Human Capital and Unemployment Dynamics: Why More Educated Workers Enjoy Greater Employment Stability

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Human Capital and Unemployment Dynamics: Why More Educated Workers Enjoy Greater Employment Stability Isabel Cairo and Tomaz Cajner 2014-09 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS: WHY MORE EDUCATED WORKERS ENJOY GREATER EMPLOYMENT STABILITY ISABEL CAIRO´† AND TOMAZ CAJNER‡ Abstract. Why do more educated workers experience lower unemployment rates and lower employment volatility? A closer look at the data reveals that these workers have similar job finding rates, but much lower and less volatile separation rates than their less educated peers. We argue that on-the-job training, being complementary to formal education, is the reason for this pattern. Using a search and matching model with endogenous separations,we show that investments in match-specific human capital reduce the outside optionof workers,implying less incentives to separate. The model generates unemployment dynamics that are quantitatively consistent with the cross-sectionalempirical patterns. Keywords: unemployment, education, on-the-job training, specific human capital. JEL Classification: E24, E32, J24, J64. †Universitat Pompeu Fabra ‡Board of Governors of the Federal Reserve System E-mail addresses: isabel.cairo@upf.edu, tomaz.cajner@frb.gov. Date: 1 November 2013. The views expressed in this paper are those of the authors and do not necessarily represent the views or policies of the Board of Governors of the Federal Reserve System or its staff. We are especially grateful to Jordi Gal´ı and Thijs van Rens for their guidance, advice, and encouragement. We would also like to thank Regis Barnichon, Fabio Canova, Vasco Carvalho, Nir Jaimovich, Christian Merkl, Pascal Michaillat,ClaudioMichelacci, StaceyTevlin, AntonellaTrigari, EranYashiv, andseminarparticipantsatCREI Macroeconomics Breakfast, XXthAix-Marseille Doctoral SpringSchool, 2011 SED AnnualMeeting, 2011 EEA Annual Congress, 13th IZA/CEPR ESSLE, 2011 SAEe, IIES, IESE, ECB, Bank of Canada, Federal Reserve Board, and Bank of Spain for valuable comments and suggestions at various stages of the project. We are also grateful to Vera Brencic for help with the EOPP data. Isabel Cairo´ thanks the Ministry of Science and Innovation (BES-2009-028519) for financial support. Part of this research was conducted when Tomaz Cajner was a graduate student at the Universitat Pompeu Fabra and he gratefully acknowledges financial support from the Government of Catalonia and the European Social Fund during that period.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 1 1. Introduction “Employees with specific training have less incentive to quit, and firms have less incentive to fire them, than employees with no training or general training, which implies that quit and layoff rates are inversely related to the amount of specific training.” (Becker, 1964) More educated individuals fare much better in the labor market than their less educated peers. For example, when the U.S. aggregate unemployment rate hit 10 percent during the recent recession, high school dropouts suffered from unemployment rates close to 20 percent, whereas college graduates experienced unemployment rates of only 5 percent. As can be inferred from Figure 1, educational attainment appears to have been a good antidote to joblessness for the whole period of data availability. Moreover, the volatility of employment decreases with education as well. Indeed, enhanced job security arguably presents one of the main benefits of education. This paper systematically and quantitatively investigates possible explanations for greater employment stability of more educated people by using recent empirical and theoretical advances in the area of worker flow analysis and search and matching models. Unemployment rate (in percent) 20 18 16 14 12 10 8 6 4 2 < High school High school Some college College degree 0 1975 1980 1985 1990 1995 2000 2005 2010 Figure 1. U.S. unemployment rate by educational attainment Notes: Thesampleperiodis1976:01-2010:12. Monthlydatafortheworking-agepopulationconstructed from CPS microdata and seasonally adjusted. Shaded areas indicate NBER recessions. Theoretically, differences in unemployment across education groups can arise either because the more educated find jobs faster, because the less educated get fired more often, or due to a combination of the two factors. Empirically, the worker flow analysis in this paper finds that different education groups face roughly the same unemployment outflow rate (loosely speaking, the job finding rate). What creates the remarkably divergent patterns in unemployment by education is the unemployment inflow rate (the job separation rate). Why is it then that more educated workers lose their jobs less frequently and experience lower turnover rates? This paper provides a theoretical model in which higher educational attainment leads to greater employment stability. The model is based on vast empirical evidence showing

2 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS that on-the-jobtraining is strongly and positively related to education. As argued already by Becker (1964), higher amounts of specific training should reduce incentives of firms and workers to separate.1 We build on this insight and formalize it within a search and matching framework with endogenous separations in the spirit of Mortensen and Pissarides (1994). Inour model, all newhires lack somejob-specific skills, which theyobtainthrough the process of initial on-the-job training. More educated workers engage in more complex jobactivities, which necessitate more initial on-the-jobtraining. After gaining job-specific human capital, workers have less incentives to separate from their jobs, with these incentives being stronger for more educated workers. We parameterize the model by using detailed micro evidence from the Employment Opportunity Pilot Project (EOPP) survey. In particular, our empirical measure of training for each education group is based on the duration of initial on-the-job training and the productivity gap between new hires and incumbent workers. The simulation results demonstrate that, given the observed empirical differences in initial on-the-job training, the model is able to explain the empirical regularities across education groups on job finding, separation, and unemployment rates, both in their first and second moments. This cross-sectional quantitative success of the model is quite remarkable, especially when compared to the well-documented difficulties of the canonical search and matching model to account for the main time-series properties of aggregate labormarketdata(Shimer,2005), andthusrepresents themaincontributionofthispaper. Perhaps the most interesting is the ability of the model to generate vast differences in the separation rate, whereas at the same time the job finding rate remains very similar across education groups. The result that on-the-job training leaves the job finding rate unaltered reflects two opposing forces. On the one hand, higher training costs lower the value of a new job, leading to less vacancy creation and a lower job finding rate. On the other hand, higher training costs reduce the probability of endogenously separating once the worker has been trained, implying a higher value of a new job and a higher job finding rate. The simulation results reveal that both effects cancel out, thus an increase in training costs leaves the job finding rate virtually unaffected. This result is important, because it cannot be obtained with standard models in the literature. Indeed, because the job creation equation represents one of the central building blocks for any search and matching model, it is very likely that alternative explanations for different unemployment dynamics by education will be inconsistent with the empirical observation of almost negligible variation in job finding rates by education. The model in this paper can be also used to quantitatively evaluate several alternative explanations for differences in unemployment dynamics by education. In particular, the model nests the following alternative explanations: i) differences in the size of job profitability (match surplus heterogeneity); ii) differences in hiring costs; iii) differences in the frequency of idiosyncratic productivity shocks; iv) differences in the dispersion of 1 Similar arguments were also put forward by Oi (1962) and Jovanovic (1979).

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 3 idiosyncratic productivity shocks; and v) differences in the matching efficiency. We simulate the model under each of these alternative hypotheses and then use empirical evidence in order to discriminate between them. According to our findings, none of the economic mechanisms behind the competing explanations can generate unemployment dynamics by education that we observe in the data.2 As a final test of the theoretical mechanism embedded in our model, we provide novel empirical evidence on unemployment dynamics by required job training. In particular, we constructunemploymentrates, jobfindingratesandseparationratesbyspecificvocational preparation as measured in the Dictionary of Occupational Titles. This new evidence shows that occupations with higher specific vocational training experience substantially lower unemployment rates, which are predominantly due to lower separation rates. More strikingly, even after we condition for educational attainment, for example by focusing on high school graduates only, we find that higher specific vocational training leads to lower separation rates, but almost indistinguishable job finding rates, consistent with the theoretical mechanism advocated in this paper. Our paper contributes to three strands of literature. First, it contributes to the theoretical literature of business cycle fluctuations that attempts to move beyond the representative agent framework. The aim of this literature is twofold: first, to test the plausibility of different theories by taking advantage of cross-sectional data, and second, to further our understanding of business cycle fluctuations by studying the heterogeneous impact of aggregate shocks on different demographic groups, which seems particularly relevant for fluctuations in the labor market. Relative to the existing contributions (Kydland, 1984, Gomme, Rogerson, Rupert, and Wright, 2005), we carry out our analysis within the equilibrium search and matching framework and find that the inability of this class of models to explain aggregate unemployment fluctuations at business cycle frequencies (Shimer, 2005) is not due to a failure of these models to account for fluctuations experienced by some particular education group, but instead this models’ failure pertains equally to all education groups. Moreover, this paper shows that a tractable extension of the benchmark search and matching model delivers a framework that can account well for the cross-sectional differences in unemployment fluctuations by education and can be thus fruitfully utilized for studying cross-sectional labor market phenomena. Second, our paper contributes to the theoretical literature on search and matching models with worker heterogeneity. Contributions in this literature include Gautier (2002), Albrecht and Vroman (2002), Pries (2008), Dolado, Jansen, and Jimeno (2009), Gonzalez and Shi (2010), and Krusell, Mukoyama, and S¸ahin (2010). However, in these 2 Onealternativehypothesisthatwe cannotdirectly testwithourmodelrelatesto minimum-wagefloors, which are more likely to be binding for less educated workers, thus potentially explaining their higher unemployment rates. Nevertheless, the empirical research following Card and Krueger (1994) finds conflicting evidence on the effect of minimum wages on employment. If anything, the employment effects of minimum wages appear to be empirically modest – see, e.g., Dube, Lester, and Reich (2010) for some recent U.S. empirical evidence.

4 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS papers the worker’s exit to unemployment is assumed to be exogenous, hence they cannot be used to explain why the empirical unemployment inflow rate differs dramatically by education. Bils, Chang, and Kim (2011, 2012) allow for endogenous separations and heterogeneity in the rents from being employed; however, the latter assumption generates a substantial variation in the job finding rate and thus cannot be used to explain why the unemployment outflow rate empirically exhibits low variation by education. Relative to the existing literature, this paper provides a search and matching model with endogenous separations and on-the-jobtraining, which can generate substantial variability in job separation rates and at the same time small differences in job finding rates, which was a challenge for existing models. Third, our paper contributes to the empirical literature that studies cross-sectional differences in unemployment dynamics by education. Using Panel Study of Income Dynamics (PSID) data, Mincer (1991) finds that the incidence of unemployment is far more important than the reduced duration of unemployment in creating the educational differentials in unemployment rates; he attributes this finding to higher amount of on-the-job training for more educated workers. Our paper confirms this finding by using representative Current Population Survey (CPS) microdata, by constructing both duration-based and gross-flow labor market transition rates, and by controlling for possible biases (for example, duration dependence). Moreover, we use a combination of microdata and a theoretical model of equilibrium unemployment in order to interpret empirical evidence and to quantitatively discriminate among several possible explanations for observed empirical patterns. Following this introduction, Section 2 provides some empirical evidence on unemployment, its inflows and outflows, and on-the-job training by education. Section 3 outlines the model, which is then calibrated in Section 4. Section 5 contains the main simulation results of the model and a discussion of the mechanism driving the results. In Section 6 we quantitatively explore other possible explanations for differences in unemployment dynamics by education. Novel empirical evidence on unemployment dynamics by required job training is provided in Section 7. Finally, Section 8 concludes with a discussion of possible avenues for further research. We provide data description, some further empirical results, analytical proofs, sensitivity analysis, and additional robustness checks in the Appendix. 2. Empirical Evidence 2.1. Unemployment Rates It is a well-known and documented empirical fact that the unemployment rate differs by education level (recall Figure 1). In the United States, the jobless rate of the least educated (high school dropouts) is roughly four times greater than that of the most educated (college graduates), and this difference has been maintained since the data are available.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 5 Table 1. U.S. unemployment rates by educational attainment (in percent) males, males, males, 16 years 25 years prime age prime age, prime age, and over and over (25-54) white white, married Less than high school 12.6 9.0 9.3 8.5 7.1 High school 6.7 5.4 5.9 5.2 3.9 Some college 5.3 4.4 4.5 4.0 2.9 College degree 2.8 2.6 2.4 2.2 1.5 All individuals 6.4 4.9 5.0 4.5 3.4 Ratio LHS/CD 4.5 3.5 3.9 3.9 4.6 Notes: The sampleperiodis 1976:01- 2010:12. All variablesareconstructedfromCPSmicrodata. LHS stands for less than high school and CD for college degree. Table 1 tabulates the unemployment rate across four education groups by using the standard demographic controls (i.e., by showing the largest demographic group). As it turns out, substantial unemployment differentials across education groups represent a robust empirical finding that cannot be explained by usual demographic controls (age, gender, race, marital status). This is confirmed by results from a somewhat more formal regressionanalysis, which controlsforindividual characteristics, industry, andoccupation, and includes time dummies – these results can be found in the Appendix (Table 11). For the rest of the paper, we focus our analysis on individuals with 25 years of age and older for the following two reasons. First, by the age of 25 most individuals have presumably finished their studies, hence we avoid the possibility that our conclusions regarding unemployment properties for low educated workers could be driven by differential labor market behavior of young people. Second, further empirical exploration of unemployment rates by age reveals that young people experience somehow higher unemployment rates for all education groups, which could be related to their labor market entry that may start with an unemployment spell.3 2.2. Unemployment Flows Theoretically, a higher unemployment rate may be a result of a higher probability of becoming unemployed – a higher incidence of unemployment – or a lower probability of finding a job – higher duration of the unemployment spell.4 In order to distinguish between these possibilities, we follow the recent approach in the literature by calculating empirical unemployment flows.5 In particular, we decompose unemployment rates for 3 See Figure 10 in the Appendix. 4 Acknowledging a slight abuse of terminology, we use in this paper interchangeably expressions “inflow rates”,“separationrates” and “unemploymentincidence” to denote flow rates into unemployment. Similarly, we refer to “outflow rates” and “job finding rates” to denote flow rates out of unemployment, whereas “unemployment duration” is the inverse of the latter. 5 This approach has been used by Shimer (2012), Elsby, Michaels, and Solon (2009), and Fujita and Ramey (2009) for the analysis of aggregate data, and by Elsby, Hobijn, and S¸ahin (2010) for decompositions along various demographic groups. Note that there exists an older literature, which is not based on empirical unemployment flows, that also tries to identify the reasonbehind the observed differences in unemployment rates across education levels. It is a robust finding in this literature that

6 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS people with 25 years of age and over into unemployment inflow and outflow rates.6 As can be seen from Figure 2, we find that outflow rates from unemployment are broadly similar across education groups, whereas inflow rates differ considerably.7 Furthermore, ∗ we exploit the steady state unemployment approximation u ≈ s /(s + f ), which has t t t t been found in the literature to replicate well the actual unemployment rates (s stands t for the separation rate and f denotes the job finding rate). In Figure 3 we construct two t types of counterfactual unemployment rates to analyze separately the role of outflows and inflows in explaining the differences in unemployment rates across education groups. In particular, inthe left panel of Figure3 we calculate the counterfactual unemployment rate series for each group by taking its actual outflow rate series, but keeping the inflow rate series at the value for the aggregate economy. Analogously, in the right panel of Figure 3 we calculate the counterfactual unemployment rate series for each group by taking its actual inflow rate series, but keeping the outflow rate series at the value for the aggregate economy. These two counterfactuals clearly demonstrate that the observable differences in job finding rates have a negligible effect on unemployment rates, with separation rates accounting for almost all variability in unemployment rates across education groups.8 Moreover, the observed differences in outflow rates actually go in the wrong direction as they predict (slightly) higher unemployment rates for highly educated workers. In the Appendix we further check for two possible biases regarding our conclusion that inflow rates drive the differences in unemployment rates by education. First, the procedure to calculate outflow rates might be biased due to duration dependence. Figure 11 in the Appendix illustrates that all education groups are roughly equally represented over the whole unemployment duration spectrum, hence duration dependence is not likely to bias our conclusion that outflow rates are similar by education. Second, so far we have neglected transitions in and out of the labor force. Figures 12 and 13 in the Appendix show that the findings of similar job finding rates and vastly different separation rates across education groups remain valid when considering a three-state decomposition of unemployment flows. lower incidence of unemployment within the more educated is the main contributor to differences in unemployment rates (Ashenfelter and Ham, 1979, Nickell, 1979, Mincer, 1991). Indeed, empirical evidence on the effect of education on unemployment duration is mixed, with some studies finding a negative effect(Nickell, 1979, Mincer, 1991), some negligibleeffect (Ashenfelter and Ham, 1979), andsome positive effect (Moffitt, 1985, Meyer, 1990). 6 Details of the procedure canbe found in the Appendix. The Appendix alsoprovides analogousanalysis for people with 16 years of age and over. 7 Similar findings of nearly identical outflow rates and different inflow rates across education groups are provided by Elsby, Hobijn, and S¸ahin (2010). 8 Note that our focus here is primarily on cross-sectional variation, as opposed to time variation in unemployment rates. Therefore, we avoid the critique of Fujita and Ramey (2009) on using counterfactual unemploymentratesto assessthe roleofinflow ratesandoutflowratesinexplainingunemploymentfluctuations over time. Their critique stressedthe importance of accountingfor dynamic interactions,which imply that fluctuations in the separation rate are negatively correlated with future changes in the job finding rate.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 7 Outflow rate (in percent) Inflow rate (in percent) 80 6 70 5 60 4 50 40 3 30 2 20 1 10 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 2. Unemployment flow rates Notes: 12-month moving averages for individuals with 25 years of age and over. The role of outflow rate The role of inflow rate 20 20 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 3. Counterfactual unemployment rates Notes: The left panel shows the counterfactual unemployment rate series for each group by taking its actualoutflowrateseries,butkeepingthe inflowrateseriesatthe valuesfortheaggregateeconomy. The rightpanel shows the counterfactualunemployment rate series for eachgroupby taking its actual inflow rateseries,butkeepingthe outflowrateseriesatthevaluesforthe aggregateeconomy. 12-monthmoving averagesfor individuals with 25 years of age and over. To sum up, in order to understand why the least educated workers have unemployment rates nearly four times greater than the most educated workers, one has to identify the economic mechanisms that create a gap in their inflow rates to unemployment. 2.3. Labor Market Volatility Table 2 summarizes volatility measures for the main labor market variables of interest. In particular, we report two sets of volatility statistics. First, absolute volatilities are defined as standard deviations of the data expressed in deviations from an HP trend with smoothing parameter 105.9 Second, relative volatilities are defined analogously, except 9 For example,absolute volatility of 1.05for the aggregateunemploymentrate implies that the aggregate unemployment rate varies +/- 1.05 percentage points around its mean of 4.89.

8 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS that all variables are initially expressed in natural logarithms.10 Both sets of volatility statistics are reported in order to facilitate the comparison with the existing literature. More precisely, on the one hand macroeconomists typically avoid taking logarithms of rates and thus prefer to report absolute volatilities. On the other hand, some of the recent literature on quantitative performance of search and matching models puts more emphasisonrelativevolatilities, becausewhatmattersfromtheviewpoint ofthecanonical search and matching model are relative changes in unemployment. Table 2. Labor market volatility by education level Absolute volatility Relative volatility n u f s n u f s Less than high school 1.78 1.78 7.62 0.42 1.99 18.66 17.45 9.23 High school 1.26 1.26 7.48 0.24 1.35 20.83 18.62 9.09 Some college 1.02 1.02 8.96 0.18 1.08 21.32 20.48 8.28 College degree 0.55 0.55 8.55 0.11 0.57 20.16 21.39 9.87 All individuals 1.05 1.05 7.49 0.18 1.12 20.07 17.99 7.57 Ratio LHS/CD 3.22 3.22 0.89 3.87 3.47 0.93 0.82 0.93 Notes: Quarterly averages of seasonally-adjusted monthly data for individuals with 25 years of age and over. Absolute volatilities are defined as standard deviations of the data expressed in deviations from an HP trend with smoothing parameter 105. Relativevolatilitiesaredefinedanalogously,exceptthatallvariablesareinitially expressed in natural logarithms. The sample period is 1976:01 - 2010:12. n refers to employment rate, u to unemployment rate, f to job finding rate and s to separation rate. Our preferred volatility measure corresponds to the concept of absolute volatility. To understand why, notice that in the case of employment rates, the distinction between relative and absolute volatilities becomes immaterial.11 As the numbers in Table 2 clearly illustrate, more educated workers enjoy greater employment stability. Employment stability is arguably also the concept that matters from the welfare perspective of an individual. However, if we compare absolute and relative volatilities for unemployment rates, the numbers lead to contradictory conclusions – while absolute volatilities agree with employment volatilities by definition, relative volatilities in contrast suggest that the most educated group experiences higher unemployment volatility than the least educated group. The reason why the more educated have more volatile unemployment rates in terms of log deviations, despite having less volatile employment rates, is clearly related to their lower unemployment means.12 To avoid the distorting effect of different means on relative volatility measures, we prefer to focus on absolute volatilities. Note that the more educated experience also lower (absolute) volatility of separation rates, whereas job finding rates exhibit broadly equal variation across education groups. 10 Forexample,relativevolatilityof20.07fortheaggregateunemploymentrateimpliesthattheaggregate unemployment rate roughly varies +/- 20.07 percent around its mean of 4.89. 11 This naturally follows as log(1+x)≈x for x close to zero. 12 By definition of the employment and unemployment rates, we have nt +ut = 1. Taking log-linear approximation yields ut = −(n∗/u∗)nt ≈ −(1/u∗)nt, where hats denote steady-state deviations. Hence, logdeviationsinemploymentareamplifiedbyafactorofroughly1/u∗ whenonecalculateslogdeviations in unemployment. b b b

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 9 2.4. On-the-Job Training Economists have long recognized the importance of learning-by-doing, formal and informal on-the-job training for human capital accumulation. Despite the widely accepted importance of on-the-job training in theoretical work, empirical verifications of theoretical predictions remain rare, mainly due to limited data availability. Unlike with formal education, the data on training need to be obtained from scarce and frequently imperfect surveys, with considerable data imperfections being related especially to informal on-the-job training and learning-by-doing.13 Nevertheless, existing empirical studies of job training overwhelmingly suggest the presence of strong complementarities between education and training. The positive link between formal schooling and job training has been found in data from: i) the CPS Supplement of January 1983, the National Longitudinal Surveys (NLS) of Young Men, Older Men and Mature Women, and the 1980 EOPP survey by Lillard and Tan (1986); ii) the NLS of the High School Class of 1972 by Altonji and Spletzer (1991); iii) the Panel Study of Income Dynamics (PSID) by Mincer (1991); and iv) a dataset of a large manufacturing firm by Bartel (1995). In what follows we provide some further evidence on training by education level from the 1982EOPP survey, which will formthe empirical basis for the parameterization of our model. Table 3 summarizes the main training variables of the survey with a breakdown by education.14 The EOPPsurvey isparticularlyuseful toanalyzetraining becauseit includes measures of both formal and informal training. This is important given that the average incidence rate of receiving initial (i.e. during first three months) formal training in our sample corresponds to 13.7 percent, while the incidence rate of receiving some type of initial training is 95.0 percent. Table 3 illustrates two relevant aspects of the data for our paper. First, nearly all new hires receive some type of initial training, regardless of their level of education. Second, there are considerable differences across education groups in terms of the duration of training received and the corresponding productivity gap (the latter is defined as the percent difference in productivity of an incumbent worker with 2 years of experience and a new hire). For example, a newly hired college graduate needs 18.2 weeks on average to become fully trained, which is nearly two times the time needed for a newly hired high school dropout. Moreover, the difference between the initial productivity and 13 Barron,Berger, and Black (1997) provide a comprehensive comparison of different measures of onthe-job training across datasets and Lynch (1992) discusses shortcomings of various on-the-job training surveys. 14 We restrict the EOPP sample to individuals for whom we have information on education and, to be consistent with our data on unemployment, to individuals with 25 years of age and over. Since the distribution of training duration is highly skewed to the right, we eliminate outliers by truncating distribution at its 95th percentile, which corresponds to the training duration of 2 years. The survey questionfortrainingdurationwas: “Howmanyweeksdoesittakeanew employeehiredfor thisposition to become fully trained and qualified if he or she has no previous experience in this job, but has had the necessary school-provided training?” In order to compute the productivity gap we combine the survey questiononproductivityofa“typicalworkerwhohasbeeninthisjobfor2years”andthesurveyquestion on productivity of a “typical worker during his/her first 2 weeks of employment”. In the Appendix we provide some additional discussion of the 1982 EOPP survey.

10 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Table 3. Measures of training by education level from the 1982 EOPP survey Less than High Some College All high school school college degree individuals Incidence rate of initial training (mean, in percent) Formal 9.5 12.0 18.1 17.9 13.7 Informal by manager 89.7 85.9 89.8 88.5 87.3 Informal by coworkers 56.7 58.0 62.7 53.5 58.1 Informal by watching others 78.1 75.1 81.0 73.9 76.3 Some type of training 94.0 94.5 97.0 95.1 95.0 Time to become fully trained (mean, in weeks) Duration 10.2 12.0 15.9 18.2 13.4 Productivity gap (mean, in percent) Typical new hire vs. incumbent 32.5 36.2 45.3 48.1 39.1 Notes: The sample includes 1053 individuals with 25 years of age and older, for whom we have informationoneducation. The distributionoftrainingdurationis truncatedatits 95thpercentile. All measures of training correspond to typical new hires. the productivity achieved by an incumbent worker increases with the education level as well, from one third to one half. The objective of this paper is to study whether the observed differences in on-the-job training are able to explain the observed differences in unemployment rates across education groups by affecting the job destruction margin. In particular, the paper’s hypothesis claims that higher investments in training reduce incentives for job destruction. However, according to the argument of Becker (1964) incentives for job destruction crucially depend on the portability of training across different jobs. As we argue below, there exist strong reasons to believe that our empirical measure of on-the-job training can indeed be interpreted as being largely job-specific and hence unportable across jobs. First, the appropriate theoretical concept of specificity in our case is not whether a worker canpotentiallyusehislearnedskills inanotherfirm. Whatmattersforouranalysis is whether after going through an unemployment spell, a worker can still use his past training in a new job. To give an example, a construction worker might well be able to take advantage of his past training in another construction firm, but if after becoming unemployed he cannot find a new job in the construction sector and is thus forced to move to another sector, where he cannot use his past training, then his training should be viewed as specific. Industry and occupational mobility are not merely a theoretical curiositybut, asshownbyKambourov and Manovskii(2008), anotablefeatureoftheU.S. labor market. These authors also find that industry and occupational mobility appears to be especially high when workers go through an unemployment spell.15 Similarly, by analyzing the National Longitudinal Survey of Youth (NLSY) data Lynch (1991) reaches the conclusion that on-the-job training in the United States appears to be unportable from employer to employer. In the same vein, Lynch (1992) finds that on-the-job training 15 See Figure 10a of their paper.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 11 with the current employer increases wages, while spells of on-the-job training acquired before the current job have no impact on current wages. Second, the EOPP was explicitly designed to measure the initial training at the start of the job (as opposed to training in ongoing job relationships), which is more likely to be of job-specific nature. Moreover, the EOPP also provides data onthe productivity difference between the actual new hire during his first two weeks and the typical worker who has been in this job for two years. For the actual new hire the EOPP also reports months of relevant experience.16 Table 4 summarizes the productivity differences between the actual new hire and the typical incumbent for three age groups and also for two subsamples of new hires with at least 1 and 5 years of relevant experience. Note that one would expect to observe in the data a rapidly disappearing productivity gap (between incumbents and new hires) with rising age of workers and months of relevant experience, if this measure of on-the-job training were capturing primarily general human capital. However, the results in Table 4 indicate that initial on-the-job training remains important also for older cohorts of workers and for workers with relevant experience. Crucially for our purposes, the relative differences across education groups remain present and even increase a bit. Overall, this suggests that initial on-the-job training, at least as measured by the EOPP survey, contains primarily specific human capital. Table 4. Productivity gap between incumbents and new hires by education level from the 1982 EOPP survey Less than High Some College All high school school college degree individuals Productivity gap (mean, in percent) 16 years and over 32.2 35.4 37.9 43.9 36.4 25 years and over 24.6 29.3 37.9 39.3 31.8 35 years and over 20.2 29.3 31.7 38.6 29.6 25 years and over and at least - 1 year of relevant experience 22.7 24.5 34.4 41.7 28.8 - 5 years of relevant experience 18.2 22.6 26.6 38.9 25.0 Notes: The productivity gap is calculated as the difference in productivity between the actual new hire and the typical incumbent. We restrict the sample to individuals for whom we have information on education. Third, Figure 4 depicts the incidence rate of formal training from the NLSY cohort.17 The analysis of these data shows that the incidence rate of formal training differs across education groups, with more educated workers receiving more training and the numbers being comparable to the ones for formal training from the EOPP survey (see Table 3). Moreover, Figure 4 shows that incidence rates of training across education groups do not exhibit a notable downward trend with aging of the 1979 NLSY cohort, consistent with the argument of the previous paragraph. 16 The exact survey question was “How many months of experience in jobs that had some application to the position did (NAME) have before (he/she) started working for your company?” 17 A short description of this survey is available in the Appendix.

12 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 35 30 25 20 15 10 5 < High school High school Some college College degree 0 1987 1990 1992 1995 1997 2000 2002 2005 2007 Figure 4. Incidence rate of formal training from the 1979 NLSY cohort Finally, the traditional approach in the literature to distinguish between general and specific human capital has been to associate the wage return to overall work experience as an indication of the presence of general human capital, whereas the wage return to tenure has been typically interpreted as evidence of specific human capital. In an influential paper, Topel (1991) estimates that 10 years of job tenure raise the wage by over 25 percent, with wage growth being particularly rapid during an initial period of job, hence suggesting the presence of specific human capital.18 Moreover, Brown (1989) shows that firm-specific wage growth occurs almost exclusively during periods of on-the-job training, lending further support to the argument that on-the-job training is mostly specific. 3. The Model This section presents the model, which is an extension of the canonical search and matching model with endogenous separations (Mortensen and Pissarides, 1994). In our setting workers initially lack some job-specific skills, which they obtain during a period of on-the-job training. The model allows for worker heterogeneity in terms of productivity, directly related to their formal education. Moreover, different levels of education require different amounts on-the-job training for exogenous, technological reasons, which may reflect variety in job complexity. Intuitively, more educated workers engage in more complex job activities, which necessitate a higher degree of initial on-the-job training. 3.1. Environment The discrete-time model economy contains a finite number of segmented labor markets, indexed by h ∈ {1,2,...,hmax}, where h represents different levels of formal educational attainment. Workers in each of these markets possess a certain amount of formal human capital, denoted by H ∈ {H 1 ,H 2 ,...,H hmax}, directly related to their education. Moreover, firms in each of these markets provide initial on-the-job training to their new hires, 18 Evidence from displaced workers, as reported by Jacobson, LaLonde, and Sullivan (1993), and Couch and Placzek (2010), also indicates the importance of specific human capital.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 13 with the amount of training depending on worker’s education. The assumption of segmented labor markets is chosen because education is an easily observable and verifiable characteristic of workers, hence firms can direct their search towards desired education level for their new hires.19 Each segmented labor market features a continuum of measure one of risk-neutral and infinitely-lived workers. These workers maximize their expected discounted lifetime utility defined over consumption, E ∞ βkc , where β ∈ (0,1) represents the discount t k=0 t+k factor. Workers can be either employed or unemployed. Employed workers earn wage w , P t whereas unemployed workers have access to home production technology, which generates b consumption units per time period. In general, b also includes potential unemployh h ment benefits, leisure, saved work-related expenditures and is net of job-searching costs. Importantly, it depends onworker’s education. Weabstract fromlaborforce participation decisions, therefore all unemployed workers are assumed to be searching for jobs. A large measure of risk-neutral firms, which maximize their profits, is trying to hire workers by posting vacancies. We follow the standard approach in search and matching literature by assuming single-worker production units. In other words, each firm can post only one vacancy and for this it pays a vacancy posting cost of c units of output per time h period. Here we allow this vacancy posting cost to vary across segmented labor markets, reflecting potentially more costly searching process in labor markets that require higher educational attainment. After a match between a firm and a worker with education H is formed, they first draw an idiosyncratic productivity a. If the latter is above a certain threshold level, described more in detail below, they start producing according to the following technology: y(H,A,a) = (1−τ )HAa. h Notethatworkersareinitiallyuntrained, thustheyproduceonly(1−τ )ofregularoutput, h where τ measures the extent of job-specific skills (i.e., the productivity gap between a h new hire and a skilled worker). In each period untrained workers experience a probability φ of being upgraded to a skilled worker. Note that 1/φ yields the average duration of h h on-the-job training.20 A firm with a skilled worker of education H produces a regular output level of HAa, where A denotes the aggregate productivity and a the idiosyncratic productivity. Both aggregate and idiosyncratic productivity are assumed to be stochastic, 19 In a somewhat related setting with direct search, Mortensen and Pissarides (1999) show that even if one allows for the possibility of overqualification, whereby workers can apply for jobs that require lower formal education than their own, workers optimally self-select themselves into appropriate educational sub-markets, yielding a perfectly segmented equilibrium. For the contrasting case with random search, see for example Pries (2008). 20 Related modeling approaches are adopted in Silva and Toledo (2009) and Kambourov and Manovskii (2009). Silva and Toledo (2009) model on-the-job training without workers’ heterogeneity in order to examine the issue of aggregate volatilities in the search and matching model. In addition to onthe-job training, they also assume that upon firing a skilled worker firms need to pay a firing cost. Kambourov and Manovskii (2009) abstract from business cycle fluctuations and use their occupationspecific human capital model with experienced and inexperienced workers in order to investigate occupational mobility and wage inequality.

14 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS evolving over time according to two independent Markov chains {A,ΠA } and {a,Πa }, with finite grids A = {A ,A ,...,A } and a = {a ,a ,...,a }, transition matrices ΠA 1 2 n 1 2 m being composed of elements πA = P{A ′ = A | A = A } and Πa being composed of ij j i elements πa = P{a ′ = a | a = a }, and the initial probability vector being composed of ij j i elements πa = P{a ′ = a }. j j 3.2. Labor Markets The matching process between workers and firms is formally depicted by the existence of a constant returns to scale matching function: m(u,v) = γuαv 1−α, where the parameter γ stands for matching efficiency, the parameter α for the elasticity of the matching function with respect to unemployment, u denotes the measure of unemployed and v denotes the measure of vacancies. Each segmented labor market h features such a matching function. We can define labor market tightness as θ(H,A) ≡ v(H,A)/u(H,A) and derive the endogenously determined vacancy meeting probability, q(θ(H,A)), and job meeting probability, p(θ(H,A)), as: m(u(H,A),v(H,A)) q(θ(H,A)) = = γθ(H,A) −α, (1) v(H,A) m(u(H,A),v(H,A)) p(θ(H,A)) = = γθ(H,A) 1−α. (2) u(H,A) 3.3. Characterization of Recursive Equilibrium Bellman equations for the firm in labor market h with required education H that is employing a trainee and a skilled worker are, respectively: JT(H,A,a) = max 0,(1−τ )HAa−wT(H,A,a) (3) h (cid:8)+β(1−δ) E φ JS(H,A ′ ,a ′ )+(1−φ )JT(H,A ′ ,a ′ ) , A,a h h JS(H,A,a) = max 0,HAa−wS(H(cid:8),A,a)+β(1−δ) E JS(H,A ′ ,a ′ ) . (cid:9)(cid:9) (4) A,a Equation (4) is stand(cid:8)ard in search and matching models wit(cid:8)h endogenous(cid:9)se(cid:9)parations. Observe that we also allow for exogenous separations at rate δ, which are understood to be other types of separations that are not directly related to the productivity of a job. As explained above, equation (3) in addition involves the lost output τ that is due to h initial lack of job-specific skills and the probability φ of becoming a skilled worker. E h A,a denotes expectations conditioned on the current values of A and a. Note that at any point in time, a firm can also decide to fire its employee and become inactive in which case it obtains a zero payoff. The firm optimally chooses to endogenously separate at and below the reservation productivities a˜T(H,A) and a˜S(H,A), which are implicitly defined as the

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 15 maximum values that satisfy: JT(H,A,a˜T(H,A)) = 0, (5) JS(H,A,a˜S(H,A)) = 0. (6) The free entry condition equalizes the costs of posting a vacancy (recall that c is per h period vacancy posting cost and 1/q(θ(H,A)) is the expected vacancy duration) with the expected discounted benefit of getting an initially untrained worker: c h = βE JT(H,A ′ ,a ′ ) . (7) A q(θ(H,A)) (cid:8) (cid:9) The unemployed worker enjoys utility b and with probability p(θ(H,A)) meets with a h vacancy: U(H,A) = b +p(θ(H,A))βE WT(H,A ′ ,a ′ ) +(1−p(θ(H,A)))βE U(H,A ′ ) . (8) h A A Note that the unemployed worke(cid:8)r always starts(cid:9)a job as a trainee, due t(cid:8)o the initia(cid:9)l lack of job-specific skills.21 Bellman equations for the worker are analogous to the firm’s ones, with his outside option being determined by the value of being unemployed: WT(H,A,a) = max U(H,A),wT(H,A,a)+βδE U(H,A ′ ) (9) A (cid:8)+β(1−δ) E φ WS(H,A ′ ,(cid:8)a ′ )+(1−(cid:9)φ )WT(H,A ′ ,a ′ ) , A,a h h WS(H,A,a) = max U(H,A),wS(H,(cid:8)A,a)+βδE U(H,A ′ ) (cid:9)(cid:9)(10) A (cid:8)+β(1−δ) E WS(H,A ′ ,a ′ (cid:8)) . (cid:9) A,a Under the generalized Nash wage barg(cid:8)aining rule the(cid:9)(cid:9)worker gets a fraction η of total match surplus, defined as: ST(H,A,a) ≡ JT(H,A,a)+WT(H,A,a)−U(H,A), SS(H,A,a) ≡ JS(H,A,a)+WS(H,A,a)−U(H,A), for the job with a trainee and a skilled worker, respectively. Hence: WT(H,A,a)−U(H,A) = ηST(H,A,a), WS(H,A,a)−U(H,A) = ηSS(H,A,a). Observe that the above equations imply that the firm and the worker bothwant a positive match surplus. Therefore, there is a mutual agreement onwhen to endogenously separate. From the above surplus-splitting equations it is straightforward to show that the wage 21 The model could be extended to allow for heterogeneity in the loss of specific human capital upon becoming unemployed, as for example in Ljungqvist and Sargent(1998, 2007). Such an extension would be valuable for analyzing issues like long-term unemployment (where the loss of specific human capital is likely to be larger) and sectoral worker mobility (where the loss of specific human capital is likely to be larger when an unemployedworkerfinds a job in a new sector). We leave these extensions for further research.

16 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS equations are given by: wT(H,A,a) = η((1−τ )HAa+c θ(H,A))+(1−η)b , (11) h h h wS(H,A,a) = η(HAa+c θ(H,A))+(1−η)b , (12) h h for the trainee and the skilled worker, respectively. The wage equations imply that the worker and the firm share the cost of training in accordance with their bargaining powers. The model features a recursive equilibrium, with its solution being determined by equations (1)-(12). The solution of the model consists of equilibrium labor market tightness θ(H,A) and reservation productivities a˜T(H,A) and a˜S(H,A). Next, the following proposition establishes an important neutrality result. Proposition 1. Under the assumptions c = cH and b = bH with c,b,H > 0 the h h solution of the model is independent of H. Proof. We can combine the equilibrium conditions and write the surpluses as: ST(H,A,a) = max 0,(1−τ )HAa−b −βηp(θ(H,A)) E ST(H,A ′ ,a ′ ) h h A (cid:8)+β(1−δ) E φ SS(H,A ′ ,a ′ )+(1−(cid:8)φ )ST(H,A ′ ,a(cid:9) ′ ) , A,a h h SS(H,A,a) = max 0,HAa−b −β(cid:8)ηp(θ(H,A)) E ST(H,A ′ ,a ′ ) (cid:9)(cid:9) h A (cid:8)+β(1−δ) E SS(H,A ′ ,a ′ ) (cid:8). (cid:9) A,a Moreover, the free entry condition can be(cid:8)written in te(cid:9)rm(cid:9)s of the surplus as: c h = β(1−η) E ST(H,A ′ ,a ′ ) . A q(θ(H,A)) (cid:8) (cid:9) Introducing the free entry condition in the expressions for the surpluses we obtain the following: c η ST(H,A,a) = max 0,(1−τ )HAa−b −θ(H,A) h h h 1−η (cid:18) (cid:19) (cid:8) +β(1−δ) E φ SS(H,A ′ ,a ′ )+(1−φ )ST(H,A ′ ,a ′ ) , A,a h h SS(H,A,a) = max 0,HAa−b −θ (cid:8) (H,A) c h η +β(1−δ) E SS(H,A (cid:9)′(cid:9) ,a ′ ) . h A,a 1−η (cid:18) (cid:19) (cid:8) (cid:8) (cid:9)(cid:9) Substituting recursively, it is straightforward to check that the solution of the model is equivalent for ∀H > 0 iff c = cH and b = bH with c,b > 0. (cid:3) h h The usefulness of Proposition 1 will become clear in the following two sections with calibration and numerical results of the model. In particular, the proposition’s result enables a transparent comparison of the model results across different education groups h, with the only parameters affecting results being on-the-job training parameters. Notably, by using the proposition we avoid changing the surpluses by magnifying the difference between thefirm’soutputandthevalueofbeing unemployed. Webelieve thatthemodel’s implications when changing the value of being unemployed relative to output have been

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 17 well explored in the recent literature.22 Indeed, by assuming that more educated workers enjoy higher match surplus (with b being lower relative to output than in the case of h less educated workers) it is well documented that the model would predict a decrease in the unemployment and the separation rate, but at the same time it would also predict an increase in the job finding rate. The latter prediction strongly contradicts the empirical evidence across education groups, as documented in Section 2. Further discussion of these issues together with some empirical evidence justifying the assumptions of proportionality in c and b is provided in the next section. h h Withtheobtainedsolutionofthemodelwecangeneratenumericalresultsbysimulating it, using the law of motion for trainees and skilled workers. The mass of trainees next period with idiosyncratic productivity a is given by: j (nT) ′ (a ) = j 1 m a > a˜T(H,A ′ ) (1−δ)(1−φ ) πanT(a )+p(θ(H,A))πau(H,A) . j h ij i j " # i=1 (cid:8) (cid:9) X First notice that if a ≤ a˜T(H,A ′ ) then the mass of trainees with idiosyncratic proj ductivity a is zero, given that it is not optimal to produce at this productivity. If j a > a˜T(H,A ′ ), the mass of trainees tomorrow with idiosyncratic productivity a is comj j posed of two groups: the mass of trainees today that survive exogenous separations and that are not upgraded to skilled workers, and the mass of new matches that are created with productivity a . j Similarly, the mass of skilled workers next period with idiosyncratic productivity a is j given by: (nS) ′ (a ) = j 1 m m a > a˜S(H,A ′ ) (1−δ) πanS(a )+(1−δ)φ πanT(a ) . j ij i h ij i " # i=1 i=1 (cid:8) (cid:9) X X Again, notice that if a ≤ a˜S(H,A ′ ), the mass of skilled workers with idiosyncratic proj ductivity a is zero, given that these matches are endogenously destroyed. However, if j a > a˜S(H,A ′ ), the mass of skilled workers tomorrow with idiosyncratic productivity a is j j again composed of two groups: the mass of previously skilled workers that survive exogenous separations and the mass of upgraded trainees that were not exogenously destroyed. Finally, the aggregate employment rate n and unemployment rate u are defined as: m n(H,A) = nT(a )+nS(a ) , i i i=1 X(cid:0) (cid:1) u(H,A) = 1−n(H,A), 22 See, e.g., Mortensen and Nagypa´l (2007), Costain and Reiter (2008), and Hagedorn and Manovskii (2008).

18 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS respectively. Labor productivity is defined as total production (Y) over total employment (n), where m m Y(H,A) = (1−τ )HA a nT(a )+HA a nS(a ). h i i i i i=1 i=1 X X 3.4. Efficiency The canonical search and matching model features search externalities. It is wellknown that the equilibrium of this model yields a socially efficient outcome, provided that the Hosios condition is satisfied (Hosios, 1990). This condition equalizes the worker’s bargainingpower totheelasticity ofthematching functionwithrespect tounemployment. Does the same condition also apply to our model or is there some role for policy? Proposition 2. Abstracting from aggregate productivity shocks and assuming that idiosyncratic productivity shocks are being drawn in each period from a continuous distribution G(a), the model’s equilibrium is constrained-efficient iff η = α. The proof of the above proposition is given in the Appendix. Hence, the standard Hosios condition applies also to our setting where workers are initially untrained. In other words, there are no additional inefficiencies specific to our model, except from the standard search externalities. Therefore, differential unemployment outcomes, which are related to differential training requirements, are efficient in our model if the Hosios condition is satisfied. This result is intuitive, because training requirements in our model are merely a technological constraint. Finally, we show in the Appendix that the job destruction is maximized when the Hosios condition holds.23 4. Calibration We proceed by calibrating the model. First, we discuss the calibration of parameter values that are consistent with empirical evidence at the aggregate level. Second, we specify the on-the-job training parameter values that are specific to each education group. 4.1. Parameter Values at the Aggregate Level Themodel issimulated atmonthly frequency. Table5summarizes theparameter values at the aggregate level. The value of the discount factor is consistent with an annual interest rate of four percent. The efficiency parameter γ in the matching function targets a mean monthly 23 Whether violation of the Hosios condition affects more the job destruction margin for trainees or for skilled workers depends on parameter values. The exact analytical condition is given in the Appendix, where we also provide a numerical example for our original model (with aggregate productivity shocks andsome persistence inidiosyncraticproductivity),showingthat the jobdestructionis maximizedwhen the worker’s bargaining power is equal to the elasticity of the matching function with respect to unemployment.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 19 Table 5. Parameter values at the aggregate level Parameter Interpretation Value Rationale β Discount factor 0.9966 Interest rate 4% p.a. γ Matching efficiency 0.45 Job finding rate 45.3% (CPS) α Elasticity of the matching 0.5 Petrongolo and Pissarides (2001) function η Worker’s bargaining power 0.5 Hosios condition c Vacancy posting cost 0.106 1982 EOPP survey b Value of being unemployed 0.82 See text σ Standard deviation for 0.0064 Labor productivity (BLS) A log aggregate productivity ρ Autoregressive parameter for 0.98 Labor productivity (BLS) A log aggregate productivity µ Mean log idiosyncratic 0 Normalization a productivity σ Standard deviation for log 0.249 Separation rate 2.24% (CPS) a idiosyncratic productivity λ Probability of changing 0.3333 Fujita and Ramey (2012) idiosyncratic productivity δ Exogenous separation rate 0.0075 JOLTS data φ Probability of training upgrade 0.3226 1982 EOPP survey τ Training costs 0.196 1982 EOPP survey H Worker’s productivity 1 Normalization job finding rate of 45.3 percent, consistent with the CPS microevidence for people with 25 years and over as described in Section 2.2. For the elasticity of the Cobb-Douglas matching function with respect to unemployment we draw from the evidence reported in Petrongolo and Pissarides (2001) and accordingly set α = 0.5. Absent any further microevidence, we follow most of the literature and put the workers’ bargaining power equal to η = 0.5.24 Aswe show inSection 3.4, thisguarantees efficiency of theequilibrium, consistent with the Hosios condition. For the parameterization of the vacancy posting cost we take advantage of the EOPP data, which contain information on vacancy duration and hours spent during the recruitment process.25 In our sample it took on average 17.8 days to fill the vacancy, with 11.3 hours being spent during the whole recruitment process.26 Note that the expected recruitment cost in the model is equal to the product of the flow vacancy posting cost and the expected duration of the vacancy, c×(1/q). Hence, we have on a monthly basis 24 The same value is used by Pissarides (2009). The calibration in the credible bargaining model of Hall and Milgrom (2008) implies that the worker’s share of the joint surplus is 0.54. 25 Thesurveyquestionswere“Approximatelyhowmanydayswasbetweenthetimeyoustartedlookingfor someone to fill the opening and the time new hire started to work?” and “While hiring for this position, what was the total number of man hours spent by your company personnel recruiting, screening, and interviewing all applicants?” 26 We restrict the sample to individuals with 25 years of age and older, for whom we have information on education. Because of positive skewness, the vacancy duration and the hours spent distributions are truncated at their 99th percentiles, which correspond to 6 months and 100 hours, respectively.

20 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS c×(17.8/30) = 11.3/180, which gives us the flow vacancy posting cost c = 0.106.27 The vacancy posting cost equals 10.5 percent of average worker’s productivity in our simulated model, which also appears to be broadly consistent with other parameter values for the vacancy posting cost used in the literature.28 The flow value of non-market activities b in general consists of: i) unemployment insurance benefits; ii) home production and self-employment; iii) value of leisure and disutility of work; iv) expenditures saved by not working; and v) is net of job-searching costs. The literature has demonstrated that this parameter value crucially affects the results of the model. Low values of b, such as in Shimer (2005) who uses b = 0.40, imply large surpluses and low volatilities of labor market variables. High values of b, such as in Hagedorn and Manovskii (2008) who use b = 0.955, instead generate high volatilities, but as shown by Costain and Reiter (2008) also imply unrealistic responses of unemployment levels to policy changes in unemployment benefits. Here, we decided to choose an intermediate level of b = 0.82, which imply 81.2 percent of average labor productivity in our simulated model. As shown in the Appendix, our main results remain unaffected if we set b = 0.71 as in Hall and Milgrom (2008) and Pissarides (2009). Parameters for the Markov chain governing the aggregate productivity process are calibratedtomatchthecyclical propertiesofthequarterlyaverageU.S.laborproductivitybetween1976and2010.29 AftertakinglogsanddeviationsfromanHPtrendwithsmoothing parameter105, thestandarddeviationofquarterlylaborproductivityisequal to0.018and its quarterly autocorrelation is equal to 0.90. We apply the Rouwenhorst (1995) method for finite state Markov-chain approximations of AR(1) processes, which has been found to generate accurate approximations to highly persistent processes (Kopecky and Suen, 2010). In choosing the Markov chain for the idiosyncratic productivity process, we follow the standard assumption in the literature by assuming that idiosyncratic shocks are independent draws from a lognormal distribution with parameters µ and σ . As in a a Fujita and Ramey (2012), these draws occur on average every quarter (λ = 1/3), governing the persistence of the Markov chain. In order to determine the parameters of the lognormal distribution and the exogenous separation rate we match the empirical evidence on separation rates. The CPS microevidence for people with 25 years of age and over gives us a mean monthly inflow rate to unemployment of 2.24 percent. The recent 27 Thisvalue ofthe vacancyposting costmightbe toolowfortworeasons. First,the EOPPsurveyasked questions related to the last hired worker, so it is very likely to overrepresent vacancies with shorter durations. Second, it might well be that the hiring personnel consists of managers and supervisors, who arepaidmorethanthe hiredworkerinquestion. Nevertheless,asshowninthe Appendix, ourresultsare robust to different parameterizations of the vacancy posting cost. 28 Hagedorn and Manovskii (2008) argue that the flow labor cost of posting a vacancy equals to 11.0 percent of average labor productivity. Fujita and Ramey (2012) use the value of c = 0.17, Pissarides (2009) c=0.356 and Hall and Milgrom (2008) c=0.43. 29 Following Shimer (2005), the averagelabor productivity is the seasonallyadjusted real averageoutput per employed worker in the nonfarm business sector. These data are provided by the Bureau of Labor Statistics (BLS), series PRS85006163.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 21 Job Openings and Labor Turnover Survey (JOLTS) data, available from December 2000 onwards, tell us that the mean monthly layoff rate is equal to 1.5 percent. The layoffs in JOLTS data correspond to involuntary separations initiated by the employer, hence we take these to be endogenous separations. Accordingly, we set the exogenous monthly separation rate to δ = 0.75 percent, and adjust σ in order that the simulated data gena erate mean monthly inflow rates to unemployment of 2.24 percent. The parameter µ is a normalized to zero. We select parameters regarding on the-job-training from the 1982 EOPP survey as summarized in Table 3 of Section 2.4. To calibrate the duration of on-the-job training we consider the time to become fully trained in months. In particular, under the baseline calibration we parameterize the average duration of on-the-job training to 3.10 months (13.4 × (12/52)), which yields the value for φ equal to 1/3.10. To calibrate the extent of on-the-job training we use the average productivity gap between a typical new hire and a typical fully trained worker. In reality, we would expect that workers obtain jobspecific skills in a gradual way, i.e. shrinking the productivity gap due to lack of skills proportionally with the time spent on the job. Our parameterization of training costs for the aggregate economy, τ = 0.196, implies that trainees are on average 19.6 percent less productive than skilled workers. This is consistent with an average initial gap of 39.1 percent, which is then proportionally diminishing over time. Finally, the worker’s productivity parameter H is normalized to one. 4.2. Parameter Values Specific to Education Groups Next we turn to parameterizing the model across education groups. We keep fixed all theparameter values at the aggregatelevel as reported inTable 5, with the only exception being the training parameters (φ and τ). In particular, we assume that c = cH and h b = bH, making applicable the neutrality result of Proposition 1, according to which the h parameterization for H is irrelevant. We argue below that this is not only desirable from the model comparison viewpoint as we can completely isolate the effects of on-the-job training, but it is also a reasonable thing to do given available empirical evidence. Note also that a neutrality result similar to Proposition 1 would obtain if we were to assume a standard utility function in macroeconomic literature, featuring disutility of labor and offsetting income and substitution effects.30 Regarding the parameterization of parameter b , recall that this parameter should h capture several elements, including unemployment insurance benefits, home production, disutility of work, expenditures saved by not working, andjob-searching costs. Intuitively, higher educational attainment could lead to higher b through all of the mentioned eleh ments. More educated workers typically earn higher salaries and are hence also entitled to higher unemployment insurance benefits (albeit the latter are usually capped at some level). Higher educational attainment presumably not only increases market productivity, 30 See Blanchard and Gal´ı (2010).

22 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS but also home production, which incorporates the possibility of becoming self-employed. Jobsrequiring moreeducationcould bemorestressful, leading to higher disutility ofwork, and might require higher work-related expenditures (e.g., commuting, meals, clothing). Finally, more educated workers might be able to take advantage of more efficient jobsearching methods, lowering their job-searching costs. Overall, there seems to be little a priori justification to simply assume that more educated workers enjoy higher job surplus. To proceed further, we turn to empirical evidence reported in Aguiar and Hurst (2005), who among other things measure food consumption and food expenditure changes during unemployment. Focusing on food items (which include eating in restaurants) is a bit restrictive forour purposes, but theresults arenevertheless illustrative. Aguiar and Hurst (2005) report their estimates separately for the whole sample and for the “low-education” subsample, which consist of individuals with 12 years or less of schooling. They find that during unemployment food expenditure falls by 19 percent for the whole sample and by 21 percent for the low-education sample, with the difference not being statistically significant. The drop in food consumption amounts to 5 percent for the whole sample and 4 percent for the low-education sample, with the numbers being statistically significant from zero, but not from each other.31 Based on this micro evidence and the reasoning given above, we take b = bH to be a reasonable assumption. Results from robustness h checks on this assumption are provided in the Appendix. The proportionality assumption on flow vacancy posting cost would follow directly if we were to assume that hiring is a labor intensive activity as in Shimer (2009). Moreover, the textbook matching model also assumes proportionality of hiring costs to productivity (Pissarides, 2000). Nevertheless, we perform the sensitivity analysis of the quantitative results with respect to different specification of vacancy posting cost and report them in the Appendix. For the parameters regarding on-the-job training we refer the reader to Table 3 in Section 2.4. Moreover, we will report all on-the-jobtraining parameter values for different education groups in the tables with simulation results. 5. Simulation results The main results of the paper are presented in this section. First, we report baseline simulation results for the aggregate economy. Second, the model is solved and simulated for each education group. This exercise is done by changing the parameters φ and τ h h related to on-the-job training for each education group, while keeping the rest of parameters fixed at the aggregate level. Finally, we discuss the main mechanism of the model, by exploring how simulation results depend on each training parameter. This section reports simulation results with the calibration for the age group of 25 years and older. As shown in the Appendix, our conclusions remain unaffected if we calibrate the model for the whole working-age population. 31 See Table 6 of their paper.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 23 5.1. Baseline Simulation Results We begin by simulating the model, parameterized at the average aggregate level for duration of training and training costs (1/φ = 3.10 and τ = 0.196). Table 6 reports the baseline simulation results together with the actual data moments for the United States during 1976-2010. In particular, we report means, absolute and relative volatilities for the key variables of interest. The reported model statistics are means of statistics computed from 100 simulations. In each simulation, 1000 monthly observations for all variables are obtained. The first 580 months are discarded and the last 420 months, corresponding to data from 1976:01 to 2010:12, are used to compute the statistics in the same way as we do for the data. In order to assess the precision of the results, standard deviations of simulated statistics are computed across simulations. Table 6. Labor market variables: data versus model y n u f s Panel A: U.S. data, 1976 - 2010 Mean - 95.11 4.89 45.26 2.24 Absolute volatility - 1.05 1.05 7.49 0.18 Relative volatility 1.78 1.12 20.07 17.99 7.57 Panel B: Baseline simulation results Mean - 95.14 4.86 45.24 2.25 (0.61) (0.61) (2.39) (0.16) Absolute volatility - 0.80 0.80 3.22 0.23 (0.28) (0.28) (0.64) (0.07) Relative volatility 1.78 0.85 15.47 7.28 9.64 (0.34) (0.31) (3.55) (1.65) (2.18) Notes: All data variables in Panel A are seasonally-adjusted. y is quarterly real averageoutputperemployedworkerinthenonfarmbusinesssector,providedbythe BLS. The rest of variables are constructed from CPS microdata and are quarterly averagesof monthly data. Statistics for the model in PanelB are means across 100 simulations,standarddeviationsacrosssimulationsarereportedinparentheses. All means of rates are expressed in percentages. The baseline simulation results show that the model performs reasonably well at the aggregate level. It essentially hits the empirical means of the unemployment rate, the job finding rate and the separation rate by construction of the exercise. More notably, it also mirrors well the empirical volatilities. Two main reasons why the model does not suffer from an extreme unemployment volatility puzzle as in Shimer (2005) relate to a bit higher flow value of being unemployed and the inclusion of endogenous separations.32 The latter are also the reason why the model matches the volatility of the separation rate quite well.33 The model underpredicts the volatility of the job finding rate and to 32 Hagedorn and Manovskii (2008) claim that the unemployment volatility puzzle can be resolved by a calibrating higher flow value of being unemployed. Note that our value for this parameter (b = 0.82) is considerably below the one used in Hagedorn and Manovskii (2008). As shown in the Appendix, our main results remain unaffected if we set b=0.71 as in Hall and Milgrom (2008) and Pissarides (2009). 33 Fujita and Ramey (2012) also find that the inclusion of endogenous separations can help in increasing volatilities of search and matching models.

24 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS a somewhat lesser extent the volatility of the unemployment rate, which should not be surprising given that in this model productivity shocks are the only cause of fluctuations in vacancies.34 5.2. Unemployment Rates across Education Groups Next, we turn to the simulation results across different education groups. We keep fixed all the parameter values at the aggregatelevel and only vary the training parameters across education groups. Table 7 shows the simulation results for the means. As we can see, the model is able to explain the differences in unemployment rates across education groups that we observe in the data. In particular, the ratio of unemployment rates of the least educated group to the most educated group is 3.5 in the data and 3.4 in the model. Moreover, the model accounts for the observable differences in separation rates across groups, while keeping similar job finding rates. The ratio of separation rates of the least educated group to the most educated group is 4.1 in the data and 3.6 in the model. In general, thegreater is thedegree of on-the-jobtraining (longer training periodsand higher productivity gaps), the lower is the separation rate and the lower is the unemployment rate. Therefore, the observed variation in training received across education groups can explain most of the observed differences in separation rates and unemployment rates. Table 7. Education, training and unemployment properties - means (in percent) Data Parameters Model u f s 1/φ τ u f s h h Less than high school 8.96 46.85 4.45 2.35 0.163 7.93 45.51 3.83 (0.75) (2.08) (0.21) High school 5.45 45.02 2.48 2.78 0.181 6.09 45.53 2.88 (0.71) (2.38) (0.20) Some college 4.44 46.34 2.05 3.67 0.227 3.02 45.08 1.36 (0.32) (2.35) (0.08) College degree 2.56 42.80 1.09 4.19 0.240 2.35 45.27 1.06 (0.25) (2.38) (0.05) Notes: Data moments are quarterly averages of monthly seasonally-adjusted data constructed from CPS microdata. The sample period is 1976:01 - 2010:12. Statistics for the model are means across 100 simulations, with standard deviations across simulations reported in parentheses. Table 8 presents a more detailed view of the results, offering a breakdown of separation rates and employment rates for trainees and for skilled workers. As it can be seen, separation rates of trainees are roughly similar across education groups and trainees represent a small share of employment for all four education groups. Therefore, differences in separation rates for skilled workers are the main reason why more educated workers enjoy lower separation rates. 34 Mortensen and Nagypa´l (2007) argue that the empirical correlation between labor productivity and labor market tightness is 0.396, thus substantially below the model’s correlationof close to 1.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 25 Table 8. Separationandemployment ratesfortraineesandskilled workers - means (in percent) s sT sS n nT nS Less than high school 3.83 7.83 3.63 92.07 7.47 84.60 High school 2.88 7.69 2.65 93.91 6.59 87.32 Some college 1.36 7.32 1.18 96.98 4.05 92.94 College degree 1.06 7.13 0.89 97.65 3.54 94.11 All individuals 2.25 7.59 2.02 95.14 5.70 89.45 T S Notes: Statistics aremeansacross100simulations. s ands refertoseparationratesoftraineesandskilledworkersrespectively,nT andnS toemployment rate of trainees and skilled workers respectively. 5.3. Unemployment Volatility across Education Groups Panel A of Table 9 reports the simulation results for absolute volatilities. As mentioned in Section 5.1, the model underpredicts the volatilities of the job finding and the unemployment rates. This property of the model is also inherited here. Nevertheless, the model replicates well the relative differences in volatilities across education groups. In the data, the volatility of the unemployment rate for high school dropouts is 3.2 times higher than the corresponding volatility for college graduates, whereas the same ratio in the model stands at 3.7. Something similar is true for volatilities of separation rates (the ratio is 3.9 in the data and 5.5 in the model), where additionally the model also explains volatility levels quite well. The model can also account for the observed similar values of volatilities in job finding rates across education groups. Panel B of Table 9 reports the simulation results for relative volatilities. The model succeeds in replicating the ratio of relative employment volatility of the least educated group to the most educated group (the ratio is 3.5 in the data and 3.9 in the model). This finding is not surprising given the results of Panel A of Table 9, which show that the model is able to replicate the ratio of absolute employment volatility. The model also accounts well for the empirical finding that relative volatilities in unemployment, job finding, and separation rates are similar across education groups. 5.4. Unemployment Dynamics across Education Groups To provide another view of the model’s results we conduct the following experiment. Using the model’s original solution for the aggregate economy and the actual data on the aggregate unemployment rate we back out the implied realizations of the aggregate productivity innovations. Then, we feed this implied aggregate productivity series to the model’s original solution for each education group. The simulated unemployment rate series for each group are shown in Figure 5, together with the actual unemployment rates. Again, the model replicates the data remarkably well, both in terms of capturing the differences in means and volatilities across groups.

26 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Table 9. Education, training and unemployment properties - volatilities Data Parameters Model n u f s 1/φ τ n u f s h h Panel A: Absolute volatilities Less than high school 1.78 1.78 7.62 0.42 2.35 0.163 1.14 1.14 3.07 0.34 (0.28) (0.28) (0.63) (0.07) High school 1.26 1.26 7.48 0.24 2.78 0.181 0.91 0.91 3.07 0.27 (0.27) (0.27) (0.57) (0.07) Some college 1.02 1.02 8.96 0.18 3.67 0.227 0.48 0.48 3.34 0.12 (0.14) (0.14) (0.54) (0.03) College degree 0.55 0.55 8.55 0.11 4.19 0.240 0.31 0.31 3.30 0.06 (0.12) (0.12) (0.68) (0.02) Panel B: Relative volatilities Less than high school 1.99 18.66 17.45 9.23 2.35 0.163 1.25 13.65 6.88 8.55 (0.32) (2.87) (1.47) (1.66) High school 1.35 20.83 18.62 9.09 2.78 0.181 0.98 14.36 6.86 9.04 (0.30) (2.96) (1.43) (1.79) Some college 1.08 21.32 20.48 8.28 3.67 0.227 0.49 14.67 7.55 8.20 (0.15) (2.93) (1.35) (1.75) College degree 0.57 20.16 21.39 9.87 4.19 0.240 0.32 12.13 7.47 5.51 (0.13) (3.21) (1.69) (1.70) Notes: Absolute volatilities are defined as standarddeviations of the data expressedin deviations from anHPtrendwithsmoothingparameter105. Relativevolatilitiesaredefinedanalogously,exceptthatall variables are initially expressed in natural logarithms. The sample period is 1976:01 - 2010:12, with all databeingseasonallyadjusted. Statisticsforthemodelaremeansacross100simulations,withstandard deviations across simulations reported in parentheses. 5.5. Discussion of the Model’s Mechanism In order to highlight the mechanism at work in our model, two more exercises are conducted. In particular, we analyze separately the effects of training duration and productivity gap of new hires to demonstrate that both of them quantitatively play almost equally important roles for our results. In the left panel of Figure 6 we study the role of the average duration of on-the-job training, keeping the rest of the parameters constant at the aggregate level. Analogously, the right panel of Figure 6 studies the role of the productivity gap of new hires, keeping the rest of the parameters constant at the aggregate level. In both cases, we observe a decrease in the mean of the unemployment rate as we increase the degree of on-the-job training (longer training periods and higher productivity gaps). This decrease in the unemployment rate is completely driven by the decrease in the separation rate, given that the job finding rate remains roughly constant as we vary the degree of on-the-job training.35 Let’s consider first why the job finding rate virtually does not move with the average durationofon-the-jobtraining. Onewouldexpect thatanincreaseintheaverageduration 35 In fact, the simulationresults revealthat the job finding rate decreasesby roughly2 percentagepoints aswe increaseeither the trainingdurationorthe productivitygapofnew hires. Sucha decreaseleadsto approximately0.5percentagepointshigherunemploymentrate,whichquantitativelyrepresentsamodest effect, given the observed declines in the unemployment rate in Figure 6.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 27 Less than high school High school 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 Data Model Data Model 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Some college College degree 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 Data Model Data Model 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 5. Unemployment rates across education groups: model versus data Notes: Actual unemployment rates are quarterly averages of monthly seasonally-adjusted data constructed from CPS microdata. The simulated unemployment rates are generated by solving and simulating the model for each education group using the implied realizations of the aggregate productivity innovations as explained in the text. of on-the-job training reduces the value of a new job, since the worker spends more time being less productive. Consequently, firms’ incentives to post vacancies should decrease, leading to a decrease in the job finding rate. However, an increase in the average duration of on-the-job training also reduces the probability of separating endogenously once the worker becomes skilled. This second effect increases the value of a new job, and hence incentives for vacancy posting go up. It turns out that these two effects cancel out and the job finding rate hence remains almost unaffected. The same reasoning holds for the productivity gap of new hires, which measures the extent of on-the-job training. Again, we have two effects at work, which cancel each other out – a higher extent of on-the-job trainingby itself decreases the valueofa newjob, but at thesame timethelatter increases through lower endogenous separations of skilled workers. In order to understand why separation rates decrease with the degree of on-the-job training, we analyze match incentives to separate. Figure 7 shows the reservation productivities for trainees and skilled workers for different degrees of on-the-job training. As we can see, investments in match-specific human capital do not significantly affect the

28 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Unemployment rate − mean Unemployment rate − mean 10 10 0 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 Job finding rate − mean Job finding rate − mean 50 50 0 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 Separation rate − mean Separation rate − mean 10 10 5 5 0 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 Average training duration Productivity gap of new hires Figure 6. The role of training parameters Notes: Statistics are means (in percent) across 100 simulations. The left panel studies the role of the average duration of on-the-job training, keeping the rest of parameters constant at the aggregate level. The right panel studies the role of the productivity gap of new hires, keeping the rest of parameters constant at the aggregate level. incentives of trainees to separate, while they clearly reduce skilled workers’ incentives to separate. The intuition for this result is that skilled workers know that upon a job loss they will have to undergo first, a period of searching for a new job and second, a period of on-the-job training with a lower wage. Hence, reservation productivity levels drop for skilled workers as we increase the degree of on-the-job training, implying a lower rate of endogenous separations. 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 trainees skilled trainees skilled 0 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 Average training duration Productivity gap of new hires Figure 7. The effects of on-the-job training on reservation productivities Notes: Theleftpanelplotsreservationproductivitiesfortraineesandskilledworkersfordifferenttraining durations,keepingtherestofparametersconstantattheaggregatelevel. Therightpanelplotsreservation productivities for trainees and skilled workers for different productivity gaps of new hires, keeping the rest of parameters constant at the aggregate level. 6. Evaluating Other Potential Explanations This section evaluates the plausibility ofother potential explanations fordifferential unemployment dynamicsbyeducation. Inparticular, ourmodelcanencompass thefollowing

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 29 alternative hypotheses: i) differences in the size of match surplus ; ii) differences in hiring costs; iii) differences in frequency of idiosyncratic productivity shocks; iv) differences in dispersion of idiosyncratic productivity shocks; and v) differences in matching efficiency. We simulate the model under each of these alternative hypotheses and then confront the obtained simulation results with empirical evidence. In particular, for these simulations we use the parameter values for the aggregate level as given in Table 5, whereas across education groups we only allow to vary the parameter that is crucial for each alternative hypothesis. This helps us to highlight economic mechanisms behind the alternative hypotheses. Simulations results are summarized in Table 10. Table 10. Other potential explanations (means, in percent) u f s Panel A: U.S. data, 1976 - 2010 Less than high school 8.96 46.85 4.45 High school 5.45 45.02 2.48 Some college 4.44 46.34 2.05 College degree 2.56 42.80 1.09 Panel B: Size of Match Surplus b1 = 0.90 14.37 29.28 4.61 b2 = 0.85 7.12 39.31 2.89 b3 = 0.80 3.89 49.20 1.95 b4 = 0.75 2.43 58.29 1.44 Panel C: Hiring Costs c1 = 0.05 8.76 55.26 5.19 c2 = 0.10 5.13 46.06 2.42 c3 = 0.15 3.58 40.83 1.48 c4 = 0.20 2.91 37.25 1.09 Panel D: Idiosyncratic Shocks – Frequency λ1 = 1/6 15.62 33.64 6.16 λ2 = 1/4 10.24 39.80 4.46 λ3 = 1/3 4.80 45.47 2.23 λ4 = 1/2 1.52 53.22 0.81 Panel E: Idiosyncratic Shocks – Dispersion σ1 = 0.35 14.12 39.41 6.38 σ2 = 0.30 9.40 41.57 4.22 σ3 = 0.25 5.01 45.05 2.31 σ4 = 0.20 2.32 49.27 1.14 Panel F: Matching Efficiency γ1 = 0.60 7.74 53.14 4.35 γ2 = 0.50 5.78 48.32 2.89 γ3 = 0.40 3.92 42.45 1.69 γ4 = 0.30 2.70 34.78 0.95 Notes: Data moments are quarterly averages of monthly seasonallyadjusted data constructed from CPS microdata. The sample period is 1976:01 - 2010:12. Statistics for the model are means across 100 simulations.

30 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 6.1. Differences in the Size of Match Surplus One possibility why more educated workers enjoy higher employment stability might be related to higher profitability of their jobs. In the terminology of search and matching framework, more educated workers might be employed in jobs yielding a higher match surplus. The latter crucially depends on the worker’s outside option, which is in turn governed by the flow value of being unemployed. In our main simulation results as reported in Section 5, we ruled out this possibility by assuming that the flow value of being unemployed is proportional to the market labor productivity coming from education, i.e. b = bH. h Here we relax the proportionality assumption and instead assume b = 0.90, b = 0.85, 1 2 b = 0.80, b = 0.75. In other words, the size of match surplus is now increasing with 3 4 education. The simulation results, reported in Panel B of Table 10, indicate that the unemployment rate decreases with education under this alternative parameterization, as in the data. However, the model now counterfactually predicts higher job finding rates for more educated workers. Intuitively, since jobs with more educated workers yield higher surplus, firms are willing to post more vacancies in this segment of the labor market, leading in turn to higher labor market tightness and job finding rates. Additionally, further simulation results reveal exaggerated employment stability for highly educated workers; indeed, due to greater surplus the simulation results for college graduates now suffer from extreme unemployment volatility puzzle, as their unemployment rate remains virtually constant over the business cycle.36 Overall, the simulation results show that one cannot explain differences in unemployment dynamics across education groups by assuming higher match surplus for more educated. As discussed in Section 4.2, such an assumption also lacks empirical support, at the least for the case of the US. Interestingly though, Gomes (2012) finds empirical evidence that in the UK both the differences in job finding and separation rates contribute roughly equally towards generating differences in unemployment rates by education.37 Moreover, the OECD data show thattheaverageofnetreplacement ratesover60monthsofunemployment isroughlytwice as high in the UK as in the US. To the extent that this difference in net replacement rates reflects more generous welfare policies in the UK, which would in turn invalidate our baseline assumption of proportionality between market and non-market returns, differences in the size of match surplus might play a role for explaining unemployment dynamics by education in countries with similar or even more generous welfare policies as in the UK. 6.2. Differences in Hiring Costs Another possibility for differences in unemployment dynamics by education might be due to hiring costs. One could imagine that hiring costs are greater for highly skilled 36 The detailed simulation results on volatilities are available from authors upon request. 37 In the UK,high schooldropoutsexperience approximatelyfour times higher unemploymentratesthan college graduates, with their separation rates being higher by a factor of two and their job finding rates being lower by half.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 31 individuals and anecdotal evidence about head hunters in some top-skill occupations is indeed consistent with such a story. In our main simulation results in Section 5 we already assumed that flow vacancy posting costs are growing proportionally with productivity. However, it might be that this assumption understates the true differences in hiring costs by education. In what follows, we assume the following values for vacancy posting costs, which are expressed in terms of output: c = 0.05, c = 0.10, c = 0.15, c = 0.20. Hence, hiring 1 2 3 4 somebodywithacollegedegreeisnowfourtimescostlierthanhiringahighschooldropout interms of their output. Acknowledging differences intheir productivity, this implies that in absolute terms, hiring costs are more than six times higher for the most educated group relative to the least educated group. The simulation results, reported in Panel C of Table 10, reveal that under the assumed differences in hiring costs the model replicates the unemployment rates by education. However, the model now predicts sharply decreasing job finding rates with education, which is in contrast with the empirical evidence for the US as presented in Section 2.2 and even more at odds with the empirical evidence for the UK found by Gomes (2012). What is the economic mechanism behind these simulation results? Because it is costlier to hire college graduates, firms will post fewer vacancies in this labor market segments. As a consequence, the job finding rate drops. Highly educated workers that are currently employed know that upon a job loss they will face a lower job finding rate, hence they are less likely to get separated than less educated workers. The less educated workers are instead facing high job finding rates, hence they aremorewilling toleavetheir employer inthecaseoflowidiosyncratic productivity shock. As mentioned, the problem with this explanation lies in the fact that there is no empirical evidence that job finding rate for the most educated workers would be substantially lower, or in other words, that their unemployment duration would be longer. Moreover, the parameterization of the flow vacancy posting cost assumes that it is extremely expensive to hire a college graduate, whereas this cannot be seen from the EOPP data (see the Appendix for further discussion). 6.3. Differences in Frequency of Idiosyncratic Productivity Shocks Individuals with different educational attainment might work in different industries and occupations – the classical distinction between blue-collar and white-collar workers comes to mind. Therefore, it might be that differences in unemployment dynamics by education are due to industry and/or occupation specific factors. Results from estimated regression equations, as reported in the Appendix (Table 11), indicate that this might indeed be part of the story. But then the natural question is in what sense industries and occupations differ. It is quite likely that they differ in terms of initial on-the-job training requirements and this would be consistent with our main story, according to which differences in training lead to differences in unemployment. However, it might also be the case that industries and occupations are subject to heterogeneous dynamics of

32 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS idiosyncratic shocks. For example, industries and occupations with predominantly low educated workers might be subject to more frequent shocks. The simulation results reported in Panel C of Table 10 illustrate what happens when we vary the Poisson arrival rate of idiosyncratic productivity shocks from every 6 months (λ = 1/6) to every 2 months (λ = 1/2). It turns out that the faster the arrival rate of idiosyncratic productivity shocks, the lower will be the separation rate. The intuition behind this result is straightforward: if new shocks arrive often, then it is better to stay in the match even in the case of a very low idiosyncratic productivity shock, since you avoid the unemployment spell.38 But these results are then not consistent with the notion that it should be the industries and occupations with low educated workers that are facing more frequent shocks – historically, blue-collar jobs are more cyclical. Additionally, the model cannot generate different unemployment rates and similar job-finding rates. 6.4. Differences in Dispersion of Idiosyncratic Productivity Shocks Still another possibility, related to the story from the previous subsection, is that the dispersion of idiosyncratic productivity shocks varies across industries and occupations (or more generally, across jobs with different proportions of workers by education). This possibility is explored in Panel D of Table 10. The results show that higher dispersion of idiosyncratic productivity shocks generates more separations and leads to higher unemployment. But this would then imply that low educated workers should exhibit higher wage dispersion than high educated workers, which is at odds with the empirical evidence. In particular, the evidence provided in Lemieux (2006) for the US shows that highly educated workers have higher variance of wages than less educated workers, and these differences are present in both 1973-1975 and 2000-2002 time periods.39 Furthermore and similar to before, this model specification also cannot generate similar job finding rates in the presence of different unemployment rates. 6.5. Differences in Matching Efficiency Finally, imagine a situation where the extent of labor market frictions differs by education. This situation is explored in Panel E of Table 10. The simulation results show that better matching efficiency creates higher labor turnover rates. Hence, while higher matchingefficiency generateshigher unemployment, italsocreates higherjobfinding rates – and both facts cannot be consistent with the empirical evidence for the US. Additionally, higher matching efficiency for less educated is in sharp contrast with the anecdotal evidence that more educated workers take greater advantage of modern techniques for job search. 38 Note that nonlinearities are present here – after some point, lower frequency of idiosyncratic productivity shocks leads to slowly declining separation rates. 39 See Table 1A of his paper.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 33 7. Unemployment Dynamics by Training Requirements One direct testable implication of our model is that on-the-job training itself leads to greateremployment stabilitybyresulting inlower separationrates(andsimilar jobfinding rates). In order to test this prediction of the model, we provide in this section novel empirical evidence on unemployment dynamics by training requirements. The measure of training we use here is specific vocational preparation as measured in the Fourth Edition of the Dictionary of Occupational Titles (provided by the US Department of Labor). The Dictionary of Occupational Titles (DOT) defines specific vocational preparation as “the amount of lapsed time required by a typical worker to learn the techniques, acquire the information, and develop the facility needed for average performance in a specific jobworker situation.” Following the methodology of Autor, Levy, and Murnane (2003), we aggregate detailed occupations from DOT into three-digit Census occupation codes. We then merge training data from these aggregated occupations with the CPS microdata and construct unemployment rates, job finding rates, and separation rates by training. Unemployment rate, all (in percent) Unemployment rate, high school graduates (in percent) 14 14 12 12 10 10 8 8 6 6 4 4 2 2 Up to 3 months 3 months−1 year 1−2 years Over 2 years Up to 3 months 3 months−1 year 1−2 years Over 2 years 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 8. Unemployment rate by training requirements Notes: 12-month moving averages for individuals with 25 years of age and over. Figure 8 depicts unemployment rates by training requirements for all individuals with 25 years of age and over (left panel) and for high school graduates with 25 years and over (right panel). Given the strong complementaries between education and job training (see the discussion in Section 2.4) it is not surprising to see that higher training requirements are associated with lower unemployment rates. What is more striking is that even after we control for education, for example by focusing on high school graduates as in the right panel of Figure 8, higher training levels remain to be related to more stable employment. Furthermore, even after we condition for education attainment, job training leads to empirically lower separation rates and similar job finding rates as shown in Figure 9. We view this novel empirical evidence, which shows that occupations with higher specific vocational training experience substantially lower unemployment rates, predominantly through lower separation rates, as an external validation of the theoretical mechanism advocated in this paper.

34 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Outflow rate, high school graduates (in percent) Inflow rate, high school graduates (in percent) 80 6 70 5 60 4 50 40 3 30 2 20 1 10 Up to 3 months 3 months−1 year 1−2 years Over 2 years Up to 3 months 3 months−1 year 1−2 years Over 2 years 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 9. Unemployment flow rates by training requirements, high school graduates Notes: 12-month moving averages for individuals with 25 years of age and over. 8. Conclusions In this paper we build a theoretical search and matching model with endogenous separations and initial on-the-job training. We use the model in order to explain differential unemployment properties across education groups. The model is parameterized by taking advantage of detailed micro evidence fromthe EOPP survey on the duration of on-the-job training and the productivity gap between new hires and incumbent workers across four education groups. In particular, the applied parameter values reflect strong complementarities between educational attainment and on-the-job training. The simulation results reveal that the model almost perfectly captures the empirical regularities across education groups on job finding rates, separation rates and unemployment rates, both in their first and second moments. The analysis of this paper views training requirements as a technological constraint, inherent to the nature of the job. We believe that such a view is appropriate for the initial on-the-job training, for which we also have exact empirical measures that are used in the paper for the parameterization of the model. However, in reality firms provide training also to their workers in ongoing job relationships. To investigate such cases it would be worthwhiletoendogenizethetrainingdecisionsandexamineinteractionsbetween training provision and job separations. Furthermore, one could take advantage of cross-country variation in labor market institutions that are likely to affect incentives for training provision. This could provide a new explanation for differential unemployment dynamics across countries, based on supportiveness of their respective labor market institutions to on-the-job training. We leave these extensions for future research.

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HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 39 Appendix A. Data Description A.1. Current Population Survey In order to construct unemployment rates, inflows, and outflows by education group we use the Current Population Survey (CPS) basic monthly data files from January 1976 until December 2010, accessed through http://www.nber.org/cps/. From these data we obtain the total number of employed, the total number of unemployed and the number of short-term (less than 5 weeks) unemployed for each education group. The calculation of unemployment rates follows the usual definition (unemployed/labor force). In January 1992 the U.S. Census Bureau modified the CPS question on educational attainment. In particular, before 1992 the question was about the highest grade attended and completed (years of education), whereas after that the question has been about the highest degree received. We broadly follow suggestions by Jaeger (1997) on categorical recoding schemes for old and new education questions. Our education groups consist of: i) less than high school (0-12 years uncompleted according to the old question; at most 12th grade, no diploma according to the new question); ii) high school graduates (12 years completed; high school graduates); iii) some college (13-16 years uncompleted; some college, associate’s degrees); iv) college graduates (16 years completed and more; bachelor’s, master’s, professional school and doctoral degrees). Moreover, due to the January 1994 CPS redesign there is a discontinuity in the shortterm unemployment series.40 More precisely, from 1994 onwards the CPS does not ask about unemployment duration a worker who is unemployed in consecutive months, but instead his duration is calculated as the sum of unemployment duration in the previous month plus the intervening number of weeks. Nevertheless, workers in the incoming rotation groups (1st and 5th) are always asked about unemployment duration, even after 1994. This allows to calculate the ratio of the short-term unemployed share for the 1st and 5th rotation groups relative to the short-term unemployed share in the full sample. One can then multiply the short-term unemployment series after 1994 by this ratio. Since the ratio turns out to be quite volatile over time, we follow the suggestion by Elsby, Michaels, and Solon (2009) and multiply the series by the average value of the ratio for the period February 1994 - December 2010. We apply this correction for each education group separately, although the ratios are very similar across groups. More precisely, the ratio equals to 1.14 (1.17 when limiting the sample to 16 years of age and over) for high school dropouts, 1.14 (1.16) for high school graduates, 1.14 (1.14) for people with some college, 1.13 (1.15) for college graduates, and 1.14 (1.16) for aggregate numbers. Note that the aggregate number for the whole sample is very close to the one calculated by Elsby, Michaels, and Solon (2009), who find an average ratio of 1.15 for the period February 1994 - January 2005. 40 See also Shimer (2012) and references therein.

40 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Next, we seasonally adjust the series using the X-12-ARIMA seasonal adjustment program (version 0.3), provided by the U.S. Census Bureau. Then we compute the monthly outflow and inflow rates. The outflow rate can be obtained from the equation describing the law of motion for unemployment: u = (1 − F )u + us , where u denotes t+1 t t t+1 t unemployed, us short-term unemployed and F the monthly outflow probability. The t t latter is hence given by F = 1 − (u − us )/u , with the outflow hazard rate being t t+1 t+1 t f = −log(1 − F ). To calculate inflow rates, we use the continuous-time correction for t t time aggregation bias from Shimer (2012), which takes into account that some workers who become unemployed, manage to find a new job before the next CPS survey arrives. A.2. Employment Opportunity Pilot Project Survey The 1982 Employment Opportunity Pilot Project (EOPP) was a survey of employers in the United States conducted between February and June 1982. The survey had three parts. The first part collected information on general hiring practices, the second part asked the employer about the last hired worker and the last part dealt with government programs. We focus only on the central part of the survey, given that it provides specific information about the relationship between education and the degree of on-the-job training. In particular, employers were asked to think about the last new employee the company hired prior to August 1981 regardless of whether that person was still employed by the company at the time of the interview. A series of specific questions were asked about the training received by the new employee during the first three months in the company. Themainadvantageofthe1982EOPPsurveyisthatitincludesbothmeasuresofformal and informal training. Nevertheless, some drawbacks of the 1982 EOPP survey need to be mentioned as well. First, the sample of employers interviewed is not representative. In particular, the sample was intentionally designed to overrepresent low-paid jobs. Second, given that questions were related to the last hire in the company, the sample also most likely overrepresents workers with higher turnover rates. Finally, although the survey has been widely used to study several aspects of on-the-job training, it is becoming outdated and thus perhaps less relevant. To overcome some of these concerns, we use the data from the 1979 National Longitudinal Survey of Youth as a supplementary data source on (formal) on-the-job training. A.3. National Longitudinal Survey of Youth The 1979 National Longitudinal Survey of Youth (NLSY) contains a nationally representative sample of 12,686 young men and women who were 14-22 years old when they were first surveyed in 1979. These individuals were interviewed annually through 1994 and are currently interviewed on a biennial basis. The measure of training incidence used in the text comes from the following question in the survey: “Since [date of the last interview], did youattend anytraining programor anyon-the-jobtrainingdesigned toimprove

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 41 job skills, help people find a job, or learn a new job?”. Notice that this question has a 1-year reference period in 1989-1994, while it has a 2-year reference period in 1988 and from1996 onwards. As mentioned in the text, the analysis of the NLSY data supports the main empirical findings from the 1982 EOPP data regarding the existence of on-the-job training differences across education groups. Appendix B. Supplementary Results B.1. Unemployment Rates by Education Table 11 shows results from estimated regression equations, where the probability of being unemployed is being regressed on the standard set of controls. These results show that education remains an important predictor of the probability of being unemployed, evenwhencontrollingfordemographiccharacteristics, industry, occupation, andincluding time dummies. Table 11. Unemployment and education (1) (2) (3) (4) (5) (6) Less Than High School 0.0986*** 0.0749*** 0.0764*** 0.0487*** 0.0402*** 0.0372*** (0.0005) (0.0005) (0.0005) (0.0005) (0.0005) (0.0005) High School 0.0430*** 0.0327*** 0.0334*** 0.0233*** 0.0165*** 0.0152*** (0.0003) (0.0003) (0.0003) (0.0003) (0.0003) (0.0003) Some College 0.0253*** 0.0137*** 0.0140*** 0.0108*** 0.0068*** 0.0061*** (0.0002) (0.0002) (0.0002) (0.0002) (0.0003) (0.0003) Individual controls yes yes yes yes yes Time dummies yes yes yes yes Industry controls yes yes Occupation controls yes yes Observations 6,701,078 6,701,078 6,701,078 6,670,335 6,670,335 6,670,335 R-squared 0.015 0.0321 0.0385 0.0367 0.0355 0.0389 Notes: Dependentvariable: probabilityofbeingunemployed. Theomittededucationdummycorresponds to college graduates. The sample period is 2003:01 - 2010:12. All variables are obtained from CPS microdata. Individual controls: age, age squared, gender, marital status, race. Time dummies: month and year. Industry controls: 52 2-digit industries. Occupation controls: 23 2-digit occupations. Robust standard errors in parentheses. Significance levels: *** p<0.01, ** p<0.05, * p<0.1.

42 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS B.2. Unemployment Rates by Age U.S. unemployment rates Shares of education groups 40 100 < High school < High school 35 H So ig m h e s c c h o o lle o g l e 90 H So ig m h e s c c h o o lle o g l e College degree College degree 80 30 70 25 60 20 50 40 15 30 10 20 5 10 0 0 20 30 40 50 60 20 30 40 50 60 Age Age Figure 10. U.S. unemployment rates, educational attainment and age Notes: The sample period is 1976:01-2010:12. All variables are constructed from CPS microdata. B.3. Unemployment Duration Shares by Education Groups Figure 11. Unemployment duration shares by education groups Notes: The sample period is 2003:01-2010:12. All variables are constructed from CPS microdata.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 43 B.4. Unemployment Gross Flows Employment−Unemployment transition rate Employment−Inactivity transition rate 5 5 4.5 4.5 4 4 3.5 3.5 3 3 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Unemployment−Employment transition rate Unemployment−Inactivity transition rate 50 50 45 45 40 40 35 35 30 30 25 25 20 20 15 15 10 10 5 5 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Inactivity−Employment transition rate Inactivity−Unemployment transition rate 10 5 9 4.5 8 4 7 3.5 6 3 5 2.5 4 2 3 1.5 2 1 1 0.5 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 12. Gross flow rates (25+ years of age) Notes: 12-month moving averages.

44 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS The role of Employment−Unemployment transition rate The role of Employment−Inactivity transition rate 20 20 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 The role of Unemployment−Employment transition rate The role of Unemployment−Inactivity transition rate 20 20 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 The role of Inactivity−Employment transition rate The role of Inactivity−Unemployment transition rate 20 20 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 13. Counterfactual unemployment rates (25+ years of age) Notes: Thetopleftpanelshowsthecounterfactualunemploymentrateseriesforeachgroupbytakingits actualemployment-unemploymenttransitionrate series, but keeping the restof transitionrates seriesat the values for the aggregate economy. The rest of the panels are constructed analogously, but analyzing the role of different transition rates. 12-month moving averages.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 45 B.5. Unemployment Flows for Working-Age Population Outflow rate (in percent) Inflow rate (in percent) 100 10 90 9 80 8 70 7 60 6 50 5 40 4 30 3 20 2 10 1 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 14. Unemployment flow rates (16+ years of age) Notes: 12-month moving averages. The role of outflow rate The role of inflow rate 25 25 20 20 15 15 10 10 5 5 < High school High school Some college College degree < High school High school Some college College degree 0 0 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Figure 15. Counterfactual unemployment rates (16+ years of age) Notes: The left panel shows the counterfactual unemployment rate series for each group by taking its actualoutflow rate series, but keeping the inflow rate series at the value for the aggregateeconomy. The rightpanel shows the counterfactualunemployment rate series for eachgroupby taking its actual inflow rate series,but keeping the outflow rate series at the value for the aggregateeconomy. 12-monthmoving averages.

46 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Appendix C. Proofs and Computational Strategy C.1. Proof of Proposition 2 C.1.1. The Constrained-Efficient Allocation In order to investigate the efficiency properties of the model, we derive the constrainedefficient allocation by solving the problem of a benevolent social planner. Given the assumption onrisk neutrality of agents inthe model, we naturallyabstract fromdistributive inefficiency and instead examine inefficiency arising exclusively due to search externalities. The social planner takes as given the search frictions and the training requirements. We abstract from aggregate productivity shocks and assume that idiosyncratic shocks are being drawn in each period from a continuous distribution G(a), which simplifies some of the derivations. The benevolent social problem chooses θ, a˜T and a˜S in order to maximize the utility of the representative worker by solving the following Bellman equation for each submarket h: ∞ ∞ V NT(x),NS(x) = max (1−τ )HA anT(a)dG(a)+HA anS(a)dG(a) h (cid:16) (cid:17) θ,a˜T,a˜S (cid:26) Za˜T Za˜S +(1−n)b −θ(1−n)c +βV (NT) ′ (x),(NS) ′ (x) , h h (cid:27) (cid:16) (cid:17) with x x NT(x) = nT(a)dG(a), NS(x) = nS(a)dG(a), −∞ −∞ Z Z ∞ ∞ n = nT(a)dG(a)+ nS(a)dG(a), Za˜T Za˜S subject to the following laws of motion for employment: ∞ (NT) ′ (x) = (1−δ)(1−φ ) nT(a)dG(a)+γθ 1−α(1−n) G(x), h (cid:20) Za˜T (cid:21) ∞ ∞ (NS) ′ (x) = (1−δ) nS(a)dG(a)+(1−δ)φ nT(a)dG(a) G(x). h (cid:20) Za˜S Za˜T (cid:21) Note that NT(x) and NS(x) denote employment distributions after idiosyncratic productivity shocks take place and before the social planner decides the optimal destruction thresholds.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 47 The first order conditions are: ′ ∂V (·) 0 =−c (1−n)+β γ(1−α)θ −α(1−n)G(x), h ∂(NT)′(x) 0 =(1−τ )HA(−a˜TnT(a˜T))−b (−nT(a˜T))+c θ(−nT(a˜T)) h h h ′ ∂V (·) +β (1−δ)(1−φ )(−nT(a˜T)−γθ 1−α(−nT(a˜T)) G(x) ∂(NT)′(x) h (cid:16) (cid:17) ′ ∂V (·) +β (1−δ)φ (−nT(a˜T))G(x), ∂(NS)′(x) h 0 =HA(−a˜SnS(a˜S))−b (−nS(a˜S))+c θ(−nS(a˜S)) h h ′ ′ ∂V (·) ∂V (·) +β −γθ 1−α(−nS(a˜S)) G(x)+β (1−δ)(−nS(a˜S))G(x). ∂(NT)′(x) ∂(NS)′(x) (cid:16) (cid:17) The envelope conditions are: ∞ ∂V(·) G(x) =(1−τ )HA adG(a)−b (1−G(a˜T))+c θ(1−G(a˜T)) ∂(NT)(x) h h h Za˜T ′ ∂V (·) +β (1−δ)(1−φ )−γθ 1−α (1−G(a˜T))G(x) ∂(NT)′(x) h (cid:16) (cid:17) ′ ∂V (·) +β (1−δ)φ (1−G(a˜T))G(x), ∂(NS)′(x) h ∞ ∂V(·) G(x) =HA adG(a)−b (1−G(a˜S))+c θ(1−G(a˜S)) ∂(NS)(x) h h Za˜S ′ ∂V (·) +β (−γθ 1−α)(1−G(a˜S))G(x) ∂(NT)′(x) ′ ∂V (·) +β (1−δ)(1−G(a˜S))G(x). ∂(NS)′(x) After some rearrangements, the following optimal job creation condition can be obtained: ∞ c α (1−δ)(1−φ )c h h h =β(1−α) (1−τ )HAa−b − c θ + (13) γθ−α h h 1−α h (1−α)γθ−α Za˜T n ∞ β(1−δ)φ α h + HAa−b − c θ dG(a) dG(a). 1−β(1−δ)(1−G(a˜S)) h 1−α h Za˜S n o o Similarly, the optimal job destruction conditions are given by: α (1−δ)(1−φ )c 0 =(1−τ )HAa˜T −b − c θ + h h (14) h h 1−α h (1−α)γθ−α ∞ β(1−δ)φ α h + HAa−b − c θ dG(a), 1−β(1−δ)(1−G(a˜S)) h 1−α h Za˜S α n o 0 =HAa˜S −b − c θ (15) h h 1−α ∞ β(1−δ) α + HAa−b − c θ dG(a). 1−β(1−δ)(1−G(a˜S)) h 1−α h Za˜S n o

48 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS C.1.2. Decentralized Allocation Again, we abstract from aggregate productivity shocks and assume that idiosyncratic shocks are being drawn in each period from a continuous distribution G(a). The main equilibrium conditions are: ∞ ST(H,A,a) =(1−τ )HAa−b −βηγθ 1−α ST(H,A,a)dG(a) h h Za˜T ∞ +β(1−δ)φ SS(H,A,a)dG(a) h Za˜S ∞ +β(1−δ)(1−φ ) ST(H,A,a)dG(a), h Za˜T ∞ SS(H,A,a) =HAa−b −βηγθ 1−α ST(H,A,a)dG(a) h Za˜T ∞ +β(1−δ) SS(H,A,a)dG(a), Za˜S ∞ c h =β(1−η) ST(H,A,a)dG(a). γθ−α Za˜T Notice that we can write: ∞ ∞ η 1−β(1−δ)(1−G(a˜S)) SS(H,A,a)dG(a) = HAa−b − c θ dG(a). h h 1−η Za˜S Za˜S n o (cid:0) (cid:1) So, we have the following job creation condition: ∞ c η (1−δ)(1−φ )c h h h =β(1−η) (1−τ )HAa−b − c θ+ (16) γθ−α h h 1−η h (1−η)γθ−α Za˜T n ∞ β(1−δ)φ η h + HAa−b − c θ dG(a) dG(a). 1−β(1−δ)(1−G(a˜S)) h 1−η h Za˜S n o o The job destruction conditions can be derived as: η (1−δ)(1−φ )c 0 =(1−τ )HAa˜T −b − c θ+ h h (17) h h 1−η h (1−η)γθ−α ∞ β(1−δ)φ η h + HAa−b − c θ dG(a), 1−β(1−δ)(1−G(a˜S)) h 1−η h Za˜S η n o 0 =HAa˜S −b − c θ (18) h h 1−η ∞ β(1−δ) η + HAa−b − c θ dG(a). 1−β(1−δ)(1−G(a˜S)) h 1−η h Za˜S n o By comparing the constrained-efficient equilibrium conditions (13)-(15) with the decentralized equilibrium conditions (16)-(18) it follows that the decentralized allocation replicates the constrained-efficient allocation when η = α, reflecting the standard Hosios condition.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 49 C.1.3. Worker’s bargaining power and job destruction - analytical results Subtracting ST(H,A,a˜T) = 0 from ST(H,A,a) and SS(H,A,a˜S) = 0 from SS(H,A,a) we get: ST(H,A,a) =(1−τ )HA(a−a˜T), h SS(H,A,a) =HA(a−a˜S). Using the above in the job creation condition gives: ∞ c h = β(1−η)(1−τ )HA (a−a˜T)dG(a). γθ−α h Za˜T Taking derivative of the above job creation with respect to η yields: ∂θ −θ γθ1−α ∂a˜T = − β(1−η)(1−τ )HA(1−G(a˜T)) . h ∂η α(1−η) c α ∂η h Making an analogous substitutions and taking derivative of the job destruction condition for trainees with respect to η yields: ∂a˜T 1 c θ ∂θ (1−τ )HA 1−β(1−φ )(1−δ)(1−G(a˜T)) = h +ηc h h h ∂η 1−η 1−η ∂η (cid:18) (cid:19) (cid:0) (cid:1) ∂a˜S +β(1−δ)φ HA(1−G(a˜S)) . h ∂η Making an analogous substitutions and taking derivative of the job destruction condition for skilled workers with respect to η yields: ∂a˜S 1 c θ ∂θ HA 1−β(1−δ)(1−G(a˜S)) = h +ηc . h ∂η 1−η 1−η ∂η (cid:18) (cid:19) (cid:0) (cid:1) Combining the above and rearranging gives: ∂a˜T c θ α−η Θ h = , ∂η (1−η)2 α ∆ (cid:18) (cid:19) ∂a˜S c θ α−η Ψ h = , ∂η (1−η)2 α ∆ (cid:18) (cid:19) where: 1−β(1−φ )(1−δ)(1−G(a˜S)) h Θ ≡ , 1−β(1−δ)(1−G(a˜S)) (1−τ ) 1−β(1−φ )(1−δ)(1−G(a˜T)) h h Ψ ≡ , 1−β(1−δ)(1−G(a˜S)) (cid:0) (cid:1) γθ1−α ∆ ≡ (1−τ )HA 1−β(1−φ )(1−δ)(1−G(a˜T)) + ηβ(1−G(a˜T))Θ . h h α (cid:26) (cid:27) (cid:0) (cid:1) Note that ∆, Θ and Ψ are all positive. Hence ∂a˜S and ∂a˜T reach their maximum when ∂η ∂η η = α.

50 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS As we move away from the Hosios efficiency condition, we have: ∂a˜T ∂a˜S 1−β(1−φ )(1−δ)(1−G(a˜S)) h = . ∂η ∂η (1−τ )(1−β(1−φ )(1−δ)(1−G(a˜T))) h h Thus, whether search externalities impose greater inefficiencies on job destruction of jobs with trainees or jobs with skilled workers depends on parameter values. C.1.4. Worker’s bargaining power and job destruction - numerical results Figure16illustrateshowdifferent valuesofbargainingpower affect bothjobdestruction margins under our baseline calibration. Note that in this numerical exercise we allow for aggregate productivity shocks and some persistence in idiosyncratic productivity shocks. 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 trainees skilled 0.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 bargaining power of workers Figure 16. The effects of workers’ bargaining power on reservation productivities Notes: Resultsfromsolvingthemodelfordifferentvaluesofworkers’bargainingpower,keepingthe rest of parameters constant at the aggregate level. C.2. Computational Strategy In order to solve the model numerically, we discretize the state space. In particular, the aggregate shock A is approximated with a Markov chain of 11 equally spaced gridpoints, whereas the idiosyncratic shock a is approximated by a discrete lognormal distribution with its support having 700 equally spaced gridpoints. We truncate the lognormal distribution at 0.01 percent and 99.99 percent and then normalize probabilities so that they sum up to one. The solution algorithm consists of value function iteration until convergence. The final model’s solution consists of equilibrium labor market tightness θ(H,A) and reservation productivities a˜T(H,A) and a˜S(H,A). This solution is then used to simulate the model.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 51 Appendix D. Sensitivity Analysis of the Quantitative Results Here we provide the sensitivity analysis of our main quantitative results from Section 5 of the paper where differences in unemployment dynamics by education are explained by differences in on-the-job training. We perform two types of robustness checks for our quantitative results. First, we explore the role of parameter for the flow value when beingunemployed, bothregardingitsoverall level anddifferences acrosseducationgroups. Second, we consider different specification for the flow vacancy posting costs. Simulations results for all robustness checks are summarized in Table 12. Table 12. Sensitivity analysis of the main quantitative results - means (in percent) Parameters u f s Panel A: U.S. data, 1976 - 2010 Less than high school 8.96 46.85 4.45 High school 5.45 45.02 2.48 Some college 4.44 46.34 2.05 College degree 2.56 42.80 1.09 Panel B: Value of being unemployed – level 1/φ τ b h h Less than high school 2.35 0.163 0.71 7.26 45.32 3.52 High school 2.78 0.181 0.71 5.89 45.06 2.80 Some college 3.67 0.227 0.71 2.98 45.51 1.38 College degree 4.19 0.240 0.71 2.27 45.75 1.06 Panel C: Constant value of being unemployed 1/φ τ b h h h Less than high school 2.35 0.163 0.82 39.98 17.29 10.98 High school 2.78 0.181 0.82 12.16 34.24 4.52 Some college 3.67 0.227 0.82 1.91 54.79 1.05 College degree 4.19 0.240 0.82 0.98 80.05 0.79 Panel D: Actual vacancy posting costs 1/φ τ c h h h Less than high school 2.35 0.163 0.090 7.67 45.89 3.73 High school 2.78 0.181 0.104 5.93 44.77 2.74 Some college 3.67 0.227 0.121 2.87 44.12 1.27 College degree 4.19 0.240 0.128 2.47 46.60 1.15 Panel E: Constant vacancy posting costs 1/φ τ c h h h Less than high school 2.35 0.163 0.106 6.79 43.69 3.11 High school 2.78 0.181 0.106 5.67 44.82 2.63 Some college 3.67 0.227 0.106 3.12 46.19 1.45 College degree 4.19 0.240 0.106 2.76 49.12 1.35 Panel F: Vacancy posting costs – level 1/φ τ c h h h Less than high school 2.35 0.163 0.212 7.79 45.67 3.78 High school 2.78 0.181 0.212 6.14 45.37 2.89 Some college 3.67 0.227 0.212 2.99 45.13 1.35 College degree 4.19 0.240 0.212 2.34 45.32 1.06 Notes: Data moments are quarterly averages of monthly seasonally-adjusted data constructed from CPSmicrodata. The sample period is 1976:01- 2010:12. Statistics for the model are means across100 simulations.

52 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS D.1. Value of Being Unemployed D.1.1. Value of being unemployed - overall level Here we set b = 0.71 as in Hall and Milgrom (2008) and Pissarides (2009). Consistent with our calibration procedure we adjust the matching efficiency parameter to γ = 0.33 in order to target the average job finding rate and we adjust the standard deviation of idiosyncratic productivity shocks to σ = 0.385 in order to hit the average separation a rate. The rest of the numerical exercise follows the same steps as in Section 5, including the same parameter values for on-the-job training by education. The simulation results are provided in Panel B of Table 12 and are to be compared with results in Table 7. Note that with b = 0.71 our results remain basically unchanged with respect to our baseline calibration. The unemployment ratio between high school dropouts and college graduates was 3.4 under our baseline calibration, whereas with b = 0.71 it is 3.2 (to be compared with 3.5 in the data). The only noticeable difference concerns the volatility results. In particular, now the aggregate volatilities of labor market variables are lower by half – the unemployment volatility puzzle becomes more evident and this is also the only reason that we chose a somewhat higher b in our baseline calibration. Nevertheless, also with b = 0.71 the relative differences in volatilities across education groups remain present; the unemployment volatility ratio between high school dropouts and college graduates was 3.7 under our baseline calibration, whereas now it is 3.2, the same as in the data.41 D.1.2. Constant value of being unemployed across education groups Below we present a robustness check when we deviate from the proportionality assumption and we keep b constant at 0.82 for all four education groups. As the result of h Proposition 1 does not apply anymore, we need to parameterize differences in the market labor productivity across education groups, H. We do so by taking advantage of the 1982 EOPP data, which contain information on hourly wage. Hourly wage data allow us to impute productivity differences H, which are reported in Table 13. The parametrized productivity differences are broadly in line with estimates obtained by the literature on returns to schooling.42 After simulating the model, we can express the flow value of being unemployed relative to the effective productivity. The obtained values for the effective flow value of being unemployed are 88.7 percent for high school dropouts, 85.0 percent for high school graduates, 77.2 percent for people with some college, and 61.2 percent for college graduates. In short, the size of match surplus is now increasing with education. Panel C of Table 12presents thesimulation results. Inparticular, we solve and simulate the model for each education group, by using the corresponding training parameters (φ and τ ), the constant flow value of being unemployed (c = 0.82) and productivity h h h 41 The detailed simulation results on volatilities are available from authors upon request. 42 In asearchandmatching model, the wagedepends onproductivity, hiringcosts andthe value ofbeing unemployed, with weights determined by the worker’s bargaining power – c.f. the wage equation (12). The imputation procedure adopted here is thus likely to understate the true differences in productivity to the extent that hiring costs and the value of being unemployed are not proportional to productivity.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 53 Table 13. Productivity (H) by education Hourly Wage Implied Productivity H Less than high school 5.60 0.84 High school 6.21 0.93 Some college 7.07 1.06 College degree 8.96 1.35 All individuals 6.65 1 Notes: Productivity differences, H, are imputed from the hourly wage data in the 1982EOPP survey. We normalize the averageproductivity in the economy to 1. parameters(H)for eacheducation group, while keeping therest ofparameters constant at theaggregatelevel. Itturnsoutthatwhenwedeviatefromtheproportionalityassumption b = bH, the model yields highly counterfactual predictions. In particular, the job finding h rate for college graduates is now more than four times higher than the one for high school dropouts, whereas in the data they are practically identical. Additionally, the simulation results for college graduates suffer from extreme unemployment volatility puzzle, as their unemployment rate remains virtually constant over the business cycle.43 The simulation results with constant absolute flow value of being unemployed also severely overpredict differences in unemployment and separation rates across education groups. D.2. Vacancy posting costs Next, we examine the quantitative implications of the model when considering different assumptions regarding the vacancy costs. In particular, three robustness exercises will be carried out. The first one considers the actual data from the 1982 EOPP survey to infer the vacancy posting cost for each education group. The second exercise considers the same absolute value of vacancy posting costs for all education groups. In the last exercise we double the vacancy posting cost used in our baseline calibration. D.2.1. Actual vacancy posting costs from the 1982 EOPP survey The 1982 EOPP data contain evidence on vacancy duration and recruitment costs. Table 14 summarizes these data across education groups.44 The column denoted “c” presents vacancy posting costs expressed in terms of output for each corresponding education group. As it can be seen, the vacancy posting costs across education groups remain close to the aggregate level, which is consistent with our assumption c = cH. h The calculated vacancy posting costs exhibit very little variation across education groups due to two counteracting effects in the data. On the one hand, recruitment costs in terms of hours spent are indeed much higher for more educated workers. On the other hand, 43 The detailed simulation results on volatilities are available from authors upon request. 44 As before, we restrict the sample to individuals with 25 years of age and older, for whom we have information on education. Because of positive skewness, the vacancy duration and the hours spent distributions are truncated at their 99th percentiles, which correspond to 6 months and 100 hours, respectively.

54 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS the 1982 EOPP data also show higher vacancy duration for more educated workers. Note that the latter observation is inconsistent with the empirical evidence of similar job finding rates across education groups, under the assumption of identical matching efficiency across groups. However, longer vacancy duration for more educated workers might not be due to lower vacancy meeting probability, but might simply reflect that the recruitment processitself islongerforthisgroupofworkers, perhapsforadministrative reasons. Inthis respect, van Ours and Ridder (1993) provide evidence that the vacancy duration consists of an application period, during which applicants arrive, and a selection period, during which a new employee is chosen fromthe pool of applicants. They conclude that the mean selection period increases with the required level of education, while required education has no effect on the applicant arrival rate. The applicant arrival rate is arguably the empirical counterpart for the vacancy meeting probability of a theoretical search model. Finally note that in the calibration of search and matching models, vacancy duration is merely a normalization, as its changes can be undone by adjusting the flow vacancy posting cost and matching efficiency.45 Table 14. Vacancy posting cost by education level from the 1982 EOPP survey Vacancy Recruitment c Wage H c =cH h duration (in days) costs (in hours) Less than high school 12.2 7.8 0.107 5.60 0.84 0.090 High school 14.2 9.4 0.111 6.21 0.93 0.104 Some college 20.2 13.9 0.114 7.07 1.06 0.121 College degree 33.8 19.3 0.095 8.96 1.35 0.128 All individuals 17.8 11.3 0.106 6.65 1 0.106 Sincesomedifferences inflowvacancypostingcostsarepresent acrosseducationgroups, we use the exact information on these costs to parameterize our model as a robustnesses check. In order to do that, we express all flow vacancy posting costs in terms of aggregate output and again parameterize differences in productivity across education groups. The column denoted “Wage” corresponds to the 1982 EOPP hourly wage, from which we impute productivity differences H. The last column of Table 14 gives us the parameter values to use in the simulations for each education group. We solve and simulate the model for each education group, by using the corresponding training parameters (φ and h τ ), actual vacancy posting cost (c ) and productivity parameters (H) for each education h h group, while keeping the rest of parameters constant at the aggregate level.46 Panel D of Table 12 reports the simulation results and, as we can see, they do not differ much from our simulation results in Section 5. Therefore, our simulation results are robust when considering the actual vacancy posting costs from the 1982 EOPP survey. 45 See Costain and Reiter (2008). 46 We would obtain the same numerical results by using c, the flow vacancy posting cost expressed in terms of output for each corresponding education group, and setting H =1.

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 55 D.2.2. Constant vacancy posting costs across education groups Panel E of Table 12 reports simulation results when we set c = 0.106 for all four h education groups, hence deviating from the assumption of proportionality in vacancy posting costs. We solve and simulate the model for each education group, by using the corresponding training parameters (φ and τ ), vacancy posting cost (c = 0.106) h h h and productivity parameters (H) for each education group, while keeping the rest of parameters constant at the aggregate level. Note that this exercise presents an extreme case, in the sense that the vacancy posting cost is the same in absolute value across education groups, implying that in terms of output it is decreasing with education. The simulation results remain virtually unchanged, implying again that the parameterization of c is not crucial for our conclusions. D.2.3. Doubling vacancy posting costs In the last robustness exercise with respect to the vacancy posting cost we double the value used in our baseline calibration, increasing c from 0.106 to 0.212. Following the discussion of calibration strategy in the text (see Section 4), changing the vacancy posting cost affects the calibration of the matching efficiency in order to maintain a mean monthly job finding rate of 45.3 percent. Therefore, under the alternative calibration of c = 0.212, the efficiency parameter γ is set to 0.635. The rest of parameters remain unchanged at the aggregate level (see Table 5). Panel F of Table 12 reports simulation results for all four education groups. Again, the simulation results remain consistent with the ones under our baseline calibration. Overall, the simulation results for different specifications of the flow vacancy posting cost illustrate that our proportionality assumption c = cH is not crucial for our concluh sions. D.3. Working-Age Population Here we investigate if observed differences in training can also explain unemployment patterns across education groups, when we consider the whole working-age population (persons with 16 years of age and older). Two main reasons, why we focused our main analysisonpersonswith25yearsofageandolder, arethefollowing: first, bythatagemost individuals finish their formal schooling, and second, we avoid new labor market entrants who might exhibit different unemployment dynamics. However, such an approach also has a drawback, because highschool dropoutshave on average higher overall labor market experience as we disregard their initial labor market period by construction. In order to proceed, we calibrate the training parameters using the 1982 EOPP survey, restricting the sample to individuals with 16 years and over. In particular, under the baseline calibration we parameterize the average duration of on-the-job training to 3.00 months (13.0×(12/52)), which yields the value for φ equal to 1/3.00. Our parameterization of training costs for the aggregate economy is τ = 0.203, which implies that trainees

56 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS are on average 20.3 percent less productive than skilled workers. This is consistent with an average initial gap of 40.6 percent, which is then proportionally diminishing over time. Following the calibration strategy in Section 4, we also need to adjust the efficiency parameter in the matching function (from 0.45 to 0.59) to target a mean monthly job finding rate of 53.9 percent, consistent with the CPS microevidence for people with 16 years of age and over. Moreover, we also need to adjust the standard deviation of the distribution of idiosyncratic productivity (from0.249 to 0.237)in order that thesimulated datageneratemeanmonthlyinflowratestounemployment of3.55percent, consistent with the CPS microevidence for people with 16 years of age and over. The rest of parameters remain unchanged at the aggregate level (see Table 5). As in Section 5, we first present baseline simulation results for the aggregate economy and then the model is solved and simulated for each education group. The last exercise is done by changing the parameters φ and τ related to on-the-job training for each group, h h while keeping the rest of parameters fixed. Panel A of Table 15 presents the actual data moments for the United States during 1976-2010 for people with 16 years of age and older, which can be compared with the simulation results for the aggregate economy presented in Panel B of the same Table 15. Table 15. Labor market variables: data versus model y n u f s Panel A: U.S. data, 1976 - 2010 Mean - 93.64 6.36 53.93 3.55 Absolute volatility - 1.17 1.17 8.40 0.20 Relative volatility 1.78 1.26 17.34 16.92 5.56 Panel B: Baseline simulation results Mean - 93.52 6.48 53.24 3.59 (0.79) (0.79) (3.20) (0.25) Absolute volatility - 0.99 0.99 3.95 0.31 (0.27) (0.27) (0.63) (0.07) Relative volatility 1.78 1.06 14.61 7.56 8.52 (0.28) (0.31) (2.63) (1.40) (1.48) Notes: All data variables in Panel A are seasonally-adjusted. y is quarterly real averageoutputperemployedworkerinthenonfarmbusinesssector,providedbythe BLS.TherestofvariablesareconstructedfromCPSmicrodataforindividualswith 16 years of age and older, and are quarterly averages of monthly data. Statistics for the model in Panel B are means across 100 simulations, standard deviations across simulations are reported in parentheses. All means of rates are expressed in percentages. Table 16 reports simulation results on unemployment levels across education groups. As we can see, the observed variation in training received across education groups can explain most of the observed differences in separation rates and unemployment rates. In particular, the ratio of unemployment rates of the least educated group to the most educated group is 4.5 in the data and 4.0 in the model and the ratio of separation rates of the least educated group to the most educated group is 6.6 in the data and 4.5 in the

HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS 57 model. Thus, the observed differences intraining canalso explain unemployment patterns across education groups for the whole working-age population. Table 16. Education, training and unemployment properties - means (in percent) Data Parameters Model u f s 1/φ τ u f s h h Less than high school 12.58 59.75 8.36 2.16 0.172 9.72 54.48 5.75 (0.82) (2.60) (0.25) High school 6.72 50.13 3.46 2.83 0.196 6.98 54.05 3.95 (0.73) (2.83) (0.23) Some college 5.29 57.00 3.06 3.38 0.218 4.83 53.48 2.63 (0.47) (2.30) (0.14) College degree 2.80 45.91 1.27 4.25 0.254 2.43 53.27 1.29 (0.28) (3.22) (0.07) Notes: Data moments are quarterly averages of monthly seasonally-adjusted data constructed from CPS microdata for individuals with 16 years of age and over. The sample period is 1976:01 - 2010:12. Statistics for the model are means across 100 simulations, standard deviations across simulations are reported in parentheses. Panel A of Table 17 reports simulation results on absolute volatilities across education groups. As in Section 5, the model underpredicts the volatilities of the job finding rate and unemployment rates. However, the model can replicate remarkably well the relative differences in volatilities across education groups, even when considering the whole working-age population. In particular, the volatility of the unemployment rate for high school dropouts is 3.4 times higher than the corresponding volatility for college graduates, whereas the same ratio in the model also stands at 3.4. Something similar holds for volatilities of separation rates (the ratio is 4.0 in the data and 4.3 in the model), where the model can also account reasonably well for volatility levels. The model delivers also similar volatilities for the job finding rate across education groups, as in the data. Panel B of Table 17 presents the simulation results for relative volatilities. Also here the results are broadly consistent with the ones from Section 5. Overall, the simulation results for the whole working-age population are consistent with the ones for individuals with 25 years of age and older.

58 HUMAN CAPITAL AND UNEMPLOYMENT DYNAMICS Table 17. Working-age population - volatilities Data Parameters Model n u f s 1/φ τ n u f s h h Panel A: Absolute volatilities Less than high school 1.97 1.97 8.61 0.48 2.16 0.172 1.18 1.18 3.79 0.37 (0.27) (0.27) (0.69) (0.08) High school 1.40 1.40 8.13 0.26 2.83 0.196 0.99 0.99 3.85 0.32 (0.29) (0.29) (0.67) (0.08) Some college 1.07 1.07 10.00 0.20 3.38 0.218 0.79 0.79 3.94 0.25 (0.23) (0.23) (0.81) (0.06) College degree 0.58 0.58 8.80 0.12 4.25 0.254 0.35 0.35 4.00 0.09 (0.12) (0.12) (0.73) (0.03) Panel B: Relative volatilities Less than high school 2.29 14.83 15.65 5.73 2.16 0.172 1.32 11.78 7.08 6.36 (0.31) (2.23) (1.35) (1.15) High school 1.53 18.80 18.00 7.26 2.83 0.196 1.08 13.58 7.27 7.76 (0.32) (2.65) (1.43) (1.51) Some college 1.14 19.08 18.52 6.63 3.38 0.218 0.83 15.35 7.51 9.06 (0.25) (3.33) (1.65) (1.89) College degree 0.60 19.53 20.48 9.41 4.25 0.254 0.36 13.33 7.68 6.46 (0.13) (3.14) (1.59) (1.73) Notes: Absolute volatilities are defined as standarddeviations of the data expressedin deviations from anHPtrendwithsmoothingparameter105. Relativevolatilitiesaredefinedanalogously,exceptthatall variables are initially expressed in natural logarithms. The sample period is 1976:01 - 2010:12, with all databeingseasonallyadjusted. Statisticsforthemodelaremeansacross100simulations,withstandard deviations across simulations reported in parentheses.