Education Policy, Occupation-Mismatch and the Skill Premium

Transcription

1 Edcation Policy, Occpation-Mismatch and the Skill Premim F. Obiols-Homs V. Sánchez-Marcos November 16, 2015 Abstract A relatively low tertiary edcation wage premim and a large occpational mismatch are two salient featres of the Spanish labor market that distingish it with respect to the labor markets in other developed contries. In this paper we provide an eqilibrim model of the labor market with frictions in which workers are heterogeneos in terms of ability and edcation. We specifically model an edcation policy as delivering either a particlar selection of individals into the tertiary edcation system or a higher ability of individals, or both. Or model economy is calibrated to mimic several of the Spanish labor market statistics together with key aspects of the achievement levels from the Programme for International Stdent Assessment (PISA) and the Programme for the International Assessment of Adlt Competencies (PIIAC). We then explore the implications of alternative edcation policies on mismatch and tertiary edcation wage premim. We find that nder an edcation policy able to prodce ability levels of tertiary edcated workers comparable to the average of the OECD contries a 60% lower fraction of mismatched workers and a 11% higher tertiary edcation wage premim wold be observed in Spain. Keywords: occpational-mismatch, tertiary edcation wage premim, ability JEL Classification: I26, J21, J24 F. Obiols-Homs Universitat Atònoma de Barcelona and Barcelona GSE; V. Sánchez-Marcos Universidad de Cantabria. Part of this research was carried ot while V. Sánchez-Marcos was visiting the Departament d Economia i d Història Econòmica at Universitat Atònoma de Barcelona and F. Obiols-Homs was visiting the IAE (CSIC). V. Sánchez-Marcos thanks the Spanish Ministry of Science and Technology for Grant ECO F. Obiols-Homs acknowledges the spport of the Spanish Government throgh grant ECO

2 1 Introdction In the years preceding the last recession the nemployment rate in Spain reached the lowest vale of the last two decades, both for tertiary edcated workers and dropots (see Table 1 below). This was a remarkable achievement for Spain after several years reporting mch higher nemployment rates than other similarly developed contries. However, two less well-known aspects of the Spanish labor market dring that period are a sbstantially lower tertiary edcation wage premim than in other OECD contries, and a prominent higher fraction of occpationmismatched workers. First, as reported in Table 1 the tertiary edcated worker s wage is 51% higher than the non-edcated worker s wage in Spain, whereas the average of the OECD for that figre is 72%. Second, the fraction of occpation-mismatched male workers in Spain is abot 0.34, 14 points above the average of the OECD contries. 1 We follow here the definition of vertical mismatch by Erostat: a worker is considered to be occpational mismatched if her edcational attainment is at least ISCED 5 2, bt her occpation is not considered to be ISCO 3 1, 2 or 3. 4 Interestingly, the fraction of the poplation with tertiary edcation in Spain is however similar to the average of the OECD. In section 2 we provide a more accrate description of this occpational mismatch phenomena that in Spain is spread across fields of specialization and age grops. Table 1: Spain verss OECD Spain OECD Unemployment Rate of Tertiary Edc Unemployment Rate of Dropots Tertiary Edc. Wage Premim Fraction of Tertiary Edc. Mismatched Fraction of Workers with Tertiary Edc Average Skills Tertiary Edc., PIIAC (2012) Sorce: Edcation al Glance (2010) and Erostat. All statistics are for male in 2007, except average skills of tertiary edcated. The fraction of tertiary edcated mismatched workers is for the UE-27 in Why is then the retrn to edcation and the fraction of mismatched workers so different in Spain? In this paper we claim that the qality of the edcated labor is an important variable to accont for these facts. There are signs of a poor performance of the edcation system in Spain -and specially the tertiary edcation level- and we think of it as a promising candidate to explain the aforementioned facts. In particlar according to the Programme for the International 1 The fraction of mismatched male workers in the EU-27 ranges from 3% in Lxemborg to 34% in Spain. The mode is 21%, and the standard deviation is 8. 2 International Standard Classification of Edcation (ISCED): levels 0 to 4 inclde edcation between preprimary school and pper-secondary edcation. - Levels 5 and 6 are tertiary edcation levels (respectively, not leading/leading to an advanced research qalification). 3 International Standard Classification of Occpations (ISCO): Categories 1, 2 and 3 inclde legislators, senior officials, managers, professionals, technicians and associate professionals. Categories 4 to 9 inclde clerks, service workers, etc., to elementary occpations. 4 In the literatre this notion of mismatch is sometimes called over-edcation or over-qalification and there are several alternatives to measre it. See for instance Leven and Oosterbeeck (2011) and the many references therein. 2

3 Assessment of Adlt Competencies (PIAAC, 2013) in 2013 the average score of the tertiary edcated individals in Spain is 278, whereas the average for the OECD contries is 295. This difference may not seem large, bt the fact is that the average score in Spain for this edcation grop is similar to the average score for secondary edcated individals in contries like Sweden, the Netherlands or Astria. Or view is that this sort of indicators are to a large extent the reslt of the policy stance with respect to edcation in different contries. For instance, the low scores observed in Spain cold be seen as the reslt of either a poor selection of high ability stdents into tertiary edcation, or a poor performance of the tertiary edcation system in shaping the capacities of the poplation, or of a combination of both. 5 The bottom line is that changes in the tertiary edcation system are likely to modify the average qality of both edcated and non edcated workers, which may have sizable implications on the eqilibrim in the labor market. Hence, or aim is to provide a model taking into accont the effects of edcation and qantitatively explore its ability to explain the facts of the Spanish labor market relative to the performance observed in other developed contries. An important featre of or model is that we distingish between innate ability or skills, and effective ability, a point made in jst a few preceding papers sch as Albrecht and Vroman (2002) [AV] and Cadras-Morató and Mateos-Planas 2013 [CMMP]. This is an essential ingredient in or model becase we think of edcation as a technology to increase the prodctivity of ability in the labor market, in contrast to [AV] and [CMMP]. Althogh we do not model edcation decisions here we think it is important to consider a framework in which those individals who wold end p being mismatched wold still have an incentive to enroll in college edcation. 6 Unlike previos papers we consider a continm of abilities, hence edcation is instrmented by a selection margin (what abilities receive edcation) and by a qality margin (by how mch the prodctivity of ability in the labor market increases). Finally, in or model we incorporate frictions in the labor market à la Mortensen and Pissarides. Given the qantitative natre of or exercise, a model with frictions is needed to captre the interaction between edcation policy, nemployment, and mismatch. In or qantitative work we calibrate the model to mimic key observations of the Spanish economy in the mid 2000 s. We condct several conter-factal experiments to asses the effects of alternative edcational policies regarding tertiary edcation. We find that a lower occpational mismatch and a higher tertiary edcation wage premim cold have been observed in Spain if the edcation policy had been more selective or if it had provided individals with more capacities. 7 We also asses the impact of the hosing boom. Or reslts sggest that the hosing boom effects have gone in the direction of increasing occpational mismatch and decreasing the wage premim for tertiary workers (albeit in absence of the hosing boom a slightly larger nemployment rate wold had been observed). 5 In the same way, one can think that the widespread increase in the fraction of tertiary edcated workers in developed contries cold have been achieved by simply relaxing the criteria to access tertiary edcation, or, alternatively, by agmenting the chances of those with higher ability to complete tertiary edcation (this may involve increasing the fnding for high-ability stdents belonging to poor families rather than simply increasing the nmber of stdents that receive some fnding to complete tertiary edcation). 6 Blazqez and Jansen 2008 stdy the efficiency of eqilibrim allocations in the AV model. Regarding edcation choices, Charlot and Decrese 2010 stdy the efficiency in a similar model and show that overedcation (in the sense of too many individals choosing to acqire edcation) arises since workers do not internalize the impact of their decision on the wage and employment perspectives of others. 7 Hence or findings are consistent with empirical literatre spporting the view that over- edcated workers have lower skills than the same level of edcation workers who are well-matched, see Nieto

4 A closely related paper to or work is CMMP where the athors pt forth skill bias technological change (SBTC) as an explanation for the overedcation observed in the U.S. 8 In particlar, CMMP show that as a reslt of the SBTC over-edcation increases becase firms opening vacancies with college reqirement may reject candidates that hold a college degree bt that are poorly skilled (their ability endowment is small). This reslt critically hinges on the fact that only innate ability is an inpt in the prodction fnctions of goods. We depart from the model in CMMP in that we characterize technologies by a sector specific component, which is independent of the ability of the worker operating the technology, and by an additional component that depends on her ability and edcation level. These assmptions allow s to state a condition for the existence of occpation mismatch in terms of the characteristics of the technologies, sch that mismatch can only arise when the ability of an edcated worker displays comparative advantage in the technologically advanced sector. Alternative explanations of the facts that we discssed above have been considered. For instance Díaz and Franjo (2014) provide evidence of poor investment in Specific Technical Change in Spain. So one cold possibly arge that, compared to other OECD contries, in Spain labor prodctivity in high-skilled sectors is low relative to that in low-skilled sectors de to a rather small investment in eqipment. Their model, however, is silent with respect to the specific isses regarding the labor market that are central in or work. Finally, Marimon and Zilibotti (1999) explore the differences in the generosity of nemployment benefits across contries as a mechanism to explain the differences between Continental Erope and the United States in nemployment rates, in the growth rate of prodctivity per worker, and in wage ineqality. In their analysis nemployment benefits act as a sbsidy to search for better jobs, which promotes a more efficient allocation albeit at the cost of larger nemployment rate. Hence, the more generos nemployment benefits the smaller shold be the mismatch, which rns conter to the particlar sitation in Spain. The paper is organized as follows. In section 2 we provide a more detailed description of the facts that we discss in this Introdction. Next in section 3 we describe the model economy that we se as framework for or analysis. In section 4 we ndertake the qantitative analysis to assess the ability of different edcation policies to accont for the differences between Spain and the average of the OECD contries in terms of labor market otcomes. In addition we explore the conseqences of a hosing boom. Finally, section 5 concldes. 2 Facts In this section we introdce a more detailed accont of the facts that motivate or research and that were reported in the Introdction. Figre 1 portrays a graphical representation of the differences in mismatch across several Eropean contries sing the notion of vertical mismatch sed in this paper. The fraction of poplation aged with higher edcation in Spain is similar to that in Eropean contries sch as U.K., Sweden, France, Belgim or Finland, and yet, Spain is the contry with the highest degree of mismatch, way above the levels observed in the previos contries. We arge first that the distribtion of stdents in higher edcation (ISCED levels 5A, 5B, 8 See also Krsell et al The literatre on the SBTC tries to accont for mismatch and the skill premim by changes in the relative demand of edcated workers. Or approach here is to asses the ability of changes in the relative spply of skilled labor. 4

5 Figre 1: High edcational attainment (ISCED 5-6) and vertical mismatch 25-34) 2007 (age grop 45 Percentage of vertically mismatched (not in ISCO 1, 2 or 3) tertiary gradates TR 25 AT IT 20 HR 15 RS SK RO 10 CZ 5 PT DE MD HU MT BG EL PL Bologna * LV SI IS ES LT UK FR BE EE CH SE NO FI NL DK LU IE CY Percentage of poplation with a high edcational attainment Sorce: Table Figre D.5b in Erostat (2009). 5

6 Table 2: Distribtion of stdents in higher ISCED levels as a percentage of all tertiary stdents, ISCED 5A 5B 6 5A 5B 6 5A 5B 6 5A 5B 6 5A 5B 6 5A 5B 6 EU ES Sorce: UIS, UOE (The Bologna process in higher edcation in Erope 2009, Table 0 p. 189). and 6) in Spain is comparable to Eropean contry average, so that the explanation for the higher mismatch is not de disproportionately large/small fraction of stdents involved in scientific/academic activity. 9 The Statistical Book of Erostat corresponding to the Bologna Process in Higher Edcation in Erope (2009) reports the distribtion of tertiary stdents in the ISCED levels 5A, 5B, and 6 as a percentage of all tertiary stdents in private and pblic instittions for the period 2001 to 2006 (see the table 2). It is clear from the table that the differences between Spain and the average EU-27 are remarkably small. We now wonder whether the distribtion of the poplation across fields of specialization in Spain is similar or not to the average of the EU contries. Obviosly, given that the incidence of occpational mismatch varies across fields of specialization, it cold be the case that the higher fraction of mismatched workers in Spain was de to a higher concentration of workers in certain fields of specialization. According to the statistics calclated from the Research into Employment and professional FLEXibility database (REFLEX srvey, ) and reported in Table 2 this is not the case. Roghly speaking the fraction of workers in Hmanities, Edcation, Agricltre, Health and Social sciences is similar in Spain to the average of the EU contries. There are only moderate differences in the fraction of workers in Science (abot 12% in the EU in contrast to 19% in Spain) and Engineering (abot 32% in the EU in contrast to 27% in Spain). Therefore we conclde that the phenomena of occpational mismatch is not de to compositional differences in terms of the fraction of edcated workers in each field of specialization. We report in table 2 the fraction of workers aged 25 to 34 who are considered to be mismatched by field of edcation. The incidence of mismatch by field of specialization in Spain is higher than the Eropean average (with the sole exception of Agricltre and Veterinary). It is clear that the average fraction of occpational mismatched workers across fields of specialization is sbstantially higher in Spain than in EU-27, and also that mismatch is not a phenomenon concentrated in a very specific sbset of fields. In EU-27 the highest fraction of mismatched workers is fond in Services (49) and it is followed by Agricltre (39) and Social Sciences (29). In Spain the highest fraction if fond in Services (64) and it is followed by Engineering field (50) and Social Science (44). Both in Spain and in the average of the EU-27 the lowest fraction of 9 ISCED level 5A are tertiary programs that are largely theoretically based and are intended to provide sfficient qalifications for gaining entry into advanced research programs and profession with high skills reqirements. Programs in ISCED 5B are typically shorter than those in 5A and focs on occpationally specific skills geared for entry into the labor market, althogh some theoretical fondations may be covered. Level ISCED 6 is reserved for tertiary programs which lead to the award of an advanced research qalification (they typically reqire the sbmission of a thesis or dissertation of pblishable qality (see the Statistical book of Erostat pp for frther details). 6

7 Table 3: Distribtion of Recently Gradated Individals Across Fields of Edcation 2000 UE Spain Edcation 5 5 Hmanities and Arts 7 7 Social sciences, Bsiness and Law Science, Mathematics and Compting Engineering, Manfactring and Constrction Agricltre and Veterinary 5 4 Heath and Welfare 7 7 Services 3 1 Sorce: REFLEX UE incldes Portgal, Spain, Italy, France, Switzerland, Astria, Germany, Netherlands, Belgim, United Kingdom, Norway, Sweden and Finland. Table 4: Percentage of Workers Vertical Mismatched, aged by Field of Edcation UE-27 Spain Edcation Hmanities and Arts Social sciences, Bsiness and Law Science, Mathematics and Compting Engineering, Manfactring and Constrction Agricltre and Veterinary Heath and Welfare Services Sorce: Erostat, EU-LFS, mismatched workers is fond in Health fields (12 in UE-27 in contrast to 27 in Spain) and in Edcation (13 in EU-27 and 28 in Spain). The largest gap between Spain and the UE-27 (more than doble) is fond in Edcation field and it is followed by Engineering field. In view of the facts above, we explore the possibility of the mismatch in Spain is affecting jst a redced age-specific grop of workers. With this regard, Hidalgo-Pérez et al. (2015) se a sample of the Social Secrity Records of the Spanish poplation (Mestra Contina de Vidas Laborales, MCVL) to explore the pzzling fall in the wage skill premim in Spain over the last decades. They stdy the evoltion of occpational mismatch among college gradated workers. According to their analysis the fraction of mismatched college workers decreases with age, bt very moderately (from 60% in the age grop 30 to 34 to 50% in the age grop 50 to 54). This persistence of over-qalification is consistent with the findings in Montalvo (2013). They se the Spanish School to Work Transition database to stdy these qestions and find that overqalification is a very absorbing state since transition matrices show that the probability to contine overqalified after moving to a new job is 76%. Finally, one may wonder abot the comparability of tertiary edcated workers in terms of the official nmber of years of edcation across contries. In Table 2 we can see that for the selected sample of contries there are noticeable differences in the distribtion of years in primary, secondary and high school. However, looking specifically at tertiary edcation the differences 7

8 Table 5: Eropean edcation systems Formal Prim.+sec. Voc. edc. Univ. Univ. edc. school +high s. starts starts (min. years) Astria / Denmark Finland France Germany Italy Spain UK (+2) Sorce: Erydice, The strctre of the Eropean Edcation systems seem rather small: in Spain higher edcation starts a year before than in other contries, bt it takes one more year (together with Germany) to complete college edcation. Given this, we wold find difficlt to jstify the lower performance of tertiary edcated workers in Spain in terms of PIAAC scores simply on a lower nmber of years of edcation. We now briefly trn to the otcome of the Spanish edcation system. We mentioned in the introdction the poor performance of the Spanish edcation system, which is reflected in the lower average score of the tertiary edcated individals in the PIAAC, 278 in Spain in contrast to 295 for the OECD contries. According to OECD Skills Otlook 2013, an additional year of edcation roghly represents abot 7 additional points in the score (see p. 61). Hence, Spanish adlts wold need abot two years of additional edcation to eliminate the difference with respect to the average adlt in the OECD. There are other signs of poor performance of the Spanish edcation system that are worrisome. The fraction of stdents at the 2 higher proficiency levels of the Programme for International Stdent Assessment (PISA) on the science scale is among the lowest in the OECD: in Spain only 5% of the stdents are classified in those categories, in contrast to the 9% average of the OECD. The pictre that emerges from the previos discssion is that the Spanish edction system in terms of length and in terms of the distribtion of stdents over the degree and field of specialization is comparable to the systems in place in other similar contries. In addition, the empirical evidence reported above sggests that mismatch is a widespread phenomena across fields of specialization and age, rather than a specific isse of a particlar sbset of workers. For these reasons we think it is natral to consider the qality of edcation as a relevant aspect to explain the mismatch observed in the Spanish labor market Obviosly the qality of edcation has sizable implications beyond the labor market. For instance, Hanshek and Kimko (2010) find that direct measres of labor-force qality from international mathematics and science test scores are strongly related to growth. 8

9 3 The Model Time is continos and in the economy there is a mass one of infinitely lived workers which are endowed with an ability level a. The key featre of or model is that ability is distribted according to a continos density λ(a) on a set of possible abilities A. We also assme that workers differ in their edcation level: some of them are edcated, denoted e, and some of them are not, denoted ne. Ths, nlike ability, edcation is a discrete variable with only two mass points. We think of the differences in edcation as the reslt of an edcational policy σ(a) : A [0, 1], which indicates the fraction of agents with edcation amongst those with ability level a. We se µ(a) = σ(a)λ(a) to denote the fraction of (edcated) e-agents with ability level a. Edcation in the economy is valable becase it increases the effective ability at work (i.e., the efficient nits of labor) of edcated workers. Specifically, the term ã j measres the effective ability of the worker at the work place which takes into accont not only the innate ability of the worker bt also the effect of edcation. Specifically, we assme that ã j = ψ j a, (1) with ψ e ψ ne = 1. Ths it is natral to think of ψ e as the qality of edcation becase it measres the increase in the efficiency nits of labor of a worker de to edcation. In the prodction side of the economy there are firms/jobs that are either vacant or filled. These jobs differ in the minimm edcation reqirement that a worker needs to satisfy to be able to sccessflly operate the corresponding technology. This means that there are firms with a technology sch that ne-workers are nable to properly operate. We refer to these firms as high-tech firms, denoted h. Also, there are firms sch that their technology can be operated by both edcated and non edcated workers, which we informally label as low-tech firms, and denote them by l. We denote by y ij (a) the otpt of a firm type i = h, l employing a worker with edcation j = e, ne, and ability level a A. We assme that y ij (a) > 0, so that for all worker types and sectors otpt is larger the larger is the ability of the worker. Creating a vacancy has a cost c v, and once the vacancy is filled with a worker, there is a cost c i, i = h, l of operating the technology. Finally, an employment relationship breaks p at exogenos rate δ i, and once nemployed a worker receives nemployment benefits b. We follow the Mortensen-Pissarides tradition and we assme that there are frictions in the labor market, sch that both firms and workers need to spend some resorces before a prodctive match can be formed. These frictions are captred by a matching fnction relating the nmber of new matches to the nmber of nemployed workers and to the nmber of otstanding vacancies. Hence, in this formlation of the labor market externalities de to congestion natrally arise and play an important role in shaping the eqilibrim configration. Notice that given the technological constraint abot the edcation reqirements, it is clear that ne-workers wold never look for a job in the h-sector, hence in this sense the labor market is segmented by edcation. The assmptions on technology place no restriction on edcated workers being able to operate the low-tech technology, and yet, we cannot rle ot that the labor market be additionally segmented by ability: it is possible that some edcated workers choose to search jobs in the low-tech sector. This is the notion of mismatch that we stdy in this paper. 11 In order to better focs on this isse, we will assme that nemployed workers can only search for a job in one market, hence edcated workers mst choose beforehand whether to search for a 11 See Herz and Van Rens 2011 for a notion of mismatch based on inefficient nemployment: the excessive nemployment above the level a planner wold have chosen. 9

10 job in the high or in the low sector. Likewise, a firm willing to create a vacancy needs to choose beforehand the sector in which it will be created. Given these assmptions the nmber of prodctive matches in sector i = h, l is given by a constant retrns to scale matching fnction M(v i, µ i ) defined on the nmber of vacancies (v i) and the mass of nemployed workers (µ i ) participating in the corresponding market. The matching fnctions satisfy M(v i, µ i ) = m(θ i)µ i, where θ i = v i /µ i and m(θ i ) = M(θ i, 1). This means that the probability of an nemployed worker finding a vacancy, and the probability of a vacant position to be filled with an nemployed worker, are given respectively by m(θ i ) and m(θ i )/θ i. 3.1 The problem of a worker Workers are assmed to be risk netral and ths they maximize the present vale of income: wages and nemployment benefits. We denote w ij (a) the wage of a worker type j = e, ne, with ability level a, who is matched to a firm in sector i = h, l, and we denote W ij (a) the vale of this match. Similarly, U ij (a) stands for the vale of searching for a job in sector i = h, l, for a type j = e, ne worker with ability level a. The asset vale of employment for a worker is given by: rw ij (a) = w ij (a) + δ i (U ij (a) W ij (a)), (2) for i = h, l, j = e, ne, all a A, and where r is the discont rate. The asset vale of looking for a job in the i-sector for a worker with edcation level j and ability level a is given by ru ij (a) = b + m(θ i ) {W ij (a) U ij (a)}. (3) In the crrent environment mismatch may arise if for some ability level we have that an e-worker looks for (and accepts) jobs in the l-sector. That is, mismatch occrs when there is a sbset à A sch that U he (a) U le (a) for a Ã. 3.2 The problem of the firm Firms create vacancies at a cost c v, irrespectively of the sector of operation. Once the vacancy is filled, however, the operation cost is c i for i = h, l. The vale of an operative match between a job in sector i and a worker type j and ability a is given by J ij (a), and it satisfies: rj ij (a) = y ij (a) w ij (a) c i + δ i [ max i {h,l} V i J ij(a)]. (4) Notice that once the crrent match is broken the firm is allowed to reconsider its sector of operation. The vale of creating a vacancy in the h-sector satisfies: rv h = c v + m(θ h) θ h {max{e µ [J he (a)] V h, 0}}, (5) The max operator reflects the fact that it may not be profitable for a firm in the h-sector to offer a job to an edcated worker. Notice also that E µ in the expression above is the expectation 10

11 conditional on meeting an edcated worker as implied by the measre µ(a). We also have rv l = c v + m(θ { l) µ le θ l µ (max{e µ [J le (a)] V l, 0}) l } + µ lne µ l (E µ [J lne (a)] V l ), (6) for the case of a vacancy in the low-tech sector. Again, the max operator in the previos eqation reflects the fact that for a firm in the l-sector it may not be profitable to hire an edcated worker (hence notice that we implicitly assme that a firm in the l-sector always finds desirable to hire a non edcated worker, irrespectively of her ability level). In the previos expression, µ le stands for the mass of edcated nemployed workers searching for a job in the low-tech sector (µ lne is the corresponding nmber of non edcated workers). Ths µ,le /µ l is the probability of meeting an e-worker who is searching in the l-sector, and µ lne /µ l is the probability of meeting an nemployed ne-worker. As before, notice also that E µ stands for the conditional expectations operator as implied by µ, the distribtion of edcation and ability. Finally, in the eqilibrim we consider we will assme free entry, so that V h = V l = 0 will hold. 3.3 Wage setting rle We assme that once an nemployed worker is matched to a posted vacancy, the firm and the worker engage in a Nash bargaining process in order to split the srpls that the match may potentially create. Under these assmptions the wages satisfy w ij (a) = argmax (W ij (a) U ij (a)) β (J ij (a) V i ) 1 β, (7) (where β (0, 1) represents the bargaining power of the workers), which is obtained by satisfying the FOC of the bargaining problem: (1 β)(w ij (a) U ij (a)) = β(j ij (a) V i ). (8) 3.4 Stationary eqilibrim Sbtitting Eq. (2), Eq. (3) and the expression for J ij (a) from Eq. (4) after imposing the free entry condition V i = 0 in Eq. (7) we obtain: w ij (a) = β(r + δ i + m(θ i ))(y ij (a) c i ) + (1 β)b(r + δ i ). (9) r + δ i + βm(θ i ) Also, inserting Eq. (2) into Eq. (3) and rewriting prodces: ru ij (a) b = m(θ i ) [w ij(a) b] r + δ i + m(θ i ). (10) It is also sefl to obtain a closed form expression for the vale of an active vacancy. Imposing again the free entry condition in Eq. (4) and rewriting: J ij (a) = y ij(a) w ij (a) c i r + δ i. (11) 11

12 Finally we write the free entry conditions as: and 0 = c v + m(θ l) θ l 0 = c v + m(θ h) θ h { E µ [J ij (a) a / Ã] }, (12) { µ le µ l } ) (E µ [J le (a) a Ã] + µ lne µ (E µ [J lne (a)]). (13) l Notice that in Eq. (12) and (13) we take into accont that in eqilibrim not all edcated workers may be searching in the high-tech sector. The previos eqations are sefl becase they help to characterize the stationary eqilibrim, which we introdce below. The definition is standard in that it involves a wage rate consistent with the wage setting rle, a labor market tightness and a stationary vale for nemployment that are consistent with free entry (see for instance Pissarides 2000, p. 18). The non standard ingredient of or economic environment is that with the possibility of mismatch and a continm of abilities the free entry conditions involve expectations defined by probability measres which are themselves endogenos. Definition: Given λ(a) and σ(a) implying µ(a), a stationary eqilibrim consists of a list θ i, a set à A, a distribtion of employment and nemployment over types and sectors (µ e h, µe le,µe lne, µ h, µ le, µ lne ) and wages w ij(a) sch that for i = h, l, j = e, ne and all a A: i) Given m(θ i ), w ij (a) satisfy Eq. (9). ii) Given m(θ i ), the set à A is consistent with the mismatch condition U he(a) U le (a), where U ij (a) satisfy Eq. (10). iii) The set à is consistent with the distribtion of employment and nemployment: µ e hc + µ hc = µ(a)da, µ e lc + µ lc = µ(a)da, and µ e lnc + µ lnc = µ(a)da. (14) a Ãc a à A where µ e ij /µ ij stand for the mass of employed/nemployed j-edcated agents in the i-sector. iv) labor markets are stationary: µ hm(θ h ) = µ e heδ h, µ lem(θ l ) = µ e leδ l, and µ lnem(θ l ) = µ e lneδ l. (15) v) The free entry conditions in Eq. (12) and (13) hold when J ij (a) is given by Eq. (11). As previosly noted in AV and in CMMP in similar models with a discrete nmber of ability levels there are three possible eqilibrim configrations which are respectively characterized by (1) ex-post segmentation, when all edcated workers work or look for jobs in the h-sector (remember that non edcated workers can operate only the technology of the l-sector), (2) employment mismatch, which is observed when some edcated workers look for and accept jobs in the l-sector, or (3) the case of mltiple eqilibria in which both types are simltaneosly possible. In addition to these possibilities, in or model with a continm of abilities we cannot rle ot the possibility of mltiple eqilibria with employment mismatch. We retrn to this isse in or qantitative work in section The possibility of a mismatched eqilibrim To fix some ideas from now on we will assme that the technology to prodce goods is linear in ability and it takes a general form that will be sefl in or qantitative analysis: y ij (a) = y i + ỹ ij ã j. (16) 12

13 The term y i captres the component of prodction that is sector-specific and nrelated to the ability of the worker operating the technology. The term ỹ ij allows s to captre the fact that marginal prodctivity of ability may be both edcation and sector specific. 12 The linearity assmption of the technology is sefl to characterize the set à by means of a simple threshold level for ability ā A. In fact, after some tedios algebra we can show that for given θ i : where and w ij (a) = w i + w ij a, (17) w i = β(r + δ i + m(θ i ))(y i c i ) + (1 β)b(r + δ i ), (18) r + δ i + βm(θ i ) w ij = β(r + δ i + m(θ i ))y ij, (19) r + δ i + βm(θ i ) end where we have simplified notation by letting y ij = ỹ ij ψ j. The above characterization is sefl becase it allows s to write the asset vale of nemployment in each sector also as a linear fnction of a. That is, the right hand side of Eqations (3) satisfies: ru ij (a) b = i + ij a, (20) with and where i = m(θ i ) β(y i c i b) r + δ i + βm(θ i ), (21) βy ij ij = m(θ i ) r + δ i + βm(θ i ). (22) With the linearity in a of U ij (a) it is clear that there can be mismatch if the straight lines described by U he (a) < U le (a) for some a A. That is, we conclde that there can be an eqilibrim with mismatch only if h l and he le (with at least one strict ineqality), or if h l and he le (also with at least one strict ineqality). In the former case there is ā sch that U he (ā) = U le (ā) and U he (a) > U le (a) a ā. That is, à = {a A : a ā} and the eqilibrim with mismatch is characterized by positive assortative matching: y h c h b y he < y l c l b y le (23) In this case ability displays comparative advantage in the h-sector and ths edcated bt lowability workers end p looking for jobs in the l-sector. 13 If the opposite ineqality holds then the eqilibrim is characterized by negative assortative matching, and so high-ability workers end p looking for jobs in the l-sector, hence à = {a A : a ā}.14 Figre 2 below portrays examples of the different types of mismatch. 12 We discss in Section 4.2 that by considering separately the effect of edcation on ability (by the term ψ e), and the associated marginal prodctivity of effective ability in prodction (by the term ỹ ij) will help s to calibrate the model in a transparent way and consistently with the empirical observations on the distribtion of ability and the average effective ability of tertiary edcated workers. 13 See Sattinger (1975) for an early development of a sorting condition along this lines. 14 The case of positive sorting is the one empirically relevant (see CMMP and the references therein), ths in or qantitative analysis we disregard negative sorting. For completeness, it is worth mentioning that the theoretical model admits additional forms of mismatch bt they violate the assmption that y ij > 0. 13

14 Figre 2: Different types of eqilibrim (a) U ij h + he a l + le a a a U ij ij (a) l + le a h + he a a a U ij ij (a) h + he a a l + le a 14

15 Whether the eqilibrim with mismatch is niqe or not is nclear (to the very best of or knowledge no general reslts are available on this isse), and sch a characterization is ot of the scope of this paper. For ftre reference, however, notice that for an eqilibrim candidate with à = (i.e., the one obtained when all edcated agents look for jobs in the h-sector) to fail to constitte a segmented eqilibrim it sffices to check that the edcated agents endowed with the lowest ability level wold be better off by looking for jobs in the l-sector. We will relay on this simple test to establish the niqeness of the eqilibrim with mismatch we stdy in Section It is clear from the Eqation (23) on the condition for positive sorting that there are many parameter configrations that will favor the existence of sch mismatch. At this stage however it is not possible to trace back the effect of the edcational policy on the eqilibrim vale of ā throgh θ i s, on the size of the occpational-mismatch nor on the edcated workers wage premim. Therefore in the following section we resort to qantitative methods in order to explore the implications for labor market otcomes of alternative edcation policies. Before we contine, however, we briefly discss the connections between the previos condition and the reslts in AV and CMMP. Remarks Remark 1: In line with the reslts in CMMP, it is clear from Eqation (23) that SBTC consisting in increasing y he relative to y le (the marginal prodctivity of ability in the h-sector relative to the l-sector) will favor the existence of mismatch. Hence or condition in Eqation (23) offers a new insight for the existence of mismatch based on increased comparative advantage of higher ability e-workers in the h-sector. Remark 2: The fact that the above sort of SBTC is able to give rise to mismatch is not possible in the AV model, in which search is ndirected (there is a single labor market) and ths increasing y he relative to y le tends to redce mismatch favoring an eqilibrim with ex-post segmentation. 16 Withot disregarding the importance of ndirected search, we notice that in or model with directed search a SBTC consisting in increasing y h relative to y l (that is, the sector specific parameter in the technology) will prodce the same effects as in the AV model. Remark 3: In the particlar case in which c l = c h = 0 there may be mismatch as long as y l is large relative to y h. Ths, the costs of operating a vacancy stressed in CMMP as a necessary condition to generate mismatch appear to be irrelevant once prodction depends not only on the ability of the agent bt also on the sector where she is (potentially) employed. 4 Qantitative Analysis The aim of the qantitative analysis in this section is to shed light on the determinants of the position of Spain relative to other similarly developed contries in terms of the labor market statistics that we highlighted in the Introdction. With this goal in mind we introdce additional assmptions that facilitate the analysis and we discipline or qantitative exercise with 15 Therefore with concave technologies in principle it wold be possible to generate several intervals of abilities in which there wold be mismatch with positive and negative sorting, as well as no mismatch. 16 The intition is that with a single labor market, skilled workers find profitable to remain nemployed and wait for the arrival of an offer from a h-tech firm only when the wage rate in that sector is sfficiently large relative to the l-sector. In the AV model the wage premim increases with this sort of SBTC. 15

16 a calibration of model parameters gronded on relevant statistics of the Spanish economy. 4.1 Fnctional forms We assme that the matching fnctions are Cobb-Doglas of the form M(v i, µ i ) = m i v η i (µ i ) 1 η, i = h, l, (24) where η (0, 1) measre the vacancy-elasticity of the matching fnction. This assmption is in line with most of the qantitative literatre abot frictional labor markets (see for instance the closely related papers by AV and CMMP). We assme that the distribtion of ability λ(a) is Pareto of parameters a m and α, so that the density satisfies λ(a) = α aα m a α+1 (25) if a a m and zero otherwise. We reqire this density to have finite mean, hence we assme α > With respect to the edcational policy we explore the implications of a general form sch that for all a a m : ( σ(a) = σ 0 + σ 1 1 a ) m. (26) a Notice that if σ 1 = 0, then the fraction of edcated workers is the same for all ability levels, and that if σ 1 > 0, then the fraction of edcated workers increases with the level of ability. Finally, notice that the fnction σ(a) is bonded, strictly increasing and strictly concave. Under these assmptions we have that µ(a) = σ(a)λ(a) = µ 0 a α+1 µ 1, (27) aα+2 where µ 0 = (σ 0 + σ 1 )αa α m, and that µ 1 = σ 1 αa 1+α m. The two-parameter family of edcational policies is convenient becase it allows s not only to control for the mass of edcated agents, bt also to disentangle the effects of the policy on the average ability in the edcated grop. To see this, notice that µ = µ(a)da = σ 0 + σ α, (28) A hence the fraction of edcated workers increases with both σ 0 and σ 1. In addition, the average ability of edcated workers satisfies a e = µ 1 A aµ(a)da = aα m(1 + α) α 1 ασ 0 + σ 1. (29) (1 + α)σ 0 + σ 1 If is straight forward to show that a e / σ 0 < 0, bt that a e / σ 1 > 0. Hence, σ 0 and σ 1 have opposite effects on a e. Following a similar reasoning we wold find that a ne / σ 0 > 0 and that a ne / σ 1 < 0 (a ne stands for the average ability of non edcated workers). Hence, changes in σ 0 and σ 1 have opposite effects on a e and a ne. This is important becase as it will be seen, the amont of mismatch and the tertiary edcation wage premim critically depend on whether the edcational policy increases or decreases the average qality of the edcated workers. Intitively, and increase in σ 0 increases the fraction of edcated agents, and it improves a ne bt worsens a e. Hence opening vacancies in the l-sector is more attractive than before (and opening vacancies 17 In fact, we will assme that α > 2, which in addition assres that the distribtion of ability has finite variance. 16

17 in the h-sector is less so), and ths, we expect a redction in the wage premim and higher mismatch. It will be seen below that this intitive reasoning rightly sggests that increasing σ 1 will have the opposite effects. 4.2 Calibration In or calibration strategy there is a first set of parameter vales that we borrow directly from existing stdies in the related literatre. This is the case of the worker s bargaining power β, which we fix at 0.5, the parameters that govern the matching technology (m h = m l = 1, η = 0.5) and the qarterly interest rate r, which is set to These are all the same as in AV. The job separation rates δ h and δ l for the Spanish economy are taken from Hobijn and Sahin (2009), who estimate a qarterly separation rate of Second, we fix the parameters that govern the distribtion of ability and the policy edcation fnction. To this end we se the distribtion of ability according to PISA and PIIAC in the mid 2000 s and the distribtion of edcation of the working poplation according to Eropean Union Srvey of Income and Living Conditions (EU-SILC) in In particlar we identify a m and α by targeting the mean and dispersion in the PISA scores (Science) in These two parameters pin down the distribtion of innate ability (i.e., before any effect of edcation). Given the distribtion of innate ability we then calibrate σ 0 and σ 1 to target the fraction of individals with tertiary edcation, 0.31, and the mean score in math test of individals with tertiary edcation relative to non edcated individals of 1.2, as calclated from the Programme for the International Assessment of Adlt Competencies (PIAAC, 2012). A difficlty in matching this statistic is de to the fact that it is hard to disentangle the role played by selection of abilities that receive edcation and the qality of edcation in shaping the relative higher mean score of tertiary edcated workers with respect to non edcated workers. 19 As a starting reasonable compromise, we assme that ψ e = 1.15 (remember that ψ ne is normalized to 1), that is, we assme that as a reslt of tertiary edcation effective ability is increased by 15%, and the rest of the differences between edcated and non edcated workers will be explained by selection. Given this choice, for or model to accont for the 1.2 ratio of PIIAC abilities of tertiary to non-tertiary edcated workers, the average effective ability of a tertiary edcated worker has to be eqal to Table 6 contains this second set of parameters vales and it also reprodces the relevant statistics in the model and in the data. Finally there are seven parameters that we calibrate to match specific targets of the Spanish labor market, which are reported in Table 7 (We try to be parsimonios and normalize the l-sector: c l = 0 and ỹ lj = 1). Most of the statistics related to the labor market otcomes are calclated sing the Eropean Union Srvey of Income and Living Conditions (EU-SILC) in 2007: the tertiary edcation wage premim is 1.47, the nemployment rate by edcation (4% for tertiary edcated workers and 9% for dropots) and the standard deviation to the mean of wages by edcation (0.47 for tertiary edcated and 0.36 for dropots). 21 Unfortnately, this 18 Cbas, Ravikmar and Ventra 2013 also proxy the distribtion of talent in several contries sing the distribtion of PISA scores. 19 As discssed in Hendricks and Lekhina (2014) it is an open empirical qestion what is the importance of self-selection into edcation in acconting for differences in life-time earnings and this qestion goes beyond the aim of this paper. 20 The difference in this figre between Table 6 and Table 1 is de to the difference between the normalization of effective ability in the model and in PIIAC scores. 21 Or sample is made of male individals aged 25 to 54. Statistics of wages are for the sample of fll-time 17

18 srvey does not provide information on the qality of the job match for each worker, so we cannot compte the fraction of mismatched workers in this data set. As an alternative we target the fraction of mismatched workers (those with tertiary edcation who hold a job beneath their edcational level) as reported by Erostat in 2009, which is 33%. As we stated above this is the highest figre amongst the EU contries, where the average is 20%. An important target in the calibration is the wage of workers with tertiary edcation relative to dropots conditioning on the type of job match. According to Hidalgo et al. (2014) sing the Mestra Contina de Vidas Laborales (this is a sample of Social Secrity Administration records) the average wage of college to non-college workers is abot 1.15 when the college worker is mismatched. Since or focs here is on tertiary edcated instead of college edcated individals we think it is appropriate to target a smaller vale and ths we prse a 10% premim. 22 In the nmerical calclations to determine the eqilibrim we proceed iteratively: given initial gesses for θ i we find the implied wages and a potential threshold level ā. Once this is fond we integrate the vales of active matches and check if the free entry conditions are close to zero. We iterate on the θ i ntil the free entry conditions are approximately satisfied. Once a candidate eqilibrim with mismatch is fond it is straightforward to perform the test explained at the end of Section 3.4 (whether U he (a m ) > U le (a m ) or not). Frthermore, once a candidate eqilibrim is fond we also check that no other eqilibrim with mismatch can be fond nearby: we restart the algorithm from many different initial conditions and check that we always converge to the same candidate. Ths, the mismatch eqilibrim reported in Tables 6 and 7 appears to be niqe. Parameter a m 4.10 α 6.30 σ σ Target Data Model PISA mean score science (OECD 2006) PISA standard deviation to mean (OECD 2006) Fraction of workers with tertiary edc. (EU-SLIC 2007) Average skills tertiary edc. (PIAAC 2012) Table 6: Calibrated Parameters and Targets I workers after trimming the bottom and top 1% of the distribtion of wages in each edcation grop. 22 A negative vale for the operation cost of the high-tech sector is needed to bring the fraction of mismatched workers to the level observed in the data. 18

19 Parameter b 7.5 c v 0.82 c h 3.5 y h ỹ he 4.10 ỹ le 3.15 ỹ lne 2.60 Target Data Model Unemp. rate dropots (EU-SLIC 2007) Unemp. rate tertiary edc. (EU-SLIC 2007) Frac. tertiary edc. mismatched (Erostat 2009) Tertiary edc. wage premim (EU-SLIC 2007) Std. dev. to mean wages, tertiary (EU-SLIC 2007) Std. dev. to mean wages, dropots (EU-SLIC 2007) Tertiary edc. wage premim, mismatched (Hidalgo et al. 2014) Table 7: Calibrated Parameters and Targets II 4.3 Benchmark As a reslt of or benchmark calibration we obtain that the eqilibrim with mismatch in the model is able to accont reasonably well for the differences in nemployment rates across edcational levels, for the within edcation grops ineqality, for the relative ability of tertiary edcated workers as well as for the observed tertiary edcation wage premim. In or view this is a comprehensive set of the statistics that characterizes relevant dimensions of the Spanish labor market. All in all, the model involves a rather large nmber of parameters and ths it is hard to find additional statistics that can be sed as over-identifying restrictions to asses the sitability of the benchmark calibration. To gain additional confidence along these lines we explore the implications of changing the fraction of tertiary edcated workers to the one observed in the mid 90 s. In Table 8 we compare the labor market otcomes of or benchmark economy with those in an economy in which the fraction of edcated workers is eqal to 0.21 (this is what we call mid 90s), a figre that is similar to the one observed in Spain in the mid 90s. 23 We obtain that the fraction of mismatched workers decreases from 0.33 to 0.29 and the tertiary edcation wage premim increases from 1.46 o This evoltion is consistent with empirical evidence for Spain as reported by Hidalgo et al. (2014), Dolado et al. (2000) and Pijoan-Mas and Sánchez- Marcos (2010) (these papers docment a decrease in the tertiary edcation wage premim and an increase in the fraction of mismatched workers over the period 1997 to 2007). In other words, 23 In order to do that we set σ 0 = 0.15, instead of the σ 0 = 0.25 in or benchmark. 19