogeneity. We assume that v i is Gamma distributed 5 : ( 1, ) V X ~ Γ θ (5) The unit of time is one month and the covariates are fixed to their values at the beginning of each spell. The individual contribution to the likelihood function of an incomplete (right censored) spell, that is, the probability of surviving in unemployment state until time t, can be expressed as follows: c c ( t W ; Ω ) = exp{ Λ( t W ; Ω) } S (6) i i i i where: Λ = t j 0 i ( s W ; Ω) λ s (7) i i is the corresponding integrated hazard function, W i = {x i, v i } is the vector of all observed and unobserved variables and Ω is the vector of all unknown parameters (β,θ). The individual contribution to the likelihood function of a completed spell of duration t c i spent in the unemployment state that ends in the employment state is therefore: c c c ( t W ; Ω ) = S( t W ; Ω) ( t W ; Ω) f λ (8) i i i i i i The presence of the unobserved heterogeneity term implies that it is not possible to condition the individual probabilities on v i since they are unobservable. To overcome this difficulty, and as usual, we integrate out v i over all possible values to get the unconditional probabilities. The individual sublikelihood function is: 5 Heckman and Singer (1984) proposed Non-Parametric Maximum Likelihood Estimation that approximates the distribution function of unobservable with a finite mixture distribution, to avoid biased estimates in a MPH model due to a misspecification of unobservable terms. However, Abbring and Van den Berg (2006) proved that in a large class of hazard models with proportional unobserved heterogeneity, the distribution of heterogeneity among survivors converges, often rapidly, to a gamma distribution. 7

9 L i + Ci Ci c c d ci r i c c ( Ω ti, xi ) = f ( ti xi, vi; Ω) S( ti xi, vi; Ω) dγ( vi ) (9) c= 1 c= 1 c indicates the c th spell in the unemployment state, d c is an indicator variable equal to one if the individual changed from the unemployment state to the employment state and zero otherwise, and r c is a dummy variable equal to one if the c th spell is incomplete and zero otherwise. The log-likelihood function reads: N c ( L( Ω ti, xi ) = ln( Li ) ln (10) i= 1 The Cox PH model is a semi-parametric model that makes no assumptions about the form of the baseline hazard. Relaxing the restriction of monotone duration dependence, the Cox PH model allows for flexible time dependence, and assumes a parametric form for the effect of the predictors on the hazard rate. The general specification of the hazard rate is quite similar to the MPH specification, except that it does not control for unobserved heterogeneity and the constant term is included in the baseline hazard. The parameters are estimated using the Cox partial likelihood estimator (see Cox, 1972), and the Breslow method is used for handling tied failures in the calculation of the model and residual. The pseudo log-likelihood function is similar to that of the MPH model, with the notable aforementioned exception that it does not allow for unobserved heterogeneity. As anticipated, in this case, the standard errors are estimated using the Huber-White estimator in order to obtain consistent estimates for them. As the usual standard errors may be incorrect because of the effects of clustered data, we employ the following variance estimator: [ I( b) ] 1 B[ I( )] 1 Var = b (11) where B is a correction factor. As anticipated, two possible searching processes are analysed here. The first one consists in the random matching approach that assumes that unemployed workers sample a vacant job at random and apply for it at each time, repeating applications also for jobs considered in the previous periods. This involves that the stock of unemployed workers (U) apply at each time while unemployed for all available vacancies, i.e. the stock of vacant jobs (V). The second search process consists in the stockflow matching approach and assumes that job seekers have complete information about the number of available job vacancies and apply to all the ones that they think are likely to be acceptable (see Coles and Smith, 1998; Petrongolo and Pissarides, 2001). The main difference from the previous approach 8

10 consists in the fact that the unemployed workers sample the entire stock of vacancies during the first period they search. From the second period on, in the event they remain unemployed after the first round of search (here, one month), they only apply for new vacancies, i.e. the gross inflow of vacant jobs (v). 3. Data The data used are drawn from an IEFP dataset that provides information on individuals registered at job centres in (Mainland) Portugal since 1997 to The IEFP is the agency responsible for running the public employment services 6, and it is a division of the Ministry of Labour and Solidarity. The IEFP is also responsible for job broking, vocational guidance, administering employment subsidies, vocational training, and apprenticeship training, but it does not administer unemployment benefits (see Addison and Portugal, 2001). However, being registered at a job centre is necessary to collect unemployment benefits. The IEFP dataset also includes information about job vacancies offered by firms, even if employers are not obliged to notify job centres of vacancies- The original sample containing information on individuals is composed by more than 3 million observations. In order to avoid computational problems, we drew a randomized sub-sample equal to 10% of the original sample 7, and focus only on unemployment spells starting since June 1998 in order to have at our disposal complete information on all covariates considered (described below) 8. The IEFP dataset provides daily information about the date of registration at the job centre and the date of placement, making it possible to identify multiple spells of unemployment for each individual. The IEFP dataset contains a plethora of personal and job related characteristics. Spells without the date of placement are considered censored. However, individuals may drop out of the job centres if they fail to present themselves at the job centres control interviews. We eliminate from our sample spells that terminate in failure to report to the control interviews in order to avoid misleading identification of censored unemployment durations. In order to make our results, on the one hand, more readable in economic terms, and, on the other, easily comparable to previous studies found in the literature, unemployment duration is analysed on a monthly basis rather than a daily basis. We follow arguments found in Petrongolo (2001) and analyse males and females separately as coefficients estimates may differ remarkably by gender. Hence, two sub-samples are used to estimate 6 IEFP does not have a placement monopoly, since both temporary work agency and private employment agencies are allowed. 7 Descriptive statistics of variables contained in the original IEFP dataset and descriptive statistics of our randomized sample are available upon request. 8 Only since June 1998 was introduced training activity during the registration at the job centres. 9

11 our hazard functions. We only consider individuals, aged 16-60, for whom all information with respect to all the covariates considered is available. This selection leaves us two unbalanced panels composed by observations and individuals for the male sample, and observations and individuals for the female sample. We remark that 84% of females and 88% of males only experiment one spell of unemployment in our samples. This is mainly due to the (1) quite long duration of unemployment spells that characterize the Portuguese labour market and to the (2) short period analysed in this paper (55 months). Both of these two factors (1) and (2) concur to explain the high percentage of censored spells in our sample (about 68%-69%). We consider a number of covariates to control for observed heterogeneity at the individual level. Table 1 contains descriptive statistics. To be more specific, we control for the following individual or family variables: age introduced in a non-linear way, educational level, marital status, number of dependent persons in the household, and a dummy indicating if the individual is disabled. Individuals composing our samples are on average respectively 33.4 years old and 32 years old for males and females, respectively. 41% of males and 48% of females are married, and 67% of males and 57% of females do not report any dependents. Perhaps as expected, only a very small percentage of the individuals in our samples is disabled (0.4% and 0.9% for males and females, respectively). Finally, the educational levels considered are quite equally present in our samples (about 20% for each level) across the so-called intermediate educational classes (4 years, 6 years, 9 years and years of education). Between 50% (for males) and 50.9% (for females) of individuals have maximum 6 years of education and between 7% (for males) and 10% (for females) report more than 12 years of education (including bachelors, masters or Ph.D. degrees). We also control for job related characteristics. We introduce a variable indicating if the individual is looking for his or her first job, meaning that he or she has no previous work experience. We note that individuals with no prior work experience constitute 17.5% of the male sample and 20.4% of the female sample. We also control if the individual is looking for a full time job or for a part time one. About 99% of the individuals in both of our samples were looking for a full time job. We consider a set of dummy variables indicating the motivation of the registration at the job centre. These dummy variables flag if the individual: was formerly a student (6.5% in the male sample and 6.9% in the female one), finished his or her educational career (between 8.6% and 9.7%), finished a training period (without any prior registration at the job centre; only represent 1.5%-2% of our samples), was dismissed (respectively 19.3% and 16.8%), resigned (respectively 14.1% and 11.2%) and if the individual registered because of the termination of a temporary contract. The latter group constitutes the largest one in our samples: 35.9% in the male sample and 37.3% in the female sample. The base category dummy is constituted by individuals with no previous job experiences. We also control for a set of dummy variables indicating the profession of the individual, distinguishing between managers, direction activities and specialists, technicians, administrative workers, service workers, agricultural and fishing workers, blue collars, 10

12 and individuals without professions (interpreted here as no qualifications). In the male sample, blue collar workers are the largest group (36.7%), followed by white collar workers (13.1%) and technicians (11.6%). In the female sample, individuals with services professions represent the largest group (27.5%), followed by white collars (19.6%) and blue collars (11.4%). Both samples present a very low percentage of managers, specialist and similar professions, and quite a high percentage of individuals with no declared occupation (respectively 17.3% and 22.2%). Two variables are introduced to control if the individuals received unemployment benefits (28.8% in the male sample and 31.4% in the female sample) or underwent a training period during the registration at the job centre (respectively 42.6% and 50.8%). Year and seasonal dummies are introduced to control business cycle and seasonal effects, respectively. Regional dummies are introduced to control for possible specific local labour markets effects. As anticipated, the probability of accepting a job offer is related to the expected wage distribution, and, hence, we introduce the mean wage offered by firms, evaluated monthly at the job centre level. Labour market tightness variables are also introduced and are evaluated monthly at the job centre level. To implement both the random matching process and the stock-flow matching process, we use stock and flow values of unemployed workers and vacancies in the following way. The IEFP data provide daily information of gross inflows of unemployed workers and vacancies that allow us to construct the monthly magnitude of gross inflows of labour market tightness variables and to reconstruct their stock values. To be more specific, to construct stock values we use information from the IEFP dataset since January 1997, hence at the starting of the period analyzed we have at our disposal the accumulated flow values until June In the random matching approach, unemployed workers and vacant jobs are measured at their stock values and fixed accordingly to the starting date of the unemployment spell. Hence, we preserve our no-time varying covariates framework. The stock flow approach, in turn, is implemented using time-varying labour market tightness variables, under the hypothesis that individuals look at the pool of vacancies only in the first round (one month) of their search process, and, afterwards, look at the gross inflow in the following rounds (months) of the search process. Average tightness of the labour market expressed in terms of stock values (V/U) is about 0.013, while it is about 0.20 if expressed in gross flow terms (v/u). These differences are strongly suggestive that mean unemployment duration far exceeds mean vacancy duration, a result in line with other studies in the literature. Finally, the mean value of the heterogeneity index is in the male sample and 0,282 in the female sample. 11

13 4. Contract Types Heterogeneity and Unemployment Duration The availability of unemployed and job vacancy data at a disaggregate level as possible is required to construct mismatch indexes. Many datasets fall to provide information on job vacancies, making it impossible to analyze both labour market side conditions. IEFP dataset gathers information from 85 job centres for each month under investigation including the number of job vacancies available, therefore we potentially can analyze labour market demand side at a well-disaggregated level. Specifically, in order to evaluate the effects of (contract type) heterogeneity between permanent contracts searched by unemployed workers and permanent contracts offered by firms, we introduce a simple index (HI, Heterogeneity Index) measured monthly (m) at the job centre level (j). The index that we propose is quite similar to the first Jackman and Roper (1987) mismatch indicator 9, with the difference that we do not consider it at aggregate level and we do not take its absolute value. The latter point is an important issue, since positive heterogeneity may be quite different from negative heterogeneity in the case of contract mismatch. For example, full positive heterogeneity (i.e. the index takes value one) indicates that all unemployed workers look for a permanent contract and no permanent contract is available, possibly implying higher incidence of refuse of contract offered and higher unemployment duration. On the contrary, full negative heterogeneity (i.e. the index takes value minus one) indicates that all unemployed workers look for a temporary contract and no temporary contracts are available. In this case, the probability of refusing the offered contract, i.e. a permanent one, could be lower, and also unemployment duration should be less affected, since the utility deriving from to be employed with a permanent contract should be larger than to be employed with a temporary one. Therefore, in the case of contract type heterogeneity, using the absolute value of the index could lead to wrong interpretation of the phenomenon. Analytically, we define the index as the difference between the ratio of the unemployed workers looking for a permanent contract and the pool of unemployed workers and the ratio of permanent contracts offered by firms and the pool of vacancies: HI jm PC PC U jm V jm = with HI jm = [-1, +1] (12) U V jm jm HI takes the value of zero in the absence of heterogeneity, i.e. the percentage of permanent contracts searched is equal to the percentage of permanent contracts offered. This situation should 9 The first indicator proposed by Jackman and Roper (1987) reads: M = u v M [ 0,1] ui = U i U and i vi = Vi i 1, where i i i 2 V where U i and V i are the number of unemployed workers and vacancies in i category i (where i may indicate the sector, skill, region and so on). i 12

14 imply that no frictions in the matching process arise from the eventual mismatch associated with contract type searched and contract type offered. HI takes the value of one or minus one in presence of full heterogeneity, i.e. in the extreme case in which all unemployed workers look for a permanent contract and firms only offer temporary contracts, or all unemployed workers look for a temporary contract and firms only offer permanent contracts. This situation should imply a higher degree of mismatch in the labour market, everything else the same. Hence, increasing values of HI should be associated with higher degrees of mismatch. The mean value of the heterogeneity index, as indicated above, is about 0.28, which represents the mean value of the difference between unemployed workers looking for a permanent relationship (about 97%-98% of the total unemployed workers) and the percentage of permanent jobs offered by firms (about 69-70% of total job offers). Table 2 and graph 1(related to the male sample) illustrate the distribution of HI s values across the job-centres, Obviously, our index show some limitations, since it only takes into account the relative percentages of searched/offered permanent contracts, but it does not consider the absolute values of searched/offered permanent contracts. Consequently, a zero value of the index is not always indicative of a potential full placement of unemployed workers looking for a permanent contract, and a no zero value not always implies a potential no full placement. However, it remains rather effective to describe contract type heterogeneity, since it is representative of the potential mismatch at contract level. Moreover, since we can interpret the job-centres role as a matcher role, i.e. the job-centres gather the information about searched/offered contract types and make the matches accordingly the searched/offered contract, there is not mismatch due to jobs being randomly offered 10. Preliminary evidences of the relationship between unemployment duration and searched/offered contract type heterogeneity are provided by a simple graph analysis (graph 2). Specifically, we graph the prediction of unemployment duration from estimation of a fractional polynomial of heterogeneity index and plot the resulting curve. The use of a fractional polynomial rather than of a linear or a quadratic prediction allows us to obtain a more flexible result, since it also admits a non monotonic pattern. According to our hypothesis, we expect a positive shape of the unemployment durationheterogeneity index curve for non negative values of the index, i.e. unemployment duration should increase as the searched/offered contract type heterogeneity also increases. In fact, a larger positive 10 To clarify the term randomly offered jobs we propose the following example. We consider a job centre in which two unemployed workers are registered (one looking for a permanent contract) and two vacancies (one permanent contract) are available. The matcher (i.e. the job centre) will propose the permanent job offered to the unemployed worker looking for permanent contract, and the temporary job offered to the unemployed worker looking for temporary contract. A cross offer, i.e. permanent job offered to unemployed worker looking for a temporary contract and vice versa, only arise in presence of over supply of permanent or temporary contracts. Consequently, unemployed workers do not randomly select the offered job, and an eventual refuse of the offered contract would be not imputable to the offered contract type. The absence of a matcher, i.e. the absence of a possible information channel about the nature of the offered contract, could implicate contract mismatch due to so called random selection. Following our example, it could implicate that in the first round-search the unemployed worker looking for the permanent contract before meets for a temporary contract may imply a possible increase of mismatch probability. 13

15 missmatch at the searched/offered contract level should imply higher probability of refusing the job offered by unemployed workers hence, in the average, higher unemployment duration. With regard to negative values of the heterogeneity index, larger negative heterogeneity could imply an unclear effect on unemployment duration. It will depend by the choices of the unemployed workers looking for temporary jobs when a permanent contract is offered to them. To better explain, we can consider the two possible extreme cases. In the first one, i.e. all individuals looking for temporary jobs strictly prefer a temporary job, and then the unemployment duration-heterogeneity index curve should display a negative shape (the reverse case of positive heterogeneity index). In the second one, i.e. all individuals looking for temporary jobs declare that they prefer a temporary job only because they believe this increases their reemployment probabilities, but they would accept a permanent job if it is offered. In this case, the unemployment duration-heterogeneity index curve should display an unclear slope, or a positive slope if the acceptance rate of permanent contracts should be higher than the acceptance temporary contract, since the benefits deriving from the a permanent contract, could compensate eventual other bad characteristics of the offered job. Graph 2 overlaid unemployment duration-heterogeneity index curves of male and female samples. Because of the scarcity of heterogeneity index values lower than -0.7, male graph does not present predictions for strong negative heterogeneity index values. However, when predictions are available, among males we find a positive relationship between predicted unemployment duration and the heterogeneity index 11. This finding is consistent with our hypothesis of higher mismatch probability, hence larger unemployment duration, in presence of higher positive contract type heterogeneity. The positive slope also found for negative values of the heterogeneity index, may be explained as suggested above, i.e. unemployed workers looking for a temporary job also accept, and in some cases more rapidly permanent jobs if offered. We have full information about predicted unemployment duration and heterogeneity index among females. The unemployment durationheterogeneity index curve for the female sample displays a similar pattern to that of the male sample. Interestingly. Predicted unemployment duration display the lowest values (about five months) for very high negative values of heterogeneity index, with a strong raise of predicted unemployment duration in correspondence of full negative contract type heterogeneity. It could be suggestive that, at least a part (probably a residual part), of unemployed workers looking for a temporary jobs have strong preferences for temporary contract, and when only permanent jobs are offered they face very long unemployment duration. On the contrary, as explained above, unemployed workers looking for a temporary jobs as a second best solution, and they are ready to accept permanent contracts if it is offered, have lower expected unemployment duration, since the acceptance rate for permanent jobs is likely to be greater than the acceptance rate for temporary contracts. Finally, it is also interesting to 11 We also plot a linear and a quadratic prediction of unemployment duration on the heterogeneity index. In both cases we find a positive shape of the unemployment duration-heterogeneity index curve. 14

16 make a gender comparison at unemployment duration-heterogeneity index curve level. According to graph 2, we firstly find that women experiment longer unemployment spells than males, except that for the highest and positive values of the heterogeneity index. Secondly, and more interestingly, we find evidence that, at least for positive values of the heterogeneity index, the slope of females curve is smaller than the slope of males curve. It is potentially suggestive of a greater adaptability of women with respect to men, in the acceptance of temporary contracts when they are looking for a permanent job. This evidence is confirmed by table 3, in which we report the destination contract of the unemployed workers. In fact, as explained above, we find that 70% of men unemployed workers looking for a permanent contract really are employed with a permanent job, but this percentage goes down to 65% among females. 5. Estimation Results Tables 3 to 5 present preliminary evidence. Table 3 informs us about the distribution of the spells with respect to their end, distinguishing by the type of contract sought. Inspection of Table 3 reveals that there are no great differences in the numbers of censored spells by type of contract sought after by the unemployed workers. Females leaving unemployment and looking for a permanent contract seem to be more likely to find a job via job centres (about 46%), with respect to the other sub-groups (about 39%-40%). Finally, and quite interestingly, Table 3 shows that only 70% of male and 65% of female unemployed workers looking for a permanent contract effectively are employed in a permanent relationship. Table 4 reports mean values of unemployment durations distinguishing by type of contract sought. With respect to all observed spells, both censored and uncensored, those unemployed workers looking for permanent contracts have on average an unemployment spell about 3 months longer than those unemployed workers looking for a temporary contract. Such greater duration is found both for males and females, yet on average females spend about 2 months more unemployed than males. We find similar results when we consider only uncensored spells. Table 5 displays the mean unemployment duration, focusing only on individuals with uncensored spells and for whom the destination contract is available. Differences in mean values are not significant, for both males and females, for those unemployed workers looking for temporary contracts. Rather interestingly, both males and females looking for a permanent contract experience a longer unemployment duration if they end up employed in a temporary relationship (about one month more for males and about two months more for females). This preliminary finding is consistent with the hypothesis that individuals looking for a permanent job are likely to first refuse temporary job offers to accept them later on only if they do not find a permanent job. 15

17 Tables 6a and 6b present the estimation results for the stock-flow matching models respectively for the male sample and the female sample, while Tables 7a and 7b present the estimation results for the random matching models respectively for the male sample and the female sample. Moreover, we present our hazard model estimates separating them between spells related to non-negative values [0, +1] of the heterogeneity index and spells related to non-positive values [-1, 0] of the heterogeneity index. In other words, we apply our hazard models to two sub-samples for the male sample and two sub-samples for the female sample. Making it possible to catch the effect of the contract type heterogeneity on reemployment probabilities without misinterpretation of the estimated heterogeneity index coefficients. It is important to highlight that, quite reassuringly, no differences in the signs of the coefficients are found when the hazard models are estimated separately with respect to non-negative and non-positive values of the heterogeneity index, both estimates of the coefficient are statistically significant. While we do not find differences in the signs of the coefficients, there are differences in the coefficients magnitude. The same, i.e. no differences in the signs of the coefficients but differences in the coefficients magnitude, are found with respect to stock-flow matching models and random matching models. Before proceeding to our analysis of our econometric results, we note the consistency of the Weibull MPH model with the data. The Weibull MPH model assumes a parametric distribution of unemployment duration, and it implies a monotone relationship between unemployment duration and reemployment probabilities. Figures 1 to 4 and 5 to 8, in turn, display evidence, from the estimated Cox PH model and from the MPH model with piece-wise constant baseline hazard, that highlights the existence of a monotone and negative relationship between unemployment duration and hazard rates 12. To be more specific, and focusing on the Cox PH model, we find that the baseline contribution to the hazard rate is continuously decreasing in the time spent in unemploymen. In addition, the Figures related to the non-parametric MPH model portray hazard rates that monotonically decrease. Therefore, both models seem to confirm the goodness of the chosen parametric model. The Weibull baseline hazard parameter (p) estimate takes a value smaller than one both in the random matching and in the stock-flow matching approach and both for the non-negative values of the heterogeneity index and for the non-positive values of the heterogeneity index,. Hence, we find overwhelming evidence of negative duration dependence. Moreover, we always find, both for the male sample and for the female sample, larger values of the duration dependence parameter for the micro labour markets characterized by non-positive heterogeneity index and in the stock-flow matching approach, i.e. less strong negative duration dependence. With reference to the heterogeneity index, the less strong negative duration 12 Graphs, both using stock-flow matching mechanism and random matching approach, show the trend described above. As we expected the hazard rates, or the baseline contributions to the hazard rate, are higher in the random matching since this mechanism, allowing the application tat the pool of vacancies in each round search, implies higher probability of matching. 16

18 dependence for the non-positive values, in correspondence of which there are smaller unemployment duration, could be indicative of a slower loss of skills in the first months of unemployment and faster for later ones. With reference to matching model approaches, even if predicted reemployment probabilities are higher, in their absolute values, using the random matching approach, the reduction in the probability of finding a job is less rapid using the stock-flow matching approach. It is suggestive that in the random matching model after the first round of the job-search, even if the probability of receiving a job offer is higher than in the stock-flow matching model, the acceptance rate is higher in the latter one. It occurs because in the random matching model the probability of receiving an old offer, previously refused, is higher than in the stock-flow matching model (where this probability is zero), and it could contribute to broaden the unemployment duration, overall for long spells. As anticipated, our MPH models also allow for the presence of unobserved heterogeneity at the individual level (theta parameter estimates). Our results show a non statistically significant presence of unobserved heterogeneity in the piece-wise constant specification, and a significant presence of unobserved heterogeneity in the Weibull MPH model, for both the stock-flow matching approach and the random matching approach. The presence of unobserved heterogeneity is more relevant in the female sample than in the male one. The estimation of the Weibull model without unobserved heterogeneity provides us a confirmation of the bias problems arising from a model specification that does not control for the presence of omitted variables. In fact, using this simpler model we find a stronger negative duration dependence, and, for example, an underestimation of the effect of the heterogeneity index. In particular, we find that the p parameter takes the values of 0.67 and 0.73 (the first one for non-negative heterogeneity index and the second one for non-positive heterogeneity index) for males and 0.73 and 0.74 for females under the stock-flow approach, and 0.64 and 0.68 for males and 0.70 and 0.69 for females, under the random matching approach. The estimated hazard ratios of the heterogeneity index are more or less halved. For brevity, in presenting our results we focus on the stock-flow matching model. We note that that the signs of the coefficients are quite stable across models, and, usually, when the signs do change across models the estimates turn out to be not significant. The magnitudes of the coefficients are quite similar in the parametric MPH model and in Cox PH model, while they are lower in the non parametric MPH model. Age shows the usual inverted U effect with significance at the 1% level both for males and females and both for non-negative and non-positive heterogeneity index values. Being married increases the probability of leaving unemployment with the effect being larger for males and for nonnegative heterogeneity index values. When significant, the presence of one or two dependent persons increases the hazard rate of males, but the probability of leaving unemployment decreases in the presence of three or more dependent persons (the coefficient is significant only in the Weibull model 17

19 for non-negative heterogeneity index values). Interestingly, when the relevant estimates are significant, the presence of dependent persons decreases the probability of leaving unemployment for females. Such gender duality may be explained in terms of caring services offered by female members in their respective households. In fact, they may contribute to reduce search effort or compel women to accept only jobs consistent with their obligations within the household. Being disabled, as expected, strongly reduces reemployment probabilities. Finally, unemployed workers with a higher educational levels are less likely to find a job. This somewhat counter intuitive finding may be explained by the fact that low educated individuals are over represented at the job centres, implying that jobs offered by firms likely present low skill requirements. We turn to this issue below. With respect to job related characteristics, we find that females looking for their first job are more likely to experience longer unemployment durations, meaning that the accumulation of previous job experiences may be important to increase skills or to act as a signal, leading to a higher reemployment probability. Estimates related to male samples, only are significant for Weibull and Cox model and for non-positive values of the heterogeneity index, and they display a positive effect on reemployment probabilities. Looking for a full time job increases the hazard rate for both males and females. This coefficient significant only for non-negative values of the heterogeneity index. Motivations underlying the registration at the job centre also contribute to explain reemployment probabilities. The base category dummy refers to unemployed workers with no previous dependent job relationship (i.e. ex housewife or ex self-employed). Interestingly, individuals who registered at the job centre after the end of a training period experience higher hazard rates (estimates are significant only for the Weibull model, and for non-negative heterogeneity index in the Cox model for the female sample). A similar effect, in magnitude, is found for ex students. An unexpected strong and positive effect is found for individuals who registered after being dismissed. However, the strongest effect is found for those individuals who registered after the end of a temporary job. We take this finding as suggestive of the importance of accumulating job experience in order to reduce unemployment duration. With respect to the professions considered (workers without a declared occupation are the reference category), we find that individuals better qualified, i.e. managers, specialists and technicians, are more likely to spend more time unemployed. On the contrary, a higher probability of leaving unemployment is found for agricultural and fishing workers and blue collar workers. This finding also suggests that the jobs offered by firms in job centres are quite likely to present low skill requirements. When estimates are significant, we find an unexpected positive effect of receiving unemployment benefits on reemployment probabilities, contrary to the predictions of moral hazard based unemployment insurance models. Receiving training during the registration period has ambiguous effects on reemployment probabilities. On the one hand, non parametric models (Cox PH and piece-wise MPH) predict the expected positive effect of training on the probability of leaving unemployment. This 18

20 finding is suggestive of the importance of providing training to prevent loss of skills. However, we remark that an unexpected negative effect is found using the Weibull specification. The variable identifying the mean wage offered by firms was introduced to control for the determinant of the probability of accepting the job offer as reservation wages quite likely depend on the expected wage distribution. Our estimates are not always significant for non-negative values of the heterogeneity index, while most of the times they are significant for non-positive values of the heterogeneity index. In particular, and as expected, the mean wage offered by firms has a positive sign. We also considered regional dummies to control for specific effects of regional labour markets. Lisbon is the reference region. We find that unemployed workers living in the North region experience a lower probability of leaving unemployment, while unemployed workers living in the other regions (Centre, Algarve and Alentejo) experience higher reemployment probabilities, even if some exception exist. We include yearly and seasonal dummies to control for possible business cycle and seasonal effects. The Weibull model estimates show a stronger negative effect for the period 2001 and 2002 on the reemployment probabilities of males. This result is consistent with the observed lower GDP growth in Portugal after A quite similar effect is found for females. With respect to the seasonal dummies, overall, we do not reject the expected seasonal pattern. Labour market tightness variables present the expected signs in all specifications (with the exception of the Weibull model in the stock-flow matching approach). We find that an increase in the value of the logarithm of the gross flow of unemployed workers reduces reemployment probabilities, most likely owing to congestion problems, while an increase in the value of the logarithm of the gross flow of vacancies increases reemployment probabilities, as implied by thick market externalities. We obtain the same results under the random matching approach. Tightness variables allow us to test the hypothesis of constant return to scale. We find unclear evidences as estimation result tables report. Finally, we focus on the coefficient of the heterogeneity index which describes the heterogeneity level between permanent contracts searched and permanent contracts offered. Estimation results are reported separately from hazard model results, in table 8. We find that for non-negative values of the index, the Weibull model and Cox model (the piece-wise constant model display no significant estimates), under either stock-flow matching or random matching processes, predict a negative effect of higher heterogeneity of contracts searched-offered on reemployment probabilities. For non-positive values of the index we always find non-significant estimates, possibly indicating an unclear effect on reemployment probabilities. In particular, it seems consistent with the non linear trend of the predicted unemployment duration-heterogeneity index curve for the female sample. All these findings are in line with our predictions and they support the notion that overly optimistic expectations about the probability of becoming employed in a permanent relationship may build in frictions in the search process, thus lengthening unemployment durations. 19