Description
The term business cycle (or economic cycle) refers to economy-wide fluctuations in production, trade and economic activity in general over several months or years in an economy organized on free-enterprise principles.
ABSTRACT
Title of dissertation:
JOB COMPETITION OVER THE BUSINESS CYCLE Antri N. Chasampoulli, Ph.D., 2005
Dissertation directed by:
Professor John Haltiwanger and Professor Je?rey Smith, Department of Economics
My thesis explores the following question: how workers of di?erent skill are allocated across jobs and unemployment over the business cycle. I am interested in understanding the “over-quali?cation”of workers that occurs during periods of high unemployment, as increased congestion in the labor market hinders workers from ?nding a suitable match. I focus on the skill mismatch that takes the form of high-skilled workers transitorily accepting low-skill jobs, thereby in?uencing the labor market prospects of low-skilled workers. In the ?rst chapter, I develop a business cycle matching model with heterogeneous workers and jobs, which helps understand the role of over-quali?cation on labor productivity and across-skill unemployment dynamics. I capture the acrossskill search externalities and spillover e?ects that arise when low- and high-skilled workers compete for low-skill jobs, by relaxing the common assumption that all
workers qualify for any type of vacancy. I show that the skill mix of vacancies changes over the cycle, thus altering the allocation of workers of di?erent skill across jobs and unemployment. In addition, my model explains observed di?erences in labor market outcomes of di?erent skill groups, including the higher sensitivity of low-skilled unemployment to changes in economic activity. In the second chapter, I test the empirical relevance of over-quali?cation. I ask whether the risk of unemployment induces high-skilled workers to accept transitorily low-skill jobs until a better job comes along. To this end, I study the mismatch rates and job level dynamics of high-skilled workers. Unlike existing studies that only examine how the business cycle a?ects job level probabilities, I adopt dynamic panel data estimation methods, in which the worker’s lagged state (i.e., whether unemployed or mismatched) enters the model as an explanatory variable. I ?nd evidence suggestive of the existence of over-quali?cation. The mismatch rates of higher educational groups are higher and exhibit more cyclical variation. Moreover, I ?nd that high-skilled workers are more likely to move into lower job levels when they are unemployed and the unemployment rate is high. In addition, my results point to the existence of an upgrading in the job levels of mismatched high-skilled workers when the unemployment rate is low.
JOB COMPETITION OVER THE BUSINESS CYCLE
by Antri N. Chasampoulli
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial ful?llment of the requirements for the degree of Doctor of Philosophy 2005
Advisory Committee: Professor Professor Professor Professor Professor John Haltiwanger, Co-Chair Je?rey Smith, Co-Chair John Shea Michael Pries John Horowitz
c Copyright by Antri N. Chasampoulli 2005
This dissertation is dedicated to my mother.
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TABLE OF CONTENTS List of Tables List of Figures 1 Job Competition Over the Business Cycle: Implications for Labor Productivity and Unemployment Rates by Skill 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Main Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Timing and Flow Equations . . . . . . . . . . . . . . . . . . . 1.3.4 Asset Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Surpluses and Zero Pro?t Conditions . . . . . . . . . . . . . . 1.3.6 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Aggregate Productivity Fluctuations . . . . . . . . . . . . . . 1.4.2 Job Separation Fluctuations . . . . . . . . . . . . . . . . . . . 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Cyclical Variation in Match Quality: The Role of Unemployment Risk 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Mismatch Rates Over the Business Cycle . . . . . . . . . . . . . . . 2.4 Linear Probability and Logit Models . . . . . . . . . . . . . . . . . 2.4.1 The E?ect of Business Cycle and Education on High- JobLevel Probability . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 The E?ect of Business Cycle and Education on Low- Job-Level Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Dynamic Panel Data Models . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Are Unemployed High-Skilled Workers More Likely to Take Low-Skill Jobs in Recessions? . . . . . . . . . . . . . . . . . 2.5.2 Are Unemployed High-Skilled Workers Less Likely to Take High-Skill Jobs in Recessions? . . . . . . . . . . . . . . . . . 2.5.3 Are Mismatched High-Skilled More Likely to Take High-Skill Jobs in Booms? . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Markov Chain Multinomial Logit Model of Job level Transitions . . 2.6.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Conditional Maximum Likelihood Estimation . . . . . . . . 2.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Prestige Scores iii . . . . v vi 1 1 7 12 12 17 18 18 21 23 23 25 34 40 43 43 48 50 57
. 58 . 59 . 60 . 62 . 65 . . . . . . 68 70 70 74 76 79 89
Bibliography
100
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LIST OF TABLES
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Job Levels Based on Prestige Scores . . . . . . . . . . . . . . . . . . . 81 Sample Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . 81 Linear Probability and Logistic Regression Results: High-Job-Level Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Linear Probability and Logistic Regression Results: Low-Job-Level Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Dynamic Panel Data Models: unemployment to low-job-level transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Dynamic Panel Data Models: unemployment to high-job-level transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Dynamic Panel Data Models: low-job-level to high-job-level transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Estimated parameters Markov Chain Multinomial Logit model, full sample, yearly transitions . . . . . . . . . . . . . . . . . . . . . . . . 87 Estimated parameters Markov Chain Multinomial Logit model, highschool graduates, yearly transitions . . . . . . . . . . . . . . . . . . . 88
A.1 Prestige Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
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LIST OF FIGURES
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
E?ect of a Negative Productivity Shock on the Fraction of Low-skill Vacancies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 E?ect of a Negative Productivity Shock on the Fraction of Low-skilled Workers in the Mass of Job Seekers. . . . . . . . . . . . . . . . . . . . 26 E?ect of a Negative Productivity Shock on the Fraction of Highskilled Workers in the Mass of Job Seekers. . . . . . . . . . . . . . . . 27 E?ect of a Negative Productivity Shock on the Worker-Vacancy Meeting Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 E?ect of a Negative Productivity Shock on the Probability of Finding a High-Skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 E?ect of a Negative Productivity Shock on the Probability of Finding a Low-Skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 E?ect of a Negative Productivity Shock on Average Match Productivity. 29 E?ect of a Negative Productivity Shock on Unemployment and Mismatch Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 E?ect of a Separation Rate Shock on the Fraction of Low-Skill Vacancies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.10 E?ect of a Separation Rate Shock on the Fraction of High-skilled Job Seekers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.11 E?ect of a Separation Rate Shock on the Probability of Finding a High-skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.12 E?ect of a Separation Rate Shock on the Probability of Finding a Low-skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.13 E?ect of a Separation Rate Shock on Average Match Productivity. . . 37 1.14 E?ect of a Separation Rate Shock on Unemployment and Mismatch Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1 2.2 Mismatch Rate of College Graduates (90% cuto? point) . . . . . . . . 52 Mismatch Rate of College Graduates (95% cuto? point) . . . . . . . . 53 vi
2.3 2.4 2.5
Mismatch Rates by Education (90% prestige cuto? point) . . . . . . . 54 Fraction of Unemployed by Education . . . . . . . . . . . . . . . . . . 55 Degrees of Mismatch: College Graduates . . . . . . . . . . . . . . . . 56
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Chapter 1 Job Competition Over the Business Cycle: Implications for Labor Productivity and Unemployment Rates by Skill 1.1 Introduction
An open theoretical question is how the quality of job-worker matches evolves over the business cycle. Evidence that matches created during recessions are of lower productivity and dissolve faster has increased attention on the role of search frictions in exacerbating skill-mismatches during recessions.1 This chapter focuses on the type of skill-mismatch that takes the form of highskilled workers taking transitorily low-skill jobs, i.e., becoming “over-quali?ed”, in order to avoid the distress of being unemployed, while continuing to search on the job for high-skill jobs. I analyze the implications of over-quali?cation for unemployment and labor productivity dynamics, by developing a business cycle matching model in which high-skilled workers can take both high- and low-skill jobs, whereas low-skilled workers can only take low-skilled jobs.
1
For evidence on the procyclicality of match quality, see for example, Bowlus (1995), Davis,
Haltiwanger, and Schuh (1996), Bils (1985), Shin (1994), Bowlus, Liu and Robinson (2002), and Liu (2003). Moreover, worker surveys indicate that workers are more likely to report being employed at jobs below their skill level during recessions (e.g., Akerlof Rose and Yellen, 1988; and Acemoglu, 1999).
1
The existing literature on the role of search frictions in exacerbating skill mismatch during recessions neglects the fact that workers face restrictions in the type of vacancies they can ?ll. Existing studies assume that all workers, independent of their skill level, qualify for any type of vacancy ?rms create. In reality, however, the matching technology is asymmetric: workers of high skill qualify for a wider range of job types, while jobs with low skill requirements can be ?lled by a wider range of worker types. Hence, when low-skilled workers compete with high-skilled workers for low-skilled jobs, the asymmetric nature of the matching technology entails search externalities and across-skill spillover e?ects that existing studies fail to incorporate. In turn, the job competition externalities that arise have important consequences for how workers of di?erent skill are allocated across jobs and unemployment over the cycle. Typically, workers of di?erent skill experience di?erent labor market outcomes on a variety of dimensions, which the assumption that all workers can be employed in any type of vacancies ?rms create (i.e., a single job-worker matching rate for all skill groups) cannot explain. Low-skilled workers have lower exit rates from unemployment and lower propensity to search on the job than high-skilled workers (e.g., Blau and Robins, 1990; Pissarides and Wadsworth, 1994; and Belzil, 1996). Moreover, low-skilled unemployment is higher and exhibits higher cyclical sensitivity than high-skilled unemployment (e.g., Topel, 1993). These di?erences in labor market outcomes for workers of di?erent skill, are consistent with the existence of job competition externalities, as high-skilled workers take temporary jobs below their
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skill level, thereby a?ecting the labor market prospects of low-skilled workers.2 There is increasing interest in modeling over-quali?cation to explain why many EU countries in the recent decades have su?ered an uneven increase in low-skilled unemployment relative to high-skilled unemployment (Albrecht and Vroman, 2002; Gautier, 2002; Dolado et al., 2003). These studies focus on across-skill job competition externalities and investigate whether high-skilled workers “crowd-out” lowskilled workers as they compete for jobs. Since their goal is to explain long term uneven developments in unemployment rates, they only look at steady states. The notion that search frictions exacerbate skill-mismatches during recessions has been formalized in Barlevy (2002), via a business cycle matching model with twosided heterogeneity and on-the-job search. Prior to Barlevy, a series of theoretical papers argued that recessions promote e?cient allocation of resources by “cleansing” out the less e?cient production arrangements.3 However, the “cleansing” view is at odds with the evidence that recessions encourage the creation of less productive matches. Barlevy (2002) is a ?rst attempt at reconciling the theoretical literature on the “cleansing” e?ect of recessions with the evidence. In his model recessions kill marginal production arrangements, but also hinder the transition of mismatched workers into more productive uses (labeled as the “sullying” e?ect), because ?rms
2
The ?ndings of Bowlus (1995) that the quality of matches falls during recessions more evidently
in white collar than blue collar activities gives additional support to this view.
3
Examples are Hall (1991, 2000), Mortensen and Pissarides (1994), Caballero and Hammour
(1994, 1996) and Gomes, Greenwood, and Rebelo (1999). These studies have been inspired by the work of Davis and Haltiwanger (1992), who argue that recessions are associated with increased job reallocation in the manufacturing sector.
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create fewer vacancies per job seeker. The latter e?ect dominates, and accounts for the lower match quality observed during recessions. Barlevy’s model adopts a symmetric framework (i.e., ?rms create equal amounts of each type of vacancy and all workers can be employed in any type of vacancy ?rms open), making the role of aggregate shocks more transparent. However, a symmetric framework implies identical unemployment rates across skill groups, and therefore cannot account for the observed uneven cyclical ?uctuations in unemployment rates of di?erent skill cohorts. More importantly, it ignores the externalities and spillover e?ects across skill groups arising from job competition. In this paper, I relax the symmetry assumption and incorporate both business cycle ?uctuations and job competition externalities into the model, thus bringing the two strands of literature together. I investigate the dynamic e?ects on unemployment of two types of shocks: an exogenous shock to productivity that a?ects output of all matches and shock to the rate at which matches dissolve. Given the asymmetric nature of the matching technology, changes in the skill composition of vacancies alter the way high- and low-skilled workers are allocated across types of jobs and unemployment. I show that the skill composition of vacancies changes over the cycle, as ?rms respond to changes in the relative value of opening high- and low-skill vacancies. My model delivers the conventional result that in periods of low aggregate productivity workers have greater di?culty escaping unemployment, as ?rms create fewer vacancies per job seeker, but it also shows that downturns generate two countervailing e?ects. On the one hand, an exogenous reduction in aggregate productivity raises 4
the relative value of opening high-skill vacancies and encourages ?rms to upgrade the skill composition of vacancies. In turn, the skill upgrading in the vacancy mix facilitates the transition of both unemployed and overquali?ed (i.e., in low-skill jobs) high-skilled workers into high-skill jobs, increasing average match productivity. On the other hand, a rise in exogenous job separation rates induces ?rms to downgrade the skill composition of vacancies: since low-skill jobs can be ?lled by both types of workers, their relative pro?tability increases when matches dissolve faster and thus is a greater supply of job seekers. The skill downgrading, together with the increase in the number of unemployed high-skilled workers, enhances the likelihood that unemployed high-skilled workers take low-skill jobs, while sti?ing the transition into high-skill jobs. The net e?ect on the degree of over-quali?cation and thus average match productivity depends on the relative importance of exogenous aggregate productivity and separation rate shocks over the business cycle. Once I allow for the skill composition of vacancies to vary over the cycle, Barlevy’s (2002) result that recessions sti?e the transition of mismatched workers into appropriate jobs no longer holds unless the fall in aggregate productivity is accompanied by a su?ciently high increase in job separation. Further, contrary to the “cleansing” view, under which higher job separation during recessions eliminates marginally productive arrangements, higher job separation in this paper actually exacerbates over-quali?cation and lowers average match productivity. Hence, my model gives a view of skill-mismatch over the cycle that puts more emphasis on job separation rather than aggregate productivity ?uctuations, and calls for further investigation on the link between the two impulses. 5
In addition, by relaxing the common assumption of a single matching rate for all skill groups, my model allows for the unemployment rate not only to vary over the cycle, but across skill groups as well. Therefore, my model allows for an examination of why low-skilled unemployment is more sensitive to slowdowns in economic activity than high-skilled unemployment, and whether this is due to intensi?ed job competition between high- and low-skilled workers. Consistent with the evidence, I ?nd that low-skilled unemployment is higher and more volatile than high-skilled unemployment. However, contrary to the common belief, the main reason is not that high-skilled workers crowd out low-skilled ones when competing for jobs; instead, high-skilled workers are eligible for both high- and low-skill jobs and are therefore less vulnerable to the changes in the skill composition of vacancies that occur over the cycle. As it turns out, regardless of whether or not over-quali?cation and job competition externalities increase during recessions, the low-skilled unemployment rate still rises relatively more. The rest of the paper is organized as follows. Section 1.2 is devoted to the description of related literature. Section 1.3 describes worker and ?rm behavior and the labor market mechanisms (matching process, wage bargaining). In sections 1.4 and 1.5, I examine the properties of the model through comparative statics and dynamic simulation exercises, by considering separately the e?ects of aggregate productivity and separation rate ?uctuations. Finally, in section 1.6, I conclude with a few remarks and discuss how future research will build upon this contribution.
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1.2 Related Literature
Several modi?cations to the conventional search equilibrium model have been made to incorporate the signi?cance of skill mismatches which occur during periods of high congestion in the labor market, mainly by allowing for some heterogeneity in job productivities and/or workers skills. The literature on matching models with heterogeneous agents dates back to the contribution by Pissarides (1994), where onesided heterogeneity is assumed: there are two types of jobs (good and bad jobs) but workers are homogeneous. Workers who take bad jobs stay in them as their wages increase with job tenure, so that employment in good jobs is no longer attractive to them.4 The more recent contributions of Acemoglu (1999) and Mortensen and Pissarides (1999) set up the foundations of the role of search frictions in matching models with skill heterogeneity. Assuming a constant contact rate between unemployed workers and vacancies, thus eliminating any possible interactions between workers with di?erent skills, Acemoglu (1999) o?ers a theory of how the unemployment rates of high- and low-skilled workers and between-group wage dispersion change endogenously depending on the vacancy creation strategy of ?rms. In particular, ?rms ?nd it pro?table to either create only low-skill jobs or to create both low-skill and high-skill jobs and search for the appropriate candidates. Similarly, in Mortensen and Pissarides (1999), the distribution of workers over a continuum of skill levels is exogenous, whereas the distribution of job types is endogenous. They examine the
4
A relevant contribution in this line of research is also McKenna (1996).
7
consequences of skilled-biased technological change on unemployment rates across skill groups. However, they do not deal with across skill search externalities and spillover e?ects associated with skill-mismatches, because in their model there is a perfect match between workers skills and ?rms skill requirements. Similar models have also been considered in studies that investigate the role of unemployment risk in how e?ciently workers are allocated across jobs, and the corresponding welfare implications of unemployment insurance policy. In Acemoglu (2001), workers are identical and only job productivities are heterogeneous. Similarly, Acemoglu and Shimer (1999) assume that workers are identical in terms of their skills, while jobs are heterogeneous in terms of speci?city with higher speci?city jobs being more productive. Marimon and Zilibotti (1999) go one step further and allow for two-sided skill heterogeneity, thus capturing the negative impact that skill mismatch has on labor productivity. They model match productivity to be lower the higher the distance between the workers’ skill level and the vacancies’ required skill level. However, they impose a convenient symmetry in the production technology that is very restrictive: as long as the distance between the ?rms required skill level and the worker’s skill level is the same, the productivity of the match will be equal. This implies that an overquali?ed worker can produce as much as an under-quali?ed worker (a nurse can do the job of a doctor as well as a doctor can do the job of a nurse). Although the strands of literature described above set the foundations for studying search frictions in models with skill-heterogeneity, they do not deal with spillover e?ects of high-skilled workers onto the creation and ?lling of low-skill jobs 8
and their connection to the observed di?erences in the labor market outcomes of different skill cohorts. Some of these papers assume perfectly segmented labor markets where job competition and interactions across skill groups are not possible. In other cases, markets are not segmented, but the type of heterogeneity assumed does not incorporate di?erences in the minimum skill requirements of jobs. That is, all types of workers are quali?ed to perform any type of job entrepreneurs create and thus have identical job ?nding rates. In such a set up, the matching behavior of di?erent skill groups does not in?uence the ability of other skill groups to ?nd a job. Hence, possible job competition and crowding out phenomena that may occur in periods of high congestion in the labor market, and their implications for unemployment rate di?erences across skill groups, are ignored. The recent contributions by Albrecht and Vroman (2002), Gautier (2002) and Dolado et al. (2003) extend this type of model to include job competition and spillover e?ects across skill groups and address issues such as over-quali?cation and crowding-out more directly. In these studies, for simplicity, there are only two types of jobs (low-skill and high-skill) and only two skill groups (low-skilled and highskilled workers). Both the distribution of skills and job destruction are exogenous, but the vacancy mix is endogenous and is determined by free entry conditions. The key feature of these models, ?rst introduced by Albrecht and Vroman (2002), is the type of production technology assumed: low- and high-skill workers can be hired for low-skill jobs, whereas only the latter can perform high-skill jobs. In this context, high- and low-skill submarkets can endogenously segregate or merge depending on the matching behavior of workers. It may be worthwhile for unemployed high-skilled 9
workers to mismatch, i.e., take low-skill jobs. If this is the case, job creation and unemployment in the low-skill market can a?ect job creation and unemployment in the high-skill market. Therefore, job competition takes place and crowding out may occur.5 Although these studies provide important insights into the externalities associated with searching and matching behavior of workers and shed some light on the implications of job competition for unemployment, they are limited in that they only perform comparative static exercises on the steady-state equilibrium, investigating
5
The most notable di?erences between these three studies rest on their assumptions regarding
the nature of job search. In both Gautier (2002) and Dolado et al. (2003) mismatched workers (high-skilled workers on low-skilled jobs) are allowed to search on-the-job and quit as soon as better jobs come along, while in the Albrecht and Vroman model, on-the-job search is not allowed. In the latter study, there are two main results. First, when high-skilled workers are willing to take low-skill jobs (cross-skill matching), unemployment duration among low-skilled workers is higher than among high-skilled workers, while the expected match duration is higher for highthan low-skill jobs. Second, in equilibria with cross-skill matching, high-skilled workers “crowd out”, that is, take jobs away from low-skilled workers, but at the same time, their willingness to accept low-skill jobs leads to an overall expansion of low-skill vacancy supply. Therefore, the net impact on low-skilled unemployment depends on which of these e?ects is stronger. Gautier (2002) and Dolado et al. (2003) ?nd that on-the-job search provides an additional mechanism through which the labor market position of low-skill workers is weakened when high-skilled workers move into low-skill jobs. In particular, the higher quit rate of mismatched workers exerts a negative externality on low-skill jobs, which lowers the value of posting a low-skill vacancy and thus, leads to lower low-skill vacancy creation. Gautier (2002) additionally argues that job competition may exert a positive externality on the pro?ts of low-skill vacancies when high-skilled workers are more productive than low-skilled workers on low-skill jobs.
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how the steady-state equilibrium unemployment rates of low- and high-skilled workers are a?ected by changes in the aggregate productivity level or the job separation rate, which represent changes in overall economic activity; changes in the relative productivity of high and low-skill jobs, which are interpreted as skill-biased technological shocks; and changes in the mass of high-skilled workers in the economy.6 Comparative static results do not provide insights into the dynamic impact of shocks. Therefore, the studies described above do not establish a clear connection between job competition and the observed di?erences in the cyclical patterns of unemployment across skill groups. To characterize the allocation of workers across di?erent types of matches and unemployment over the business cycle, we need to allow for deviations from the steady state. Mortensen and Pissarides (1994) do precisely this in their model without heterogeneity and only o?-the-job search, by allowing aggregate productivity to ?uctuate over time. However, on-the-job search and heterogeneity make the transitional dynamics associated with deviations from the steady state di?cult to characterize analytically. Barlevy (2002) incorporates both of these features but turns to a discrete-time version of the model and a collocation method to approximate the value function in order to analyze transitional dynamics. His study establishes that recessions exacerbate mismatch while booms
6
More recently, Pierrard and Sneesens (2003) examine the dynamic adjustment process to a
skill-bias shock and to skill upgrading by allowing for these changes to take place progressively over time. Their scope is to investigate how these changes in combination with job competition externalities a?ect the dispersion between the high- and low-skilled unemployment rates. However, they do not look at the cyclical implications of job competition for the across-skill unemployment dynamics.
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promote allocative e?ciency by allowing mismatched workers to quit and move into better jobs. The matching technology assumed in Barlevy, however, does not allow for the possibility of job competition and the resulting search externalities and spillover e?ects across skill groups.7 Moreover, by assuming a symmetric equilibrium where ?rms create equal amounts of each type of vacancy, his model predicts that all types of workers face the same labor market prospects. This is inconsistent with the evidence that changes in aggregate economic conditions have di?erent impacts on unemployment ?ows and rates of di?erent skill groups. In this paper, I unite the literature examining matching models with skillmismatches and business cycles with the recent literature examining matching models of job competition. The section that follows gives a description of the model.
1.3 The Model 1.3.1 Main Assumptions
I assume that time is discrete. An exogenous fraction of workers ? is low-skilled (l), while the remaining fraction (1 ? ? ) is high-skilled (h). Similarly, vacancies are high-skill (h) and low-skill (l). The distribution of skill requirement across vacancies is endogenous. Interactions between high- and low-skilled submarkets are embedded into the model by incorporating heterogeneity in terms of jobs’ minimum skill requirements. Both low- and high-skilled workers can be hired for low-skill jobs, but a high-skill job
7
The matching technology in Barlevy is identical to that in Marimon and Zilibotti (1999).
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can be ?lled only by a high-skilled worker. Consequently, workers of di?erent skill not only have di?erent productivity distributions across types of jobs but di?erent job ?nding rates as well; high-skill workers have a higher job ?nding rate, while low-skill vacancies enjoy a higher arrival rate of workers than high-skill vacancies. High- and low-skilled workers are assumed to be equally productive in low-skill jobs, but high-skilled workers are more productive when matched to a high-skill job. The ?ow output of each match is assumed to be the product of an aggregate component y , and a match speci?c component aj i , where i denotes the type of job and j the type of worker. More formally, let yaj i denote the ?ow of output of a job of type i = (h, l) that is ?lled by a worker of type j = (h, l). Then, the production
h l l technology assumptions can be summarized by yah h > yal = yal > yah = 0.
Given that job-to-job movements represent a substantial fraction of worker ?ows (e.g., Gautier, 1998), I allow for on-the-job search. Mismatched high-skilled workers search on the job for high-skill jobs and quit as soon as they ?nd one, while low-skilled workers have no reason to search on the job. Firms can open at most one job and the choice of type is irreversible. The mass of each type of vacancy is determined endogenously by a free-entry condition. The exogenous component of job separation follows a Poisson process with arrival rate s. Although s is common to both types of job, the e?ective separation rate of low-skill jobs is higher due to on-the-job search by mismatched workers. Whenever a match is destroyed the job becomes vacant and bears a maintenance cost c, while the worker becomes unemployed and receives a ?ow of income b, which is to be interpreted as home production or leisure. 13
I introduce productivity and separation rate ?uctuations into the model by allowing aggregate labor productivity y and the separation rate s to follow a Markov process. Aggregate productivity takes the value of y0 in recessions and y1 > y0 in booms, while the separation rate takes the value s0 in recessions and s1 < s0 in booms. Both variables switch between the two levels with a transition probability p. At every point in time the current values of productivity and separation are common knowledge. The condition that ensures a match is formed in equilibrium is simply that the ?ow of output generated from the match is higher than the unemployment bene?t, i.e., aj i > b, ?i, j . It is optimal for unemployed high-skilled workers to take low-skill jobs as long as their productivity is higher than the unemployment bene?t, because they retain their chances of ?nding a high-skilled job by searching on the job.8 The meeting process is undirected in the sense that a low-skill worker encounters a high-skill vacancy (in which case a match is not formed) with a probability per unit of time that is proportional to the fraction of high-skill vacancies. Similarly, a high-skill worker encounters a low-skill vacancy with a probability per unit of time that is proportional to the fraction of low-skill vacancies.9
8
Dolado et al. (2003) derive conditions that rule out a corner solution in which ?rms create
only low-skill vacancies in a steady state equilibrium. They also derive the conditions under which a steady-state cross-skill matching equilibrium (i.e. an equilibrium in which high-skill workers take low-skill jobs) is unique.
9
I assume the meeting process is undirected (i.e., workers cannot distinguish the vacancy type
before applying) to capture the impact of changes in the skill mix of vacancies on the ?ow rates of di?erent skill groups. In reality even if job seekers can distinguish the type of vacancy before they
14
The total number of matches between a worker and a ?rm is determined by a constant returns to scale function, m vh + vl , uh + ul + eh l (1 ? s) , where vh and vl denote the mass of high- and low-skill vacancies, uh and ul the mass of highand low-skilled unemployed workers, and eh l (1-s) the number of high-skilled workers in low-skill jobs (which I label as mismatched henceforth) that survive separation. m [·, ·] is strictly increasing in both arguments. The “labor market tightness” is denoted by ? =
vh +vl , uh +ul +e h (1?s) l
so that in a tighter market there are more vacancies
available per job seeker. The pool of job seekers is composed of unemployed high- and low-skilled workers and mismatched workers. For convenience, I de?ne the following shares: ul ul + uh ul + uh ? = ul + uh + eh l (1 ? s) ? = (1.1) The rate at which ?rms meet a job seeker of any type is equal to q (?) = m(1, 1 ), ? which is decreasing in ? and exhibits the standard properties of: lim??0 q (?) = lim??? ?q (?) = ? and lim??? q (?) = lim??0 ?q (?) = 0. A mismatched high-skilled worker has no incentive to change employer unless the new employer o?ers him a high-skill job. Accordingly, some low-skill vacancies will meet mismatched workers who will refuse to match. Likewise, employers with high-skill jobs will not hire
apply there are still search frictions involved that prevent workers from ?nding the right match. For example, it is harder for a high-skilled worker to ?nd a high-skill job if only 5% of the vacancies are high-skill than when 95% of the vacancies are high-skill, even if he/she can distinguish the vacancy type. This type of search friction is captured by assuming random instead of directed search.
15
the low-skilled workers they meet. Therefore, the e?ective matching rate of a lowskill vacancy with a low-skilled worker is given by ??q (?), while the corresponding rate with a high-skilled worker is ? (1 ? ?) q (?) . High-skill vacancies match only with either mismatched or unemployed high-skilled workers, and thus their e?ective matching rate can be written as (1 ? ??) q (?). Assuming that ? =
vl vl +vh
denotes
the fraction of low-skill vacancies, the e?ective matching rate of low-skilled workers is ?m(?), while mismatched high-skilled ?nd a high-skill job with a rate (1 ? ? )m(?). Finally, unemployed high-skilled workers can take either a high- or a low-skill job and thus their e?ective matching rate is equal to m(?) (i.e., ?m(?) + (1 ? ? )m (?)). The asymmetric nature of the matching technology generates the following across-skill externalities and spillover e?ects: i) Vacancy Composition E?ect (VCE). An increase in the fraction of high-skill vacancies (1 ? ? ) decreases the unemployment-to-employment ?ow probability of low-skilled workers, but also decreases the unemployment-to-mismatch ?ow probability of high-skilled workers; ii) Negative Quit Externality (NQE). The higher quit rate of mismatched highskilled workers lowers the pro?ts of low-skill jobs. As a result, an increase in the fraction of high-skilled unemployed job seekers ? (1 ? ?), which in turn increases the likelihood of high-skilled workers taking low-skill jobs, lowers the pro?ts of low-skill jobs. Hence, low-skill vacancy creation declines with higher fractions of unemployed high-skilled workers, making it harder for low-skill workers to ?nd a job; iii) Negative Congestion Externality (NCE henceforth). High-skilled job seekers exert a negative externality on low-skilled employa16
bility by creating additional congestion in the market, thus making it harder for low-skilled workers to encounter a low-skill job, and for low-skill vacancies to encounter a low-skilled worker. To be more speci?c, an increase in the number of high-skilled job seekers eh l + uh , lowers the probability that a low-skill worker will meet a low-skill vacancy, given by ?m(?), through a lower ?, and the probability that a low-skill vacancy will encounter a low-skilled worker, given by ??q (?), through a lower ??. In short, an increase in ? implies a VCE that bene?ts low-skilled employability but at the same time facilitates the transition of high-skilled workers into low-skill jobs. An increase in the fraction of high-skilled job seekers (both unemployed and mismatched), given by (1 ? ??), exacerbates both the NCE and NQE on low-skill employability.
1.3.2 Bargaining
In equilibrium there are three possible types of matches: (i) high-skilled workers in high-skill jobs, (ii) high-skilled workers in low-skill jobs and (iii) low-skilled workers in low-skill jobs. The surplus of each match is divided according to a Nash bargaining solution. The share of surplus that workers receive is exogenous and denoted by ? . I adopt the following standard notation: U j denotes the value of unemployment for a worker of type j , Vi denotes the value of a vacant job of type i, Wij denotes the value of employment for a worker of type j in a job of type i, and ?nally Jij denotes the value to the ?rm of ?lling a job of type i with a worker of type
17
j . Accordingly, the surplus of a match can be expressed as Sij = Wij + Jij ? U j ? Vi
j and the wage wi satis?es
(1 ? ? ) Wij ? U j = ? Jij ? Vi
(1.2)
1.3.3 Timing and Flow Equations
h l Let e = eh h , el , el be the mass of high-skilled workers in high-skill jobs, the
mass of high-skilled workers in low-skill jobs and the mass of low-skilled workers in low-skill jobs, respectively, at the beginning of period t. At this stage, the Markov shock hits the economy and a new pair (y, s) arrives that is common knowledge to
h l all agents in the economy. After e = eh h , el , el and (y, s) are observed, production
takes place, exogenous separations occur, and vacancies are posted by ?rms to insure zero pro?ts. Search takes place and workers change jobs, leading to the following distribution of workers in the subsequent period:
l e?ll = el l (1 ? s) + ?m(? ) ? ? el (1 ? s) h h e?h = eh h (1 ? s) + (1 ? ? )m(? ) (1 ? ? ? eh (1 ? s) h h e?lh = eh l (1 ? s) + ?m(? ) 1 ? ? ? (el + eh )(1 ? s)
(1.3) (1.4)
?(1 ? ? )m(?)eh l (1 ? s)
(1.5)
1.3.4 Asset Values
Workers are risk neutral, time is discrete and the interest rate r is constant. The asset value of an unemployed low-skilled worker at aggregate state (y, s) and 18
a given distribution of employment e = satis?es U l (y, s, e) = b +
h l eh h , el , el
is denoted by U l (y, s, e) and
1 [?m(?)E [Wll (y ? , s?, e? /)/y, s, e] (1 + r ) (1.6)
+(1 ? ?m(?))E [U l (y ? , s? , e? )/y, s, e]
Equation (1.6) states that the value of an unemployed low-skilled worker is equal to his value of leisure b, plus the present value of the probability he ?nds a low-skill job times the resulting expected value conditional on the current state (y, s, e), given by E [Wll (y ?, s? , e? )/y, s, e], plus the probability he does not ?nd a job, times the expected value of staying unemployed given by E [U l (y ?, s? , e? )/y, s, e]. (y ?, s? ) and e? =
h ?h ?l e?h , el , el
denote the realization of aggregate shocks and the distribution
of employment next period, respectively. Similarly, given that high-skilled workers accept both types of jobs, the corresponding value of unemployment for high-skilled workers, U h (y, s, e) satis?es U h (y, s, e) = b + 1 [?m(?)E [Wlh (y ? , s? , e? )/y, s, e] (1 + r )
h ? ? ? +(1 ? ? )m(?)E [Wh (y , s , e )/y, s, e]
+(1 ? m(?))E [U h (y ?, s? , e? )/y, s, e]]
(1.7)
The rest of the asset values are similar. The asset values of high- and low-skilled workers in high- and low-skill jobs, respectively, satisfy
h h ? ? ? Wh (y, s, e) = wh (y , s , e ) +
1 [sE [U h (y ? , s? , e? )/y, s, e] (1 + r ) (1.8)
h ? ? ? +(1 ? s)E [Wh (y , s , e )/y, s, e]]
Wll (y, s, e) = wll (y ?, s? , e? ) +
1 [sE [U l (y ?, s? , e? )/y, s, e] (1 + r )
19
+(1 ? s)E [Wll (y ?, s? , e? )/y, s, e]]
(1.9)
while the asset value of employment for mismatched high-skilled workers is given by Wlh (y, s, e) = wlh (y ? , s?, e? ) + 1 [sE [U h (y ?, s? , e? )/y, s, e] (1 + r )
h ? ? ? +(1 ? s)(1 ? ? )m(?)E [Wh (y , s , e ) ? Wlh (y ?, s? , e? )/y, s, e]
+(1 ? s)E [Wlh (y ?, s? , e? )/y, s, e]]
(1.10)
Mismatched high-skilled workers search on the job for high-skill jobs. Therefore, the last term in the above equation represents the value of on-the-job search: given that the match survives to the next period with a probability (1 ? s) a mismatched highskilled worker can ?nd a high-skill job with a probability (1 ? ? ) m(?), in which case
h ? ? ? he gains the expected capital gain from switching jobs, given by E (Wh (y , s , e /y, s, e)?
Wlh (y ? , s? , e? /y, s, e)). The values of opening high- and low-skill vacancies are given by Vh (y, s, e) = ?c + 1 h ? ? ? [(1 ? ??)q (?)E [Jh (y , s , e )/y, s, e] (1 + r ) (1.11)
+(1 ? (1 ? ??)q (?))E [Vh (y ?, s? , e? )/y, s, e]] Vl (y, s, e) = ?c + 1 [??q (?)E [Jll (y ?, s? , e? )/y, s, e] (1 + r )
+? (1 ? ?)q (?)E [Jlh (y ?, s? , e? )/y, s, e] +(1 ? ?q (?))E [Vl (y ?, s? , e? )/y, s, e]] whereas the values to the employer of ?lling those vacancies satisfy
h h Jh (y, s, e) = yah h ? wh (y, s, e) +
(1.12)
1 [sE [Vh (y ?, s? , e? )/y, s, e] (1 + r ) (1.13)
h ? ? ? +(1 ? s)E [Jh (y , s , e )/y, s, e]]
20
l Jll (y, s, e) = yal l ? wl (y, s, e) +
1 [sE [Vl (y ? , s? , e? )/y, s, e] (1 + r ) (1.14)
(1 ? s)E [Jll (y ? , s? , e? )/y, s, e]] Finally, the value to a low-skill ?rm with a high-skilled worker is
h Jlh (y, s, e) = yal l ? wl (y, s, e) +
1 [sE [Vl (y ?, s? , e? )/y, s, e] (1 + r )
+(1 ? s)E [Jlh (y ?, s? , e? )/y, s, e] ?(1 ? s)(1 ? ? )m(?)E [(Jlh (y ?, s? , e? ) ? Vl (y ?, s? , e? ))/y, s, e]] (1.15) where the last term represents the reduction in the value to the ?rm of hiring a high-skilled worker, as the latter searches on the job and thus will quit as soon as a high-skill job arrives.
1.3.5 Surpluses and Zero Pro?t Conditions
Using the Nash bargaining condition given by equation (1.2) and the asset value equations described above we can write the surplus functions as follows: Sll (y, s, e) = yal l ?b+ 1 [(1 ? s)E [Sll (y ?, s? , e? )/y, s, e] (1 + r ) (1.16)
???m(?)E [Sll (y ? , s? , e? )/y, s, e]
h Sh (y, s, e) = yah h?b+
1 h ? ? ? [(1 ? s)E [Sh (y , s , e )/y, s, e] (1 + r )
h ? ? ? ?? (1 ? ? )m(?))E [Sh (y , s , e )/y, s, e]
???m(?)E [Slh (y ?, s? , e? )/y, s, e]]
(1.17)
21
Slh (y, s, e) = yal l?b+
1 [(1 ? s)E [Slh (y ?, s? , e? )/y, s, e] (1 + r )
h ? ? ? +(1 ? s)(1 ? ? )m(?)E [(?Sh (y , s , e ) ? Slh (y ? , s? , e? ))/y, s, e]
???m(?)E [Slh (y ?, s? , e? )/y, s, e]
h ? ? ? ?? (1 ? ? )m(?)E [Sh (y , s , e )/y, s, e]]
(1.18)
The surplus of a low-skill job ?lled by a low-skilled worker Sll , takes the standard form: the ?rst term, gives the net ?ow of output the match generates; given that the match survives to the next period with a probability (1 ? s), the second term gives the expected present value of future surplus; the last term re?ects the workers’ forgone search opportunity (i.e., their ability to search for a job) while employed, and is subtracted from the surplus.
h The surplus of a ?lled high-skill job Sh , takes a similar form. The only dif-
ference is that once high-skilled workers ?nd a job, they lose their opportunity to search for both high- and low-skill job jobs once employed. Hence, the surplus function changes accordingly. The surplus of a low-skill-job ?lled by a high-skill worker Slh , takes a slightly di?erent form. When high-skilled workers take low-skill jobs, they can still search for high-skill jobs. The value of this option is added to the surplus and is given by the third term in the equation (1.18). Given that the match survives to the next period with a probability (1 ? s), mismatched workers search on the job and with probability (1 ? ? )m (?) ?nd high-skill jobs, in which case they
h ? ? ? gain a share ? of E [Sh (y , s , e )/y, s, e] while losing E [Slh (y ? , s? , e? )/y, s, e].
After substituting the surplus expressions into the values of vacancies, given
22
by equations (1.11) and (1.12), I de?ne the following free entry conditions: c = (1 ? ? )q (?) ??ESll (y ?, s? , e? ) + ? (1 ? ?)ESlh (y ? , s? , e? ) (1 + r ) (1 ? ? )q (?) h ? ? ? c = (1 ? ??)ESh (y , s , e ) (1 + r ) (1.19) (1.20)
These conditions imply that ?rms keep opening vacancies until the cost of keeping a vacancy un?lled c equals the expected future pro?ts of a ?lled job. The conditions implicitly de?ne ?y,s,e and ?y,s,e as a function of the current aggregate state (y, s) and the current distribution of employment across types of matches given by e =
h l eh h , el , el .
1.3.6 Equilibrium
The equilibrium is given by a vector {?, ?, ?, ?, e} that satis?es the following: (i) the three types of matches are formed voluntarily, i.e., yaj i > b ?i, j for which matches are formed; (ii) the two free entry conditions in (1.19) and (1.20), are satis?ed so that the values of maintaining low- and high-skill vacancies are zero;
h l and (iii) the state variables eh h , el , and el follow the ?ow equations (1.3) to (1.5)
above.
1.4 Simulations
The purpose of this section is to gauge qualitatively the e?ects of business cycle ?uctuations on job competition, skill mismatches, average match productivity and unemployment rates by skill group. I consider aggregate productivity and separation
23
rate shocks separately in order to illustrate their individual e?ects and highlight their di?erences. I turn to numerical techniques to analyze the model. I use the free entry conditions given by equations (1.19) and (1.20) above to ?nd the state-contingent market tightness ?y,s,e and fraction of low-skill vacancies ?y,s,e . I then simulate the model as follows: ?rst, I generate a sequence of aggregate state (y, s) realizations; then, starting with the ?rst realization of aggregate state, and an initial distribution
h l of employment e = eh h , el , el I use the laws of motion given by equations (1.3) to
(1.5) to compute the new distribution of employment at the beginning of the next period; and then I repeat. At the end of each period, I record the aggregate state and employment distribution and generate series of unemployment rates and labor productivity along a sequence of aggregate state realizations. The exogenous variables are set at the following values: ? = .5, r = .03,
l c = .5, b = .1, ? = .75, ah h = .8 and al = .45. The matching function m [·, ·] is
a Cobb Douglas function in which job seekers and vacancies are assumed to have equal elasticities of 0.5. In section 1.5.1, where I examine the e?ects of an aggregate productivity shock, I normalize the high value of aggregate productivity to y1 = 1 and set the low value equal to y0 = .9, while keeping the separation rate ?xed at s = .1. In section 1.5.2, I keep aggregate productivity at its high level and let the separation rate ?uctuate between s1 = .1 and s0 = .11. For the purpose of solving the free entry conditions to determine the state-contingent ?y,s,e and ?y,s,e , the stochastic variable in each case follows a Markov process, with a transition probability .3. To compute impulse responses to each shock, I simulate the model 24
assuming that once the shock arrives it follows a sample path in which it persists for 20 periods, although the agents believe that the shock persists only with probability 0.3 each period. Since the purpose of this section is to illustrate qualitative implications the parameters have been chosen in a rather ad hoc manner. However, the results presented in this section are robust to changes in the underlying parameter con?guration.
1.4.1 Aggregate Productivity Fluctuations
In this section, I simulate the model allowing for aggregate productivity ?uctuations. As already mentioned, the heart of the model is the skill composition of vacancies. Hence, I begin this section by characterizing the evolution of this skill composition. As we can see from Figure 1.1, the immediate e?ect of a negative productivity shock is to lower the fraction of low-skill vacancies (? ).
Figure 1.1: E?ect of a Negative Productivity Shock on the Fraction of Low-skill Vacancies.
Over time, the initial decline is gradually partially reversed. The reason for 25
the partial recovery is the increase in the fraction of low-skilled unemployed in the mass of jobs seekers immediately after the shock. In response to the increase in the fraction of high-skill vacancies following the fall in productivity, the fraction of unemployed low-skilled workers in the mass of job seekers increases, while the corresponding fraction of high-skilled (both unemployed and mismatched) workers decreases. These are illustrated in Figures 1.2 and 1.3, respectively. Firms with low-skill vacancies bene?t from the increased fraction of low-skilled workers in the pool of searchers, because low-skilled workers do not search on the job and thus provide more surplus than mismatched high-skilled workers. Thus, the change in the skill composition of job seekers stimulates low-skill vacancy creation so that the fraction of low-skill vacancies partially recovers from the initial decline.
Figure 1.2: E?ect of a Negative Productivity Shock on the Fraction of Low-skilled Workers in the Mass of Job Seekers.
The conventional result that periods of low productivity hurt the matching process is present in this model as well. This takes the standard form of a lower vacancy-job seeker ratio ? and thus a lower meeting rate m (?) during downturns. As can be veri?ed in Figure 1.4, the meeting rate follows a pattern similar to the
26
Figure 1.3: E?ect of a Negative Productivity Shock on the Fraction of High-skilled Workers in the Mass of Job Seekers. fraction of low-skill vacancies and for similar reasons: vacancy creation falls initially due to lower productivity and surplus, then gradually rises, as rising unemployment increases the worker arrival rate.
Figure 1.4: E?ect of a Negative Productivity Shock on the Worker-Vacancy Meeting Rate.
Although the model delivers the conventional result of a lower vacancy-job seeker ratio (?) during downturns, it does not replicate Barlevy’s (2002) result that recessions sti?e the transition of mismatched workers into the jobs they are best suited for, and therefore increase the degree of skill-mismatch in the market. Instead, 27
the model suggests that economic slowdowns generate a reduction in the number of mismatched high-skilled workers.
Figure 1.5: E?ect of a Negative Productivity Shock on the Probability of Finding a High-Skill Job.
Figure 1.6: E?ect of a Negative Productivity Shock on the Probability of Finding a Low-Skill Job. The key to this novel result is the VCE described above, namely that periods of low productivity involve an upgrading in the skill composition of vacancies (i.e. an increase in (1 ? ? )). More precisely, the VCE dominates the reduction in the meeting rate, so that the probability of ?nding a high-skill job (1 ? ? ) m (?) increases, while the probability of ?nding a low-skill job ?m (?) decreases. The paths 28
of these probabilities are illustrated in Figures 1.5 and 1.6, respectively. As soon as the shock arrives, the former increases, while the latter decreases, hindering the transition of unemployed high-skilled workers into low-skill jobs and facilitating the transition of both unemployed and mismatched high-skilled workers into high-skill jobs. Later on, these probabilities partially revert towards their initial values, re?ecting the gradual recovery in the fraction of low-skill vacancies as ?rms try to take advantage of the higher arrival rate of low-skilled job seekers.
Figure 1.7: E?ect of a Negative Productivity Shock on Average Match Productivity.
As illustrated in Figure 1.7, these changes in probabilities that occur during periods of low productivity shift the mass of the distribution of high-skilled workers towards high-skill jobs and therefore increase average match productivity (i.e. the average of aj i across all matches). This result is in line with previous work that argues that recessions should promote allocative e?ciency (e.g. Hall 1991, 2000; Mortensen and Pissarides 1994; Caballero and Hammour 1994, 1996; and Gomes, Greenwood, and Rebelo 1999), but rests on a di?erent mechanism: an upgrading in the skill composition of vacancies facilitates the transition of overquali?ed workers into the jobs for which they are best suited. This mechanism is new in the theo29
retical literature on business cycles and worker reallocation, because it results from asymmetries in the matching rates of di?erent skill groups that have been neglected in previous research. The notion that the lower meeting rate m (?) during recessions sti?es the transition of mismatched workers into the jobs they are best suited for has been labeled by Barlevy (2002) as the “sullying” e?ect of recessions. However, the “sullying” e?ect rests on the assumption of symmetry. To be more speci?c, Barlevy (2002) focuses only on equilibria in which the production technology is symmetric, the skill composition of the labor force is symmetric and ?rms create equal amounts of each type of vacancy.10 Under these assumptions, neither the distribution of workers across match quality and unemployment nor the number of vacancies posted varies with skill type. Moreover, this type of framework implies that all workers are equally likely to form a match of any given quality. Hence, such framework leaves no room for search externalities and spillover e?ects across skill groups. Given that by assumption in equilibrium ?rms create equal amounts of each type of vacancy, the VCE that arises in my model during periods of low productivity is not present in Barlevy’s model. The only e?ect of recessions in Barlevy is the lower meeting rate that impedes mismatched workers from reallocating into more e?cient uses. I next characterize the evolution of unemployment rates across skill groups.
10
According to the production technology assumed in Barlevy the productivity of a match de-
pends negatively on the distance between the worker’s and job’s skill level. However, an underquali?ed worker is as productive as an over-quali?ed worker on a particular job, as long as the distance between the worker-job skill level is the same.
30
Figure 1.8: E?ect of a Negative Productivity Shock on Unemployment and Mismatch Rates. As mentioned in the introduction, the low-skilled unemployment rate is higher and more sensitive to changes in economic activity than the high-skilled unemployment rate. The model con?rms this observation. Figure 1.8 illustrates the evolution of unemployment rates of the two skill groups and the evolution of the mismatch rate (de?ned as the fraction of high-skilled workers who are mismatched). Independent of the level of aggregate productivity, the low-skill unemployment rate is higher than the high-skilled one, because high-skilled workers qualify for both types of jobs and thus can ?nd a job more easily. When aggregate productivity falls, mismatch in the form of high-skilled workers taking low-skill jobs declines, yet the low-skilled
31
unemployment rate still rises more than the high-skilled unemployment rate. The latter converges to a level only 0.2 percentage points higher than the original, while the former converges to a level 0.6 percentage points higher than the original. The explanation I o?er for the higher sensitivity of the low-skilled unemployment rate to changes in economic activity is conceptually simple but contrary to the common belief that high-skilled workers “crowd-out” low-skilled workers in a competition for jobs.11 As illustrated above, periods of low aggregate productivity involve less job competition and fewer high-skilled workers taking low-skilled jobs. Instead, the model suggests that high-skilled employability is less sensitive to changes in economic
11
Among the studies that investigate the implications of job competition externalities on low-
skilled employability, only Gautier (2002) looks at the steady-state e?ects of changes in aggregate productivity. He con?rms that low-skilled unemployment rises more than high-skilled unemployment when aggregate productivity falls, but suggests that this is due to high-skilled workers crowding out low-skilled workers. This result, however, rests on two assumptions. First he assumes that unemployment bene?ts are a ?xed fraction of workers’ productivity. Therefore, changes in economic activity do not alter the relative net productivities of high- and low-skill jobs, leaving the skill composition of vacancies unchanged. Second, he assumes that search is directed. Directed search implies that changes in the skill mix of vacancies do not a?ect workers probability of ?nding a job. Consequently, under directed search the VCE is no longer relevant. The only e?ect captured in Gautiers model is that high-skilled workers’ exert a negative externality on low-skill job profitability because of their higher quit probability (NQE), so that when unemployment is higher and high-skilled workers’ take low-skill jobs more frequently, low-skill vacancy creation declines. The validity of this result depends on the extend to which changes in the skill composition of vacancies do not a?ect workers’ probabilities of ?nding a particular type of job.
32
activity because high-skilled workers can be employed in a wider range of job types and thus can more easily bu?er against unfavorable changes in the skill composition of vacancies. High-skilled workers qualify for both types of jobs, which implies an e?ective unemployment-to-employment probability for high-skilled workers equal to m(?), which depends only on market tightness (?). Low-skilled workers, on the other hand, qualify for only low-skill jobs. Therefore, their e?ective matching rate is ?m (?) and ?uctuates both with changes in market tightness and changes in the skill composition of vacancies. As a result, during periods of low productivity, lowskilled workers su?er both the consequences of a more sluggish labor market (lower ?) and skill upgrading in vacancy mix (lower ? ), whereas high-skilled workers su?er only the consequences of the former. The reduction in the fraction of high-skilled job seekers (both unemployed and mismatched) implies a lower NCE and NQE on low-skilled employability. Given that there are relatively fewer high-skilled job seekers low-skill vacancies are more likely to encounter a low- than a high-skilled job seeker, and low-skilled workers su?er lower congestion from high-skilled workers. However, low-skill unemployment still rises more in response to the fall in productivity, indicating that the VCE dominates. Hence, what is hidden behind the higher sensitivity of low-skilled unemployment is not job competition externalities but the change in the skill composition of vacancies. The ?nding that an upgrading in the skill composition of vacancies facilitates a more e?cient allocation and improves average match productivity following a decline in aggregate productivity, does not square with empirical ?ndings that match quality is procyclical. As will be explained in the next section, however, the model performs 33
better along this dimension when periods of low productivity are driven by shocks to the separation rate and thus a high ?ow of workers into unemployment. Before I proceed with characterizing the dynamic response to a separation rate shock, I discuss the robustness of the results presented so far to changes in the parameter con?guration. The results are not sensitive to changes in the relative productivity of high- and low-skilled jobs or changes in the magnitude of the shock. A smaller productivity gap between skill types results in a smaller gap between highand low-skilled unemployment rates, while larger shocks result in higher dispersion between high- and low-skilled unemployment rates. However, the implications of changes in aggregate productivity for unemployment and mismatch rates remain the same. I also examined changes in the skill composition of the labor force.12 I ?nd that the relevant variables follow the patterns described above independent of the skill composition of the labor force.
1.4.2 Job Separation Fluctuations
In this section, I keep aggregate productivity ?xed and allow the job separation rate to ?uctuate over time. As illustrated in Figure 1.9, on impact of a negative separation rate shock, the fraction of low-skill vacancies increases as ?rms take advantage of the increase in their relative pro?tability. Over time, the fraction of
12
This exercise was motivated by the work of Pierard and Sneezes (2003) and Dolado et al. (2003)
that suggests the uneven increase in low-skilled unemployment, may be the result of an increase in the fraction of high-skilled workers in the labor force, which exacerbates job competition and crowding out of low-skilled workers.
34
low-skill vacancies gradually decreases, but remains higher than the original level.
Figure 1.9: E?ect of a Separation Rate Shock on the Fraction of Low-Skill Vacancies. The gradual reversion is due to intensi?ed negative quit externalities following the initial increase, which reduce low-skill job pro?tability and thus vacancy creation. The sharp initial increase in the fraction of low-skill vacancies, together with the sharp increase in high-skilled unemployment due to the separation rate shock, facilitate the transition of high-skilled workers into low-skill jobs while sti?ing transitions out of them, exacerbating negative quit externalities on low-skill job pro?tability. Figure 1.10 shows the evolution of the fraction of high-skilled job seekers (both unemployed and mismatched), which re?ects the evolution of negative job competition externalities (NCE and NQE) on low-skilled employability. On impact, the fraction declines, re?ecting the sharp increase in unemployment. Subsequently the fraction increases as more high-skilled workers move into low-skilled jobs. In turn, the rise in NCE and NQE results in a gradual reduction in the fraction of low-skill vacancies. To clarify this further, I report the evolution of probabilities of ?nding a highand a low-skill job in Figures 1.11 and 1.12, respectively. On impact of the shock, the 35
Figure 1.10: E?ect of a Separation Rate Shock on the Fraction of High-skilled Job Seekers. ?rst decreases while the latter increases. Therefore, a higher mass of high-skilled workers is misallocated into low-skill jobs, while the lower probability of ?nding high-skill jobs implies that they remain overquali?ed for a longer period. Over time the resulting negative job competition externalities lower the probability of ?nding a low-skill job, while increasing the probability of ?nding a high-skill job.
Figure 1.11: E?ect of a Separation Rate Shock on the Probability of Finding a High-skill Job.
Given these changes in job probabilities in response to the increase in job separation, the model suggests that a higher degree of over-quali?cation during recessions is the result of an increase in job separation and ?ow of workers into unemployment. 36
Figure 1.12: E?ect of a Separation Rate Shock on the Probability of Finding a Low-skill Job. If indeed recessions are characterized by sharp increases in job separation then the model can explain the observed procyclicality in match quality. As can be veri?ed from Figure 1.13, in response to the separation rate shock, average match productivity decreases gradually, as more high-skilled workers become overquali?ed, and converges to a lower level.
Figure 1.13: E?ect of a Separation Rate Shock on Average Match Productivity.
The question that remains is whether separation rate ?uctuations can also explain higher and more volatile low-skilled relative to high-skilled unemployment. One would expect that the shift in the vacancy mix towards low-skill vacancies in
37
response to the shock, and the resulting higher probability of ?nding a low-skill job, would improve the position of low-skilled workers relative to high-skilled workers in the labor market. However, this is not the case. The shift in the vacancy mix exerts a positive VCE on low-skilled employability, but at the cost of the strong negative job competition externalities that follow. The evolution of unemployment and mismatch is illustrated in Figure 1.14. Both unemployment rates increase in response to the shock, but the low-skilled unemployment rate continues to increase even further as the mismatch rate increases. Eventually, the low-skilled unemployment rate converges to a level 1.6 percentage points above the original, while the high-skilled unemployment rate converges to a level only 1.2 percentage points above the original. As in the case of a negative productivity shock, the impact of a separation rate shock on unemployment and mismatch rates is not qualitatively sensitive to changes in parameters such as the relative productivity of high-skilled workers or the skill composition of the labor force. What drives the evolution of mismatch and unemployment rates in response to the separation rate shock is the increase in the fraction of low-skill vacancies, following the increase in the relative pro?tability of low-skill jobs. In turn, the increase in the relative pro?tability of low-skill jobs rests solely on the fact that low-skill vacancies can be re-?lled faster once dissolved, because they can be ?lled by both types of workers. This advantage is never reversed, no matter the skill-composition of labor force or the productivity dispersion between high- and low-skill jobs. I close this section by discussing the impact of job competition externalities 38
Figure 1.14: E?ect of a Separation Rate Shock on Unemployment and Mismatch Rates. on low-skilled employability. Unquestionably, the negative externalities arising from intensi?ed job competition for low-skill jobs in response to the job separation shock harm low-skilled employability. However, the job competition externalities are not the only driving force behind the relatively higher sensitivity of low-skilled unemployment to cyclical ?uctuations. The changes in the skill mix of vacancies that occur over the business cycle are also important, as low-skilled workers are more vulnerable to these changes than high-skilled workers. In response to a negative productivity shock, job competition externalities decline, but still low-skilled unemployment rises relatively more, because of the skill upgrading in the skill composition 39
of vacancies that hurts low-skilled employability. On the other hand, a negative separation rate shock exacerbates the negative job competition externalities on low-skill employability, but only because low-skill vacancies become relatively more plentiful. Hence, regardless of the e?ect of the co-movement between aggregate productivity and job separation on competition for low-skill jobs, recessions hurt low-skilled employability relatively more.13
1.5 Conclusion
In this paper I develop a model that examines the impact of skill-mismatch, in the form of high-skilled workers taking temporarily low-skill jobs, on labor productivity and unemployment dynamics by skill. I capture negative job competition
13
Job competition may actually bene?t low-skilled employability by stimulating low-skill vacancy
creation. I simulated the model assuming that searching on the job is costly enough that highskilled workers are no longer willing to take low-skill jobs (i.e., separate markets). I found that unemployment for both types is higher when markets are separated than when cross-skill matching takes place. The high-skilled unemployment rate is higher in the absence of cross-skill matching for the obvious reason: given that they cannot take low-skill jobs they have a harder time escaping unemployment. What is somewhat surprising is that low-skilled unemployment is higher, but the explanation is also reasonable: when high-skilled workers are not willing to take low-skill jobs, the value of opening a low-skill vacancy is lower, as the option value of hiring a high-skilled worker is forgone, resulting in lower vacancy creation and higher unemployment in the low-skill market. This explanation does not contradict my previous argument that ?rms with low-skill vacancies prefer hiring low- instead of high-skilled workers. The intuition is that low-skill ?rms prefer hiring low- to high-skilled workers because the latter are likely to quit, but they are still better o? having the option of hiring a high-skilled worker in case they meet one.
40
externalities on low-skilled employability, by incorporating into the model the fact that low-skilled workers qualify only for jobs with low skill requirements. Previous work has argued that recessions hurt the matching process as ?rms post fewer vacancies per job seeker. As a result, mismatched workers who search onthe-job for better matches remain mismatched for a longer period, aggravating the allocation of workers into mediocre matches. However, as this paper illustrates, this is not the whole story. Recessions also involve an increase in the relative number of high-skill vacancies that facilitates the transition of high-skilled workers into highskill jobs, thus bringing down the degree of over-quali?cation in the labor market. Accounting for the asymmetric nature of the matching technology, and the resulting job competition externalities, shows that recessions involve a higher degree of overquali?cation only when associated with higher job turnover and ?ow of workers into unemployment. Hence, my model provides insights into skill-mismatch over the cycle that stress the role of increases in job separation when aggregate productivity is low. Further, my model explains observed di?erences in labor market outcomes of di?erent skill cohorts. The asymmetry explains the relatively low exit rates of lowskilled workers from unemployment, and their relatively low propensity to search on the job. My model can also explain why low-skilled unemployment exhibits relatively higher cyclical sensitivity. The common belief is that, during recessions, high-skilled workers “crowd-out” low-skilled workers as they compete for jobs. However, in this paper I illustrate that the higher sensitivity of low-skill unemployment to changes in economic activity is not due to crowding out per se. Instead, the primary reason is that high-skilled workers qualify for both high- and low-skill jobs, and therefore 41
are less vulnerable to changes in economic activity, because they are less vulnerable to the changes in the skill mix of vacancies that occur simultaneously. By highlighting the vacancy composition e?ect of recessions, which has been overlooked in previous research, my model improves our understanding of how recessions a?ect the matching process and the employability of di?erent skill cohorts, and suggests a closer look at the evolution of the skill mix of vacancies. In addition, by laying out the e?ects of aggregate productivity and job separation on the skill composition of vacancies, I stress the importance of understanding the relation between the two impulses. Modeling endogenous responses of the separation rate to changes in aggregate labor productivity as in Mortensen and Pissarides (1994), for instance, is therefore, the natural extension of the model. The nature of the model in this paper requires the endogenous variables to depend on the aggregate state and also on the distribution of workers across types of matches. Therefore, introducing aggregate productivity ?uctuations alone is a signi?cant contribution and makes the task of endogenizing job separation much more plausible. Future research will build upon this contribution by endogenizing separations.
42
Chapter 2 Cyclical Variation in Match Quality: The Role of Unemployment Risk 2.1 Introduction
Studies show that the unemployment rate of low-skilled workers is higher and more sensitive to changes in economic activity compared to that of high-skilled workers.1 Some have suggested that this may in part be caused by “crowding out”, i.e. the phenomenon in which high-skilled workers occupy simple jobs during recessions, thereby pushing low-skilled workers into unemployment, and move on to better jobs in booms.2 Existing research has not yielded clear conclusions about the empirical relevance of such a cyclical pattern in the matching behavior of high-skilled workers. Hence, its empirical relevance remains a question, the answer of which forms the basic goal of this chapter. To this end, I study the mismatch rates and job level dynamics using a panel of 15748 individuals constructed from the yearly family ?les of the Panel Study of
1
For evidence on the cyclicality of low-skilled unemployment rate, see for example, van Ours
and Ridder (1995). For evidence on the distribution of jobless time and unemployment being heavily concentrated among the least skilled individuals see e.g. Topel (1993); Bovengerg (1997) Ashenfelter and Ham (1979); Nickell (1979).
2
See e.g., and Teulings and Koopmanschap (1989).
43
Income Dynamics (PSID), which covers the years from 1968 to 1993.3 By job levels I refer to categories of occupations that di?er in terms of skill requirements and prestige (i.e., high job levels are jobs that require more education and have higher prestige scores than low job levels). First, to give a general idea of the cyclical patterns in match quality across di?erent skill groups, I look at how mismatch rates vary over the business cycles and across workers with di?erent education. Second, I use linear probability and Logit regression analysis to characterize how the probability of moving either to high- or low-skill jobs is a?ected by the overall unemployment rate and the education of the worker. Third, by adopting dynamic panel data estimation methods, I measure the e?ect of the workers’ lagged state (i.e., whether unemployed or mismatched), as well as the e?ect of its interactions with overall the overall unemployment rate and workers’ education level, on the probability of transitions to either high- or low-job levels. Finally, by modeling the dynamics of transitions as a ?rst order Markov process, which is heterogeneous among individuals I investigate how workers’ transitions between job levels vary with skill and over the business cycle. To characterize the transitions, I adopt a ?xed e?ects multinomial Logit estimation procedure designed by Honor´ e and Kyriazidou (2000), which is based on conditional likelihood maximization (Chamberlain, 1984).
3
Existing studies test for crowding out phenomena mainly in Europe. In the U.S. crowding out
as an explanation for the high and more cyclical low-skill unemployment received less attention. To my knowledge, this is the ?rst study that tests for crowding out phenomena using data from the U.S.
44
The comparison of job level probabilities across groups of workers with di?erent education years of high employment growth to those of low employment growth is a common methods of testing for cyclical variation in match quality. Such a comparison reveals whether workers with a given level of education achieve lower job levels in years with low employment growth, as the crowding out hypothesis assumes. Examples are Gautier, Pomp and Zijl (1997), and Gautier (1998) who separate workers into educational levels and estimate multinomial Logit models (one for each level of education). Empirical tests also compare educational levels per job level. Teulings and Koopmanschap (1989), for example, explain regional changes in the distribution of educational levels per job level, using regional changes in unemployment rates. In a similar analysis, Hartog (1992) uses survey answers to questions regarding labor market tightness of the form: do people with your education, skills and age, in your area, easily ?nd a job to match this? Others test the crowding out hypothesis by looking at the ?ows of ?lled vacancies. For example, van Ours and Ridder (1995) test whether lower stock of vacancies and higher number of unemployed job seekers at the beginning of the period, leads to higher ?ow of ?lled vacancies at lower levels. Their test of crowding out also involves estimating whether the correlation between the unemployment rate of higher educated workers and the ?ow of ?lled vacancies at lower job levels is positive and signi?cant. There are considerations, however, as to whether the empirical methodologies described above are accounting for the cause of the cyclical variation in match quality if such phenomenon exists. Higher probabilities, higher fractions of high45
skilled workers, or higher ?ows of ?lled vacancies, at low job levels when employment growth is low, do not necessarily imply that the risk of unemployment induces workers to accept jobs below their skill level, as they can also be due to other reasons. For example, changes in the hiring and ?ring policies of ?rms (i.e., ?rms require more schooling at given job complexity during bad times), or higher turnover rates of low-skilled can also produce similar patterns.4 Similarly, the opposite ?ndings do not necessarily reject the existence of over-quali?cation. High-skilled workers may accept low-skill jobs to avoid the distress of being unemployed, but higher overall unemployment may not have the same e?ect on the behavior of high-skilled workers. In order to account for this limitation, the main innovation of my empirical methodology is that it allows for job level probabilities to vary not only with overall economics activity, but with the workers’ lagged state. In particular, I adopt dynamic panel data estimation methods, in which the worker’s lagged state enters the model as an explanatory variable. By controlling for the lagged state I capture some
4
Other explanations include skill-biased technological change, minimum wages, search frictions
in combination with higher turnover rates of low-skilled workers, and incentive structures (e.g. high replacement rates, high reservation wages) that induce low-skilled workers to search less e?ectively. To my knowledge the only study that takes some of these considerations into account is Gautier et al. (2002). Unlike the studies mentioned above, which restrict crowding out to be an in?ow phenomenon only, they allow for changes in the educational attainment per job level to be the result of a combination of in?ow and out?ow policies at the ?rm level. Hence, they observe whether upgrading at given job levels is associated with the out?ow of relatively low educated workers or the in?ow of relatively high educated workers. Nevertheless, this methodology does not distinguish crowding out from the rest of the possible explanations.
46
propensity to experience a certain job level, which has been previously unmeasured by focusing only on how overall economic conditions a?ect job level probabilities.5 In particular, I am able to address whether unemployed high-skilled workers are more likely to move into low job levels, while mismatched workers are more likely to move into higher job levels when economic conditions improve. Although existing studies reach mixed conclusions regarding the empirical relevance of cyclical variation in match quality of high-skilled workers, I ?nd evidence highly suggestive of it. The mismatch rate of college graduates is higher and exhibits higher cyclical variation than the mismatch rate of workers without a college degree. Moreover, I ?nd that in periods of high unemployment rate, the high-joblevel probability of college graduates is lower, while the low-job-level probability is higher. The results of the dynamic panel data regression analysis show that when the origin state is unemployment, workers with a college degree are more likely to move into low-job-levels when the overall unemployment rate is high. Moreover, the results point to the existence of an upgrading in the job levels of mismatched college graduates when the unemployment rate is low. Consistent with the crowding out hypothesis, the estimates of the Markov
5
In a similar spirit, Teulings (1993) also accounts directly for the role of the risk of unemploy-
ment plays on job level transitions. He follows a di?erent estimation procedure than the studies described above. On the basis of a number of job characteristics he ranks jobs from the most desirable to the least desirable and estimates whether higher expected search duration decreases the probability of ?nding an attractive job. His results con?rm that this indeed the case, suggesting crowding out, but Teulings admits that other explanations may also be consistent with his ?ndings.
47
Chain Multinomial Logit model of job level transitions suggest that the odds of moving to a lower job level, as opposed to a higher job level, are larger when the lagged state is unemployment and vice versa. Moreover, I ?nd that the negative impact of higher unemployment rate on each job level probability declines with education and more evidently for “mediocre” job levels. Thus, I conclude that workers of higher education are more likely to accept jobs below their skill level than become unemployed. The rest of the chapter is organized as follows. In section 2.2, I describe the data set. Following this, in section 2.3, by grouping occupations into categories using prestige scores and information on educational attainment, I show how mismatch rates vary over the business cycle and across di?erent education groups. Sections 2.4 to 2.6, describe the empirical models, estimation methodologies, and results. Finally, in section 2.7, I conclude this chapter with some remarks.
2.2 Data
Each year the Panel Study of Income Dynamics (PSID) asks the head of each family participating in the study to report his/her employment status, i.e. whether unemployed, employed or out of the labor force and their occupation. Occupations are reported using the 3-digits code from 1970 Census of Population. I use the PSID family ?les to construct an unbalanced panel of 15748 heads who have been in the labor force for at least one year. The panel covers the years from 1968 to 1993. I consider individuals who report being students, retired, or keeping a house, to be
48
out of the labor force. Since I am only interested in analyzing movements across occupational categories and unemployment, I am not considering transitions in and out of the labor force. Hence, these transitions are excluded from the sample. Responders also report their years of schooling, which can be used as proxy for their skill level. A better approximation of skill would be a combination of education and work experience. Unfortunately, the questions regarding experience and job training asked in the PSID vary from year to year. I can only use both education and work experience as a proxy for workers’ skill level, if I concentrate on a smaller subperiod, in which case, the sample size declines considerably. To capture the e?ect of aggregate economic activity on job level transitions, I use the yearly average unemployment rate as a time varying covariate in the estimation procedures. I construct the time series of yearly average unemployment rates, using the seasonally adjusted monthly unemployment rates for the years 1968 to 1993, available from the Current Population Survey (CPS). I separate occupations into categories (job levels) based on the Hodge-SiegelRossi (HSR) prestige scores, which are conveniently assigned to the 3-digit U.S Census of Population classi?cation.6 Table A.1 in Appendix A gives a detailed description of the scores.
6
One could argue that the use of the term “job level” is misleading, because I am essentially
referring to occupation and not job categories. It may be the case that workers with the same occupation perform jobs or tasks of di?erent complexity. Hence, there may be variation in skill requirements within occupations. The reason I am using occupation and not job categories is simply the lack of such information.
49
The problem with prestige scores is that they do not necessarily measure the complexity of the jobs or the skill level required to do the job. Ideally, occupations would be categorized based on their skill requirements rather than their socioeconomic status. Such a ranking could be constructed by measuring workers’ quali?cation in each occupation. However, the PSID is a relatively small data set and the number of workers within each occupation is sometimes too small to obtain accurate estimates of skill requirements.7 Although no information regarding educational attainment was used to derive these scores, this caveat is partly surpassed by the fact that the scores are highly correlated with the level of educational attainment of the workers in each occupation. Occupations with high prestige scores are occupations that employ workers with high levels of education. Table 2.1 illustrates the resulting job levels using prestige scores. Some additional descriptive statistics of are in Table 2.2. On average, 5% of the individuals is unemployed and the majority of employed individuals is found in job levels 1 and 2. Only 14% of the employed is found in the lowest job level and only 4% in the highest.
2.3 Mismatch Rates Over the Business Cycle
The hypothesis discussed in the introduction, and investigated theoretically in the ?rst chapter of my thesis, is that mismatch rates increase during recessions
7
An alternative methodology would be to rank occupations into skill categories using residual
wages. I could regress real wages on education, experience, and other individual characteristics like and create a ranking based on the average residual wage of workers in each occupation.
50
when there is greater congestion in the labor market, and especially among the more educated who are quali?ed for a greater variety of jobs. Here I test this hypothesis by looking at how mismatch rates vary over the business cycles and across workers with di?erent education. As already mentioned, in the absence of information on the skill requirements of each occupation, I group occupations as low-skill and high-skill based on educational attainment and prestige scores. First, I consider as high-skill, occupations with prestige score 37 and above, and low-skill occupations with prestige score below 37. Based on this cuto? point, on average, 90% of college graduates in each year are in high-skill occupations. Then, I consider a lower prestige score cuto? point, 21, which results in an average of 95% of college graduates being in high-skill occupations each year. The lower the prestige score cuto? point that divides occupations between high- and low-skill, the higher the “degree” of mismatch of college graduates who happen to be in low-skill occupations. Figure 2.1 shows the fraction of mismatched college graduates (i.e., in lowskill occupations) using the 90% cuto? prestige point. There is an obvious upward trend. This may re?ect the introduction of new technologies so that traditionally simple or “low-specialization” tasks now require more knowledge and training. We also observe cyclical variation in the fraction of mismatched workers. There was a recession starting at the end of 1973 and ending at the beginning of 1975. As we can see from the graph, the mismatch rate increases in 74. From 1980 to 1982, there were two recessions, one shorter, beginning in 1980 and ending half year later, and one beginning in the middle of 1981 until the end of 1982. The mismatch rate obviously 51
9.8 8.8 7.8 6.8 5.8 4.8 69 71 73 75 77 79 81 83 85 87 89 91 93
Year
Figure 2.1: Mismatch Rate of College Graduates (90% cuto? point) increases during that period. It decreases in subsequent years and increases again in the years 90 and 91 re?ecting the July 90-March 91 recession. As expected, when a lower cuto? prestige score is used the mismatch rate is lower. Figure 2.2 shows the fraction of workers with a college degree that are in jobs below the 95% percent cuto? prestige score. Both the upward trend and the relationship between business cycles and the mismatch rate are less clear in this case, but we still observe an increase in the mismatch rate around the years 74, 80 to 82 and 91. The main assumption of the model in the ?rst chapter of my thesis, upon which the crowding out hypothesis rests, is that there is asymmetric matching: while highskilled workers can be employed in both high- and low-skill jobs, low-skilled workers 52
1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 69 71 73 75 77 79 81
Year
83
85
87
89
91
93
Figure 2.2: Mismatch Rate of College Graduates (95% cuto? point) do not qualify for high-skill jobs. This is a realistic assumption given that in reality jobs have minimum skill requirements that some workers satisfy, but some others do not. However, asymmetric matching does not automatically imply that mismatch rates increase with education as possible “scarring” e?ects or career considerations may prevent high-skilled workers from taking low-skill jobs. If this was the case, then we should observe similar levels and patterns in the mismatch rates across workers with di?erent education. To test this, I compare the mismatch rates of workers with a college degree to those without a college degree. I measure the mismatch rates of workers without college degree in a similar fashion. I ?nd the cuto? prestige score that implies on average 90% of workers without a college degree each year are in occupations 53
10 9 8 7 6 5 4 3 2 1 69 71 73 75 77 79 81 83 85 87 89 91 93 College Degree No College Degree
Figure 2.3: Mismatch Rates by Education (90% prestige cuto? point) above the cuto? prestige point. The mismatch rates for the 90% cuto? prestige score for workers with and without a college degree, respectively are in Figure 2.3. The mismatch rate of workers without a college degree is much lower overall and relatively constant over time. One the other hand, the mismatch rate of college graduates is much higher, has an upward trend and exhibits cyclical variation. If high-skilled workers are eligible for more types of jobs and hence, as shown above are more likely to mismatch during recessions, the question that follows naturally is whether the fraction of unemployed workers decreases with education and exhibits more cyclical variation. Is it the case that high-skilled workers, as opposed to low-skilled workers, mismatch and search on the job instead of staying or becoming unemployed during recessions? Figure 2.4 shows the fraction of workers with 54
14 12 10 8 6 4 2 0 69 71 73 75 77 79 81 83 85 87 89 91 93 College Degree No College Degree
Figure 2.4: Fraction of Unemployed by Education and without a college degree reporting unemployed each year. The fraction is always higher for workers without a college degree. In addition, it exhibits higher cyclical variation. While both fractions follow a similar pattern, the fraction for workers without a college degree increases more evidently in recessions (around 74-75, 80-82 and 90-91). Another interesting question that arises is whether the higher mismatch rates in recessions are due to workers moving into “stop-gap” jobs as opposed to a general type of mismatch. Stop-gap jobs are considered to be part-time jobs and temporary arrangements in low-paying industries. A more general type of mismatch occurs when workers simply lower their standards when ?nding a suitable job is di?cult, and accept jobs of slightly lower level, but not necessarily stop-gap jobs. If what 55
observed is a stop-gap phenomenon we should expect a higher fraction of mismatched workers to be concentrated in jobs with very low prestige scores.
10 9 8 7 6 5 4 3 2 1 0 69 71 73 75 77 79 81 83 85 87 89 91 93 prestige score below 21 prestige score 21-36 prestige score 37-44
Figure 2.5: Degrees of Mismatch: College Graduates
In Figure 2.5, I compare the fraction of college graduates in jobs with lower prestige scores to that in jobs with higher prestige scores. As we can see from the ?gure, the fraction of college graduates in jobs with prestige scores 37-44 is higher than the fraction in jobs with prestige scores 21-36. Moreover, the latter is higher than the fraction of college graduates in jobs with prestige score below 20. In addition, the fraction of college graduates in middle prestige category (21-36) follows the business cycle most closely (i.e., it increases in recessions and decreases in booms). This indicates that workers are mainly taking “mediocre” jobs to avoid unemployment rather than stop-gap jobs. 56
2.4 Linear Probability and Logit Models
In this section, I estimate linear probability (LP) and Logit models to characterize how the probability of moving to either high or low job levels is a?ected by the overall unemployment level and the education level of the worker. I consider as high job levels, occupations above the 90% prestige score cuto? point. Low jobs levels are occupations below this cuto? point. Moreover, throughout the analysis, I consider as high-skilled workers who hold a college degree. The model to be estimated is the following: yit = ?1 UNEi,t?1 + ?2 EDUi,t?1 + ?3 (UNE ? EDU )i,t?1 + ?it (2.1)
The latent variable yit describes the propensity to be either in high or low job levels, depending on the question of interest. The variable UNE is a dummy that takes the value of 1 when the unemployment rate is above 6%, and EDU is a dummy that takes the value of 1 when the worker has a college degree and zero otherwise. The EDU*UNE variable is an interaction term that takes the value of 1 when both the unemployment rate is high and the worker has a college degree.8 The subscript
8
I model the unemployment rate as a dummy instead of a continuous variable because it makes
it easier to interpret the marginal e?ects of the unemployment rates and its interaction with the education dummy on the probability. Moreover, in the sections that follow, I estimate dynamic models where whether the worker is mismatched or not, enters as an explanatory variable. By modeling the unemployment rate as a dummy allows me to ask what is the e?ect on the probability of high job levels when the worker is mismatched and the unemployment rate is low (i.e., is below 6%). Hence, I model the unemployment rate in the same fashion here to be able to compare the estimates. However, the reader should know that the results that follow do not change when a
57
i is for individual and t is for time. I model individual e?ects as ?xed. Hausman tests show that ?xed e?ects are more appropriate, but the results are similar in both cases.
2.4.1 The E?ect of Business Cycle and Education on High- Job-Level Probability
The results in the ?rst two columns of Table 2.3 show the marginal e?ects estimates of the LP and Logit model, respectively, when the interaction term between education and unemployment is not included in the set of regressors. As expected, education has a positive and signi?cant e?ect on the probability of high job levels. The unemployment dummy, on the other hand, has no signi?cant e?ect on the probability. However, the question of most interest is not how higher unemployment in general a?ects the probability, but whether higher unemployment reduces the probability high-skilled workers move into high job levels. To address this question we need to look at the interaction between the education and the unemployment dummy. The 3rd and 4th columns show the results when this interaction term is included. The interaction has a negative and signi?cant marginal e?ect in both cases. The LP model suggests that when overall unemployment is high the probability workers with a college degree will be in a high job level next period is approximately 1.5% lower, while the Logit model suggests that the probability is approximately
continuous variable is used.
58
5.5% lower. According to the likelihood ratio test chi-squared statistic, which is statistically signi?cant at the 5% level, the model with the interaction term is superior to the partial model. The results are consistent with the view that in periods of high unemployment high-skilled workers have a more di?culty moving into the jobs they are best suited for. Although having a college degree increases the probability of moving into high job levels, when unemployment is high, the e?ect of education on the probability is lower.
2.4.2 The E?ect of Business Cycle and Education on Low- Job-Level Probability
The results above suggest that in periods of high unemployment high-skilled workers have more di?culty moving into the jobs they are best suited for. However, this does not necessarily imply that high-skilled workers take jobs below their skill instead. It may be the case they just become or stay unemployed. To clarify this I also estimate the e?ects of overall unemployment, education and their interaction on low-job-level probability. The results are in Table 2.4. I ?nd that when the unemployment rate is high, workers with a college degree are more likely to be in low job levels next period. Having a college degree has a negative and signi?cant e?ect on the probability. The e?ect of unemployment rate, on the other hand, although quite small, is negative and signi?cant. Again, the question of interest it is whether high-skilled workers are
59
more likely to move into low job levels when the unemployment rate is high. Hence to address this question we need to look at the e?ect of the interaction between UNE and EDU. The interaction of the two has a positive and signi?cant e?ect. The negative impact of overall unemployment on the probability of moving into low-job levels is lower when the worker is high-skilled. Equivalently, the negative impact of having a college degree on low job levels probability is lower when overall unemployment is high. The LP model suggests that is approximately 2% lower, while the Logit model suggests is approximately 7% lower. Moreover, the likelihood ratio test statistic, which is statistically signi?cant at the 5% level indicates that the interacted model is superior to the model without interaction term.
2.5 Dynamic Panel Data Models
Individuals’ decisions on whether or not to accept a particular job depend not only on the overall unemployment rate and their education level, but also on their state at the time the decision is made. In this section, account for this e?ect by including workers lagged state in the set of regressors. In particular, I consider the following model: yitk = ?1 UNEi,t?1 + ?2 EDUi,t?1 + ?3 (UNE ? EDU )i,t?1 + ?1 1{yi,t?1 = j } +?2 [1{yi,t?1 = j } ? (UNE ? EDU )i,t?1 ] + ?it (2.2)
where UNE and EDU are as de?ned above. The latent variable yitk indicates the propensity the current state is k , while yi,t?1 indicates the lagged state. There three 60
possible states: high job level, low job level and unemployment. Depending on the question of interest, I model k to be either high or low job level and j to be unemployment. I divide occupations into low and high job levels using the 90% prestige score described above. The possibility of unobserved unit e?ects, unfortunately makes the estimation of dynamic panel data models complicated. If a lagged depended variable model is estimated in the presence of unit e?ects, these e?ects are transferred to the disturbance term, violating the strict exogeneity assumption. I get around this problem by following 3 di?erent estimation approaches. First, I adopt the Anderson and Hsiao (1981) instrument al variables approach in the ?rst di?erences of the model. According to this approach the coe?cients can be estimated consistently by instrumenting the lagged depended variable. Anderson and Hsiao (A-H, henceforth) suggested using the second lag of the depended variable as instrument. Second, I use a generalized method of moment estimator proposed by Arellano and Bond (1991), which is based on the same idea. The ArellanoBond (A-B) approach, ?rst identi?es how many lags of the dependent variables are valid instruments. Then, it combines these lagged levels and ?rst di?erences of the strictly exogenous variables into an instrument matrix, and then, it derives the corresponding one-step and two-step GMM estimators. Finally, I estimate a non-linear probability model by adopting Chamberlain’s (1980) conditional MLE approach. Chamberlain proposed a procedure that speci?es the density of (yi1 , ...yiT ) given yi0 and the vector of explanatory variables (xi ) for each i . What is convenient with this approach is that I can use standard random 61
e?ects software to estimate the parameters. The only di?erence is that the list of explanatory variables is expanded to include the include yi0 and xi in each period.
2.5.1 Are Unemployed High-Skilled Workers More Likely to Take Low-Skill Jobs in Recessions?
I begin with investigating the probability of low job levels. I model k to be high job levels and j the state of unemployment. With each of the estimation procedure described above I estimate three speci?cations. First, I estimate the main model in which the set of regressors contains only UNE, EDU and 1{yi,t?1 = j }. Then, I add the interaction term between UNE and EDU in the model. The third speci?cation, which I call fully interacted model, includes in addition the three-way interaction term between UNE, EDU and 1{yi,t?1 = j }. Table 2.5 summarizes the results in three panels, one for each estimation procedure. The result that education has a negative e?ect on the probability of low job levels is carried over in the dynamic model, but the results regarding the constituent e?ect of a UNE are mixed. It is insigni?cant according to the A-H and A-B procedure, but negative and signi?cant according to the Chamberlain approach. Hence, we reach mixed conclusions regarding the impact of unemployment on low-job-level probability. However, unemployment at the individual level seems to be important. With the exception of A-B procedure, where the e?ect of LAG is signi?cant only in the fully interacted model, the other two approaches suggest that being unemployed
62
has a negative impact on the probability of low job levels. This result does not represent rejection of the hypothesis that the risk of unemployment induces highskilled workers to accept low job levels. To test this hypothesis, the variables of interest are the interaction terms. When the interaction term between EDU and UNE is included in the set of regressors (second row of each panel) the rest of the coe?cients retain their signs, but in contrast to the LP and Logit models presented above, the e?ect of this interaction here is not always positive. The A-H and A-B procedures reach similar conclusions regarding the impact of this interaction. While the constituent e?ect of higher unemployment rate is insigni?cant, its e?ect conditional on the worker having a college degree is negative (although, only marginally signi?cant in the AB procedure). Therefore, the results of these two procedures suggest that higher overall unemployment reduces the low job level probability of workers with a college degree even further. In both cases, however, when this term is further interacted with the lagged unemployment dummy (third row of each panel) it becomes positive and signi?cant, suggesting that college graduates are more likely to move into low job levels when they are unemployed and the unemployment rate is high. The results of both estimation procedures imply that the probability a worker with a college degree will be in a low job level next period is lower when overall unemployment is high, but conditional in addition on the worker being unemployed, the probability is higher. In both cases, the negative impact of education on low job level probability is weaker when unemployment is high and the worker is experiencing unemployment. 63
The results of the Chamberlain approach are most strongly supportive of the view that the risk of unemployment induces high-skilled workers to take low-skill jobs, especially in periods of high unemployment. Not only the three-way interaction term has a positive e?ect on the probability, but the two way interaction between unemployment and education has a positive e?ect on the probability as well. The last row of the table contains the results of Logit estimates of the fully interacted model assuming no unobservable e?ects. The results are consistent with the Chamberlain results. Both the two-way and the three-way interaction terms are positive and signi?cant, while the constituent e?ects of higher unemployment rate and having a college degree are negative and signi?cant. In sum, all estimation procedures suggest the negative e?ect of holding a college degree on the probability of low job levels is weaker when the origin state is unemployment and overall unemployment is high. Moreover, in comparison with the LP and Logit estimated presented earlier, the dynamic model puts more emphasis on the risk of unemployment at the individual level. The dynamic model suggests that what may induce high-skilled workers to accept jobs below their skill level is being unemployed while overall unemployment rate is high, rather than just the fact that the overall unemployment rate is high.
64
2.5.2 Are Unemployed High-Skilled Workers Less Likely to Take HighSkill Jobs in Recessions?
Here I investigate the impact of the same set of regressors and their interactions on the probability of moving into high job levels (i.e., k = high job level). The variation in the results across the di?erent estimation procedures is higher in this case. While most procedures contribute to the conclusion that interactions between unemployment, either at the aggregate level or the individual level and education have a negative impact on the probability of high job levels, we cannot argue that this is certainly the case. The results of the three estimation procedures are in Table 2.6. In accordance with the results so far, the A-H and A-B approach, show that the constituent e?ect of higher unemployment on high-job-level probability is insigni?cant. In the Chamberlain approach, however, the constituent e?ect of higher unemployment rate is insigni?cant, but when the interaction terms are included, it becomes positive and signi?cant. The constituent e?ect of the lagged unemployment dummy is in general insigni?cant. The only case this is negative and signi?cant is in the Chamberlain approach. However, even in this case, it is signi?cant only when the three-way interaction term is not included in the set of regressors. As can be veri?ed from the third row of the bottom panel, when LAG is interacted with EDU and UNE, its constituent e?ect is no longer signi?cant. The conclusion that could be drawn from both the A-H and Chamberlain
65
approach is that when the worker is unemployed, or when the unemployment rate is high, does not necessarily imply lower high-job-level probability, unless the worker has a college degree. In other words, those more likely to have a harder time moving into high-skill jobs when they are unemployed or when the unemployment rate is high, are those quali?ed for high-skilled jobs (i.e., those who hold a college degree). In the A-H case, the only way higher unemployment rate a?ects negatively the high-job-level probability is when the worker both has a college degree and is experiencing unemployment. In fact, we get the counterintuitive result that the effect of the interaction between UNE and EDU, although quite small (approximately 1%) is positive and signi?cant. The only way this results can be justi?ed is if this interaction is actually picking up some of the e?ect of education. The constituent e?ect of having a college degree, as expected, and as the results indicate, is positive. Comparing the interacted model (row 2 and 3) to the constituent model (row 1) we can see that when the interaction between UNE and EDU is included the constituent e?ect of having a college degree declines by approximately 1 percentage point. Similarly, in the Chamberlain approach, the thee-way interaction e?ect is negative, although only marginally signi?cant at the 5% level, but in addition, the e?ect of the two-way interaction term between UNE and EDU on the probability is negative and signi?cant. Thus, the positive impact of having a college degree on high-job-level probability is lower in periods of high unemployment. The results of the A-B approach are di?erent. The e?ect of the interaction between overall unemployment and education is very small and only marginally signi?cant at the 5 % level in the fully interacted model. Moreover, the A-B approach 66
gives the paradoxical result that when this term is further interacted with the lagged unemployment dummy it has a positive and signi?cant e?ect on the probability of high job levels. This implies that in periods of high unemployment, workers who have a college degree, can more easily move into a high job level when unemployed than when employed. While the A-H results suggest that the positive impact of having a college degree on high-job-level probability is lower when overall unemployment rate is high and the worker is unemployed, the A-B approach contradicts this ?nding. The strongest support for the hypothesis that unemployment both at the individual level and at the aggregate level reduces the probability of high-skilled (college graduates) workers ?nding an appropriate match can be found in the Chamberlain estimates. In this case, both when education is interacted with overall unemployment and when it is further interacted with the lagged unemployment dummy it has a negative and signi?cant coe?cient (although, the latter is only marginally signi?cant at the 5% level). Given the variation in the estimates across the di?erent estimation procedures, it is useful to take a look at the estimates assuming no unobserved e?ects. These are given in the last row of the table. The only signi?cant coe?cients are those of EDU and UNE*EDU. The former is positive, while the latter is negative, con?rming the LP and Logit estimates presented earlier. The estimates of the model with unobserved e?ects are also consisted with the Chamberlain estimates. They suggest that higher unemployment rate reduces the positive impact of having a college degree on high-job-level probability. The overall conclusion from this analysis is that there some evidence suggestive 67
of the hypothesis that high-skilled workers have more di?culty moving into high-skill jobs when unemployment is high. However, these evidence are not concrete.
2.5.3 Are Mismatched High-Skilled More Likely to Take High-Skill Jobs in Booms?
The results in section 2.5.1 suggested that college graduates are more likely to move into low job levels when unemployed, and overall unemployment is high. Hence, they support the view that the risk of unemployment induces workers to take jobs below their skill level. Here, I ask the question of whether this phenomenon is temporary or not. Do college graduates accept job below their skill level transitorily, until overall economic conditions improve, and a better job comes along? To address this question I investigate how the unemployment rate a?ects the high-job-level probability of mismatched workers. I consider as mismatched workers who hold a college degree and are in low job levels (i.e., j = low job levels). As mentioned at the beginning of this section, this implies that they are in jobs the on average employ approximately only 10% college graduates each year. In addition, I model the overall unemployment rate dummy to be the reverse of the unemployment dummy in previous regressions. UNE takes the value of 1 when the unemployment rate is below 6% and 0 otherwise. Given this speci?cation, the two-way interaction term between EDU and UNE, takes that value of 1 when unemployment is low and the workers has a college degree, while the three-way interaction term between EDU, UNE and LAG takes the value of 1, when in addition, the worker is in a low job
68
level (i.e., mismatched). The results are in Table 2.7. According to all three estimation procedures being in a low job level a?ects the high-job-level probability negatively. The coe?cient of the lagged depended variable is negative and signi?cant in all cases. This result is not surprising. One cannot argue that being in a low job level as opposed to a high job level increases your chances of being in a high job level next period. For the hypothesis to be tested here, the interaction e?ects of overall unemployment and education with this dummy variable are of most interest. First, we are interested on whether when the unemployment rate is low workers with a college degree are more likely to be in high-skill jobs next period (i.e., the coe?cient of EDU*UNE is positive). Second, we are interested to see whether mismatched college graduates are more likely to move into high job levels next period when the overall unemployment rate is low (i.e., the coe?cient of UNE*EDU*LAG is positive). Both the results of the A-H and A-B approach indicate that mismatched college graduates are more likely to move into high job levels when overall unemployment rate is high. In both cases, the three-way interaction term has a positive and significant coe?cient. The two-way interaction term, however, has a negative coe?cient in the ?rst case and has an insigni?cant coe?cient in the second. Hence, in both cases, a positive e?ect on high-job-level probability when overall unemployment rate is low, arises when then worker in addition to having a college degree, is mismatched. The Chamberlain approach gives the opposite result. The coe?cient of the two-way interaction term is positive and signi?cant, suggesting that when overall unemployment is low, college graduates are more likely to move into high job levels, 69
independent of their origin state. The coe?cient of the three-way interaction term, on the other hand, is negative suggesting that conditional on a college graduate being mismatched, the positive impact of lower unemployment rate on high-joblevel probability is lower. The A-H and A-B results emphasize the tendency of mismatched college graduates to move into higher job levels when the overall unemployment rate is low, while the results of the chamberlain approach emphasize the positive e?ect of overall unemployment being low on the high-job-level probability of college graduates. Overall, we can conclude that the results of this regression analysis point to the existence of an upgrading in the job level of college graduates when the overall unemployment rate is low.
2.6 Markov Chain Multinomial Logit Model of Job level Transitions 2.6.1 The Model
The purpose of this section is to characterize job level transitions. To describe transitions between job levels, I adopt the latent propensity framework a la McFadden (1974). At each period, the latent variable ykit describes the propensity level to be in state k out of states 0, ....., m for individual i at time t. States are unemployment k = 0 and ?ve job levels k = 1, ..., m with m = 5. Assuming N individuals i are observed at T + 1 points in time t = 0, ..., T , the propensity function
70
is determined by
m
ykit = xit ?k +
j =0
?jk 1{yi(t?1) = j } + ?ki + ?kit
(2.3)
where xit is a vector of observable covariates, 1 is the indicator function, yi(t?1) indicates the lagged state, yi(t?1) = j if the individual was in state j at time t ? 1, ?ki is an unobservable individual speci?c e?ect and ?kit is an unobservable error term. This speci?cation assumes that each individual has a speci?c propensity for each alternative depending on the lagged state. The parameters ? = (?0 , ..., ?m ) and ?j = (?j 0, ?j 1, ..?jm ) ? j = 0, ....m capture how the observed covariates and the lagged state, respectively, a?ect the propensity to be in each state. For example, the parameter ?k captures how the observed covariates in?uence the propensity of being in state k , while the parameter ?jk captures the feedback e?ect when the state j at time t ? 1 is followed by the state k at time t. In total, there are m2 feedback parameters ? to be estimated. For the question of interest, the dependent variable ykit is the propensity of individual i being in job level k at time t. I separate occupations 5 levels, from the lowest –job level 1– to the highest –job level 5– based on the HSR prestige scores. Table 2.1 shows the prestige scores corresponding to each job level. The vector of observable covariates xit includes the education dummy and overall unemployment rate dummy, as de?ned in sections 2.5.1 and 2.5.2. Assuming that the error terms ?kit are independent across alternatives and over time conditional on (xi , ?i , yi0 ) and identically distributed according to the Type1 extreme value distribution, the probability of individual i of being in state k at time 71
t, is given by P (yit = k \ yi(t?1) = j, xi , ai ) = exp(xit ?k + ?jk + ?ki ) 1+ m l=1 exp(xit ?l + ?jl + ?li ) (2.4)
The parameters ? and ? can be estimated based on a sequence of states where the individual switches alternatives at least once during periods 1 to T ? 1. Given that only (m2 ? (2m ? 1)) feedback parameters can be identi?ed, we need to impose some identi?cation restriction. I follow Weber(2002) and assume that all parameters with respect to the reference state k = 0 are equal to zero. More speci?cally, I impose the following identi?cation restrictions: ?0 = 0 ?0 = (?00 , ..., ?mo ) = 0 ?0k = 0 ? k = 1, ..., m ?i0 = 0 ? i = 1, ..., N (2.5)
The problem with imposing parameter restrictions is that it complicates the interpretation of the parameters. For the purpose of the empirical analysis in this paper, it is convenient to choose unemployment as a reference state, as it makes the interpretation easier. The advantages of this empirical methodology compared to the dynamic panel estimation procedures presented earlier are ?rst, that it allows for the analysis of the impact of the covariates on multiple job level probabilities simultaneously. Second, it characterizes the e?ect of multiple lagged states on this probability simultaneously. Third, it allows us to compare not only the sign of the e?ect of the covariates on the 72
probability of each job level, but also the magnitude of the e?ect across di?erent job levels. For example, we are able to address a question of the following form: does a higher overall unemployment rate reduce the probability of higher job level more than it reduces the probability of lower job level? Forth, in a similar fashion, it allows us to compare the e?ect of di?erent lagged states on the probability of a particular state. To give an example, we are able to address whether the e?ect of being in job level 1 as opposed to being in job level 2 on the probability of job level 3 is higher or not. Overall, this methodology allows for a more detailed description of job level transitions. To clarify the advantages of this estimation methodology, let us interpret the parameters to be estimated. The odds ration of moving from state j to state k relative to a movement from the same origin to the reference state 0, which in our case is unemployment, is given by the following expression: P (yit = k \ yi(t?1) = j, xi , ai ) = exp(xit ?k + ?jk + ?ki ) P (yit = 0 \ yi(t?1) = j, xi , ai ) (2.6)
Therefore, a high value of ?ki implies a high propensity of moving to state k as opposed to unemployment conditional on any lagged state j . Hence, the parameter ?k represents the e?ect of the covariate x on the log odd’s ratio. P (yit = k \ yi(t?1) = j, xi , ai ) ? ln = ?k ?x P (yit = 0 \ yi(t?1) = j, xi , ai ) (2.7)
The di?erence ?k ? ?k? measures the e?ect of the covariate x on the log odd’s ratio of moving from any state j to k relative to moving from any state j to k ? . In order to interpret the parameter ?jk , it is convenient to remove the individual speci?c e?ects 73
by calculating the following ratio:
P (yit =k \yi(t?1) =j,xi ,ai ) P (yit =0\yi(t?1) =j,xi ,ai ) P (yit =k \yi(t?1) =0,xi ,ai ) P (yit =0\yi(t?1) =0,xi ,ai )
= exp(?jk )
(2.8)
The above expression is identical across individuals and thus, it captures only the state dependence. According to the expression if ?jk is positive, the odds of being in state k with respect to unemployment when the lagged state is j are larger than when the lagged state is unemployment. It is obvious that the e?ects of lagged states j and j ? on the probability of moving to state k relative to unemployment can be measured by ?jk ? ?j ?k . More speci?cally, ln[ P (yit = k \ yi(t?1) = j ? , xi , ai ) P (yit = k \ yi(t?1) = j, xi , ai ) ] ? ln[ ] = ?jk ? ?j ? k P (yit = 0 \ yi(t?1) = j, xi , ai ) P (yit = 0 \ yi(t?1) = j ? , xi , ai ) (2.9) Moreover, by comparing the same origin feedback parameters ?jk and ?jk? , we can measure whether the odds of being in state k with respect to k ? when the lagged state is j are larger or smaller than when the lagged state is unemployment. After some simple algebra we derive: ln[ P (yit = k ? \ yi(t?1) = 0, xi , ai ) P (yit = k ? \ yi(t?1) = j, xi , ai ) ] ? ln [ ] = ?jk? ? ?jk P (yit = k \ yi(t?1) = j, xi , ai ) P (yit = k \ yi(t?1) = 0, xi , ai ) (2.10)
2.6.2 Conditional Maximum Likelihood Estimation
I model individual e?ects as ?xed, and pick up the method presented in Honor´ e and Kyriazidou (2000). The method concerns the estimation of panel data ?xed e?ects discrete choice models when the explanatory variable set includes strictly 74
exogenous variables, lags of the endogenous dependent variable as well as unobservable individual speci?c e?ects.9 Based on the idea applied by Chamberlain (1984), Honor´ e and Kyriazidou (2000) provide conditions under which the probabilities of the events are independent of the individual e?ects. This approach allows for estimating the individual ?xed e?ects parameters ?ki consistently. The conditions are also extended to the case of multinomial discrete choice variables, and therefore cover the model speci?ed above. The estimation of the ? and ? parameters can be based on the maximization of a likelihood function, which regards events where the state variable y switches from say state k to state l or reverse between two points in time, say s and t with 1 ? t < s ? T ? 1. Conditional on such a switch and on the constancy of the explanatory variables in the following periods xi(t+1) = xi(s+1) , the probabilities of the events are independent of the individual e?ects.10 De?ning the binary variable yhit = 1 if the individual i is in state h ? {0, 1, ..., m} in period t and yhit = 0
9
Whether individual e?ects should be modeled as random or ?xed is an important issue in
panel estimation. The latter is more common (Arellano and Honor´ e, 2001) even though the speci?cation of the distribution function of random e?ects is di?cult. In nonlinear models the numerical implementation of a random e?ects becomes even more di?cult as multiple integrals need to be evaluated. For these reasons, I follow Weber (2002) and model individual e?ects as ?xed.
10
Given this condition, modeling the overall unemployment rate as a dummy instead of a con-
tinuous variable helps increase the number of observations that contribute to the likelihood. An alternative method to avoid this limitation would be to incorporate the unemployment rate as a continuous exogenous variable and replace the exact equality condition by weighting the di?erences with a Kernel function and giving the observations with smallest di?erences the highest weights.
75
otherwise, the maximum likelihood function takes the following form:
N
L =
i=1 1?t<s?T ?1 k =l
1{ykit + ykis = 1}1{ylit + ylis = 1} 1{xi(t+1) = xi(s+1) }ln
N
exp(D1 ) 1{s ? t = 1} 1 + exp(D1 )
1{ykit + ykis = 1}1{ylit + ylis = 1}
i=1 1?t<s?T ?1 k =l
1{xi(t+1) = xi(s+1) }ln where
exp(D2 ) 1{s ? t > 1} 1 + exp(D2 )
(2.11)
D1 = (xit ? xis )(?k ? ?l ) + ?yi(t?1) ,k + ?kl + ?l,yi(s+1) ??yi(t?1) ,l ? ?lk ? ?k,yi(s+1) and D2 = (xit ? xis )(?k ? ?l ) + ?yi(t?1) ,k + ?k,yi(t+1) + ?l,yi(s+1) ??yi(t?1) ,l ? ?l,yi(t+1) ? ?yi(s?1) ,k ? ?k,yi(s+1) (2.13) (2.12)
In the objective function above I impose the identi?cation restrictions given in 2.3. For an observation to contribute to the likelihood at least four periods of observations are required and at least some variability in states in the periods between the dates 1 and T ? 1.
2.6.3 Results
Estimation results are given for the whole sample and a sample that excludes individuals with no high-school degree in Tables 2.8 and 2.8, respectively. The analysis is conducted separately for those two samples to compare the parameter 76
estimates and verify whether workers of higher education are more likely to move into lower levels than become unemployed during downturns.11 The period in which transitions are observed is one year. In both cases all the feedback parameters ? are positive, indicating that individuals are more likely to move to each of the job levels from employment, as opposed to unemployment. Moreover, the feedback parameters decline the further the origin state from the destination state. For example, ?15 < ?25 < ?35 < ?45 . Similarly, ?51 < ?41 < ?31 < ?21 , and so on. Hence, the odds ratio of moving to a particular job level with respect to unemployment are higher the closer the origin job level to the destination job level. In some cases, when the destination state is to far from the origin state the feedback parameter becomes insigni?cant indicating that this type of transitions are rare or impossible. For example, the feedback parameters when the origin state is job level 1 is positive and signi?cant for destination states 2 and 3 but becomes insigni?cant for destination states 4 and 5. The feedback parameters below the diagonal correspond to movements into job levels lower than the origin job level, while the parameters above the diagonal to movements into job levels higher than the origin job level. The parameters to
11
Ideally I would like to compare the model estimated on a low-skill sample to one estimated
on a high-skill sample. However, the full sample is too small to allow for meaningful estimates on high-skill and low-skill sub-samples. The majority of the workers in the sample have at most a high-school diploma. Focusing only on either college graduates or workers without a high-school diploma would imply a considerably smaller sample. This estimation methodology, in particular, requires a su?cient number of across state transitions for the estimates to be meaningful, making such a comparison even harder.
77
the left of the diagonal tend to be smaller than those to the right (i.e., ?21 < ?23 , ?32 < ?34 , ?31 < ?35 , etc.). This implies that workers are less likely to move from a higher job level to a lower one than from unemployment, and more likely to move from a lower job level to a higher one than from unemployment. In other words, the odds of moving into a lower job level as opposed to a higher job level are larger when the lagged state is unemployment and vice versa. This ?nding supports the hypothesis of interest as it indicates that workers experiencing unemployment are more likely to move into lower job levels. The e?ect of higher unemployment on the odds ratio of moving to each of the job levels relative to moving into unemployment are given in the last row of each table. In both cases, higher unemployment rate reduces the probability of being in each of the alternatives relative to being unemployed. In other words, higher unemployment reduces the probability of employment, as one would expect. The crowding out hypothesis implies that workers of higher skill are more likely to move into lower job levels than become unemployed during periods of high unemployment compared to workers of lower skill. Hence, the negative impact of unemployment on the probabilities of being in low job levels should be lower for workers of higher skill. Comparing the unemployment rate parameters for the sample that includes individuals with no high-school education to the one that excludes them, we note that this is indeed the case. The parameters are still negative in the second case, but lower in absolute value. Thus, for the more educated sample, higher unemployment reduces the odds of being employed as opposed to being unemployed next period 78
but to a lower degree. In fact, the parameters corresponding to job levels 2 and 3 become insigni?cant. Hence, when workers with less than a high-school diploma are excluded from the sample higher unemployment does not reduce the odds of moving to job levels 2 or 3 as opposed to unemployment. This supports the view that when the unemployment rate is high, workers with higher education are more likely to move into “mediocre” occupations than become unemployed relative to workers with lower education. The parameter corresponding to job level 1 is smaller in absolute value, but to a lower degree (i.e., it is still signi?cant). This is reasonable to expect, as the lower the level of the job the less willing one would be to accept it to avoid unemployment.
2.7 Conclusion
This chapter tests the hypothesis that high-skilled workers accept transitorily jobs below their skill level in order to escape unemployment, and move on to better jobs when times get better. The hypothesis is tested by studying the mismatch rates and job level dynamics using a panel sample of individuals constructed from the yearly family ?les of the Panel Study of Income Dynamics (PSID), which covers the years from 1968 to 1993. My empirical methodology departs from existing studies that investigate the cyclical patterns of mismatch across di?erent skill groups, in that it accounts for the e?ect of the workers’ lagged state on the propensity of being in each of the occupational categories. While existing studies test the hypothesis by focusing only
79
on the impact of economic activity on job level probabilities, I also incorporate the workers lagged state as an explanatory variable and use dynamic panel data estimation methodologies. Modeling state dependence captures some propensity to experience a certain job level, which has been previously unmeasured by focusing only on how overall economic conditions a?ect job level probabilities. I am able to capture directly the impact the risk of unemployment at the individual level, has on job level transitions. I ?nd evidence suggestive of the existence of a cyclical pattern in match behavior of high-skilled workers (college graduates). The mismatch rate of college graduates is higher and exhibits higher cyclical variation than the mismatch rate of workers without a college degree. Moreover, I ?nd that the positive impact of having a college degree on the probability of achieving higher job levels is lower when the unemployment rate is high. Similarly, the negative impact of having a college degree on low-job-level probability is lower when the unemployment rate is high. The results of the dynamic panel data regression analysis indicate that unemployed high-skilled workers are more likely to take low-skill jobs when the unemployment rate is high. In particular, the negative impact of holding a college degree on low-job-level probability is weaker when the origin state is unemployment and overall unemployment rate is high. In addition, the results point to the existence of an upgrading in the job levels of mismatched college graduates when the unemployment rate is low. Finally, the estimates of a Markov Chain Multinomial Logit model of job level transitions suggest that the odds of moving to a lower job level as opposed to a 80
higher job level are larger when the lagged state is unemployment and vice versa. In addition, the results suggest that higher unemployment rate reduces the probability of being in each job level relative to being unemployed. However, consistent with the crowding out hypothesis, the negative impact of higher unemployment rate on each job level probability declines with education and more evidently for “mediocre” job levels. Thus, I conclude that workers of higher education are more likely to accept jobs below their skill level than become unemployed. Table 2.1: Job Levels Based on Prestige Scores Job Job Job Job Job Level Level Level Level Level 1: 2: 3: 4: 5: Prestige Scores 6-21 Prestige Scores 22-36 Prestige Scores 37-51 Prestige Scores 52-66 Prestige Scores 67-83
Table 2.2: Sample Descriptive Statistics Mean Unemployed Job Job Job Job Job Level Level Level Level Level 1 2 3 4 5 0.05 0.14 0.36 0.38 0.08 0.04 533908 15748
Observations Individuals
81
Table 2.3: Linear Probability and Logistic Regression Results: High-Job-Level Probabilities Depended Variable: High-job-level Probability LP Variable UNE -.001 (.001) -.012 (.010) .001 (.001) .071 (.005) -.014 (.003) 6804.4 48.66 69.96 0.2711 2817.6 53.15 0.2695 7.6 3067.14 2810.62 3062.19 .012 (.013) .198 (.024) -.054 (.019) -6804.6 56.26 Logit LP Logit
EDU
.062 .170 (.005) (.023)
UNE*EDU
Log-likelihood value LR Chi-squared F-test R-squared LR test Chi-squared (signi?cance of UNE*EDU) Huasman test Chi-squared
Bolded coe?cients are signi?cant at the 5% level.
82
Table 2.4: Linear Probability and Logistic Regression Results: Low-Job-Level Probabilities Depended Variable: Low-job-level Probability LP Variable UNE -.003* (.002) -.013 (.006) -.007 -.029 (.002) (.008) -.073 -.179 (.008) (.022) .021 .071 (.005) (.016) -14676.8 42.44 32.32 .1526 906.30 603.77 28.35 .1508 19.55 909.45 -14667 62.00 Logit LP Logit
EDU
-.061 -.140 (.008) (.021)
UNE*EDU
Log-likelihood value LR Chi-squared F-test R-squared LR test Chi-squared (signi?cance of UNE*EDU) Huasman test Chi-squared
628.74
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level.
83
Table 2.5: Dynamic Panel Data Models: unemployment to low-job-level transitions Depended Variable: Low-job-level Probability Variables Anderson- Hsiao IV: UNE -.001 (.002) .002 (.003) .002 (.003) Arellano-Bond GMM: -.001 (.002) .000 (.002) .001 (.002) Chamberlain CML: -.146 (.027) -.233 (.031) -.230 (.031) No Unobserved E?ects: -.106 (.031) EDU -.044 (.016) -.036 (.016) -.036 (.016) -.039 (.016) -.035 (.016) -.038 (.016) -.275 (.099) -.469 (.104) -.459 (.104) .926 (.100) LAG -.074 (.010) -.074 (.010) -.083 (.011) -.029 (.046) -.025 (.046) -.089 (.043) -.452 .051 -.439 (.051) -.461 (.052) -.260 (.039) .342 (.062) .333 (.062) .258 (.063) .384* (.235) .443 (.196) -.011* (.006) -.009* (.006) .439 (.099) -.016 (.006) -.016 (.006) .168 (.045) UNE*EDU UNE*EDU*LAG
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level UNE: takes the value of 1 when the unemployment rate is above 6% EDU: takes the value of 1 when the worker has a college degree UNE*EDU: two-way interaction between UNE and EDU LAG: takes the value of 1 when the worker was unemployed in the previous period UNE*EDU*LAG: three-way interaction between UNE, EDU and LAG
84
Table 2.6: Dynamic Panel Data Models: unemployment to high-job-level transitions Depended Variable: High-job-level probability Variables Anderson-Hsiao IV: UNE .001 (.001) -.001 (.001) -.001 (.002) EDU .066 (.010) .060 (.010) .060 (.010) LAG -.007 (.006) -.007 (.006) .001 (.007) .012 (.004) .011 (.004) -.146 (.028) UNE*EDU UNE*EDU*LAG
Arellano-Bond GMM:
-.002 (.002) .003 (.002) .003 (.002)
.047 (.010) .053 (.010) .053 (.010) .250 (.105) .395 (.111) .398 (111) 1.145 (.111)
.005 (.019) -.000 ( .019) .007 (.019) -.310* (.177) -.284 ( .137) -.173 (.153) -.182 (.140) -.286 (.074) -.282 (.074) -.244 (.078) -.517* (.326) -.389 (.269) -.005 (.004) -.006* (.004) .152 (.059)
Chamberlain CML:
.009 (.036) .122 (.046) .121 (.047)
No Unobserved E?ects:
.067 (.538)
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level. UNE: takes the value of 1 when the unemployment rate is above 6% EDU: takes the value of 1 when the worker has a college degree UNE*EDU: two-way interaction between UNE and EDU LAG: takes the value of 1 when the worker was unemployed in the previous period UNE*EDU*LAG: three-way interaction between UNE, EDU and LAG
85
Table 2.7: Dynamic Panel Data Models: low-job-level to high-job-level transitions Depended Variable: High-job-level Probability Variables Anderson-Hsiao IV: UNE .001 (.001) .001 (.001) .001 (.001) Arellano-Bond GMM: EDU LAG UNE*EDU UNE*EDU*LAG
.065 -.015 (.009) (.005) .071 -.015 (.009) (.005) .069 -.019 (.009) (.005) -.012 (.004) -.008 (.003) .046 (.015)
.003 .044 -.119 (.001) (.010) (.028) .002 (.002) .002 (.001) .045 -.110 (.010) (.028) .032 -.095 (.010) (.026) .156* (.117) .081 (.123) .125 (.123) -1.330 (.043) -1.32 (.043) -1.258 (.045) .159 (.081) .258 (.084) -.001 (.088) -.455 (.099) -.008 (.092) .003 (.004) -.001 (.003) .010* (.005)
Chamberlain CML:
-.037 (.038) -.021 (.049) -.024 (.048)
No Unobserved E?ects:
.056 (.058)
.739 -1.606 (.115) (.044)
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level. UNE: takes the value of 1 when the unemployment rate is below 6% EDU: takes the value of 1 when the worker has a college degree UNE*EDU: two-way interaction between UNE and EDU LAG: takes the value of 1 when the worker was in a low job level in the previous period UNE*EDU*LAG: three-way interaction between UNE, EDU and LAG
86
Table 2.8: Estimated parameters Markov Chain Multinomial Logit model, full sample, yearly transitions Destination State Job Job Job Job Job Level 1 Level 2 Level 3 Level 4 Level 5 Origin State Job Level 1 1.444 (0.044) 0.348 (0.040) 0.308 (0.048) 0.129 (0.124) 0.049 (0.173) 0.581 (0.039) 1.428 (0.034) 0.519 (0.039) 0.293 (0.087) 0.09 (0.141) 0.478 (0.048) 0.615 (0.039) 1.678 (0.042) 0.576 (0.08) 0.544 (0.122) 0.099 (0.118) 0.349 (0.084) 0.625 (0.077) 1.658 (0.097) 0.543 (0.135) 0.116 (0.167) 0.161 (0.136) 0.409 (0.119) 0.613 (0.132) 1.525 (0.161)
Job Level 2
Job Level 3
Job Level 4
Job Level 5
Un. Rate> 6%
-0.151 (0.038)
-0.144 (0.032)
-0.158 (0.033)
-0.287 (0.051)
-0.238 (0.064)
Mean log-likelihood: -0.268 Number of cases: 85481 Number of individuals 15748
87
Table 2.9: Estimated parameters Markov Chain Multinomial Logit model, highschool graduates, yearly transitions Destination State Job Job Job Job Job Level 1 Level 2 Level 3 Level 4 Level 5
Origin State Job Level 1 1.442 (0.076) 0.369 (0.065) 0.258 (0.072) 0.140 (0.140) 0.109 (0.192) 0.640 (0.064) 1.455 (0.052) 0.500 (0.055) 0.258 (0.098) -0.007 (0.157) 0.421 (0.071) 0.641 (0.055) 1.661 (0.056) 0.649 (0.090) 0.503 (0.135) 0.117 (0.133) 0.339 (0.093) 0.565 (0.086) 1.673 (0.105) 0.609 (0.148) 0.188 (0.182) 0.216 (0.150) 0.438 (0.131) 0.565 (0.145) 1.520 (0.175)
Job Level 2
Job Level 3
Job Level 4
Job Level 5
Un. Rate> 6%
-0.101 (0.056)
-0.0031 (0.045)
-0.082 (0.045)
-0.234 (0.059)
-0.103 (0.072)
Mean log-likelihood: -0.26 Number of cases: 53507 Number of individuals 9441
88
Appendix A Prestige Scores
Table A.1: Prestige Scores 1970 Occupational Classi?cation Codes 65 102 103 104 105 110 111 112 113 114 115 116 120 121 122 123 124 125 126 130 131 132 133 134 135 Prestige Scores
Physicians, including osteopaths Agriculture teachers Atmospheric, earth, marine, and space teachers Biology teachers Chemistry teachers Physics teachers Engineering teachers Mathematics teachers Health specialists teachers Psychology teachers Business and commerce teachers Economics teachers History teachers Sociology teachers Social science teachers, n.e.c. Art, drama, and music teachers Coaches and physical education teachers Education teachers English teachers Foreign language teachers Home economics teachers Law teachers Theology teachers Trade, industrial, and technical teachers Miscellaneous teachers, college and university
82 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78
89
Teachers, college and university, subject not speci?ed Judges Lawyers Physicists and astronomers Dentists Bank o?cers and ?nancial managers Architects Aeronautical astronautical engineers Psychologists Airplane pilots Electrical and electronic engineers Chemists Clergymen Civil engineers Atmospheric and space scientists Biological scientists Marine scientists Life and Physical scientists, n.e.c. Chemical engineers Petroleum engineers Engineers, n.e.c. Geologists Archivists and curators Political scientists Sociologists Urban and regional planners Social scientists, n.e.c. Mathematicians Secondary school teachers Mechanical engineers Mining engineers Optometrists Registered nurses Pharmacists Clinical laboratory technologists and technicians Dental hygienists Health record technologists and technicians Radiologic technologists and technicians Assessors, controllers, and treasurers, local public administration Health administrators
140 30 31 53 62 202 2 6 93 163 12 45 86 11 43 44 52 54 10 21 23 51 33 92 94 95 96 35 144 14 20 63 75 64 80 81 82 83
78 76 76 74 74 72 71 71 71 70 69 69 69 68 68 68 68 68 67 67 67 67 66 66 66 66 66 65 63 62 62 62 62 61 61 61 61 61
201 61 212 61
90
O?cials and administrators; public administration, n.e.c. School administrators, college Chiropractors Veterinarians Elementary school teachers Pre-kindergarten and kindergarten teachers Authors O?cers, pilots, and pursers; ship School administrators, elementary and secondary Designers O?cials of lodges, societies, and unions Postmasters and mail superintendents Accountants Economists Public relations men and publicity writers Metallurgical and materials engineers Agricultural scientists Personnel and labor relation workers Religious workers, n.e.c. Draftsmen Painters and sculptors Librarians Actuaries Statisticians Actors Sheri?s and baili?s Industrial engineers Farm management advisers Foresters and conservationists Home management advisers Surveyors Dieticians Social workers Embalmers Funeral directors Computer programmers Computer systems analysts Computer specialists, n.e.c. Sales engineers Operations and systems researchers and analysts Health practitioners, n.e.c. Vocational and educational counselors Athletes and kindred workers
222 235 61 72 142 143 181 221 240 183 223 224 1 91 192 15 42 56 90 152 190 32 34 36 175 965 13 24 25 26 161 74 100 165 211 3 4 5 22 55 73 174 180
61 61 60 60 60 60 60 60 60 58 58 58 57 57 57 56 56 56 56 56 56 55 55 55 55 55 54 54 54 54 53 52 52 52 52 51 51 51 51 51 51 51 51
91
Editors and reporters Radio and television announcers Writers, artists, and entertainers, n.e.c. Research workers, not speci?ed Professional, technical, and kindred workers–allocated Stocks and bonds salesmen Locomotive engineers Opticians, and lens grinders and polishers Buyers, wholesale and retail trade O?ce managers, n.e.c. Sales managers and department heads, retail trade Sales managers, except retail trade Managers and administrators, n.e.c. Managers and administrators, except farm–allocated Bank tellers Recreation workers Credit Men industries Electricians Purchasing agents and buyers, n.e.c Bookkeepers Insurance adjusters, examiners, and investigators Job and die setters, metal Machinists Aircraft Dental assistants Health aides, except nursing Policemen and detectives Health technologists and technicians, n.e.c. Agriculture and biological technicians, except health Chemical technicians Electrical and electronic engineering technicians Industrial engineering technicians Mechanical engineering technicians Mathematical technicians Flight engineers Tool programmers, numerical control Technicians, n.e.c. Insurance agents, brokers, and underwriters Automobile accessories installers Carpet installers Dental laboratory technicians
184 193 194 195 196 271 455 506 205 220 231 233 245 246 301 101 210 281 430 225 305 326 454 461 471 921 922 964 85 150 151 153 154 155 156 170 172 173 265 401 420 426
51 51 51 51 51 51 51 51 50 50 50 50 50 50 50 49 49 49 49 48 48 48 48 48 48 48 48 48 47 47 47 47 47 47 47 47 47 47 47 47 47 47
92
Craftsmen and kindred workers, n.e.c. Former members of the Armed Forces Craftsmen and kindred workers–allocated Current members of the Armed Forces Musicians and composers Secretaries, legal Secretaries, medical Secretaries, n.e.c. Marshals and constables Billings clerks Bookkeeping and billing machine operators Calculating machine operator Computer and peripheral equipment operators Duplicating machine operators Keypunch operators Tabulating machine operators O?ce machine operators, n.e.c. Foremen, n.e.c. Real estate agents and brokers Telegraph operators Farm managers Firemen, ?re protection Adult education teachers Teachers, except college and university, n.e.c. Air tra?c controllers Radio operators Postal clerks Real estate appraisers Stenographers Advertising agents and salesmen Mail carriers, post o?ce Tool and die makers Practical nurses Photographers Buyers and shippers, farm products Construction inspectors, public administration Inspectors, except construction, public administration Railroad conductors Library attendants and assistants Payroll and timekeeping clerks Typists
575 580 586 590 185 370 371 372 963 303 341 342 343 344 345 350 355 441 270 384 802 961 141 145 164 171 361 363 376 260 331 561 926 191 203 213 215 226 330 360 391
47 47 47 47 46 46 46 46 46 45 45 45 45 45 45 45 45 45 44 44 44 44 43 43 43 43 43 43 43 42 42 42 42 41 41 41 41 41 41 41 41
93
Electrician apprentices Engravers, except photoengravers Machinist apprentices Mechanic, except auto, apprentices Plumber and pipe ?tters Plumber and pipe ?tter apprentices Tailors Tool and die maker apprentices Speci?ed craft apprentices, n.e.c. Not speci?ed apprentices Farmers (owners and tenants) Farmers and farm managers–allocated trade Telephone operators Carpenters Carpenter apprentices Printing trades apprentices, except pressmen Floor layers, except tile setters Millwrights Photoengravers and lithographers Pressmen and plate printers, printing Pressmen apprentices Welders and ?ame-cutters Restaurant, cafeteria and bar managers Receptionists Cabinetmakers Cranemen, derrickmen, and hoistmen Electric power linemen and cablemen Molders, metal Molder, apprentices Pattern and model makers, except paper Power station operators Telephone installers and repairmen Telephone linemen and splicers Chainmen, rodmen, and axmen; surveying Dancers Managers and superintendents, building Compositors and typesetters Electrotypers and stereotypers Barbers Podiatrists Therapists Therapy assistants
431 435 462 491 522 523 551 562 571 572 801 806 282 385 415 416 423 440 502 515 530 531 680 230 364 413 424 433 503 504 514 525 552 554 605 182 216 422 434 935 71 76 84
41 41 41 41 41 41 41 41 41 41 41 41 40 40 40 40 40 40 40 40 40 40 40 39 39 39 39 39 39 39 39 39 39 39 39 38 38 38 38 38 37 37 37
94
Decorators and window dressers Jewelers and watchmakers Air conditioning, heating, and refrigeration Automobile body repairmen Automobile mechanics Automobile mechanic apprentices Railroad and car shop Sheetmetal workers and tinsmiths Sheetmetal apprentices Boatmen and canalmen Clerical assistants, social welfare Clerical supervisors, n.e.c Counter clerks, except food Enumerators and interviewers Estimators and investigators, n.e.c. Expediters and production controllers Mailhandlers, except post o?ce Meter readers, utilities Proofreaders Statistical clerks Teacher aides, except school monitors Weighers Miscellaneous clerical workers Not speci?ed clerical workers Clerical and kindred workers–allocated Blacksmiths Brickmasons and stonemasons Brickmasons and stonemasons, apprentices Forgemen and hammermen Heat treaters, annealers, and temperers Locomotive ?remen Rollers and ?nishers, metal Ship?tters Structural metal craftsmen Tile setters Checkers, examiners, and inspectors; manufacturing Photographic process workers Health trainees Nursing aides, orderlies, and attendants Airline stewardesses Housekeepers, except private households Ticket, station, and express agents Furriers
425 453 470 472 473 474 486 535 536 701 311 312 314 320 321 323 332 334 362 375 382 392 394 395 396 403 410 411 442 446 456 533 540 550 560 610 645 923 925 931 950 390 444
37 37 37 37 37 37 37 37 37 37 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 35 35
95
Radio and television Miscellaneous mechanics and repairmen Not speci?ed mechanics and repairmen Stationary engineers Railroad brakemen Farm foremen Salesmen and sales clerks, n.e.c. Salesmen of services and construction Sales workers–allocated Dispatchers and starters, vehicle Bakers Data processing machine repairmen O?ce machines Motion picture projectionists Sailors and deckhands Bulldozer operators Excavating, grading and road machine operators, except bulldozer Farm implements Heavy equipment mechanics, including diesel Household appliance and accessory installers and mechanics Plasterers Plasterer apprentices Shoe repairmen Stone cutters and stone carvers Furnacemen, smeltermen, and pourers Graders and sorters, manufacturing Heaters, metal Milliners Stationary ?remen Railroad switchmen Hairdressers and cosmetologists Auctioneers Cement and concrete ?nishers Piano and organ tuners and repairmen Blasters and powdermen Dressmakers and seamstresses, except factory Meat cutters and butchers, except manufacturing Shoemaking machine operatives Machine operatives, miscellaneous speci?ed Machine operatives, not speci?ed Miscellaneous operatives
485 492 495 545 712 821 280 285 296 315 402 475 484 505 661 412
35 35 35 35 35 35 34 34 34 34 34 34 34 34 34 33
436 33 480 33 481 33 482 520 521 542 546 622 624 626 636 666 713 944 261 421 516 603 613 631 664 690 692 694 33 33 33 33 33 33 33 33 33 33 33 33 32 32 32 32 32 32 32 32 32 32
96
Not speci?ed operatives Operatives, except transport–allocated Bus drivers Truck drivers Cashiers Boilermakers Bookbinders Inspectors, scalers, and graders Inspectors, n.e.c. Roofers and slaters File clerks Telegraph messengers Loom ?xers Painters, construction and maintenance Painter apprentices Sign painters and letterers Upholsterers Fishermen and oystermen Sales clerks, retail trade Salesmen, retail trade Shipping and receiving clerks Furniture and wood ?nishers Metal platers Mixing operatives Painters, manufactured articles Drill press operatives Grinding machine operatives Lathe and milling machine operatives Precision machine operatives, n.e.c Punch and stamping press operatives Riveters and fasteners Solderers Carding, lapping, and combing operatives Knitters, loopers, and toppers Textile operatives, n.e.c. Winding operatives, n.e.c. Fork lift and tow motor operatives Transport equipment operatives–allocated Animal caretakers, except farm Demonstrators Asbestos and insulation workers Meat cutters and butchers, manufacturing Sawyers
695 696 703 715 310 404 405 450 452 534 325 383 483 510 511 543 563 752 283 284 374 443 635 641 644 650 651 652 653 656 660 665 670 671 674 681 706 726 740 262 601 633 662
32 32 32 32 31 31 31 31 31 31 30 30 30 30 30 30 30 30 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 28 28 28
97
Conductors and motormen, urban rail transit Deliverymen and routemen Assemblers Drillers, earth Dry wall installers and lathers Motormen; mine, factory, logging camp, etc. Farm service laborers, self-employed Collectors, bill and account Glaziers Cutting operatives, n.e.c. Mine operatives, n.e.c. Lumbermen, raftsmen, and woodchoppers Cooks, except private household Millers; grain, ?our, and feed Dyers Sewers and stitchers Spinners, twisters, and winders Weavers Child care workers, except private households household–allocated Housekeepers, private household Paperhangers Oilers and greasers, except auto Longshoremen and stevedores Crossing guards and bridge tenders Stock clerks and storekeepers Bottling and canning operatives Carpenters’ helpers Gardeners and groundkeepers, except farm Midwives Child care workers, private household Garage workers and gas station attendants Parking attendants Taxicab drivers and chau?eurs Busboys Dishwashers Food service workers, except private household Boarding and lodging housekeepers School monitors Guards and watchmen Elevator operators
704 705 602 614 615 710 824 313 445 612 640 761 912 501 620 663 672 673 942 976 982 512 642 760 960 381 604 750 755 924 980 623 711 714 911 913 916 940 952 962 943
28 28 27 27 27 27 27 26 26 26 26 26 26 25 25 25 25 25 25 25 25 24 24 24 24 23 23 23 23 23 23 22 22 22 22 22 22 22 22 22 21
98
Warehousemen, n.e.c. Bartenders Waiters Messengers and o?ce boys Filers, polishers, sanders, and bu?ers Produce graders and packers, except factory and farm Meat wrappers, retail trade Packers and wrappers, n.e.c Farm laborers, farm foremen, and kindred workers Hucksters and peddlers Clothing ironers and pressers Laundry and dry cleaning operatives, n.e.c. Farm laborers, wage workers Farm laborers, unpaid family workers Cooks, private household Laundresses, private household Maids and servants, private household Private household workers–allocated Construction laborers Freight and material handlers Garbage collectors Stockhandlers Vehicle washers and equipment cleaners Miscellaneous laborers Not speci?ed laborers Laborers, except farm–allocated Janitors and sextons Newsboys Food counters and fountain workers Attendants, recreation and amusement Ushers, recreation and amusement Chambermaids and maids, except private household Attendants, personal service, n.e.c. Baggage porters and bell hops Personal service apprentices Welfare service aides Teamsters Cleaners and charwomen Bootblacks Engineering and science technicians
770 910 915 333 621 625 634 643 846 264 611 630 822 823 981 983 984 986 751 753 754 762 764 780 785 796 903 266 914 932 953 901 933 934 945 954 763 902 941 162
20 20 20 19 19 19 19 19 19 18 18 18 18 18 18 18 18 18 17 17 17 17 17 17 17 17 16 15 15 15 15 14 14 14 14 14 12 12 9 7
99
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[15] Caballero, Ricardo and Mohammad Hammour (1996), “On the timing and e?ciency of creative destruction,” Quarterly Journal of Economics, 111, 805852. [16] Chamberlain, Gary (1984), “Panel Data,” J. J. Heckman and E. Leamer (eds.): Handbook of Econometrics, 2. [17] Koopmanschap, M. and Teulings Coen (1989). “An econometric model of crowding out of lower educational levels,” European Economic Review, 33,165364. [18] Cole, Harold and Richard Rogerson (1999), “Can the Mortensen-Pissarides matching model match the business-cycle facts?,” International Economic Review, 40(4), 933-958. [19] Davis, Steven and John C. Haltiwanger (1992), “Gross job creation, gross job destruction, and employment reallocation,” Quarterly Journal of Economics, 107, 819-863. [20] Davis, Steven, John C. Haltiwanger and Scott Schuh (1996), “Job creation and destruction,” The MIT Press. [21] Dolado, Juan, Marcel Jansen, and Juan Jimeno (2003),“A matching model of crowding-out and on-the-job search,” IZA discussion paper, No. 866. [22] Francesconi, Marco, J. Michael Orszag, Edmund S. Phelps and Gyl? Zoega (2000), “Education and the natural rate of unemployment,” Oxford Economic Papers, 52, 204-223. [23] Gautier, Pieter A., van den Berg, Gerard, Jan C. van Ours and Geert Ridder (1999), “Separations at the ?rm level,” in: Haltiwanger J., Lane J. Theeuwes J., Troske K. (Eds), The creation and analysis of matched employer-employee data, North Holland, Amsterdam, 313-328 [24] Gautier, Pieter A., van den Berg, Gerard, Jan C. van Ours and Geert Ridder (2002), “Worker turnover at the ?rm level and crowding out of lower educated workers,” European Economic Review, 46, 523-538 [25] Gautier, Pieter A. (1998) “Do more high skilled workers occupy simple jobs during bad times?,” mimeo, Free University Amsterdam. [26] Gautier, Pieter A. (2002), “Unemployment and search externalities in a model with heterogeneous jobs and heterogeneous workers,” Economica, 69, 21-40 [27] Gautier, Pieter A., Marc Pomp and Marloes Zijl (1997), “Does crowding out explain low-skilled unemployment?,” CPB report 97/3. [28] Gautier, Pieter A. and Marc Pomp (1999), “Crowding out and unskilled unemployment,” CPB report 99/1. 101
[29] Gomes, James, Greenwood, Jeremy and Sergio Rebelo (1999), “Equilibrium Unemployment,” mimeo, University of Rochester. [30] Hall, Robert (1991), “Labor demand, labor supply and employment volatility,” in NBER Macroeconomics Annual (Cambridge: MIT Press) [31] Hall, Robert (2000), “Reorganization,” Carnegie-Rochester Conference Series on Public Policy. [32] Hartog, Joop, (1992), Capabilities, allocation and earnings, Boston: Kluwer. [33] Honor` e, Bo and Ekaterini, Kyriazidou (2000), “Panel data discrete choice models with lagged dependent variables,” Econometrica,68,839-874. [34] Hoynes, Hilary (1999) “The employment, earnings and income of less skilled workers over the business cycle,” mimeo, University of California, Berkeley [35] Liu, Haoming, 1997. “Labor quality and the cyclicality of real wages,” mimeo, University of Western Ontario, Working paper 9712. [36] Liu, Haoming (2003). “A cross-country comparison of the cyclicality of real wages,” ”Canadian Journal of Economics, Canadian Economics Association, 36(4), 923-948. [37] Marimon, Ram´ on and Fabrizio Zilibotti (1999), “Unemployment vs. mismatch of talents: reconsidering unemployment bene?ts,” The Economic Journal, 109, 266-291 [38] McKenna, C.J. (1996), “Education and the Distribution of Unemployment,” European Journal of Political Economy, 12, 113-132. [39] Mortensen, Dale and Christopher Pissarides (1994), “Job creation and job destruction in the theory of unemployment,” The Review of Economic Studies, 61(3), 397-415. [40] Mortensen, Dale and Christopher Pissarides (1999), “Unemployment responses to “skill-biased” technology shocks: the role of labour market policy,” Economic Journal, Royal Economic Society, 109(127), 242-65. [41] Moscarini, Giuseppe (2001), “Excess worker reallocation,” The Review of Economic Studies, 68, 593-612 [42] Moscarini, Giuseppe (2003), “Skill and luck in the theory of turnover,” mimeo, Yale University. [43] Moscarini, Giuseppe and Francis Vella (2003), “Occupational mobility and employment reallocation: evidence from the NLSY79,” mimeo, Yale University. [44] Nickell, Stephen, (1979). “Education and lifetime patterns of unemployment,”Journal of Political Economy, University of Chicago Press,87(5), 117-31. 102
[45] van Ours, Jan C. and Geert Ridder (1995), “Job matching and job competition: are lower educated workers at the back of job queues?,” European Economic Review, 39, 1717-1731 [46] Pierrard, Olivier and Henri Sneessens (2003), “Low-skilled unemployment, biased technological shocks and job competition,” IZA Discussion Paper No.784. [47] Pissarides, Christopher (1994), “Search unemployment with on-the-job search,” The Review of Economic Studies, 61, 457-475. [48] Pissarides, Christopher and Jonathan Wadsworth (1994), “On-the-job search: some empirical evidence from Britain,” European Economic Review,38(2), 385401 [49] Plesca, Miana (2005), “Accounting for general equilibrium e?ects in programm evaluation,” mimeo, University of Guelph. [50] Rogerson, Richard, Robert Shimer and Randall Wright (2004), “Searchtheoretic models of the labor market: a survey,” mimeo, Arizona State University. [51] Royalty, Anne (1998), “Job-to-job and Job-to-nonemployment turnover by gender and education level,” Journal of Labor Economics, 16(2), 392-443. [52] Shimer, Robert (2003), “Dynamics in a model of on-the-job search,” mimeo, University of Chicago. [53] Shimer, Robert (2004), “The cyclical behavior of equilibrium unemployment and vacancies,” mimeo, University of Chicago. [54] Shin, D (1994), “Cyclicality of real wages among young men,” Economics Letters, 46, 137-142. [55] Topel, Robert (1993), “What have we learned from empirical studies of unemployment and turnover?,” The American Economic Review, 83, 110-115 [56] Weber, Andrea (2002), “State dependence and wage dynamics: a heterogeneous Markov chain model for wage mobility in Austria,” mimeo, Institute for Advance Studies.
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doc_512562895.pdf
The term business cycle (or economic cycle) refers to economy-wide fluctuations in production, trade and economic activity in general over several months or years in an economy organized on free-enterprise principles.
ABSTRACT
Title of dissertation:
JOB COMPETITION OVER THE BUSINESS CYCLE Antri N. Chasampoulli, Ph.D., 2005
Dissertation directed by:
Professor John Haltiwanger and Professor Je?rey Smith, Department of Economics
My thesis explores the following question: how workers of di?erent skill are allocated across jobs and unemployment over the business cycle. I am interested in understanding the “over-quali?cation”of workers that occurs during periods of high unemployment, as increased congestion in the labor market hinders workers from ?nding a suitable match. I focus on the skill mismatch that takes the form of high-skilled workers transitorily accepting low-skill jobs, thereby in?uencing the labor market prospects of low-skilled workers. In the ?rst chapter, I develop a business cycle matching model with heterogeneous workers and jobs, which helps understand the role of over-quali?cation on labor productivity and across-skill unemployment dynamics. I capture the acrossskill search externalities and spillover e?ects that arise when low- and high-skilled workers compete for low-skill jobs, by relaxing the common assumption that all
workers qualify for any type of vacancy. I show that the skill mix of vacancies changes over the cycle, thus altering the allocation of workers of di?erent skill across jobs and unemployment. In addition, my model explains observed di?erences in labor market outcomes of di?erent skill groups, including the higher sensitivity of low-skilled unemployment to changes in economic activity. In the second chapter, I test the empirical relevance of over-quali?cation. I ask whether the risk of unemployment induces high-skilled workers to accept transitorily low-skill jobs until a better job comes along. To this end, I study the mismatch rates and job level dynamics of high-skilled workers. Unlike existing studies that only examine how the business cycle a?ects job level probabilities, I adopt dynamic panel data estimation methods, in which the worker’s lagged state (i.e., whether unemployed or mismatched) enters the model as an explanatory variable. I ?nd evidence suggestive of the existence of over-quali?cation. The mismatch rates of higher educational groups are higher and exhibit more cyclical variation. Moreover, I ?nd that high-skilled workers are more likely to move into lower job levels when they are unemployed and the unemployment rate is high. In addition, my results point to the existence of an upgrading in the job levels of mismatched high-skilled workers when the unemployment rate is low.
JOB COMPETITION OVER THE BUSINESS CYCLE
by Antri N. Chasampoulli
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial ful?llment of the requirements for the degree of Doctor of Philosophy 2005
Advisory Committee: Professor Professor Professor Professor Professor John Haltiwanger, Co-Chair Je?rey Smith, Co-Chair John Shea Michael Pries John Horowitz
c Copyright by Antri N. Chasampoulli 2005
This dissertation is dedicated to my mother.
ii
TABLE OF CONTENTS List of Tables List of Figures 1 Job Competition Over the Business Cycle: Implications for Labor Productivity and Unemployment Rates by Skill 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Main Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Timing and Flow Equations . . . . . . . . . . . . . . . . . . . 1.3.4 Asset Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Surpluses and Zero Pro?t Conditions . . . . . . . . . . . . . . 1.3.6 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Aggregate Productivity Fluctuations . . . . . . . . . . . . . . 1.4.2 Job Separation Fluctuations . . . . . . . . . . . . . . . . . . . 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Cyclical Variation in Match Quality: The Role of Unemployment Risk 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Mismatch Rates Over the Business Cycle . . . . . . . . . . . . . . . 2.4 Linear Probability and Logit Models . . . . . . . . . . . . . . . . . 2.4.1 The E?ect of Business Cycle and Education on High- JobLevel Probability . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 The E?ect of Business Cycle and Education on Low- Job-Level Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Dynamic Panel Data Models . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Are Unemployed High-Skilled Workers More Likely to Take Low-Skill Jobs in Recessions? . . . . . . . . . . . . . . . . . 2.5.2 Are Unemployed High-Skilled Workers Less Likely to Take High-Skill Jobs in Recessions? . . . . . . . . . . . . . . . . . 2.5.3 Are Mismatched High-Skilled More Likely to Take High-Skill Jobs in Booms? . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Markov Chain Multinomial Logit Model of Job level Transitions . . 2.6.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Conditional Maximum Likelihood Estimation . . . . . . . . 2.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Prestige Scores iii . . . . v vi 1 1 7 12 12 17 18 18 21 23 23 25 34 40 43 43 48 50 57
. 58 . 59 . 60 . 62 . 65 . . . . . . 68 70 70 74 76 79 89
Bibliography
100
iv
LIST OF TABLES
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Job Levels Based on Prestige Scores . . . . . . . . . . . . . . . . . . . 81 Sample Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . 81 Linear Probability and Logistic Regression Results: High-Job-Level Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Linear Probability and Logistic Regression Results: Low-Job-Level Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Dynamic Panel Data Models: unemployment to low-job-level transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Dynamic Panel Data Models: unemployment to high-job-level transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Dynamic Panel Data Models: low-job-level to high-job-level transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Estimated parameters Markov Chain Multinomial Logit model, full sample, yearly transitions . . . . . . . . . . . . . . . . . . . . . . . . 87 Estimated parameters Markov Chain Multinomial Logit model, highschool graduates, yearly transitions . . . . . . . . . . . . . . . . . . . 88
A.1 Prestige Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
v
LIST OF FIGURES
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
E?ect of a Negative Productivity Shock on the Fraction of Low-skill Vacancies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 E?ect of a Negative Productivity Shock on the Fraction of Low-skilled Workers in the Mass of Job Seekers. . . . . . . . . . . . . . . . . . . . 26 E?ect of a Negative Productivity Shock on the Fraction of Highskilled Workers in the Mass of Job Seekers. . . . . . . . . . . . . . . . 27 E?ect of a Negative Productivity Shock on the Worker-Vacancy Meeting Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 E?ect of a Negative Productivity Shock on the Probability of Finding a High-Skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 E?ect of a Negative Productivity Shock on the Probability of Finding a Low-Skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 E?ect of a Negative Productivity Shock on Average Match Productivity. 29 E?ect of a Negative Productivity Shock on Unemployment and Mismatch Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 E?ect of a Separation Rate Shock on the Fraction of Low-Skill Vacancies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.10 E?ect of a Separation Rate Shock on the Fraction of High-skilled Job Seekers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.11 E?ect of a Separation Rate Shock on the Probability of Finding a High-skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.12 E?ect of a Separation Rate Shock on the Probability of Finding a Low-skill Job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.13 E?ect of a Separation Rate Shock on Average Match Productivity. . . 37 1.14 E?ect of a Separation Rate Shock on Unemployment and Mismatch Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1 2.2 Mismatch Rate of College Graduates (90% cuto? point) . . . . . . . . 52 Mismatch Rate of College Graduates (95% cuto? point) . . . . . . . . 53 vi
2.3 2.4 2.5
Mismatch Rates by Education (90% prestige cuto? point) . . . . . . . 54 Fraction of Unemployed by Education . . . . . . . . . . . . . . . . . . 55 Degrees of Mismatch: College Graduates . . . . . . . . . . . . . . . . 56
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Chapter 1 Job Competition Over the Business Cycle: Implications for Labor Productivity and Unemployment Rates by Skill 1.1 Introduction
An open theoretical question is how the quality of job-worker matches evolves over the business cycle. Evidence that matches created during recessions are of lower productivity and dissolve faster has increased attention on the role of search frictions in exacerbating skill-mismatches during recessions.1 This chapter focuses on the type of skill-mismatch that takes the form of highskilled workers taking transitorily low-skill jobs, i.e., becoming “over-quali?ed”, in order to avoid the distress of being unemployed, while continuing to search on the job for high-skill jobs. I analyze the implications of over-quali?cation for unemployment and labor productivity dynamics, by developing a business cycle matching model in which high-skilled workers can take both high- and low-skill jobs, whereas low-skilled workers can only take low-skilled jobs.
1
For evidence on the procyclicality of match quality, see for example, Bowlus (1995), Davis,
Haltiwanger, and Schuh (1996), Bils (1985), Shin (1994), Bowlus, Liu and Robinson (2002), and Liu (2003). Moreover, worker surveys indicate that workers are more likely to report being employed at jobs below their skill level during recessions (e.g., Akerlof Rose and Yellen, 1988; and Acemoglu, 1999).
1
The existing literature on the role of search frictions in exacerbating skill mismatch during recessions neglects the fact that workers face restrictions in the type of vacancies they can ?ll. Existing studies assume that all workers, independent of their skill level, qualify for any type of vacancy ?rms create. In reality, however, the matching technology is asymmetric: workers of high skill qualify for a wider range of job types, while jobs with low skill requirements can be ?lled by a wider range of worker types. Hence, when low-skilled workers compete with high-skilled workers for low-skilled jobs, the asymmetric nature of the matching technology entails search externalities and across-skill spillover e?ects that existing studies fail to incorporate. In turn, the job competition externalities that arise have important consequences for how workers of di?erent skill are allocated across jobs and unemployment over the cycle. Typically, workers of di?erent skill experience di?erent labor market outcomes on a variety of dimensions, which the assumption that all workers can be employed in any type of vacancies ?rms create (i.e., a single job-worker matching rate for all skill groups) cannot explain. Low-skilled workers have lower exit rates from unemployment and lower propensity to search on the job than high-skilled workers (e.g., Blau and Robins, 1990; Pissarides and Wadsworth, 1994; and Belzil, 1996). Moreover, low-skilled unemployment is higher and exhibits higher cyclical sensitivity than high-skilled unemployment (e.g., Topel, 1993). These di?erences in labor market outcomes for workers of di?erent skill, are consistent with the existence of job competition externalities, as high-skilled workers take temporary jobs below their
2
skill level, thereby a?ecting the labor market prospects of low-skilled workers.2 There is increasing interest in modeling over-quali?cation to explain why many EU countries in the recent decades have su?ered an uneven increase in low-skilled unemployment relative to high-skilled unemployment (Albrecht and Vroman, 2002; Gautier, 2002; Dolado et al., 2003). These studies focus on across-skill job competition externalities and investigate whether high-skilled workers “crowd-out” lowskilled workers as they compete for jobs. Since their goal is to explain long term uneven developments in unemployment rates, they only look at steady states. The notion that search frictions exacerbate skill-mismatches during recessions has been formalized in Barlevy (2002), via a business cycle matching model with twosided heterogeneity and on-the-job search. Prior to Barlevy, a series of theoretical papers argued that recessions promote e?cient allocation of resources by “cleansing” out the less e?cient production arrangements.3 However, the “cleansing” view is at odds with the evidence that recessions encourage the creation of less productive matches. Barlevy (2002) is a ?rst attempt at reconciling the theoretical literature on the “cleansing” e?ect of recessions with the evidence. In his model recessions kill marginal production arrangements, but also hinder the transition of mismatched workers into more productive uses (labeled as the “sullying” e?ect), because ?rms
2
The ?ndings of Bowlus (1995) that the quality of matches falls during recessions more evidently
in white collar than blue collar activities gives additional support to this view.
3
Examples are Hall (1991, 2000), Mortensen and Pissarides (1994), Caballero and Hammour
(1994, 1996) and Gomes, Greenwood, and Rebelo (1999). These studies have been inspired by the work of Davis and Haltiwanger (1992), who argue that recessions are associated with increased job reallocation in the manufacturing sector.
3
create fewer vacancies per job seeker. The latter e?ect dominates, and accounts for the lower match quality observed during recessions. Barlevy’s model adopts a symmetric framework (i.e., ?rms create equal amounts of each type of vacancy and all workers can be employed in any type of vacancy ?rms open), making the role of aggregate shocks more transparent. However, a symmetric framework implies identical unemployment rates across skill groups, and therefore cannot account for the observed uneven cyclical ?uctuations in unemployment rates of di?erent skill cohorts. More importantly, it ignores the externalities and spillover e?ects across skill groups arising from job competition. In this paper, I relax the symmetry assumption and incorporate both business cycle ?uctuations and job competition externalities into the model, thus bringing the two strands of literature together. I investigate the dynamic e?ects on unemployment of two types of shocks: an exogenous shock to productivity that a?ects output of all matches and shock to the rate at which matches dissolve. Given the asymmetric nature of the matching technology, changes in the skill composition of vacancies alter the way high- and low-skilled workers are allocated across types of jobs and unemployment. I show that the skill composition of vacancies changes over the cycle, as ?rms respond to changes in the relative value of opening high- and low-skill vacancies. My model delivers the conventional result that in periods of low aggregate productivity workers have greater di?culty escaping unemployment, as ?rms create fewer vacancies per job seeker, but it also shows that downturns generate two countervailing e?ects. On the one hand, an exogenous reduction in aggregate productivity raises 4
the relative value of opening high-skill vacancies and encourages ?rms to upgrade the skill composition of vacancies. In turn, the skill upgrading in the vacancy mix facilitates the transition of both unemployed and overquali?ed (i.e., in low-skill jobs) high-skilled workers into high-skill jobs, increasing average match productivity. On the other hand, a rise in exogenous job separation rates induces ?rms to downgrade the skill composition of vacancies: since low-skill jobs can be ?lled by both types of workers, their relative pro?tability increases when matches dissolve faster and thus is a greater supply of job seekers. The skill downgrading, together with the increase in the number of unemployed high-skilled workers, enhances the likelihood that unemployed high-skilled workers take low-skill jobs, while sti?ing the transition into high-skill jobs. The net e?ect on the degree of over-quali?cation and thus average match productivity depends on the relative importance of exogenous aggregate productivity and separation rate shocks over the business cycle. Once I allow for the skill composition of vacancies to vary over the cycle, Barlevy’s (2002) result that recessions sti?e the transition of mismatched workers into appropriate jobs no longer holds unless the fall in aggregate productivity is accompanied by a su?ciently high increase in job separation. Further, contrary to the “cleansing” view, under which higher job separation during recessions eliminates marginally productive arrangements, higher job separation in this paper actually exacerbates over-quali?cation and lowers average match productivity. Hence, my model gives a view of skill-mismatch over the cycle that puts more emphasis on job separation rather than aggregate productivity ?uctuations, and calls for further investigation on the link between the two impulses. 5
In addition, by relaxing the common assumption of a single matching rate for all skill groups, my model allows for the unemployment rate not only to vary over the cycle, but across skill groups as well. Therefore, my model allows for an examination of why low-skilled unemployment is more sensitive to slowdowns in economic activity than high-skilled unemployment, and whether this is due to intensi?ed job competition between high- and low-skilled workers. Consistent with the evidence, I ?nd that low-skilled unemployment is higher and more volatile than high-skilled unemployment. However, contrary to the common belief, the main reason is not that high-skilled workers crowd out low-skilled ones when competing for jobs; instead, high-skilled workers are eligible for both high- and low-skill jobs and are therefore less vulnerable to the changes in the skill composition of vacancies that occur over the cycle. As it turns out, regardless of whether or not over-quali?cation and job competition externalities increase during recessions, the low-skilled unemployment rate still rises relatively more. The rest of the paper is organized as follows. Section 1.2 is devoted to the description of related literature. Section 1.3 describes worker and ?rm behavior and the labor market mechanisms (matching process, wage bargaining). In sections 1.4 and 1.5, I examine the properties of the model through comparative statics and dynamic simulation exercises, by considering separately the e?ects of aggregate productivity and separation rate ?uctuations. Finally, in section 1.6, I conclude with a few remarks and discuss how future research will build upon this contribution.
6
1.2 Related Literature
Several modi?cations to the conventional search equilibrium model have been made to incorporate the signi?cance of skill mismatches which occur during periods of high congestion in the labor market, mainly by allowing for some heterogeneity in job productivities and/or workers skills. The literature on matching models with heterogeneous agents dates back to the contribution by Pissarides (1994), where onesided heterogeneity is assumed: there are two types of jobs (good and bad jobs) but workers are homogeneous. Workers who take bad jobs stay in them as their wages increase with job tenure, so that employment in good jobs is no longer attractive to them.4 The more recent contributions of Acemoglu (1999) and Mortensen and Pissarides (1999) set up the foundations of the role of search frictions in matching models with skill heterogeneity. Assuming a constant contact rate between unemployed workers and vacancies, thus eliminating any possible interactions between workers with di?erent skills, Acemoglu (1999) o?ers a theory of how the unemployment rates of high- and low-skilled workers and between-group wage dispersion change endogenously depending on the vacancy creation strategy of ?rms. In particular, ?rms ?nd it pro?table to either create only low-skill jobs or to create both low-skill and high-skill jobs and search for the appropriate candidates. Similarly, in Mortensen and Pissarides (1999), the distribution of workers over a continuum of skill levels is exogenous, whereas the distribution of job types is endogenous. They examine the
4
A relevant contribution in this line of research is also McKenna (1996).
7
consequences of skilled-biased technological change on unemployment rates across skill groups. However, they do not deal with across skill search externalities and spillover e?ects associated with skill-mismatches, because in their model there is a perfect match between workers skills and ?rms skill requirements. Similar models have also been considered in studies that investigate the role of unemployment risk in how e?ciently workers are allocated across jobs, and the corresponding welfare implications of unemployment insurance policy. In Acemoglu (2001), workers are identical and only job productivities are heterogeneous. Similarly, Acemoglu and Shimer (1999) assume that workers are identical in terms of their skills, while jobs are heterogeneous in terms of speci?city with higher speci?city jobs being more productive. Marimon and Zilibotti (1999) go one step further and allow for two-sided skill heterogeneity, thus capturing the negative impact that skill mismatch has on labor productivity. They model match productivity to be lower the higher the distance between the workers’ skill level and the vacancies’ required skill level. However, they impose a convenient symmetry in the production technology that is very restrictive: as long as the distance between the ?rms required skill level and the worker’s skill level is the same, the productivity of the match will be equal. This implies that an overquali?ed worker can produce as much as an under-quali?ed worker (a nurse can do the job of a doctor as well as a doctor can do the job of a nurse). Although the strands of literature described above set the foundations for studying search frictions in models with skill-heterogeneity, they do not deal with spillover e?ects of high-skilled workers onto the creation and ?lling of low-skill jobs 8
and their connection to the observed di?erences in the labor market outcomes of different skill cohorts. Some of these papers assume perfectly segmented labor markets where job competition and interactions across skill groups are not possible. In other cases, markets are not segmented, but the type of heterogeneity assumed does not incorporate di?erences in the minimum skill requirements of jobs. That is, all types of workers are quali?ed to perform any type of job entrepreneurs create and thus have identical job ?nding rates. In such a set up, the matching behavior of di?erent skill groups does not in?uence the ability of other skill groups to ?nd a job. Hence, possible job competition and crowding out phenomena that may occur in periods of high congestion in the labor market, and their implications for unemployment rate di?erences across skill groups, are ignored. The recent contributions by Albrecht and Vroman (2002), Gautier (2002) and Dolado et al. (2003) extend this type of model to include job competition and spillover e?ects across skill groups and address issues such as over-quali?cation and crowding-out more directly. In these studies, for simplicity, there are only two types of jobs (low-skill and high-skill) and only two skill groups (low-skilled and highskilled workers). Both the distribution of skills and job destruction are exogenous, but the vacancy mix is endogenous and is determined by free entry conditions. The key feature of these models, ?rst introduced by Albrecht and Vroman (2002), is the type of production technology assumed: low- and high-skill workers can be hired for low-skill jobs, whereas only the latter can perform high-skill jobs. In this context, high- and low-skill submarkets can endogenously segregate or merge depending on the matching behavior of workers. It may be worthwhile for unemployed high-skilled 9
workers to mismatch, i.e., take low-skill jobs. If this is the case, job creation and unemployment in the low-skill market can a?ect job creation and unemployment in the high-skill market. Therefore, job competition takes place and crowding out may occur.5 Although these studies provide important insights into the externalities associated with searching and matching behavior of workers and shed some light on the implications of job competition for unemployment, they are limited in that they only perform comparative static exercises on the steady-state equilibrium, investigating
5
The most notable di?erences between these three studies rest on their assumptions regarding
the nature of job search. In both Gautier (2002) and Dolado et al. (2003) mismatched workers (high-skilled workers on low-skilled jobs) are allowed to search on-the-job and quit as soon as better jobs come along, while in the Albrecht and Vroman model, on-the-job search is not allowed. In the latter study, there are two main results. First, when high-skilled workers are willing to take low-skill jobs (cross-skill matching), unemployment duration among low-skilled workers is higher than among high-skilled workers, while the expected match duration is higher for highthan low-skill jobs. Second, in equilibria with cross-skill matching, high-skilled workers “crowd out”, that is, take jobs away from low-skilled workers, but at the same time, their willingness to accept low-skill jobs leads to an overall expansion of low-skill vacancy supply. Therefore, the net impact on low-skilled unemployment depends on which of these e?ects is stronger. Gautier (2002) and Dolado et al. (2003) ?nd that on-the-job search provides an additional mechanism through which the labor market position of low-skill workers is weakened when high-skilled workers move into low-skill jobs. In particular, the higher quit rate of mismatched workers exerts a negative externality on low-skill jobs, which lowers the value of posting a low-skill vacancy and thus, leads to lower low-skill vacancy creation. Gautier (2002) additionally argues that job competition may exert a positive externality on the pro?ts of low-skill vacancies when high-skilled workers are more productive than low-skilled workers on low-skill jobs.
10
how the steady-state equilibrium unemployment rates of low- and high-skilled workers are a?ected by changes in the aggregate productivity level or the job separation rate, which represent changes in overall economic activity; changes in the relative productivity of high and low-skill jobs, which are interpreted as skill-biased technological shocks; and changes in the mass of high-skilled workers in the economy.6 Comparative static results do not provide insights into the dynamic impact of shocks. Therefore, the studies described above do not establish a clear connection between job competition and the observed di?erences in the cyclical patterns of unemployment across skill groups. To characterize the allocation of workers across di?erent types of matches and unemployment over the business cycle, we need to allow for deviations from the steady state. Mortensen and Pissarides (1994) do precisely this in their model without heterogeneity and only o?-the-job search, by allowing aggregate productivity to ?uctuate over time. However, on-the-job search and heterogeneity make the transitional dynamics associated with deviations from the steady state di?cult to characterize analytically. Barlevy (2002) incorporates both of these features but turns to a discrete-time version of the model and a collocation method to approximate the value function in order to analyze transitional dynamics. His study establishes that recessions exacerbate mismatch while booms
6
More recently, Pierrard and Sneesens (2003) examine the dynamic adjustment process to a
skill-bias shock and to skill upgrading by allowing for these changes to take place progressively over time. Their scope is to investigate how these changes in combination with job competition externalities a?ect the dispersion between the high- and low-skilled unemployment rates. However, they do not look at the cyclical implications of job competition for the across-skill unemployment dynamics.
11
promote allocative e?ciency by allowing mismatched workers to quit and move into better jobs. The matching technology assumed in Barlevy, however, does not allow for the possibility of job competition and the resulting search externalities and spillover e?ects across skill groups.7 Moreover, by assuming a symmetric equilibrium where ?rms create equal amounts of each type of vacancy, his model predicts that all types of workers face the same labor market prospects. This is inconsistent with the evidence that changes in aggregate economic conditions have di?erent impacts on unemployment ?ows and rates of di?erent skill groups. In this paper, I unite the literature examining matching models with skillmismatches and business cycles with the recent literature examining matching models of job competition. The section that follows gives a description of the model.
1.3 The Model 1.3.1 Main Assumptions
I assume that time is discrete. An exogenous fraction of workers ? is low-skilled (l), while the remaining fraction (1 ? ? ) is high-skilled (h). Similarly, vacancies are high-skill (h) and low-skill (l). The distribution of skill requirement across vacancies is endogenous. Interactions between high- and low-skilled submarkets are embedded into the model by incorporating heterogeneity in terms of jobs’ minimum skill requirements. Both low- and high-skilled workers can be hired for low-skill jobs, but a high-skill job
7
The matching technology in Barlevy is identical to that in Marimon and Zilibotti (1999).
12
can be ?lled only by a high-skilled worker. Consequently, workers of di?erent skill not only have di?erent productivity distributions across types of jobs but di?erent job ?nding rates as well; high-skill workers have a higher job ?nding rate, while low-skill vacancies enjoy a higher arrival rate of workers than high-skill vacancies. High- and low-skilled workers are assumed to be equally productive in low-skill jobs, but high-skilled workers are more productive when matched to a high-skill job. The ?ow output of each match is assumed to be the product of an aggregate component y , and a match speci?c component aj i , where i denotes the type of job and j the type of worker. More formally, let yaj i denote the ?ow of output of a job of type i = (h, l) that is ?lled by a worker of type j = (h, l). Then, the production
h l l technology assumptions can be summarized by yah h > yal = yal > yah = 0.
Given that job-to-job movements represent a substantial fraction of worker ?ows (e.g., Gautier, 1998), I allow for on-the-job search. Mismatched high-skilled workers search on the job for high-skill jobs and quit as soon as they ?nd one, while low-skilled workers have no reason to search on the job. Firms can open at most one job and the choice of type is irreversible. The mass of each type of vacancy is determined endogenously by a free-entry condition. The exogenous component of job separation follows a Poisson process with arrival rate s. Although s is common to both types of job, the e?ective separation rate of low-skill jobs is higher due to on-the-job search by mismatched workers. Whenever a match is destroyed the job becomes vacant and bears a maintenance cost c, while the worker becomes unemployed and receives a ?ow of income b, which is to be interpreted as home production or leisure. 13
I introduce productivity and separation rate ?uctuations into the model by allowing aggregate labor productivity y and the separation rate s to follow a Markov process. Aggregate productivity takes the value of y0 in recessions and y1 > y0 in booms, while the separation rate takes the value s0 in recessions and s1 < s0 in booms. Both variables switch between the two levels with a transition probability p. At every point in time the current values of productivity and separation are common knowledge. The condition that ensures a match is formed in equilibrium is simply that the ?ow of output generated from the match is higher than the unemployment bene?t, i.e., aj i > b, ?i, j . It is optimal for unemployed high-skilled workers to take low-skill jobs as long as their productivity is higher than the unemployment bene?t, because they retain their chances of ?nding a high-skilled job by searching on the job.8 The meeting process is undirected in the sense that a low-skill worker encounters a high-skill vacancy (in which case a match is not formed) with a probability per unit of time that is proportional to the fraction of high-skill vacancies. Similarly, a high-skill worker encounters a low-skill vacancy with a probability per unit of time that is proportional to the fraction of low-skill vacancies.9
8
Dolado et al. (2003) derive conditions that rule out a corner solution in which ?rms create
only low-skill vacancies in a steady state equilibrium. They also derive the conditions under which a steady-state cross-skill matching equilibrium (i.e. an equilibrium in which high-skill workers take low-skill jobs) is unique.
9
I assume the meeting process is undirected (i.e., workers cannot distinguish the vacancy type
before applying) to capture the impact of changes in the skill mix of vacancies on the ?ow rates of di?erent skill groups. In reality even if job seekers can distinguish the type of vacancy before they
14
The total number of matches between a worker and a ?rm is determined by a constant returns to scale function, m vh + vl , uh + ul + eh l (1 ? s) , where vh and vl denote the mass of high- and low-skill vacancies, uh and ul the mass of highand low-skilled unemployed workers, and eh l (1-s) the number of high-skilled workers in low-skill jobs (which I label as mismatched henceforth) that survive separation. m [·, ·] is strictly increasing in both arguments. The “labor market tightness” is denoted by ? =
vh +vl , uh +ul +e h (1?s) l
so that in a tighter market there are more vacancies
available per job seeker. The pool of job seekers is composed of unemployed high- and low-skilled workers and mismatched workers. For convenience, I de?ne the following shares: ul ul + uh ul + uh ? = ul + uh + eh l (1 ? s) ? = (1.1) The rate at which ?rms meet a job seeker of any type is equal to q (?) = m(1, 1 ), ? which is decreasing in ? and exhibits the standard properties of: lim??0 q (?) = lim??? ?q (?) = ? and lim??? q (?) = lim??0 ?q (?) = 0. A mismatched high-skilled worker has no incentive to change employer unless the new employer o?ers him a high-skill job. Accordingly, some low-skill vacancies will meet mismatched workers who will refuse to match. Likewise, employers with high-skill jobs will not hire
apply there are still search frictions involved that prevent workers from ?nding the right match. For example, it is harder for a high-skilled worker to ?nd a high-skill job if only 5% of the vacancies are high-skill than when 95% of the vacancies are high-skill, even if he/she can distinguish the vacancy type. This type of search friction is captured by assuming random instead of directed search.
15
the low-skilled workers they meet. Therefore, the e?ective matching rate of a lowskill vacancy with a low-skilled worker is given by ??q (?), while the corresponding rate with a high-skilled worker is ? (1 ? ?) q (?) . High-skill vacancies match only with either mismatched or unemployed high-skilled workers, and thus their e?ective matching rate can be written as (1 ? ??) q (?). Assuming that ? =
vl vl +vh
denotes
the fraction of low-skill vacancies, the e?ective matching rate of low-skilled workers is ?m(?), while mismatched high-skilled ?nd a high-skill job with a rate (1 ? ? )m(?). Finally, unemployed high-skilled workers can take either a high- or a low-skill job and thus their e?ective matching rate is equal to m(?) (i.e., ?m(?) + (1 ? ? )m (?)). The asymmetric nature of the matching technology generates the following across-skill externalities and spillover e?ects: i) Vacancy Composition E?ect (VCE). An increase in the fraction of high-skill vacancies (1 ? ? ) decreases the unemployment-to-employment ?ow probability of low-skilled workers, but also decreases the unemployment-to-mismatch ?ow probability of high-skilled workers; ii) Negative Quit Externality (NQE). The higher quit rate of mismatched highskilled workers lowers the pro?ts of low-skill jobs. As a result, an increase in the fraction of high-skilled unemployed job seekers ? (1 ? ?), which in turn increases the likelihood of high-skilled workers taking low-skill jobs, lowers the pro?ts of low-skill jobs. Hence, low-skill vacancy creation declines with higher fractions of unemployed high-skilled workers, making it harder for low-skill workers to ?nd a job; iii) Negative Congestion Externality (NCE henceforth). High-skilled job seekers exert a negative externality on low-skilled employa16
bility by creating additional congestion in the market, thus making it harder for low-skilled workers to encounter a low-skill job, and for low-skill vacancies to encounter a low-skilled worker. To be more speci?c, an increase in the number of high-skilled job seekers eh l + uh , lowers the probability that a low-skill worker will meet a low-skill vacancy, given by ?m(?), through a lower ?, and the probability that a low-skill vacancy will encounter a low-skilled worker, given by ??q (?), through a lower ??. In short, an increase in ? implies a VCE that bene?ts low-skilled employability but at the same time facilitates the transition of high-skilled workers into low-skill jobs. An increase in the fraction of high-skilled job seekers (both unemployed and mismatched), given by (1 ? ??), exacerbates both the NCE and NQE on low-skill employability.
1.3.2 Bargaining
In equilibrium there are three possible types of matches: (i) high-skilled workers in high-skill jobs, (ii) high-skilled workers in low-skill jobs and (iii) low-skilled workers in low-skill jobs. The surplus of each match is divided according to a Nash bargaining solution. The share of surplus that workers receive is exogenous and denoted by ? . I adopt the following standard notation: U j denotes the value of unemployment for a worker of type j , Vi denotes the value of a vacant job of type i, Wij denotes the value of employment for a worker of type j in a job of type i, and ?nally Jij denotes the value to the ?rm of ?lling a job of type i with a worker of type
17
j . Accordingly, the surplus of a match can be expressed as Sij = Wij + Jij ? U j ? Vi
j and the wage wi satis?es
(1 ? ? ) Wij ? U j = ? Jij ? Vi
(1.2)
1.3.3 Timing and Flow Equations
h l Let e = eh h , el , el be the mass of high-skilled workers in high-skill jobs, the
mass of high-skilled workers in low-skill jobs and the mass of low-skilled workers in low-skill jobs, respectively, at the beginning of period t. At this stage, the Markov shock hits the economy and a new pair (y, s) arrives that is common knowledge to
h l all agents in the economy. After e = eh h , el , el and (y, s) are observed, production
takes place, exogenous separations occur, and vacancies are posted by ?rms to insure zero pro?ts. Search takes place and workers change jobs, leading to the following distribution of workers in the subsequent period:
l e?ll = el l (1 ? s) + ?m(? ) ? ? el (1 ? s) h h e?h = eh h (1 ? s) + (1 ? ? )m(? ) (1 ? ? ? eh (1 ? s) h h e?lh = eh l (1 ? s) + ?m(? ) 1 ? ? ? (el + eh )(1 ? s)
(1.3) (1.4)
?(1 ? ? )m(?)eh l (1 ? s)
(1.5)
1.3.4 Asset Values
Workers are risk neutral, time is discrete and the interest rate r is constant. The asset value of an unemployed low-skilled worker at aggregate state (y, s) and 18
a given distribution of employment e = satis?es U l (y, s, e) = b +
h l eh h , el , el
is denoted by U l (y, s, e) and
1 [?m(?)E [Wll (y ? , s?, e? /)/y, s, e] (1 + r ) (1.6)
+(1 ? ?m(?))E [U l (y ? , s? , e? )/y, s, e]
Equation (1.6) states that the value of an unemployed low-skilled worker is equal to his value of leisure b, plus the present value of the probability he ?nds a low-skill job times the resulting expected value conditional on the current state (y, s, e), given by E [Wll (y ?, s? , e? )/y, s, e], plus the probability he does not ?nd a job, times the expected value of staying unemployed given by E [U l (y ?, s? , e? )/y, s, e]. (y ?, s? ) and e? =
h ?h ?l e?h , el , el
denote the realization of aggregate shocks and the distribution
of employment next period, respectively. Similarly, given that high-skilled workers accept both types of jobs, the corresponding value of unemployment for high-skilled workers, U h (y, s, e) satis?es U h (y, s, e) = b + 1 [?m(?)E [Wlh (y ? , s? , e? )/y, s, e] (1 + r )
h ? ? ? +(1 ? ? )m(?)E [Wh (y , s , e )/y, s, e]
+(1 ? m(?))E [U h (y ?, s? , e? )/y, s, e]]
(1.7)
The rest of the asset values are similar. The asset values of high- and low-skilled workers in high- and low-skill jobs, respectively, satisfy
h h ? ? ? Wh (y, s, e) = wh (y , s , e ) +
1 [sE [U h (y ? , s? , e? )/y, s, e] (1 + r ) (1.8)
h ? ? ? +(1 ? s)E [Wh (y , s , e )/y, s, e]]
Wll (y, s, e) = wll (y ?, s? , e? ) +
1 [sE [U l (y ?, s? , e? )/y, s, e] (1 + r )
19
+(1 ? s)E [Wll (y ?, s? , e? )/y, s, e]]
(1.9)
while the asset value of employment for mismatched high-skilled workers is given by Wlh (y, s, e) = wlh (y ? , s?, e? ) + 1 [sE [U h (y ?, s? , e? )/y, s, e] (1 + r )
h ? ? ? +(1 ? s)(1 ? ? )m(?)E [Wh (y , s , e ) ? Wlh (y ?, s? , e? )/y, s, e]
+(1 ? s)E [Wlh (y ?, s? , e? )/y, s, e]]
(1.10)
Mismatched high-skilled workers search on the job for high-skill jobs. Therefore, the last term in the above equation represents the value of on-the-job search: given that the match survives to the next period with a probability (1 ? s) a mismatched highskilled worker can ?nd a high-skill job with a probability (1 ? ? ) m(?), in which case
h ? ? ? he gains the expected capital gain from switching jobs, given by E (Wh (y , s , e /y, s, e)?
Wlh (y ? , s? , e? /y, s, e)). The values of opening high- and low-skill vacancies are given by Vh (y, s, e) = ?c + 1 h ? ? ? [(1 ? ??)q (?)E [Jh (y , s , e )/y, s, e] (1 + r ) (1.11)
+(1 ? (1 ? ??)q (?))E [Vh (y ?, s? , e? )/y, s, e]] Vl (y, s, e) = ?c + 1 [??q (?)E [Jll (y ?, s? , e? )/y, s, e] (1 + r )
+? (1 ? ?)q (?)E [Jlh (y ?, s? , e? )/y, s, e] +(1 ? ?q (?))E [Vl (y ?, s? , e? )/y, s, e]] whereas the values to the employer of ?lling those vacancies satisfy
h h Jh (y, s, e) = yah h ? wh (y, s, e) +
(1.12)
1 [sE [Vh (y ?, s? , e? )/y, s, e] (1 + r ) (1.13)
h ? ? ? +(1 ? s)E [Jh (y , s , e )/y, s, e]]
20
l Jll (y, s, e) = yal l ? wl (y, s, e) +
1 [sE [Vl (y ? , s? , e? )/y, s, e] (1 + r ) (1.14)
(1 ? s)E [Jll (y ? , s? , e? )/y, s, e]] Finally, the value to a low-skill ?rm with a high-skilled worker is
h Jlh (y, s, e) = yal l ? wl (y, s, e) +
1 [sE [Vl (y ?, s? , e? )/y, s, e] (1 + r )
+(1 ? s)E [Jlh (y ?, s? , e? )/y, s, e] ?(1 ? s)(1 ? ? )m(?)E [(Jlh (y ?, s? , e? ) ? Vl (y ?, s? , e? ))/y, s, e]] (1.15) where the last term represents the reduction in the value to the ?rm of hiring a high-skilled worker, as the latter searches on the job and thus will quit as soon as a high-skill job arrives.
1.3.5 Surpluses and Zero Pro?t Conditions
Using the Nash bargaining condition given by equation (1.2) and the asset value equations described above we can write the surplus functions as follows: Sll (y, s, e) = yal l ?b+ 1 [(1 ? s)E [Sll (y ?, s? , e? )/y, s, e] (1 + r ) (1.16)
???m(?)E [Sll (y ? , s? , e? )/y, s, e]
h Sh (y, s, e) = yah h?b+
1 h ? ? ? [(1 ? s)E [Sh (y , s , e )/y, s, e] (1 + r )
h ? ? ? ?? (1 ? ? )m(?))E [Sh (y , s , e )/y, s, e]
???m(?)E [Slh (y ?, s? , e? )/y, s, e]]
(1.17)
21
Slh (y, s, e) = yal l?b+
1 [(1 ? s)E [Slh (y ?, s? , e? )/y, s, e] (1 + r )
h ? ? ? +(1 ? s)(1 ? ? )m(?)E [(?Sh (y , s , e ) ? Slh (y ? , s? , e? ))/y, s, e]
???m(?)E [Slh (y ?, s? , e? )/y, s, e]
h ? ? ? ?? (1 ? ? )m(?)E [Sh (y , s , e )/y, s, e]]
(1.18)
The surplus of a low-skill job ?lled by a low-skilled worker Sll , takes the standard form: the ?rst term, gives the net ?ow of output the match generates; given that the match survives to the next period with a probability (1 ? s), the second term gives the expected present value of future surplus; the last term re?ects the workers’ forgone search opportunity (i.e., their ability to search for a job) while employed, and is subtracted from the surplus.
h The surplus of a ?lled high-skill job Sh , takes a similar form. The only dif-
ference is that once high-skilled workers ?nd a job, they lose their opportunity to search for both high- and low-skill job jobs once employed. Hence, the surplus function changes accordingly. The surplus of a low-skill-job ?lled by a high-skill worker Slh , takes a slightly di?erent form. When high-skilled workers take low-skill jobs, they can still search for high-skill jobs. The value of this option is added to the surplus and is given by the third term in the equation (1.18). Given that the match survives to the next period with a probability (1 ? s), mismatched workers search on the job and with probability (1 ? ? )m (?) ?nd high-skill jobs, in which case they
h ? ? ? gain a share ? of E [Sh (y , s , e )/y, s, e] while losing E [Slh (y ? , s? , e? )/y, s, e].
After substituting the surplus expressions into the values of vacancies, given
22
by equations (1.11) and (1.12), I de?ne the following free entry conditions: c = (1 ? ? )q (?) ??ESll (y ?, s? , e? ) + ? (1 ? ?)ESlh (y ? , s? , e? ) (1 + r ) (1 ? ? )q (?) h ? ? ? c = (1 ? ??)ESh (y , s , e ) (1 + r ) (1.19) (1.20)
These conditions imply that ?rms keep opening vacancies until the cost of keeping a vacancy un?lled c equals the expected future pro?ts of a ?lled job. The conditions implicitly de?ne ?y,s,e and ?y,s,e as a function of the current aggregate state (y, s) and the current distribution of employment across types of matches given by e =
h l eh h , el , el .
1.3.6 Equilibrium
The equilibrium is given by a vector {?, ?, ?, ?, e} that satis?es the following: (i) the three types of matches are formed voluntarily, i.e., yaj i > b ?i, j for which matches are formed; (ii) the two free entry conditions in (1.19) and (1.20), are satis?ed so that the values of maintaining low- and high-skill vacancies are zero;
h l and (iii) the state variables eh h , el , and el follow the ?ow equations (1.3) to (1.5)
above.
1.4 Simulations
The purpose of this section is to gauge qualitatively the e?ects of business cycle ?uctuations on job competition, skill mismatches, average match productivity and unemployment rates by skill group. I consider aggregate productivity and separation
23
rate shocks separately in order to illustrate their individual e?ects and highlight their di?erences. I turn to numerical techniques to analyze the model. I use the free entry conditions given by equations (1.19) and (1.20) above to ?nd the state-contingent market tightness ?y,s,e and fraction of low-skill vacancies ?y,s,e . I then simulate the model as follows: ?rst, I generate a sequence of aggregate state (y, s) realizations; then, starting with the ?rst realization of aggregate state, and an initial distribution
h l of employment e = eh h , el , el I use the laws of motion given by equations (1.3) to
(1.5) to compute the new distribution of employment at the beginning of the next period; and then I repeat. At the end of each period, I record the aggregate state and employment distribution and generate series of unemployment rates and labor productivity along a sequence of aggregate state realizations. The exogenous variables are set at the following values: ? = .5, r = .03,
l c = .5, b = .1, ? = .75, ah h = .8 and al = .45. The matching function m [·, ·] is
a Cobb Douglas function in which job seekers and vacancies are assumed to have equal elasticities of 0.5. In section 1.5.1, where I examine the e?ects of an aggregate productivity shock, I normalize the high value of aggregate productivity to y1 = 1 and set the low value equal to y0 = .9, while keeping the separation rate ?xed at s = .1. In section 1.5.2, I keep aggregate productivity at its high level and let the separation rate ?uctuate between s1 = .1 and s0 = .11. For the purpose of solving the free entry conditions to determine the state-contingent ?y,s,e and ?y,s,e , the stochastic variable in each case follows a Markov process, with a transition probability .3. To compute impulse responses to each shock, I simulate the model 24
assuming that once the shock arrives it follows a sample path in which it persists for 20 periods, although the agents believe that the shock persists only with probability 0.3 each period. Since the purpose of this section is to illustrate qualitative implications the parameters have been chosen in a rather ad hoc manner. However, the results presented in this section are robust to changes in the underlying parameter con?guration.
1.4.1 Aggregate Productivity Fluctuations
In this section, I simulate the model allowing for aggregate productivity ?uctuations. As already mentioned, the heart of the model is the skill composition of vacancies. Hence, I begin this section by characterizing the evolution of this skill composition. As we can see from Figure 1.1, the immediate e?ect of a negative productivity shock is to lower the fraction of low-skill vacancies (? ).
Figure 1.1: E?ect of a Negative Productivity Shock on the Fraction of Low-skill Vacancies.
Over time, the initial decline is gradually partially reversed. The reason for 25
the partial recovery is the increase in the fraction of low-skilled unemployed in the mass of jobs seekers immediately after the shock. In response to the increase in the fraction of high-skill vacancies following the fall in productivity, the fraction of unemployed low-skilled workers in the mass of job seekers increases, while the corresponding fraction of high-skilled (both unemployed and mismatched) workers decreases. These are illustrated in Figures 1.2 and 1.3, respectively. Firms with low-skill vacancies bene?t from the increased fraction of low-skilled workers in the pool of searchers, because low-skilled workers do not search on the job and thus provide more surplus than mismatched high-skilled workers. Thus, the change in the skill composition of job seekers stimulates low-skill vacancy creation so that the fraction of low-skill vacancies partially recovers from the initial decline.
Figure 1.2: E?ect of a Negative Productivity Shock on the Fraction of Low-skilled Workers in the Mass of Job Seekers.
The conventional result that periods of low productivity hurt the matching process is present in this model as well. This takes the standard form of a lower vacancy-job seeker ratio ? and thus a lower meeting rate m (?) during downturns. As can be veri?ed in Figure 1.4, the meeting rate follows a pattern similar to the
26
Figure 1.3: E?ect of a Negative Productivity Shock on the Fraction of High-skilled Workers in the Mass of Job Seekers. fraction of low-skill vacancies and for similar reasons: vacancy creation falls initially due to lower productivity and surplus, then gradually rises, as rising unemployment increases the worker arrival rate.
Figure 1.4: E?ect of a Negative Productivity Shock on the Worker-Vacancy Meeting Rate.
Although the model delivers the conventional result of a lower vacancy-job seeker ratio (?) during downturns, it does not replicate Barlevy’s (2002) result that recessions sti?e the transition of mismatched workers into the jobs they are best suited for, and therefore increase the degree of skill-mismatch in the market. Instead, 27
the model suggests that economic slowdowns generate a reduction in the number of mismatched high-skilled workers.
Figure 1.5: E?ect of a Negative Productivity Shock on the Probability of Finding a High-Skill Job.
Figure 1.6: E?ect of a Negative Productivity Shock on the Probability of Finding a Low-Skill Job. The key to this novel result is the VCE described above, namely that periods of low productivity involve an upgrading in the skill composition of vacancies (i.e. an increase in (1 ? ? )). More precisely, the VCE dominates the reduction in the meeting rate, so that the probability of ?nding a high-skill job (1 ? ? ) m (?) increases, while the probability of ?nding a low-skill job ?m (?) decreases. The paths 28
of these probabilities are illustrated in Figures 1.5 and 1.6, respectively. As soon as the shock arrives, the former increases, while the latter decreases, hindering the transition of unemployed high-skilled workers into low-skill jobs and facilitating the transition of both unemployed and mismatched high-skilled workers into high-skill jobs. Later on, these probabilities partially revert towards their initial values, re?ecting the gradual recovery in the fraction of low-skill vacancies as ?rms try to take advantage of the higher arrival rate of low-skilled job seekers.
Figure 1.7: E?ect of a Negative Productivity Shock on Average Match Productivity.
As illustrated in Figure 1.7, these changes in probabilities that occur during periods of low productivity shift the mass of the distribution of high-skilled workers towards high-skill jobs and therefore increase average match productivity (i.e. the average of aj i across all matches). This result is in line with previous work that argues that recessions should promote allocative e?ciency (e.g. Hall 1991, 2000; Mortensen and Pissarides 1994; Caballero and Hammour 1994, 1996; and Gomes, Greenwood, and Rebelo 1999), but rests on a di?erent mechanism: an upgrading in the skill composition of vacancies facilitates the transition of overquali?ed workers into the jobs for which they are best suited. This mechanism is new in the theo29
retical literature on business cycles and worker reallocation, because it results from asymmetries in the matching rates of di?erent skill groups that have been neglected in previous research. The notion that the lower meeting rate m (?) during recessions sti?es the transition of mismatched workers into the jobs they are best suited for has been labeled by Barlevy (2002) as the “sullying” e?ect of recessions. However, the “sullying” e?ect rests on the assumption of symmetry. To be more speci?c, Barlevy (2002) focuses only on equilibria in which the production technology is symmetric, the skill composition of the labor force is symmetric and ?rms create equal amounts of each type of vacancy.10 Under these assumptions, neither the distribution of workers across match quality and unemployment nor the number of vacancies posted varies with skill type. Moreover, this type of framework implies that all workers are equally likely to form a match of any given quality. Hence, such framework leaves no room for search externalities and spillover e?ects across skill groups. Given that by assumption in equilibrium ?rms create equal amounts of each type of vacancy, the VCE that arises in my model during periods of low productivity is not present in Barlevy’s model. The only e?ect of recessions in Barlevy is the lower meeting rate that impedes mismatched workers from reallocating into more e?cient uses. I next characterize the evolution of unemployment rates across skill groups.
10
According to the production technology assumed in Barlevy the productivity of a match de-
pends negatively on the distance between the worker’s and job’s skill level. However, an underquali?ed worker is as productive as an over-quali?ed worker on a particular job, as long as the distance between the worker-job skill level is the same.
30
Figure 1.8: E?ect of a Negative Productivity Shock on Unemployment and Mismatch Rates. As mentioned in the introduction, the low-skilled unemployment rate is higher and more sensitive to changes in economic activity than the high-skilled unemployment rate. The model con?rms this observation. Figure 1.8 illustrates the evolution of unemployment rates of the two skill groups and the evolution of the mismatch rate (de?ned as the fraction of high-skilled workers who are mismatched). Independent of the level of aggregate productivity, the low-skill unemployment rate is higher than the high-skilled one, because high-skilled workers qualify for both types of jobs and thus can ?nd a job more easily. When aggregate productivity falls, mismatch in the form of high-skilled workers taking low-skill jobs declines, yet the low-skilled
31
unemployment rate still rises more than the high-skilled unemployment rate. The latter converges to a level only 0.2 percentage points higher than the original, while the former converges to a level 0.6 percentage points higher than the original. The explanation I o?er for the higher sensitivity of the low-skilled unemployment rate to changes in economic activity is conceptually simple but contrary to the common belief that high-skilled workers “crowd-out” low-skilled workers in a competition for jobs.11 As illustrated above, periods of low aggregate productivity involve less job competition and fewer high-skilled workers taking low-skilled jobs. Instead, the model suggests that high-skilled employability is less sensitive to changes in economic
11
Among the studies that investigate the implications of job competition externalities on low-
skilled employability, only Gautier (2002) looks at the steady-state e?ects of changes in aggregate productivity. He con?rms that low-skilled unemployment rises more than high-skilled unemployment when aggregate productivity falls, but suggests that this is due to high-skilled workers crowding out low-skilled workers. This result, however, rests on two assumptions. First he assumes that unemployment bene?ts are a ?xed fraction of workers’ productivity. Therefore, changes in economic activity do not alter the relative net productivities of high- and low-skill jobs, leaving the skill composition of vacancies unchanged. Second, he assumes that search is directed. Directed search implies that changes in the skill mix of vacancies do not a?ect workers probability of ?nding a job. Consequently, under directed search the VCE is no longer relevant. The only e?ect captured in Gautiers model is that high-skilled workers’ exert a negative externality on low-skill job profitability because of their higher quit probability (NQE), so that when unemployment is higher and high-skilled workers’ take low-skill jobs more frequently, low-skill vacancy creation declines. The validity of this result depends on the extend to which changes in the skill composition of vacancies do not a?ect workers’ probabilities of ?nding a particular type of job.
32
activity because high-skilled workers can be employed in a wider range of job types and thus can more easily bu?er against unfavorable changes in the skill composition of vacancies. High-skilled workers qualify for both types of jobs, which implies an e?ective unemployment-to-employment probability for high-skilled workers equal to m(?), which depends only on market tightness (?). Low-skilled workers, on the other hand, qualify for only low-skill jobs. Therefore, their e?ective matching rate is ?m (?) and ?uctuates both with changes in market tightness and changes in the skill composition of vacancies. As a result, during periods of low productivity, lowskilled workers su?er both the consequences of a more sluggish labor market (lower ?) and skill upgrading in vacancy mix (lower ? ), whereas high-skilled workers su?er only the consequences of the former. The reduction in the fraction of high-skilled job seekers (both unemployed and mismatched) implies a lower NCE and NQE on low-skilled employability. Given that there are relatively fewer high-skilled job seekers low-skill vacancies are more likely to encounter a low- than a high-skilled job seeker, and low-skilled workers su?er lower congestion from high-skilled workers. However, low-skill unemployment still rises more in response to the fall in productivity, indicating that the VCE dominates. Hence, what is hidden behind the higher sensitivity of low-skilled unemployment is not job competition externalities but the change in the skill composition of vacancies. The ?nding that an upgrading in the skill composition of vacancies facilitates a more e?cient allocation and improves average match productivity following a decline in aggregate productivity, does not square with empirical ?ndings that match quality is procyclical. As will be explained in the next section, however, the model performs 33
better along this dimension when periods of low productivity are driven by shocks to the separation rate and thus a high ?ow of workers into unemployment. Before I proceed with characterizing the dynamic response to a separation rate shock, I discuss the robustness of the results presented so far to changes in the parameter con?guration. The results are not sensitive to changes in the relative productivity of high- and low-skilled jobs or changes in the magnitude of the shock. A smaller productivity gap between skill types results in a smaller gap between highand low-skilled unemployment rates, while larger shocks result in higher dispersion between high- and low-skilled unemployment rates. However, the implications of changes in aggregate productivity for unemployment and mismatch rates remain the same. I also examined changes in the skill composition of the labor force.12 I ?nd that the relevant variables follow the patterns described above independent of the skill composition of the labor force.
1.4.2 Job Separation Fluctuations
In this section, I keep aggregate productivity ?xed and allow the job separation rate to ?uctuate over time. As illustrated in Figure 1.9, on impact of a negative separation rate shock, the fraction of low-skill vacancies increases as ?rms take advantage of the increase in their relative pro?tability. Over time, the fraction of
12
This exercise was motivated by the work of Pierard and Sneezes (2003) and Dolado et al. (2003)
that suggests the uneven increase in low-skilled unemployment, may be the result of an increase in the fraction of high-skilled workers in the labor force, which exacerbates job competition and crowding out of low-skilled workers.
34
low-skill vacancies gradually decreases, but remains higher than the original level.
Figure 1.9: E?ect of a Separation Rate Shock on the Fraction of Low-Skill Vacancies. The gradual reversion is due to intensi?ed negative quit externalities following the initial increase, which reduce low-skill job pro?tability and thus vacancy creation. The sharp initial increase in the fraction of low-skill vacancies, together with the sharp increase in high-skilled unemployment due to the separation rate shock, facilitate the transition of high-skilled workers into low-skill jobs while sti?ing transitions out of them, exacerbating negative quit externalities on low-skill job pro?tability. Figure 1.10 shows the evolution of the fraction of high-skilled job seekers (both unemployed and mismatched), which re?ects the evolution of negative job competition externalities (NCE and NQE) on low-skilled employability. On impact, the fraction declines, re?ecting the sharp increase in unemployment. Subsequently the fraction increases as more high-skilled workers move into low-skilled jobs. In turn, the rise in NCE and NQE results in a gradual reduction in the fraction of low-skill vacancies. To clarify this further, I report the evolution of probabilities of ?nding a highand a low-skill job in Figures 1.11 and 1.12, respectively. On impact of the shock, the 35
Figure 1.10: E?ect of a Separation Rate Shock on the Fraction of High-skilled Job Seekers. ?rst decreases while the latter increases. Therefore, a higher mass of high-skilled workers is misallocated into low-skill jobs, while the lower probability of ?nding high-skill jobs implies that they remain overquali?ed for a longer period. Over time the resulting negative job competition externalities lower the probability of ?nding a low-skill job, while increasing the probability of ?nding a high-skill job.
Figure 1.11: E?ect of a Separation Rate Shock on the Probability of Finding a High-skill Job.
Given these changes in job probabilities in response to the increase in job separation, the model suggests that a higher degree of over-quali?cation during recessions is the result of an increase in job separation and ?ow of workers into unemployment. 36
Figure 1.12: E?ect of a Separation Rate Shock on the Probability of Finding a Low-skill Job. If indeed recessions are characterized by sharp increases in job separation then the model can explain the observed procyclicality in match quality. As can be veri?ed from Figure 1.13, in response to the separation rate shock, average match productivity decreases gradually, as more high-skilled workers become overquali?ed, and converges to a lower level.
Figure 1.13: E?ect of a Separation Rate Shock on Average Match Productivity.
The question that remains is whether separation rate ?uctuations can also explain higher and more volatile low-skilled relative to high-skilled unemployment. One would expect that the shift in the vacancy mix towards low-skill vacancies in
37
response to the shock, and the resulting higher probability of ?nding a low-skill job, would improve the position of low-skilled workers relative to high-skilled workers in the labor market. However, this is not the case. The shift in the vacancy mix exerts a positive VCE on low-skilled employability, but at the cost of the strong negative job competition externalities that follow. The evolution of unemployment and mismatch is illustrated in Figure 1.14. Both unemployment rates increase in response to the shock, but the low-skilled unemployment rate continues to increase even further as the mismatch rate increases. Eventually, the low-skilled unemployment rate converges to a level 1.6 percentage points above the original, while the high-skilled unemployment rate converges to a level only 1.2 percentage points above the original. As in the case of a negative productivity shock, the impact of a separation rate shock on unemployment and mismatch rates is not qualitatively sensitive to changes in parameters such as the relative productivity of high-skilled workers or the skill composition of the labor force. What drives the evolution of mismatch and unemployment rates in response to the separation rate shock is the increase in the fraction of low-skill vacancies, following the increase in the relative pro?tability of low-skill jobs. In turn, the increase in the relative pro?tability of low-skill jobs rests solely on the fact that low-skill vacancies can be re-?lled faster once dissolved, because they can be ?lled by both types of workers. This advantage is never reversed, no matter the skill-composition of labor force or the productivity dispersion between high- and low-skill jobs. I close this section by discussing the impact of job competition externalities 38
Figure 1.14: E?ect of a Separation Rate Shock on Unemployment and Mismatch Rates. on low-skilled employability. Unquestionably, the negative externalities arising from intensi?ed job competition for low-skill jobs in response to the job separation shock harm low-skilled employability. However, the job competition externalities are not the only driving force behind the relatively higher sensitivity of low-skilled unemployment to cyclical ?uctuations. The changes in the skill mix of vacancies that occur over the business cycle are also important, as low-skilled workers are more vulnerable to these changes than high-skilled workers. In response to a negative productivity shock, job competition externalities decline, but still low-skilled unemployment rises relatively more, because of the skill upgrading in the skill composition 39
of vacancies that hurts low-skilled employability. On the other hand, a negative separation rate shock exacerbates the negative job competition externalities on low-skill employability, but only because low-skill vacancies become relatively more plentiful. Hence, regardless of the e?ect of the co-movement between aggregate productivity and job separation on competition for low-skill jobs, recessions hurt low-skilled employability relatively more.13
1.5 Conclusion
In this paper I develop a model that examines the impact of skill-mismatch, in the form of high-skilled workers taking temporarily low-skill jobs, on labor productivity and unemployment dynamics by skill. I capture negative job competition
13
Job competition may actually bene?t low-skilled employability by stimulating low-skill vacancy
creation. I simulated the model assuming that searching on the job is costly enough that highskilled workers are no longer willing to take low-skill jobs (i.e., separate markets). I found that unemployment for both types is higher when markets are separated than when cross-skill matching takes place. The high-skilled unemployment rate is higher in the absence of cross-skill matching for the obvious reason: given that they cannot take low-skill jobs they have a harder time escaping unemployment. What is somewhat surprising is that low-skilled unemployment is higher, but the explanation is also reasonable: when high-skilled workers are not willing to take low-skill jobs, the value of opening a low-skill vacancy is lower, as the option value of hiring a high-skilled worker is forgone, resulting in lower vacancy creation and higher unemployment in the low-skill market. This explanation does not contradict my previous argument that ?rms with low-skill vacancies prefer hiring low- instead of high-skilled workers. The intuition is that low-skill ?rms prefer hiring low- to high-skilled workers because the latter are likely to quit, but they are still better o? having the option of hiring a high-skilled worker in case they meet one.
40
externalities on low-skilled employability, by incorporating into the model the fact that low-skilled workers qualify only for jobs with low skill requirements. Previous work has argued that recessions hurt the matching process as ?rms post fewer vacancies per job seeker. As a result, mismatched workers who search onthe-job for better matches remain mismatched for a longer period, aggravating the allocation of workers into mediocre matches. However, as this paper illustrates, this is not the whole story. Recessions also involve an increase in the relative number of high-skill vacancies that facilitates the transition of high-skilled workers into highskill jobs, thus bringing down the degree of over-quali?cation in the labor market. Accounting for the asymmetric nature of the matching technology, and the resulting job competition externalities, shows that recessions involve a higher degree of overquali?cation only when associated with higher job turnover and ?ow of workers into unemployment. Hence, my model provides insights into skill-mismatch over the cycle that stress the role of increases in job separation when aggregate productivity is low. Further, my model explains observed di?erences in labor market outcomes of di?erent skill cohorts. The asymmetry explains the relatively low exit rates of lowskilled workers from unemployment, and their relatively low propensity to search on the job. My model can also explain why low-skilled unemployment exhibits relatively higher cyclical sensitivity. The common belief is that, during recessions, high-skilled workers “crowd-out” low-skilled workers as they compete for jobs. However, in this paper I illustrate that the higher sensitivity of low-skill unemployment to changes in economic activity is not due to crowding out per se. Instead, the primary reason is that high-skilled workers qualify for both high- and low-skill jobs, and therefore 41
are less vulnerable to changes in economic activity, because they are less vulnerable to the changes in the skill mix of vacancies that occur simultaneously. By highlighting the vacancy composition e?ect of recessions, which has been overlooked in previous research, my model improves our understanding of how recessions a?ect the matching process and the employability of di?erent skill cohorts, and suggests a closer look at the evolution of the skill mix of vacancies. In addition, by laying out the e?ects of aggregate productivity and job separation on the skill composition of vacancies, I stress the importance of understanding the relation between the two impulses. Modeling endogenous responses of the separation rate to changes in aggregate labor productivity as in Mortensen and Pissarides (1994), for instance, is therefore, the natural extension of the model. The nature of the model in this paper requires the endogenous variables to depend on the aggregate state and also on the distribution of workers across types of matches. Therefore, introducing aggregate productivity ?uctuations alone is a signi?cant contribution and makes the task of endogenizing job separation much more plausible. Future research will build upon this contribution by endogenizing separations.
42
Chapter 2 Cyclical Variation in Match Quality: The Role of Unemployment Risk 2.1 Introduction
Studies show that the unemployment rate of low-skilled workers is higher and more sensitive to changes in economic activity compared to that of high-skilled workers.1 Some have suggested that this may in part be caused by “crowding out”, i.e. the phenomenon in which high-skilled workers occupy simple jobs during recessions, thereby pushing low-skilled workers into unemployment, and move on to better jobs in booms.2 Existing research has not yielded clear conclusions about the empirical relevance of such a cyclical pattern in the matching behavior of high-skilled workers. Hence, its empirical relevance remains a question, the answer of which forms the basic goal of this chapter. To this end, I study the mismatch rates and job level dynamics using a panel of 15748 individuals constructed from the yearly family ?les of the Panel Study of
1
For evidence on the cyclicality of low-skilled unemployment rate, see for example, van Ours
and Ridder (1995). For evidence on the distribution of jobless time and unemployment being heavily concentrated among the least skilled individuals see e.g. Topel (1993); Bovengerg (1997) Ashenfelter and Ham (1979); Nickell (1979).
2
See e.g., and Teulings and Koopmanschap (1989).
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Income Dynamics (PSID), which covers the years from 1968 to 1993.3 By job levels I refer to categories of occupations that di?er in terms of skill requirements and prestige (i.e., high job levels are jobs that require more education and have higher prestige scores than low job levels). First, to give a general idea of the cyclical patterns in match quality across di?erent skill groups, I look at how mismatch rates vary over the business cycles and across workers with di?erent education. Second, I use linear probability and Logit regression analysis to characterize how the probability of moving either to high- or low-skill jobs is a?ected by the overall unemployment rate and the education of the worker. Third, by adopting dynamic panel data estimation methods, I measure the e?ect of the workers’ lagged state (i.e., whether unemployed or mismatched), as well as the e?ect of its interactions with overall the overall unemployment rate and workers’ education level, on the probability of transitions to either high- or low-job levels. Finally, by modeling the dynamics of transitions as a ?rst order Markov process, which is heterogeneous among individuals I investigate how workers’ transitions between job levels vary with skill and over the business cycle. To characterize the transitions, I adopt a ?xed e?ects multinomial Logit estimation procedure designed by Honor´ e and Kyriazidou (2000), which is based on conditional likelihood maximization (Chamberlain, 1984).
3
Existing studies test for crowding out phenomena mainly in Europe. In the U.S. crowding out
as an explanation for the high and more cyclical low-skill unemployment received less attention. To my knowledge, this is the ?rst study that tests for crowding out phenomena using data from the U.S.
44
The comparison of job level probabilities across groups of workers with di?erent education years of high employment growth to those of low employment growth is a common methods of testing for cyclical variation in match quality. Such a comparison reveals whether workers with a given level of education achieve lower job levels in years with low employment growth, as the crowding out hypothesis assumes. Examples are Gautier, Pomp and Zijl (1997), and Gautier (1998) who separate workers into educational levels and estimate multinomial Logit models (one for each level of education). Empirical tests also compare educational levels per job level. Teulings and Koopmanschap (1989), for example, explain regional changes in the distribution of educational levels per job level, using regional changes in unemployment rates. In a similar analysis, Hartog (1992) uses survey answers to questions regarding labor market tightness of the form: do people with your education, skills and age, in your area, easily ?nd a job to match this? Others test the crowding out hypothesis by looking at the ?ows of ?lled vacancies. For example, van Ours and Ridder (1995) test whether lower stock of vacancies and higher number of unemployed job seekers at the beginning of the period, leads to higher ?ow of ?lled vacancies at lower levels. Their test of crowding out also involves estimating whether the correlation between the unemployment rate of higher educated workers and the ?ow of ?lled vacancies at lower job levels is positive and signi?cant. There are considerations, however, as to whether the empirical methodologies described above are accounting for the cause of the cyclical variation in match quality if such phenomenon exists. Higher probabilities, higher fractions of high45
skilled workers, or higher ?ows of ?lled vacancies, at low job levels when employment growth is low, do not necessarily imply that the risk of unemployment induces workers to accept jobs below their skill level, as they can also be due to other reasons. For example, changes in the hiring and ?ring policies of ?rms (i.e., ?rms require more schooling at given job complexity during bad times), or higher turnover rates of low-skilled can also produce similar patterns.4 Similarly, the opposite ?ndings do not necessarily reject the existence of over-quali?cation. High-skilled workers may accept low-skill jobs to avoid the distress of being unemployed, but higher overall unemployment may not have the same e?ect on the behavior of high-skilled workers. In order to account for this limitation, the main innovation of my empirical methodology is that it allows for job level probabilities to vary not only with overall economics activity, but with the workers’ lagged state. In particular, I adopt dynamic panel data estimation methods, in which the worker’s lagged state enters the model as an explanatory variable. By controlling for the lagged state I capture some
4
Other explanations include skill-biased technological change, minimum wages, search frictions
in combination with higher turnover rates of low-skilled workers, and incentive structures (e.g. high replacement rates, high reservation wages) that induce low-skilled workers to search less e?ectively. To my knowledge the only study that takes some of these considerations into account is Gautier et al. (2002). Unlike the studies mentioned above, which restrict crowding out to be an in?ow phenomenon only, they allow for changes in the educational attainment per job level to be the result of a combination of in?ow and out?ow policies at the ?rm level. Hence, they observe whether upgrading at given job levels is associated with the out?ow of relatively low educated workers or the in?ow of relatively high educated workers. Nevertheless, this methodology does not distinguish crowding out from the rest of the possible explanations.
46
propensity to experience a certain job level, which has been previously unmeasured by focusing only on how overall economic conditions a?ect job level probabilities.5 In particular, I am able to address whether unemployed high-skilled workers are more likely to move into low job levels, while mismatched workers are more likely to move into higher job levels when economic conditions improve. Although existing studies reach mixed conclusions regarding the empirical relevance of cyclical variation in match quality of high-skilled workers, I ?nd evidence highly suggestive of it. The mismatch rate of college graduates is higher and exhibits higher cyclical variation than the mismatch rate of workers without a college degree. Moreover, I ?nd that in periods of high unemployment rate, the high-joblevel probability of college graduates is lower, while the low-job-level probability is higher. The results of the dynamic panel data regression analysis show that when the origin state is unemployment, workers with a college degree are more likely to move into low-job-levels when the overall unemployment rate is high. Moreover, the results point to the existence of an upgrading in the job levels of mismatched college graduates when the unemployment rate is low. Consistent with the crowding out hypothesis, the estimates of the Markov
5
In a similar spirit, Teulings (1993) also accounts directly for the role of the risk of unemploy-
ment plays on job level transitions. He follows a di?erent estimation procedure than the studies described above. On the basis of a number of job characteristics he ranks jobs from the most desirable to the least desirable and estimates whether higher expected search duration decreases the probability of ?nding an attractive job. His results con?rm that this indeed the case, suggesting crowding out, but Teulings admits that other explanations may also be consistent with his ?ndings.
47
Chain Multinomial Logit model of job level transitions suggest that the odds of moving to a lower job level, as opposed to a higher job level, are larger when the lagged state is unemployment and vice versa. Moreover, I ?nd that the negative impact of higher unemployment rate on each job level probability declines with education and more evidently for “mediocre” job levels. Thus, I conclude that workers of higher education are more likely to accept jobs below their skill level than become unemployed. The rest of the chapter is organized as follows. In section 2.2, I describe the data set. Following this, in section 2.3, by grouping occupations into categories using prestige scores and information on educational attainment, I show how mismatch rates vary over the business cycle and across di?erent education groups. Sections 2.4 to 2.6, describe the empirical models, estimation methodologies, and results. Finally, in section 2.7, I conclude this chapter with some remarks.
2.2 Data
Each year the Panel Study of Income Dynamics (PSID) asks the head of each family participating in the study to report his/her employment status, i.e. whether unemployed, employed or out of the labor force and their occupation. Occupations are reported using the 3-digits code from 1970 Census of Population. I use the PSID family ?les to construct an unbalanced panel of 15748 heads who have been in the labor force for at least one year. The panel covers the years from 1968 to 1993. I consider individuals who report being students, retired, or keeping a house, to be
48
out of the labor force. Since I am only interested in analyzing movements across occupational categories and unemployment, I am not considering transitions in and out of the labor force. Hence, these transitions are excluded from the sample. Responders also report their years of schooling, which can be used as proxy for their skill level. A better approximation of skill would be a combination of education and work experience. Unfortunately, the questions regarding experience and job training asked in the PSID vary from year to year. I can only use both education and work experience as a proxy for workers’ skill level, if I concentrate on a smaller subperiod, in which case, the sample size declines considerably. To capture the e?ect of aggregate economic activity on job level transitions, I use the yearly average unemployment rate as a time varying covariate in the estimation procedures. I construct the time series of yearly average unemployment rates, using the seasonally adjusted monthly unemployment rates for the years 1968 to 1993, available from the Current Population Survey (CPS). I separate occupations into categories (job levels) based on the Hodge-SiegelRossi (HSR) prestige scores, which are conveniently assigned to the 3-digit U.S Census of Population classi?cation.6 Table A.1 in Appendix A gives a detailed description of the scores.
6
One could argue that the use of the term “job level” is misleading, because I am essentially
referring to occupation and not job categories. It may be the case that workers with the same occupation perform jobs or tasks of di?erent complexity. Hence, there may be variation in skill requirements within occupations. The reason I am using occupation and not job categories is simply the lack of such information.
49
The problem with prestige scores is that they do not necessarily measure the complexity of the jobs or the skill level required to do the job. Ideally, occupations would be categorized based on their skill requirements rather than their socioeconomic status. Such a ranking could be constructed by measuring workers’ quali?cation in each occupation. However, the PSID is a relatively small data set and the number of workers within each occupation is sometimes too small to obtain accurate estimates of skill requirements.7 Although no information regarding educational attainment was used to derive these scores, this caveat is partly surpassed by the fact that the scores are highly correlated with the level of educational attainment of the workers in each occupation. Occupations with high prestige scores are occupations that employ workers with high levels of education. Table 2.1 illustrates the resulting job levels using prestige scores. Some additional descriptive statistics of are in Table 2.2. On average, 5% of the individuals is unemployed and the majority of employed individuals is found in job levels 1 and 2. Only 14% of the employed is found in the lowest job level and only 4% in the highest.
2.3 Mismatch Rates Over the Business Cycle
The hypothesis discussed in the introduction, and investigated theoretically in the ?rst chapter of my thesis, is that mismatch rates increase during recessions
7
An alternative methodology would be to rank occupations into skill categories using residual
wages. I could regress real wages on education, experience, and other individual characteristics like and create a ranking based on the average residual wage of workers in each occupation.
50
when there is greater congestion in the labor market, and especially among the more educated who are quali?ed for a greater variety of jobs. Here I test this hypothesis by looking at how mismatch rates vary over the business cycles and across workers with di?erent education. As already mentioned, in the absence of information on the skill requirements of each occupation, I group occupations as low-skill and high-skill based on educational attainment and prestige scores. First, I consider as high-skill, occupations with prestige score 37 and above, and low-skill occupations with prestige score below 37. Based on this cuto? point, on average, 90% of college graduates in each year are in high-skill occupations. Then, I consider a lower prestige score cuto? point, 21, which results in an average of 95% of college graduates being in high-skill occupations each year. The lower the prestige score cuto? point that divides occupations between high- and low-skill, the higher the “degree” of mismatch of college graduates who happen to be in low-skill occupations. Figure 2.1 shows the fraction of mismatched college graduates (i.e., in lowskill occupations) using the 90% cuto? prestige point. There is an obvious upward trend. This may re?ect the introduction of new technologies so that traditionally simple or “low-specialization” tasks now require more knowledge and training. We also observe cyclical variation in the fraction of mismatched workers. There was a recession starting at the end of 1973 and ending at the beginning of 1975. As we can see from the graph, the mismatch rate increases in 74. From 1980 to 1982, there were two recessions, one shorter, beginning in 1980 and ending half year later, and one beginning in the middle of 1981 until the end of 1982. The mismatch rate obviously 51
9.8 8.8 7.8 6.8 5.8 4.8 69 71 73 75 77 79 81 83 85 87 89 91 93
Year
Figure 2.1: Mismatch Rate of College Graduates (90% cuto? point) increases during that period. It decreases in subsequent years and increases again in the years 90 and 91 re?ecting the July 90-March 91 recession. As expected, when a lower cuto? prestige score is used the mismatch rate is lower. Figure 2.2 shows the fraction of workers with a college degree that are in jobs below the 95% percent cuto? prestige score. Both the upward trend and the relationship between business cycles and the mismatch rate are less clear in this case, but we still observe an increase in the mismatch rate around the years 74, 80 to 82 and 91. The main assumption of the model in the ?rst chapter of my thesis, upon which the crowding out hypothesis rests, is that there is asymmetric matching: while highskilled workers can be employed in both high- and low-skill jobs, low-skilled workers 52
1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 69 71 73 75 77 79 81
Year
83
85
87
89
91
93
Figure 2.2: Mismatch Rate of College Graduates (95% cuto? point) do not qualify for high-skill jobs. This is a realistic assumption given that in reality jobs have minimum skill requirements that some workers satisfy, but some others do not. However, asymmetric matching does not automatically imply that mismatch rates increase with education as possible “scarring” e?ects or career considerations may prevent high-skilled workers from taking low-skill jobs. If this was the case, then we should observe similar levels and patterns in the mismatch rates across workers with di?erent education. To test this, I compare the mismatch rates of workers with a college degree to those without a college degree. I measure the mismatch rates of workers without college degree in a similar fashion. I ?nd the cuto? prestige score that implies on average 90% of workers without a college degree each year are in occupations 53
10 9 8 7 6 5 4 3 2 1 69 71 73 75 77 79 81 83 85 87 89 91 93 College Degree No College Degree
Figure 2.3: Mismatch Rates by Education (90% prestige cuto? point) above the cuto? prestige point. The mismatch rates for the 90% cuto? prestige score for workers with and without a college degree, respectively are in Figure 2.3. The mismatch rate of workers without a college degree is much lower overall and relatively constant over time. One the other hand, the mismatch rate of college graduates is much higher, has an upward trend and exhibits cyclical variation. If high-skilled workers are eligible for more types of jobs and hence, as shown above are more likely to mismatch during recessions, the question that follows naturally is whether the fraction of unemployed workers decreases with education and exhibits more cyclical variation. Is it the case that high-skilled workers, as opposed to low-skilled workers, mismatch and search on the job instead of staying or becoming unemployed during recessions? Figure 2.4 shows the fraction of workers with 54
14 12 10 8 6 4 2 0 69 71 73 75 77 79 81 83 85 87 89 91 93 College Degree No College Degree
Figure 2.4: Fraction of Unemployed by Education and without a college degree reporting unemployed each year. The fraction is always higher for workers without a college degree. In addition, it exhibits higher cyclical variation. While both fractions follow a similar pattern, the fraction for workers without a college degree increases more evidently in recessions (around 74-75, 80-82 and 90-91). Another interesting question that arises is whether the higher mismatch rates in recessions are due to workers moving into “stop-gap” jobs as opposed to a general type of mismatch. Stop-gap jobs are considered to be part-time jobs and temporary arrangements in low-paying industries. A more general type of mismatch occurs when workers simply lower their standards when ?nding a suitable job is di?cult, and accept jobs of slightly lower level, but not necessarily stop-gap jobs. If what 55
observed is a stop-gap phenomenon we should expect a higher fraction of mismatched workers to be concentrated in jobs with very low prestige scores.
10 9 8 7 6 5 4 3 2 1 0 69 71 73 75 77 79 81 83 85 87 89 91 93 prestige score below 21 prestige score 21-36 prestige score 37-44
Figure 2.5: Degrees of Mismatch: College Graduates
In Figure 2.5, I compare the fraction of college graduates in jobs with lower prestige scores to that in jobs with higher prestige scores. As we can see from the ?gure, the fraction of college graduates in jobs with prestige scores 37-44 is higher than the fraction in jobs with prestige scores 21-36. Moreover, the latter is higher than the fraction of college graduates in jobs with prestige score below 20. In addition, the fraction of college graduates in middle prestige category (21-36) follows the business cycle most closely (i.e., it increases in recessions and decreases in booms). This indicates that workers are mainly taking “mediocre” jobs to avoid unemployment rather than stop-gap jobs. 56
2.4 Linear Probability and Logit Models
In this section, I estimate linear probability (LP) and Logit models to characterize how the probability of moving to either high or low job levels is a?ected by the overall unemployment level and the education level of the worker. I consider as high job levels, occupations above the 90% prestige score cuto? point. Low jobs levels are occupations below this cuto? point. Moreover, throughout the analysis, I consider as high-skilled workers who hold a college degree. The model to be estimated is the following: yit = ?1 UNEi,t?1 + ?2 EDUi,t?1 + ?3 (UNE ? EDU )i,t?1 + ?it (2.1)
The latent variable yit describes the propensity to be either in high or low job levels, depending on the question of interest. The variable UNE is a dummy that takes the value of 1 when the unemployment rate is above 6%, and EDU is a dummy that takes the value of 1 when the worker has a college degree and zero otherwise. The EDU*UNE variable is an interaction term that takes the value of 1 when both the unemployment rate is high and the worker has a college degree.8 The subscript
8
I model the unemployment rate as a dummy instead of a continuous variable because it makes
it easier to interpret the marginal e?ects of the unemployment rates and its interaction with the education dummy on the probability. Moreover, in the sections that follow, I estimate dynamic models where whether the worker is mismatched or not, enters as an explanatory variable. By modeling the unemployment rate as a dummy allows me to ask what is the e?ect on the probability of high job levels when the worker is mismatched and the unemployment rate is low (i.e., is below 6%). Hence, I model the unemployment rate in the same fashion here to be able to compare the estimates. However, the reader should know that the results that follow do not change when a
57
i is for individual and t is for time. I model individual e?ects as ?xed. Hausman tests show that ?xed e?ects are more appropriate, but the results are similar in both cases.
2.4.1 The E?ect of Business Cycle and Education on High- Job-Level Probability
The results in the ?rst two columns of Table 2.3 show the marginal e?ects estimates of the LP and Logit model, respectively, when the interaction term between education and unemployment is not included in the set of regressors. As expected, education has a positive and signi?cant e?ect on the probability of high job levels. The unemployment dummy, on the other hand, has no signi?cant e?ect on the probability. However, the question of most interest is not how higher unemployment in general a?ects the probability, but whether higher unemployment reduces the probability high-skilled workers move into high job levels. To address this question we need to look at the interaction between the education and the unemployment dummy. The 3rd and 4th columns show the results when this interaction term is included. The interaction has a negative and signi?cant marginal e?ect in both cases. The LP model suggests that when overall unemployment is high the probability workers with a college degree will be in a high job level next period is approximately 1.5% lower, while the Logit model suggests that the probability is approximately
continuous variable is used.
58
5.5% lower. According to the likelihood ratio test chi-squared statistic, which is statistically signi?cant at the 5% level, the model with the interaction term is superior to the partial model. The results are consistent with the view that in periods of high unemployment high-skilled workers have a more di?culty moving into the jobs they are best suited for. Although having a college degree increases the probability of moving into high job levels, when unemployment is high, the e?ect of education on the probability is lower.
2.4.2 The E?ect of Business Cycle and Education on Low- Job-Level Probability
The results above suggest that in periods of high unemployment high-skilled workers have more di?culty moving into the jobs they are best suited for. However, this does not necessarily imply that high-skilled workers take jobs below their skill instead. It may be the case they just become or stay unemployed. To clarify this I also estimate the e?ects of overall unemployment, education and their interaction on low-job-level probability. The results are in Table 2.4. I ?nd that when the unemployment rate is high, workers with a college degree are more likely to be in low job levels next period. Having a college degree has a negative and signi?cant e?ect on the probability. The e?ect of unemployment rate, on the other hand, although quite small, is negative and signi?cant. Again, the question of interest it is whether high-skilled workers are
59
more likely to move into low job levels when the unemployment rate is high. Hence to address this question we need to look at the e?ect of the interaction between UNE and EDU. The interaction of the two has a positive and signi?cant e?ect. The negative impact of overall unemployment on the probability of moving into low-job levels is lower when the worker is high-skilled. Equivalently, the negative impact of having a college degree on low job levels probability is lower when overall unemployment is high. The LP model suggests that is approximately 2% lower, while the Logit model suggests is approximately 7% lower. Moreover, the likelihood ratio test statistic, which is statistically signi?cant at the 5% level indicates that the interacted model is superior to the model without interaction term.
2.5 Dynamic Panel Data Models
Individuals’ decisions on whether or not to accept a particular job depend not only on the overall unemployment rate and their education level, but also on their state at the time the decision is made. In this section, account for this e?ect by including workers lagged state in the set of regressors. In particular, I consider the following model: yitk = ?1 UNEi,t?1 + ?2 EDUi,t?1 + ?3 (UNE ? EDU )i,t?1 + ?1 1{yi,t?1 = j } +?2 [1{yi,t?1 = j } ? (UNE ? EDU )i,t?1 ] + ?it (2.2)
where UNE and EDU are as de?ned above. The latent variable yitk indicates the propensity the current state is k , while yi,t?1 indicates the lagged state. There three 60
possible states: high job level, low job level and unemployment. Depending on the question of interest, I model k to be either high or low job level and j to be unemployment. I divide occupations into low and high job levels using the 90% prestige score described above. The possibility of unobserved unit e?ects, unfortunately makes the estimation of dynamic panel data models complicated. If a lagged depended variable model is estimated in the presence of unit e?ects, these e?ects are transferred to the disturbance term, violating the strict exogeneity assumption. I get around this problem by following 3 di?erent estimation approaches. First, I adopt the Anderson and Hsiao (1981) instrument al variables approach in the ?rst di?erences of the model. According to this approach the coe?cients can be estimated consistently by instrumenting the lagged depended variable. Anderson and Hsiao (A-H, henceforth) suggested using the second lag of the depended variable as instrument. Second, I use a generalized method of moment estimator proposed by Arellano and Bond (1991), which is based on the same idea. The ArellanoBond (A-B) approach, ?rst identi?es how many lags of the dependent variables are valid instruments. Then, it combines these lagged levels and ?rst di?erences of the strictly exogenous variables into an instrument matrix, and then, it derives the corresponding one-step and two-step GMM estimators. Finally, I estimate a non-linear probability model by adopting Chamberlain’s (1980) conditional MLE approach. Chamberlain proposed a procedure that speci?es the density of (yi1 , ...yiT ) given yi0 and the vector of explanatory variables (xi ) for each i . What is convenient with this approach is that I can use standard random 61
e?ects software to estimate the parameters. The only di?erence is that the list of explanatory variables is expanded to include the include yi0 and xi in each period.
2.5.1 Are Unemployed High-Skilled Workers More Likely to Take Low-Skill Jobs in Recessions?
I begin with investigating the probability of low job levels. I model k to be high job levels and j the state of unemployment. With each of the estimation procedure described above I estimate three speci?cations. First, I estimate the main model in which the set of regressors contains only UNE, EDU and 1{yi,t?1 = j }. Then, I add the interaction term between UNE and EDU in the model. The third speci?cation, which I call fully interacted model, includes in addition the three-way interaction term between UNE, EDU and 1{yi,t?1 = j }. Table 2.5 summarizes the results in three panels, one for each estimation procedure. The result that education has a negative e?ect on the probability of low job levels is carried over in the dynamic model, but the results regarding the constituent e?ect of a UNE are mixed. It is insigni?cant according to the A-H and A-B procedure, but negative and signi?cant according to the Chamberlain approach. Hence, we reach mixed conclusions regarding the impact of unemployment on low-job-level probability. However, unemployment at the individual level seems to be important. With the exception of A-B procedure, where the e?ect of LAG is signi?cant only in the fully interacted model, the other two approaches suggest that being unemployed
62
has a negative impact on the probability of low job levels. This result does not represent rejection of the hypothesis that the risk of unemployment induces highskilled workers to accept low job levels. To test this hypothesis, the variables of interest are the interaction terms. When the interaction term between EDU and UNE is included in the set of regressors (second row of each panel) the rest of the coe?cients retain their signs, but in contrast to the LP and Logit models presented above, the e?ect of this interaction here is not always positive. The A-H and A-B procedures reach similar conclusions regarding the impact of this interaction. While the constituent e?ect of higher unemployment rate is insigni?cant, its e?ect conditional on the worker having a college degree is negative (although, only marginally signi?cant in the AB procedure). Therefore, the results of these two procedures suggest that higher overall unemployment reduces the low job level probability of workers with a college degree even further. In both cases, however, when this term is further interacted with the lagged unemployment dummy (third row of each panel) it becomes positive and signi?cant, suggesting that college graduates are more likely to move into low job levels when they are unemployed and the unemployment rate is high. The results of both estimation procedures imply that the probability a worker with a college degree will be in a low job level next period is lower when overall unemployment is high, but conditional in addition on the worker being unemployed, the probability is higher. In both cases, the negative impact of education on low job level probability is weaker when unemployment is high and the worker is experiencing unemployment. 63
The results of the Chamberlain approach are most strongly supportive of the view that the risk of unemployment induces high-skilled workers to take low-skill jobs, especially in periods of high unemployment. Not only the three-way interaction term has a positive e?ect on the probability, but the two way interaction between unemployment and education has a positive e?ect on the probability as well. The last row of the table contains the results of Logit estimates of the fully interacted model assuming no unobservable e?ects. The results are consistent with the Chamberlain results. Both the two-way and the three-way interaction terms are positive and signi?cant, while the constituent e?ects of higher unemployment rate and having a college degree are negative and signi?cant. In sum, all estimation procedures suggest the negative e?ect of holding a college degree on the probability of low job levels is weaker when the origin state is unemployment and overall unemployment is high. Moreover, in comparison with the LP and Logit estimated presented earlier, the dynamic model puts more emphasis on the risk of unemployment at the individual level. The dynamic model suggests that what may induce high-skilled workers to accept jobs below their skill level is being unemployed while overall unemployment rate is high, rather than just the fact that the overall unemployment rate is high.
64
2.5.2 Are Unemployed High-Skilled Workers Less Likely to Take HighSkill Jobs in Recessions?
Here I investigate the impact of the same set of regressors and their interactions on the probability of moving into high job levels (i.e., k = high job level). The variation in the results across the di?erent estimation procedures is higher in this case. While most procedures contribute to the conclusion that interactions between unemployment, either at the aggregate level or the individual level and education have a negative impact on the probability of high job levels, we cannot argue that this is certainly the case. The results of the three estimation procedures are in Table 2.6. In accordance with the results so far, the A-H and A-B approach, show that the constituent e?ect of higher unemployment on high-job-level probability is insigni?cant. In the Chamberlain approach, however, the constituent e?ect of higher unemployment rate is insigni?cant, but when the interaction terms are included, it becomes positive and signi?cant. The constituent e?ect of the lagged unemployment dummy is in general insigni?cant. The only case this is negative and signi?cant is in the Chamberlain approach. However, even in this case, it is signi?cant only when the three-way interaction term is not included in the set of regressors. As can be veri?ed from the third row of the bottom panel, when LAG is interacted with EDU and UNE, its constituent e?ect is no longer signi?cant. The conclusion that could be drawn from both the A-H and Chamberlain
65
approach is that when the worker is unemployed, or when the unemployment rate is high, does not necessarily imply lower high-job-level probability, unless the worker has a college degree. In other words, those more likely to have a harder time moving into high-skill jobs when they are unemployed or when the unemployment rate is high, are those quali?ed for high-skilled jobs (i.e., those who hold a college degree). In the A-H case, the only way higher unemployment rate a?ects negatively the high-job-level probability is when the worker both has a college degree and is experiencing unemployment. In fact, we get the counterintuitive result that the effect of the interaction between UNE and EDU, although quite small (approximately 1%) is positive and signi?cant. The only way this results can be justi?ed is if this interaction is actually picking up some of the e?ect of education. The constituent e?ect of having a college degree, as expected, and as the results indicate, is positive. Comparing the interacted model (row 2 and 3) to the constituent model (row 1) we can see that when the interaction between UNE and EDU is included the constituent e?ect of having a college degree declines by approximately 1 percentage point. Similarly, in the Chamberlain approach, the thee-way interaction e?ect is negative, although only marginally signi?cant at the 5% level, but in addition, the e?ect of the two-way interaction term between UNE and EDU on the probability is negative and signi?cant. Thus, the positive impact of having a college degree on high-job-level probability is lower in periods of high unemployment. The results of the A-B approach are di?erent. The e?ect of the interaction between overall unemployment and education is very small and only marginally signi?cant at the 5 % level in the fully interacted model. Moreover, the A-B approach 66
gives the paradoxical result that when this term is further interacted with the lagged unemployment dummy it has a positive and signi?cant e?ect on the probability of high job levels. This implies that in periods of high unemployment, workers who have a college degree, can more easily move into a high job level when unemployed than when employed. While the A-H results suggest that the positive impact of having a college degree on high-job-level probability is lower when overall unemployment rate is high and the worker is unemployed, the A-B approach contradicts this ?nding. The strongest support for the hypothesis that unemployment both at the individual level and at the aggregate level reduces the probability of high-skilled (college graduates) workers ?nding an appropriate match can be found in the Chamberlain estimates. In this case, both when education is interacted with overall unemployment and when it is further interacted with the lagged unemployment dummy it has a negative and signi?cant coe?cient (although, the latter is only marginally signi?cant at the 5% level). Given the variation in the estimates across the di?erent estimation procedures, it is useful to take a look at the estimates assuming no unobserved e?ects. These are given in the last row of the table. The only signi?cant coe?cients are those of EDU and UNE*EDU. The former is positive, while the latter is negative, con?rming the LP and Logit estimates presented earlier. The estimates of the model with unobserved e?ects are also consisted with the Chamberlain estimates. They suggest that higher unemployment rate reduces the positive impact of having a college degree on high-job-level probability. The overall conclusion from this analysis is that there some evidence suggestive 67
of the hypothesis that high-skilled workers have more di?culty moving into high-skill jobs when unemployment is high. However, these evidence are not concrete.
2.5.3 Are Mismatched High-Skilled More Likely to Take High-Skill Jobs in Booms?
The results in section 2.5.1 suggested that college graduates are more likely to move into low job levels when unemployed, and overall unemployment is high. Hence, they support the view that the risk of unemployment induces workers to take jobs below their skill level. Here, I ask the question of whether this phenomenon is temporary or not. Do college graduates accept job below their skill level transitorily, until overall economic conditions improve, and a better job comes along? To address this question I investigate how the unemployment rate a?ects the high-job-level probability of mismatched workers. I consider as mismatched workers who hold a college degree and are in low job levels (i.e., j = low job levels). As mentioned at the beginning of this section, this implies that they are in jobs the on average employ approximately only 10% college graduates each year. In addition, I model the overall unemployment rate dummy to be the reverse of the unemployment dummy in previous regressions. UNE takes the value of 1 when the unemployment rate is below 6% and 0 otherwise. Given this speci?cation, the two-way interaction term between EDU and UNE, takes that value of 1 when unemployment is low and the workers has a college degree, while the three-way interaction term between EDU, UNE and LAG takes the value of 1, when in addition, the worker is in a low job
68
level (i.e., mismatched). The results are in Table 2.7. According to all three estimation procedures being in a low job level a?ects the high-job-level probability negatively. The coe?cient of the lagged depended variable is negative and signi?cant in all cases. This result is not surprising. One cannot argue that being in a low job level as opposed to a high job level increases your chances of being in a high job level next period. For the hypothesis to be tested here, the interaction e?ects of overall unemployment and education with this dummy variable are of most interest. First, we are interested on whether when the unemployment rate is low workers with a college degree are more likely to be in high-skill jobs next period (i.e., the coe?cient of EDU*UNE is positive). Second, we are interested to see whether mismatched college graduates are more likely to move into high job levels next period when the overall unemployment rate is low (i.e., the coe?cient of UNE*EDU*LAG is positive). Both the results of the A-H and A-B approach indicate that mismatched college graduates are more likely to move into high job levels when overall unemployment rate is high. In both cases, the three-way interaction term has a positive and significant coe?cient. The two-way interaction term, however, has a negative coe?cient in the ?rst case and has an insigni?cant coe?cient in the second. Hence, in both cases, a positive e?ect on high-job-level probability when overall unemployment rate is low, arises when then worker in addition to having a college degree, is mismatched. The Chamberlain approach gives the opposite result. The coe?cient of the two-way interaction term is positive and signi?cant, suggesting that when overall unemployment is low, college graduates are more likely to move into high job levels, 69
independent of their origin state. The coe?cient of the three-way interaction term, on the other hand, is negative suggesting that conditional on a college graduate being mismatched, the positive impact of lower unemployment rate on high-joblevel probability is lower. The A-H and A-B results emphasize the tendency of mismatched college graduates to move into higher job levels when the overall unemployment rate is low, while the results of the chamberlain approach emphasize the positive e?ect of overall unemployment being low on the high-job-level probability of college graduates. Overall, we can conclude that the results of this regression analysis point to the existence of an upgrading in the job level of college graduates when the overall unemployment rate is low.
2.6 Markov Chain Multinomial Logit Model of Job level Transitions 2.6.1 The Model
The purpose of this section is to characterize job level transitions. To describe transitions between job levels, I adopt the latent propensity framework a la McFadden (1974). At each period, the latent variable ykit describes the propensity level to be in state k out of states 0, ....., m for individual i at time t. States are unemployment k = 0 and ?ve job levels k = 1, ..., m with m = 5. Assuming N individuals i are observed at T + 1 points in time t = 0, ..., T , the propensity function
70
is determined by
m
ykit = xit ?k +
j =0
?jk 1{yi(t?1) = j } + ?ki + ?kit
(2.3)
where xit is a vector of observable covariates, 1 is the indicator function, yi(t?1) indicates the lagged state, yi(t?1) = j if the individual was in state j at time t ? 1, ?ki is an unobservable individual speci?c e?ect and ?kit is an unobservable error term. This speci?cation assumes that each individual has a speci?c propensity for each alternative depending on the lagged state. The parameters ? = (?0 , ..., ?m ) and ?j = (?j 0, ?j 1, ..?jm ) ? j = 0, ....m capture how the observed covariates and the lagged state, respectively, a?ect the propensity to be in each state. For example, the parameter ?k captures how the observed covariates in?uence the propensity of being in state k , while the parameter ?jk captures the feedback e?ect when the state j at time t ? 1 is followed by the state k at time t. In total, there are m2 feedback parameters ? to be estimated. For the question of interest, the dependent variable ykit is the propensity of individual i being in job level k at time t. I separate occupations 5 levels, from the lowest –job level 1– to the highest –job level 5– based on the HSR prestige scores. Table 2.1 shows the prestige scores corresponding to each job level. The vector of observable covariates xit includes the education dummy and overall unemployment rate dummy, as de?ned in sections 2.5.1 and 2.5.2. Assuming that the error terms ?kit are independent across alternatives and over time conditional on (xi , ?i , yi0 ) and identically distributed according to the Type1 extreme value distribution, the probability of individual i of being in state k at time 71
t, is given by P (yit = k \ yi(t?1) = j, xi , ai ) = exp(xit ?k + ?jk + ?ki ) 1+ m l=1 exp(xit ?l + ?jl + ?li ) (2.4)
The parameters ? and ? can be estimated based on a sequence of states where the individual switches alternatives at least once during periods 1 to T ? 1. Given that only (m2 ? (2m ? 1)) feedback parameters can be identi?ed, we need to impose some identi?cation restriction. I follow Weber(2002) and assume that all parameters with respect to the reference state k = 0 are equal to zero. More speci?cally, I impose the following identi?cation restrictions: ?0 = 0 ?0 = (?00 , ..., ?mo ) = 0 ?0k = 0 ? k = 1, ..., m ?i0 = 0 ? i = 1, ..., N (2.5)
The problem with imposing parameter restrictions is that it complicates the interpretation of the parameters. For the purpose of the empirical analysis in this paper, it is convenient to choose unemployment as a reference state, as it makes the interpretation easier. The advantages of this empirical methodology compared to the dynamic panel estimation procedures presented earlier are ?rst, that it allows for the analysis of the impact of the covariates on multiple job level probabilities simultaneously. Second, it characterizes the e?ect of multiple lagged states on this probability simultaneously. Third, it allows us to compare not only the sign of the e?ect of the covariates on the 72
probability of each job level, but also the magnitude of the e?ect across di?erent job levels. For example, we are able to address a question of the following form: does a higher overall unemployment rate reduce the probability of higher job level more than it reduces the probability of lower job level? Forth, in a similar fashion, it allows us to compare the e?ect of di?erent lagged states on the probability of a particular state. To give an example, we are able to address whether the e?ect of being in job level 1 as opposed to being in job level 2 on the probability of job level 3 is higher or not. Overall, this methodology allows for a more detailed description of job level transitions. To clarify the advantages of this estimation methodology, let us interpret the parameters to be estimated. The odds ration of moving from state j to state k relative to a movement from the same origin to the reference state 0, which in our case is unemployment, is given by the following expression: P (yit = k \ yi(t?1) = j, xi , ai ) = exp(xit ?k + ?jk + ?ki ) P (yit = 0 \ yi(t?1) = j, xi , ai ) (2.6)
Therefore, a high value of ?ki implies a high propensity of moving to state k as opposed to unemployment conditional on any lagged state j . Hence, the parameter ?k represents the e?ect of the covariate x on the log odd’s ratio. P (yit = k \ yi(t?1) = j, xi , ai ) ? ln = ?k ?x P (yit = 0 \ yi(t?1) = j, xi , ai ) (2.7)
The di?erence ?k ? ?k? measures the e?ect of the covariate x on the log odd’s ratio of moving from any state j to k relative to moving from any state j to k ? . In order to interpret the parameter ?jk , it is convenient to remove the individual speci?c e?ects 73
by calculating the following ratio:
P (yit =k \yi(t?1) =j,xi ,ai ) P (yit =0\yi(t?1) =j,xi ,ai ) P (yit =k \yi(t?1) =0,xi ,ai ) P (yit =0\yi(t?1) =0,xi ,ai )
= exp(?jk )
(2.8)
The above expression is identical across individuals and thus, it captures only the state dependence. According to the expression if ?jk is positive, the odds of being in state k with respect to unemployment when the lagged state is j are larger than when the lagged state is unemployment. It is obvious that the e?ects of lagged states j and j ? on the probability of moving to state k relative to unemployment can be measured by ?jk ? ?j ?k . More speci?cally, ln[ P (yit = k \ yi(t?1) = j ? , xi , ai ) P (yit = k \ yi(t?1) = j, xi , ai ) ] ? ln[ ] = ?jk ? ?j ? k P (yit = 0 \ yi(t?1) = j, xi , ai ) P (yit = 0 \ yi(t?1) = j ? , xi , ai ) (2.9) Moreover, by comparing the same origin feedback parameters ?jk and ?jk? , we can measure whether the odds of being in state k with respect to k ? when the lagged state is j are larger or smaller than when the lagged state is unemployment. After some simple algebra we derive: ln[ P (yit = k ? \ yi(t?1) = 0, xi , ai ) P (yit = k ? \ yi(t?1) = j, xi , ai ) ] ? ln [ ] = ?jk? ? ?jk P (yit = k \ yi(t?1) = j, xi , ai ) P (yit = k \ yi(t?1) = 0, xi , ai ) (2.10)
2.6.2 Conditional Maximum Likelihood Estimation
I model individual e?ects as ?xed, and pick up the method presented in Honor´ e and Kyriazidou (2000). The method concerns the estimation of panel data ?xed e?ects discrete choice models when the explanatory variable set includes strictly 74
exogenous variables, lags of the endogenous dependent variable as well as unobservable individual speci?c e?ects.9 Based on the idea applied by Chamberlain (1984), Honor´ e and Kyriazidou (2000) provide conditions under which the probabilities of the events are independent of the individual e?ects. This approach allows for estimating the individual ?xed e?ects parameters ?ki consistently. The conditions are also extended to the case of multinomial discrete choice variables, and therefore cover the model speci?ed above. The estimation of the ? and ? parameters can be based on the maximization of a likelihood function, which regards events where the state variable y switches from say state k to state l or reverse between two points in time, say s and t with 1 ? t < s ? T ? 1. Conditional on such a switch and on the constancy of the explanatory variables in the following periods xi(t+1) = xi(s+1) , the probabilities of the events are independent of the individual e?ects.10 De?ning the binary variable yhit = 1 if the individual i is in state h ? {0, 1, ..., m} in period t and yhit = 0
9
Whether individual e?ects should be modeled as random or ?xed is an important issue in
panel estimation. The latter is more common (Arellano and Honor´ e, 2001) even though the speci?cation of the distribution function of random e?ects is di?cult. In nonlinear models the numerical implementation of a random e?ects becomes even more di?cult as multiple integrals need to be evaluated. For these reasons, I follow Weber (2002) and model individual e?ects as ?xed.
10
Given this condition, modeling the overall unemployment rate as a dummy instead of a con-
tinuous variable helps increase the number of observations that contribute to the likelihood. An alternative method to avoid this limitation would be to incorporate the unemployment rate as a continuous exogenous variable and replace the exact equality condition by weighting the di?erences with a Kernel function and giving the observations with smallest di?erences the highest weights.
75
otherwise, the maximum likelihood function takes the following form:
N
L =
i=1 1?t<s?T ?1 k =l
1{ykit + ykis = 1}1{ylit + ylis = 1} 1{xi(t+1) = xi(s+1) }ln
N
exp(D1 ) 1{s ? t = 1} 1 + exp(D1 )
1{ykit + ykis = 1}1{ylit + ylis = 1}
i=1 1?t<s?T ?1 k =l
1{xi(t+1) = xi(s+1) }ln where
exp(D2 ) 1{s ? t > 1} 1 + exp(D2 )
(2.11)
D1 = (xit ? xis )(?k ? ?l ) + ?yi(t?1) ,k + ?kl + ?l,yi(s+1) ??yi(t?1) ,l ? ?lk ? ?k,yi(s+1) and D2 = (xit ? xis )(?k ? ?l ) + ?yi(t?1) ,k + ?k,yi(t+1) + ?l,yi(s+1) ??yi(t?1) ,l ? ?l,yi(t+1) ? ?yi(s?1) ,k ? ?k,yi(s+1) (2.13) (2.12)
In the objective function above I impose the identi?cation restrictions given in 2.3. For an observation to contribute to the likelihood at least four periods of observations are required and at least some variability in states in the periods between the dates 1 and T ? 1.
2.6.3 Results
Estimation results are given for the whole sample and a sample that excludes individuals with no high-school degree in Tables 2.8 and 2.8, respectively. The analysis is conducted separately for those two samples to compare the parameter 76
estimates and verify whether workers of higher education are more likely to move into lower levels than become unemployed during downturns.11 The period in which transitions are observed is one year. In both cases all the feedback parameters ? are positive, indicating that individuals are more likely to move to each of the job levels from employment, as opposed to unemployment. Moreover, the feedback parameters decline the further the origin state from the destination state. For example, ?15 < ?25 < ?35 < ?45 . Similarly, ?51 < ?41 < ?31 < ?21 , and so on. Hence, the odds ratio of moving to a particular job level with respect to unemployment are higher the closer the origin job level to the destination job level. In some cases, when the destination state is to far from the origin state the feedback parameter becomes insigni?cant indicating that this type of transitions are rare or impossible. For example, the feedback parameters when the origin state is job level 1 is positive and signi?cant for destination states 2 and 3 but becomes insigni?cant for destination states 4 and 5. The feedback parameters below the diagonal correspond to movements into job levels lower than the origin job level, while the parameters above the diagonal to movements into job levels higher than the origin job level. The parameters to
11
Ideally I would like to compare the model estimated on a low-skill sample to one estimated
on a high-skill sample. However, the full sample is too small to allow for meaningful estimates on high-skill and low-skill sub-samples. The majority of the workers in the sample have at most a high-school diploma. Focusing only on either college graduates or workers without a high-school diploma would imply a considerably smaller sample. This estimation methodology, in particular, requires a su?cient number of across state transitions for the estimates to be meaningful, making such a comparison even harder.
77
the left of the diagonal tend to be smaller than those to the right (i.e., ?21 < ?23 , ?32 < ?34 , ?31 < ?35 , etc.). This implies that workers are less likely to move from a higher job level to a lower one than from unemployment, and more likely to move from a lower job level to a higher one than from unemployment. In other words, the odds of moving into a lower job level as opposed to a higher job level are larger when the lagged state is unemployment and vice versa. This ?nding supports the hypothesis of interest as it indicates that workers experiencing unemployment are more likely to move into lower job levels. The e?ect of higher unemployment on the odds ratio of moving to each of the job levels relative to moving into unemployment are given in the last row of each table. In both cases, higher unemployment rate reduces the probability of being in each of the alternatives relative to being unemployed. In other words, higher unemployment reduces the probability of employment, as one would expect. The crowding out hypothesis implies that workers of higher skill are more likely to move into lower job levels than become unemployed during periods of high unemployment compared to workers of lower skill. Hence, the negative impact of unemployment on the probabilities of being in low job levels should be lower for workers of higher skill. Comparing the unemployment rate parameters for the sample that includes individuals with no high-school education to the one that excludes them, we note that this is indeed the case. The parameters are still negative in the second case, but lower in absolute value. Thus, for the more educated sample, higher unemployment reduces the odds of being employed as opposed to being unemployed next period 78
but to a lower degree. In fact, the parameters corresponding to job levels 2 and 3 become insigni?cant. Hence, when workers with less than a high-school diploma are excluded from the sample higher unemployment does not reduce the odds of moving to job levels 2 or 3 as opposed to unemployment. This supports the view that when the unemployment rate is high, workers with higher education are more likely to move into “mediocre” occupations than become unemployed relative to workers with lower education. The parameter corresponding to job level 1 is smaller in absolute value, but to a lower degree (i.e., it is still signi?cant). This is reasonable to expect, as the lower the level of the job the less willing one would be to accept it to avoid unemployment.
2.7 Conclusion
This chapter tests the hypothesis that high-skilled workers accept transitorily jobs below their skill level in order to escape unemployment, and move on to better jobs when times get better. The hypothesis is tested by studying the mismatch rates and job level dynamics using a panel sample of individuals constructed from the yearly family ?les of the Panel Study of Income Dynamics (PSID), which covers the years from 1968 to 1993. My empirical methodology departs from existing studies that investigate the cyclical patterns of mismatch across di?erent skill groups, in that it accounts for the e?ect of the workers’ lagged state on the propensity of being in each of the occupational categories. While existing studies test the hypothesis by focusing only
79
on the impact of economic activity on job level probabilities, I also incorporate the workers lagged state as an explanatory variable and use dynamic panel data estimation methodologies. Modeling state dependence captures some propensity to experience a certain job level, which has been previously unmeasured by focusing only on how overall economic conditions a?ect job level probabilities. I am able to capture directly the impact the risk of unemployment at the individual level, has on job level transitions. I ?nd evidence suggestive of the existence of a cyclical pattern in match behavior of high-skilled workers (college graduates). The mismatch rate of college graduates is higher and exhibits higher cyclical variation than the mismatch rate of workers without a college degree. Moreover, I ?nd that the positive impact of having a college degree on the probability of achieving higher job levels is lower when the unemployment rate is high. Similarly, the negative impact of having a college degree on low-job-level probability is lower when the unemployment rate is high. The results of the dynamic panel data regression analysis indicate that unemployed high-skilled workers are more likely to take low-skill jobs when the unemployment rate is high. In particular, the negative impact of holding a college degree on low-job-level probability is weaker when the origin state is unemployment and overall unemployment rate is high. In addition, the results point to the existence of an upgrading in the job levels of mismatched college graduates when the unemployment rate is low. Finally, the estimates of a Markov Chain Multinomial Logit model of job level transitions suggest that the odds of moving to a lower job level as opposed to a 80
higher job level are larger when the lagged state is unemployment and vice versa. In addition, the results suggest that higher unemployment rate reduces the probability of being in each job level relative to being unemployed. However, consistent with the crowding out hypothesis, the negative impact of higher unemployment rate on each job level probability declines with education and more evidently for “mediocre” job levels. Thus, I conclude that workers of higher education are more likely to accept jobs below their skill level than become unemployed. Table 2.1: Job Levels Based on Prestige Scores Job Job Job Job Job Level Level Level Level Level 1: 2: 3: 4: 5: Prestige Scores 6-21 Prestige Scores 22-36 Prestige Scores 37-51 Prestige Scores 52-66 Prestige Scores 67-83
Table 2.2: Sample Descriptive Statistics Mean Unemployed Job Job Job Job Job Level Level Level Level Level 1 2 3 4 5 0.05 0.14 0.36 0.38 0.08 0.04 533908 15748
Observations Individuals
81
Table 2.3: Linear Probability and Logistic Regression Results: High-Job-Level Probabilities Depended Variable: High-job-level Probability LP Variable UNE -.001 (.001) -.012 (.010) .001 (.001) .071 (.005) -.014 (.003) 6804.4 48.66 69.96 0.2711 2817.6 53.15 0.2695 7.6 3067.14 2810.62 3062.19 .012 (.013) .198 (.024) -.054 (.019) -6804.6 56.26 Logit LP Logit
EDU
.062 .170 (.005) (.023)
UNE*EDU
Log-likelihood value LR Chi-squared F-test R-squared LR test Chi-squared (signi?cance of UNE*EDU) Huasman test Chi-squared
Bolded coe?cients are signi?cant at the 5% level.
82
Table 2.4: Linear Probability and Logistic Regression Results: Low-Job-Level Probabilities Depended Variable: Low-job-level Probability LP Variable UNE -.003* (.002) -.013 (.006) -.007 -.029 (.002) (.008) -.073 -.179 (.008) (.022) .021 .071 (.005) (.016) -14676.8 42.44 32.32 .1526 906.30 603.77 28.35 .1508 19.55 909.45 -14667 62.00 Logit LP Logit
EDU
-.061 -.140 (.008) (.021)
UNE*EDU
Log-likelihood value LR Chi-squared F-test R-squared LR test Chi-squared (signi?cance of UNE*EDU) Huasman test Chi-squared
628.74
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level.
83
Table 2.5: Dynamic Panel Data Models: unemployment to low-job-level transitions Depended Variable: Low-job-level Probability Variables Anderson- Hsiao IV: UNE -.001 (.002) .002 (.003) .002 (.003) Arellano-Bond GMM: -.001 (.002) .000 (.002) .001 (.002) Chamberlain CML: -.146 (.027) -.233 (.031) -.230 (.031) No Unobserved E?ects: -.106 (.031) EDU -.044 (.016) -.036 (.016) -.036 (.016) -.039 (.016) -.035 (.016) -.038 (.016) -.275 (.099) -.469 (.104) -.459 (.104) .926 (.100) LAG -.074 (.010) -.074 (.010) -.083 (.011) -.029 (.046) -.025 (.046) -.089 (.043) -.452 .051 -.439 (.051) -.461 (.052) -.260 (.039) .342 (.062) .333 (.062) .258 (.063) .384* (.235) .443 (.196) -.011* (.006) -.009* (.006) .439 (.099) -.016 (.006) -.016 (.006) .168 (.045) UNE*EDU UNE*EDU*LAG
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level UNE: takes the value of 1 when the unemployment rate is above 6% EDU: takes the value of 1 when the worker has a college degree UNE*EDU: two-way interaction between UNE and EDU LAG: takes the value of 1 when the worker was unemployed in the previous period UNE*EDU*LAG: three-way interaction between UNE, EDU and LAG
84
Table 2.6: Dynamic Panel Data Models: unemployment to high-job-level transitions Depended Variable: High-job-level probability Variables Anderson-Hsiao IV: UNE .001 (.001) -.001 (.001) -.001 (.002) EDU .066 (.010) .060 (.010) .060 (.010) LAG -.007 (.006) -.007 (.006) .001 (.007) .012 (.004) .011 (.004) -.146 (.028) UNE*EDU UNE*EDU*LAG
Arellano-Bond GMM:
-.002 (.002) .003 (.002) .003 (.002)
.047 (.010) .053 (.010) .053 (.010) .250 (.105) .395 (.111) .398 (111) 1.145 (.111)
.005 (.019) -.000 ( .019) .007 (.019) -.310* (.177) -.284 ( .137) -.173 (.153) -.182 (.140) -.286 (.074) -.282 (.074) -.244 (.078) -.517* (.326) -.389 (.269) -.005 (.004) -.006* (.004) .152 (.059)
Chamberlain CML:
.009 (.036) .122 (.046) .121 (.047)
No Unobserved E?ects:
.067 (.538)
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level. UNE: takes the value of 1 when the unemployment rate is above 6% EDU: takes the value of 1 when the worker has a college degree UNE*EDU: two-way interaction between UNE and EDU LAG: takes the value of 1 when the worker was unemployed in the previous period UNE*EDU*LAG: three-way interaction between UNE, EDU and LAG
85
Table 2.7: Dynamic Panel Data Models: low-job-level to high-job-level transitions Depended Variable: High-job-level Probability Variables Anderson-Hsiao IV: UNE .001 (.001) .001 (.001) .001 (.001) Arellano-Bond GMM: EDU LAG UNE*EDU UNE*EDU*LAG
.065 -.015 (.009) (.005) .071 -.015 (.009) (.005) .069 -.019 (.009) (.005) -.012 (.004) -.008 (.003) .046 (.015)
.003 .044 -.119 (.001) (.010) (.028) .002 (.002) .002 (.001) .045 -.110 (.010) (.028) .032 -.095 (.010) (.026) .156* (.117) .081 (.123) .125 (.123) -1.330 (.043) -1.32 (.043) -1.258 (.045) .159 (.081) .258 (.084) -.001 (.088) -.455 (.099) -.008 (.092) .003 (.004) -.001 (.003) .010* (.005)
Chamberlain CML:
-.037 (.038) -.021 (.049) -.024 (.048)
No Unobserved E?ects:
.056 (.058)
.739 -1.606 (.115) (.044)
Bolded coe?cients are signi?cant at the 5% level. Starred coe?cients are only marginally signi?cant at the 5% level. UNE: takes the value of 1 when the unemployment rate is below 6% EDU: takes the value of 1 when the worker has a college degree UNE*EDU: two-way interaction between UNE and EDU LAG: takes the value of 1 when the worker was in a low job level in the previous period UNE*EDU*LAG: three-way interaction between UNE, EDU and LAG
86
Table 2.8: Estimated parameters Markov Chain Multinomial Logit model, full sample, yearly transitions Destination State Job Job Job Job Job Level 1 Level 2 Level 3 Level 4 Level 5 Origin State Job Level 1 1.444 (0.044) 0.348 (0.040) 0.308 (0.048) 0.129 (0.124) 0.049 (0.173) 0.581 (0.039) 1.428 (0.034) 0.519 (0.039) 0.293 (0.087) 0.09 (0.141) 0.478 (0.048) 0.615 (0.039) 1.678 (0.042) 0.576 (0.08) 0.544 (0.122) 0.099 (0.118) 0.349 (0.084) 0.625 (0.077) 1.658 (0.097) 0.543 (0.135) 0.116 (0.167) 0.161 (0.136) 0.409 (0.119) 0.613 (0.132) 1.525 (0.161)
Job Level 2
Job Level 3
Job Level 4
Job Level 5
Un. Rate> 6%
-0.151 (0.038)
-0.144 (0.032)
-0.158 (0.033)
-0.287 (0.051)
-0.238 (0.064)
Mean log-likelihood: -0.268 Number of cases: 85481 Number of individuals 15748
87
Table 2.9: Estimated parameters Markov Chain Multinomial Logit model, highschool graduates, yearly transitions Destination State Job Job Job Job Job Level 1 Level 2 Level 3 Level 4 Level 5
Origin State Job Level 1 1.442 (0.076) 0.369 (0.065) 0.258 (0.072) 0.140 (0.140) 0.109 (0.192) 0.640 (0.064) 1.455 (0.052) 0.500 (0.055) 0.258 (0.098) -0.007 (0.157) 0.421 (0.071) 0.641 (0.055) 1.661 (0.056) 0.649 (0.090) 0.503 (0.135) 0.117 (0.133) 0.339 (0.093) 0.565 (0.086) 1.673 (0.105) 0.609 (0.148) 0.188 (0.182) 0.216 (0.150) 0.438 (0.131) 0.565 (0.145) 1.520 (0.175)
Job Level 2
Job Level 3
Job Level 4
Job Level 5
Un. Rate> 6%
-0.101 (0.056)
-0.0031 (0.045)
-0.082 (0.045)
-0.234 (0.059)
-0.103 (0.072)
Mean log-likelihood: -0.26 Number of cases: 53507 Number of individuals 9441
88
Appendix A Prestige Scores
Table A.1: Prestige Scores 1970 Occupational Classi?cation Codes 65 102 103 104 105 110 111 112 113 114 115 116 120 121 122 123 124 125 126 130 131 132 133 134 135 Prestige Scores
Physicians, including osteopaths Agriculture teachers Atmospheric, earth, marine, and space teachers Biology teachers Chemistry teachers Physics teachers Engineering teachers Mathematics teachers Health specialists teachers Psychology teachers Business and commerce teachers Economics teachers History teachers Sociology teachers Social science teachers, n.e.c. Art, drama, and music teachers Coaches and physical education teachers Education teachers English teachers Foreign language teachers Home economics teachers Law teachers Theology teachers Trade, industrial, and technical teachers Miscellaneous teachers, college and university
82 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78
89
Teachers, college and university, subject not speci?ed Judges Lawyers Physicists and astronomers Dentists Bank o?cers and ?nancial managers Architects Aeronautical astronautical engineers Psychologists Airplane pilots Electrical and electronic engineers Chemists Clergymen Civil engineers Atmospheric and space scientists Biological scientists Marine scientists Life and Physical scientists, n.e.c. Chemical engineers Petroleum engineers Engineers, n.e.c. Geologists Archivists and curators Political scientists Sociologists Urban and regional planners Social scientists, n.e.c. Mathematicians Secondary school teachers Mechanical engineers Mining engineers Optometrists Registered nurses Pharmacists Clinical laboratory technologists and technicians Dental hygienists Health record technologists and technicians Radiologic technologists and technicians Assessors, controllers, and treasurers, local public administration Health administrators
140 30 31 53 62 202 2 6 93 163 12 45 86 11 43 44 52 54 10 21 23 51 33 92 94 95 96 35 144 14 20 63 75 64 80 81 82 83
78 76 76 74 74 72 71 71 71 70 69 69 69 68 68 68 68 68 67 67 67 67 66 66 66 66 66 65 63 62 62 62 62 61 61 61 61 61
201 61 212 61
90
O?cials and administrators; public administration, n.e.c. School administrators, college Chiropractors Veterinarians Elementary school teachers Pre-kindergarten and kindergarten teachers Authors O?cers, pilots, and pursers; ship School administrators, elementary and secondary Designers O?cials of lodges, societies, and unions Postmasters and mail superintendents Accountants Economists Public relations men and publicity writers Metallurgical and materials engineers Agricultural scientists Personnel and labor relation workers Religious workers, n.e.c. Draftsmen Painters and sculptors Librarians Actuaries Statisticians Actors Sheri?s and baili?s Industrial engineers Farm management advisers Foresters and conservationists Home management advisers Surveyors Dieticians Social workers Embalmers Funeral directors Computer programmers Computer systems analysts Computer specialists, n.e.c. Sales engineers Operations and systems researchers and analysts Health practitioners, n.e.c. Vocational and educational counselors Athletes and kindred workers
222 235 61 72 142 143 181 221 240 183 223 224 1 91 192 15 42 56 90 152 190 32 34 36 175 965 13 24 25 26 161 74 100 165 211 3 4 5 22 55 73 174 180
61 61 60 60 60 60 60 60 60 58 58 58 57 57 57 56 56 56 56 56 56 55 55 55 55 55 54 54 54 54 53 52 52 52 52 51 51 51 51 51 51 51 51
91
Editors and reporters Radio and television announcers Writers, artists, and entertainers, n.e.c. Research workers, not speci?ed Professional, technical, and kindred workers–allocated Stocks and bonds salesmen Locomotive engineers Opticians, and lens grinders and polishers Buyers, wholesale and retail trade O?ce managers, n.e.c. Sales managers and department heads, retail trade Sales managers, except retail trade Managers and administrators, n.e.c. Managers and administrators, except farm–allocated Bank tellers Recreation workers Credit Men industries Electricians Purchasing agents and buyers, n.e.c Bookkeepers Insurance adjusters, examiners, and investigators Job and die setters, metal Machinists Aircraft Dental assistants Health aides, except nursing Policemen and detectives Health technologists and technicians, n.e.c. Agriculture and biological technicians, except health Chemical technicians Electrical and electronic engineering technicians Industrial engineering technicians Mechanical engineering technicians Mathematical technicians Flight engineers Tool programmers, numerical control Technicians, n.e.c. Insurance agents, brokers, and underwriters Automobile accessories installers Carpet installers Dental laboratory technicians
184 193 194 195 196 271 455 506 205 220 231 233 245 246 301 101 210 281 430 225 305 326 454 461 471 921 922 964 85 150 151 153 154 155 156 170 172 173 265 401 420 426
51 51 51 51 51 51 51 51 50 50 50 50 50 50 50 49 49 49 49 48 48 48 48 48 48 48 48 48 47 47 47 47 47 47 47 47 47 47 47 47 47 47
92
Craftsmen and kindred workers, n.e.c. Former members of the Armed Forces Craftsmen and kindred workers–allocated Current members of the Armed Forces Musicians and composers Secretaries, legal Secretaries, medical Secretaries, n.e.c. Marshals and constables Billings clerks Bookkeeping and billing machine operators Calculating machine operator Computer and peripheral equipment operators Duplicating machine operators Keypunch operators Tabulating machine operators O?ce machine operators, n.e.c. Foremen, n.e.c. Real estate agents and brokers Telegraph operators Farm managers Firemen, ?re protection Adult education teachers Teachers, except college and university, n.e.c. Air tra?c controllers Radio operators Postal clerks Real estate appraisers Stenographers Advertising agents and salesmen Mail carriers, post o?ce Tool and die makers Practical nurses Photographers Buyers and shippers, farm products Construction inspectors, public administration Inspectors, except construction, public administration Railroad conductors Library attendants and assistants Payroll and timekeeping clerks Typists
575 580 586 590 185 370 371 372 963 303 341 342 343 344 345 350 355 441 270 384 802 961 141 145 164 171 361 363 376 260 331 561 926 191 203 213 215 226 330 360 391
47 47 47 47 46 46 46 46 46 45 45 45 45 45 45 45 45 45 44 44 44 44 43 43 43 43 43 43 43 42 42 42 42 41 41 41 41 41 41 41 41
93
Electrician apprentices Engravers, except photoengravers Machinist apprentices Mechanic, except auto, apprentices Plumber and pipe ?tters Plumber and pipe ?tter apprentices Tailors Tool and die maker apprentices Speci?ed craft apprentices, n.e.c. Not speci?ed apprentices Farmers (owners and tenants) Farmers and farm managers–allocated trade Telephone operators Carpenters Carpenter apprentices Printing trades apprentices, except pressmen Floor layers, except tile setters Millwrights Photoengravers and lithographers Pressmen and plate printers, printing Pressmen apprentices Welders and ?ame-cutters Restaurant, cafeteria and bar managers Receptionists Cabinetmakers Cranemen, derrickmen, and hoistmen Electric power linemen and cablemen Molders, metal Molder, apprentices Pattern and model makers, except paper Power station operators Telephone installers and repairmen Telephone linemen and splicers Chainmen, rodmen, and axmen; surveying Dancers Managers and superintendents, building Compositors and typesetters Electrotypers and stereotypers Barbers Podiatrists Therapists Therapy assistants
431 435 462 491 522 523 551 562 571 572 801 806 282 385 415 416 423 440 502 515 530 531 680 230 364 413 424 433 503 504 514 525 552 554 605 182 216 422 434 935 71 76 84
41 41 41 41 41 41 41 41 41 41 41 41 40 40 40 40 40 40 40 40 40 40 40 39 39 39 39 39 39 39 39 39 39 39 39 38 38 38 38 38 37 37 37
94
Decorators and window dressers Jewelers and watchmakers Air conditioning, heating, and refrigeration Automobile body repairmen Automobile mechanics Automobile mechanic apprentices Railroad and car shop Sheetmetal workers and tinsmiths Sheetmetal apprentices Boatmen and canalmen Clerical assistants, social welfare Clerical supervisors, n.e.c Counter clerks, except food Enumerators and interviewers Estimators and investigators, n.e.c. Expediters and production controllers Mailhandlers, except post o?ce Meter readers, utilities Proofreaders Statistical clerks Teacher aides, except school monitors Weighers Miscellaneous clerical workers Not speci?ed clerical workers Clerical and kindred workers–allocated Blacksmiths Brickmasons and stonemasons Brickmasons and stonemasons, apprentices Forgemen and hammermen Heat treaters, annealers, and temperers Locomotive ?remen Rollers and ?nishers, metal Ship?tters Structural metal craftsmen Tile setters Checkers, examiners, and inspectors; manufacturing Photographic process workers Health trainees Nursing aides, orderlies, and attendants Airline stewardesses Housekeepers, except private households Ticket, station, and express agents Furriers
425 453 470 472 473 474 486 535 536 701 311 312 314 320 321 323 332 334 362 375 382 392 394 395 396 403 410 411 442 446 456 533 540 550 560 610 645 923 925 931 950 390 444
37 37 37 37 37 37 37 37 37 37 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 35 35
95
Radio and television Miscellaneous mechanics and repairmen Not speci?ed mechanics and repairmen Stationary engineers Railroad brakemen Farm foremen Salesmen and sales clerks, n.e.c. Salesmen of services and construction Sales workers–allocated Dispatchers and starters, vehicle Bakers Data processing machine repairmen O?ce machines Motion picture projectionists Sailors and deckhands Bulldozer operators Excavating, grading and road machine operators, except bulldozer Farm implements Heavy equipment mechanics, including diesel Household appliance and accessory installers and mechanics Plasterers Plasterer apprentices Shoe repairmen Stone cutters and stone carvers Furnacemen, smeltermen, and pourers Graders and sorters, manufacturing Heaters, metal Milliners Stationary ?remen Railroad switchmen Hairdressers and cosmetologists Auctioneers Cement and concrete ?nishers Piano and organ tuners and repairmen Blasters and powdermen Dressmakers and seamstresses, except factory Meat cutters and butchers, except manufacturing Shoemaking machine operatives Machine operatives, miscellaneous speci?ed Machine operatives, not speci?ed Miscellaneous operatives
485 492 495 545 712 821 280 285 296 315 402 475 484 505 661 412
35 35 35 35 35 35 34 34 34 34 34 34 34 34 34 33
436 33 480 33 481 33 482 520 521 542 546 622 624 626 636 666 713 944 261 421 516 603 613 631 664 690 692 694 33 33 33 33 33 33 33 33 33 33 33 33 32 32 32 32 32 32 32 32 32 32
96
Not speci?ed operatives Operatives, except transport–allocated Bus drivers Truck drivers Cashiers Boilermakers Bookbinders Inspectors, scalers, and graders Inspectors, n.e.c. Roofers and slaters File clerks Telegraph messengers Loom ?xers Painters, construction and maintenance Painter apprentices Sign painters and letterers Upholsterers Fishermen and oystermen Sales clerks, retail trade Salesmen, retail trade Shipping and receiving clerks Furniture and wood ?nishers Metal platers Mixing operatives Painters, manufactured articles Drill press operatives Grinding machine operatives Lathe and milling machine operatives Precision machine operatives, n.e.c Punch and stamping press operatives Riveters and fasteners Solderers Carding, lapping, and combing operatives Knitters, loopers, and toppers Textile operatives, n.e.c. Winding operatives, n.e.c. Fork lift and tow motor operatives Transport equipment operatives–allocated Animal caretakers, except farm Demonstrators Asbestos and insulation workers Meat cutters and butchers, manufacturing Sawyers
695 696 703 715 310 404 405 450 452 534 325 383 483 510 511 543 563 752 283 284 374 443 635 641 644 650 651 652 653 656 660 665 670 671 674 681 706 726 740 262 601 633 662
32 32 32 32 31 31 31 31 31 31 30 30 30 30 30 30 30 30 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 28 28 28
97
Conductors and motormen, urban rail transit Deliverymen and routemen Assemblers Drillers, earth Dry wall installers and lathers Motormen; mine, factory, logging camp, etc. Farm service laborers, self-employed Collectors, bill and account Glaziers Cutting operatives, n.e.c. Mine operatives, n.e.c. Lumbermen, raftsmen, and woodchoppers Cooks, except private household Millers; grain, ?our, and feed Dyers Sewers and stitchers Spinners, twisters, and winders Weavers Child care workers, except private households household–allocated Housekeepers, private household Paperhangers Oilers and greasers, except auto Longshoremen and stevedores Crossing guards and bridge tenders Stock clerks and storekeepers Bottling and canning operatives Carpenters’ helpers Gardeners and groundkeepers, except farm Midwives Child care workers, private household Garage workers and gas station attendants Parking attendants Taxicab drivers and chau?eurs Busboys Dishwashers Food service workers, except private household Boarding and lodging housekeepers School monitors Guards and watchmen Elevator operators
704 705 602 614 615 710 824 313 445 612 640 761 912 501 620 663 672 673 942 976 982 512 642 760 960 381 604 750 755 924 980 623 711 714 911 913 916 940 952 962 943
28 28 27 27 27 27 27 26 26 26 26 26 26 25 25 25 25 25 25 25 25 24 24 24 24 23 23 23 23 23 23 22 22 22 22 22 22 22 22 22 21
98
Warehousemen, n.e.c. Bartenders Waiters Messengers and o?ce boys Filers, polishers, sanders, and bu?ers Produce graders and packers, except factory and farm Meat wrappers, retail trade Packers and wrappers, n.e.c Farm laborers, farm foremen, and kindred workers Hucksters and peddlers Clothing ironers and pressers Laundry and dry cleaning operatives, n.e.c. Farm laborers, wage workers Farm laborers, unpaid family workers Cooks, private household Laundresses, private household Maids and servants, private household Private household workers–allocated Construction laborers Freight and material handlers Garbage collectors Stockhandlers Vehicle washers and equipment cleaners Miscellaneous laborers Not speci?ed laborers Laborers, except farm–allocated Janitors and sextons Newsboys Food counters and fountain workers Attendants, recreation and amusement Ushers, recreation and amusement Chambermaids and maids, except private household Attendants, personal service, n.e.c. Baggage porters and bell hops Personal service apprentices Welfare service aides Teamsters Cleaners and charwomen Bootblacks Engineering and science technicians
770 910 915 333 621 625 634 643 846 264 611 630 822 823 981 983 984 986 751 753 754 762 764 780 785 796 903 266 914 932 953 901 933 934 945 954 763 902 941 162
20 20 20 19 19 19 19 19 19 18 18 18 18 18 18 18 18 18 17 17 17 17 17 17 17 17 16 15 15 15 15 14 14 14 14 14 12 12 9 7
99
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