Cyclical Employment and Learning Ability

Transcription

1 Cyclical Employment and Learning Ability Jongsuk Han University of Rochester January 24, 2013 Job Market Paper Abstract I empirically document that ability is an important determinant of individual employment rates over the business cycle. Using the Armed Forces Qualification Test score as a proxy for individual ability, I find that high ability workers have a less procyclical employment rate than low ability workers even after conditioning on experience, education or average hourly wage. Moreover, the ability and education effect on employment cyclicality decreases over the life-cycle but the ability effect decreases much more gradually than the education effect. In the second part of the paper, I build a life-cycle model with human capital accumulation through learning-by-doing where agents have heterogeneous learning ability. High ability agents have a steeper human capital accumulation slope which delivers high future labor income. In recession, employment rates for all agents fall due to low labor income. However, high ability agents employment rate decreases less than others because the current employment increases future labor income. The calibrated model, which simultaneously matches employment and wage profiles, is consistent with the major cyclical properties observed in the data. I am deeply indebted to Mark Bils for his ongoing advice and encouragement. I am also grateful to William Hawkins and Jay H. Hong for advice and numerous comments. I would also like to thank Yongsung Chang, Daniele Coen-Pirani, Marios Karabarbounis, Baris Kaymak, Joshua Kinsler, Ryan Michaels, Raul Santaeulalia- Llopis, Ronni Pavan, Byoung Hoon Seok, and Hye Mi You for their useful comments and discussion. All errors are my own. hanjs2731@hotmail.com 1

2 1 Introduction It is a well-known fact that unskilled workers have an employment rate which is lower on average and substantially more volatile over the business cycle than that of skilled workers. Previous work has found these patterns regardless of whether skill is measured by age (Clark and Summers, 1981; Gomme et al., 2005), education (Keane and Prasad, 1993), or average hourly wage (Topel, 1993). It is straightforward to replicate these findings using data from the March supplement of the Current Population Survey. Using education as a skill measure, 1 skilled workers (85 percent) have a 16% higher employment rate than unskilled workers (73 percent). The cyclical behavior of employment across skill groups is even more striking. I construct the employment rate by using weeks worked for each year filtered with a quartic time trend. 2 Employment rates in both groups are positively correlated with the aggregate employment rate. However, the employment rate of unskilled workers is twice as volatile over the business cycle as that of skilled workers. When aggregate employment drops 1 percent, the employment rate for unskilled workers drops 1.3 percent but only 0.5 percent for skilled workers. 3 In contrast to previous literature, I investigate employment cyclicality in a new aspect of workers characteristics, which is ability. Individual ability, as measured by the Armed Force Qualification Test (AFQT) score, is considered as an important factor for individual schooling decision and many papers document that high ability students are more likely to finish a higher grad and obtain a higher educational qualification (Cameron and Heckman, 1998; Belley and Lochner, 2007). The positive impact of ability on wages is also well established. Blackburn and Neumark (1993) and Castex and Dechter (2012) show that high ability workers have higher wages. Farber and Gibbons (1996) and Altonji and Pierret (2001) show that high AFQT score workers have a steeper wage profile over the life-cycle. 4 Ability is highly 1 A skilled worker is defined as an individual with a college degree or above. Unskilled workers are everyone else. 2 I use a quartic time trend to be consistent with empirical analysis in Section 2. However, other filtering methods such as HP filter deliver the same results as a quartic time trend. 3 Table 9 in the Appendix A. shows the statistics of the cyclical employment rate for alternative measures of skill. Figures, that illustrate the cyclical behavior of the employment rate based on other skill measures, such as education, age or wages, are shown in the Appendix A. 4 Farber and Gibbons (1996), and Altonji and Pierret (2001) document steeper wage profiles over experience 2

3 correlated with individual characteristics such as education or wage. If ability also affects individuals employment rate in terms of level or cyclicality, omitting ability creates serious bias for other variables. For instance, when ability is positively correlated with education level and employment rate, then the effect of education on employment rate is upward biased without controlling ability. However, much less attention has been devoted to the effect of ability on employment or labor market attachment. 5 More strikingly, ability is not commonly examined in the context of the business cycle. To the best of my knowledge, this paper is the first to empirically analyze the relationship between ability and the cyclicality of employment. In this paper, I empirically document that high ability (proxy by AFQT score) workers have less procyclical employment even conditioning on each individual s education, labor market experience, and average wage. Employment volatility of college graduates is 2/3 less than that of high school graduates. Without controlling individual education, an individual with ability one standard above the mean displays 1/2 less employment volatility compare to an individual with average ability. Hence, one standard deviation in ability has the same employment effect as 5.5 years of schooling. More importantly, high ability workers employment is 2/3 less volatile than average ability workers even conditioning on education, labor market experience and average wage. However, once I control individual ability, education has no impact on employment cyclicality. also changes over the experience profile. The impact from ability and education on employment cyclicality High ability or more educated agents have less procyclical employment rate when they first enter the labor market. Those effects decrease as labor market experience is accumulated, but the education effect vanishes much faster than the ability effect. For instance, after 15 years of labor market experience, high school graduates and college graduates have same employment volatility, but high ability agents employment rate is 0.7 less volatile than average ability agents. Given the importance of the new facts I document in the first part of the paper, the second part of the paper tries to explain those findings with a life-cycle model with endogenous labor for high AFQT score workers. The common theoretical explanation in this literature is asymmetric information: a worker has better information about her own ability than her employer has. However, their reduced-form results can be interpreted independently from their theory. Therefore, their results do not contradict an explanation based on human capital theory with heterogeneous learning. 5 Holzer and LaLonde (1999) use the AFQT score as a skill measure instead of education and investigate the job transition rate. 3

4 supply. The model also contains human capital accumulation through learning-by-doing and heterogeneous learning ability. Specifically, high ability workers are capable of learning more, and thus they accumulate more human capital during any given period of employment. Over the life-cycle profile, high ability workers have a higher future return to work due to human capital accumulation, so they provide more labor. In the business cycle context, they also the experience less cyclical movement because human capital investment is a bigger component of their return to working. I calibrate the model to match life-cycle employment and wage profiles. High ability agents have higher employment rates than low ability agents over the experience profile. However, given the same ability, agents with low initial human capital catch up with agents with high initial human capital. When I introduce aggregate fluctuations into the model, high ability workers display less procyclical employment. Quantitatively, both the data and the model show that the employment rate of workers with an AFQT score one standard deviation above the average AFQT scores drops only 25% compared to the employment rate of workers with average AFQT score. However, the marginal effect of experience on cyclical employment volatility is 7.5 times greater in the model than in the data for a worker with a score one standard deviation above the mean. The contribution of this paper is twofold. First, I empirically document that high ability (proxy by AFQT score) workers have less procyclical employment and the ability effect is more important in the earlier stages of a worker s labor market experience. Second, I develop a lifecycle model with human capital accumulation through learning-by-doing. With heterogeneous learning ability, the model can generate variation in cyclical employment across ability that is in rough agreement with the data. This paper is related to two different strands of the literature. The first is a vast empirical literature on cyclical employment across different groups. Kydland (1984) studies the relationship between labor-force heterogeneity and business cycle fluctuations. Keane and Prasad (1993) find that highly educated workers have less cyclical variability in employment. 6 Several papers focus on cyclical employment over the life-cycle (Clark and Summers, 1981; Gomme et al., 2005). There is general agreement on a U-shaped employment volatility pattern over the life-cycle. Jaimovich and Siu (2009) confirm the same life-cycle pattern for the G7 countries. 6 Their main focus is real wage cyclicality. They find that the degree of real wage cyclicality across skill groups is the same after controlling for employment cyclicality across skill groups. 4

5 Several other papers try to measure market productivity. Topel (1993) documents in the March supplement of the Current Population Survey(CPS) that the lowest quintile of wage earners has a much higher unemployment volatility than the highest quintile. Using data from the Survey of Income and Program Participation (SIPP), Bils et al. (2012) also find that workers with low market productivity experience employment fluctuations 4 times larger than those of high market productivity workers. They use long-term wages and hours worked while employed to measure comparative advantage in market work. Holzer and LaLonde (1999) is the only paper that examines labor market attachment using AFQT scores. They document that high AFQT score workers are less likely to separate from the labor market. However, they do not investigate employment fluctuations over the business cycle. The second applicable literature deals with human capital, particularly incorporating learning-by-doing into analysis of the business cycle. A number of studies have investigated learning-by-doing (LBD) in a business cycle context. Cooper and Johri (2002) and Chang et al. (2002) use a LBD mechanism to generate propagation in RBC models. Although they use LBD in a business cycle context, they focus on aggregate variables rather than micro level responses over the business cycle. The study closest to the current paper is Hansen and Imrohoroglu (2009). They test standard LBD models to explain the life-cycle pattern of working hours and the U-shaped pattern of cyclical total working hours. From a calibrated life-cycle model, they note that their LBD model generates a realistic life-cycle pattern. Although they have a richer model in terms of consumption and saving, they do not have heterogeneous learning ability. Moreover, instead of calibrating a human capital production function, they use parameter values from Chang et al. (2002). Since Chang et al. (2002) calibrate their model to match aggregate variables, the parameters used in Hansen and Imrohoroglu (2009) may not be consistent with actual individual behavior. I use micro data to calibrate a human capital production function. My calibrated values, particularly the human capital depreciation rate, are not similar to those of Chang et al. (2002). The remainder of the paper is as follows. Section 2 discusses in detail the data, sample selection, and variables used for the empirical analysis. Results follow in Section 3. Section 4 sets up the model. Calibration and steady-state results are described in Section 5. Section 6 analyzes the business cycle properties of the model. Section 7 concludes. 5

6 2 Data The empirical analysis is based on the National Longitudinal Survey of Youth 1979 (NLSY79). The NLSY79 is a nationally representative sample of 12,686 young men and women who were 14 to 22 years old when first surveyed in The cohort was interviewed annually through Since 1994, the survey has been administered biennially. One unique feature of the NLSY79 is that the dataset contains the Armed Forces Qualification Test (AFQT) score for each individual. The AFQT was originally designed by the Department of Defense to test general aptitude for enlistment. The NLSY79 sample participants were administered this test in AFQT scores are widely used in the literature to measure general skills or abilities that are not captured by an individual s observable characteristics such as education or labor market outcome (Neal and Johnson, 1996). It has also been used to measure an individual s innate ability, which cannot be observed by the econometrician or employers (Farber and Gibbons, 1996; Altonji and Pierret, 2001). Besides AFQT scores, the NLSY79 provides detailed information on education (enrollment and graduation years); labor market outcomes, such as employment status by week and wages for different jobs; and job characteristics, such as occupation and industry codes. Although the sample is restricted to a single cohort, the NLSY79 is a rich data set for analyzing labor market outcomes. In this paper, I restrict the cross-sectional sample to include males only because female labor supply decisions are sensitive to external factors such as childbearing. Starting from 3,003 individuals, I apply the following sample restrictions. Since the AFQT is the most important variable in the empirical analysis, I eliminate 182 individuals from whom this score is missing. Further, because I investigate the AFQT score effect over labor market experience, I need a complete picture of each individual s labor market experience since he first entered the labor market. Therefore, I exclude 490 individuals who graduated before 1978, since the NLSY79 does not provide employment status before Finally, I drop 55 individuals who have no associated labor market information recorded, such as employment rate, labor market experience, or average wage. The resulting sample consists of 60,333 observations from 2,276 individuals. The sample period is 1979 to Summary statistics are provided in Table. 1. 6

7 Table 1: Summary Statistics Total < 12 = 12 (12, 16) 16 num. ind (100%) (17%) (43%) (17%) (23%) num. obs (100%) (18%) (45%) (17%) (20%) black (11%) (17%) (11%) (10%) (6%) Highest Grade AFQT mean std adj. AFQT mean std First Job Year mean std minimum maximum First Job Age mean std minimum maximum Potential EXP. mean std Actual EXP. mean std Avg. Wage mean std Log. Avg. Wage mean std Employment Rate mean std

8 Now, I briefly describe the key variables used in my empirical analysis. Cyclical Measure Since I investigate the cyclical behavior of employment across different individual characteristics, I need an appropriate cyclical measure. I use the annual aggregate male employment rate from the BLS. Individual Employment Rate Individual employment rate is defined as weeks worked divided by total weeks in each year. The work history file in the NLSY79 contains the weekly employment status for each individual. I use this weekly employment status variable to construct weeks worked for each individual in every calendar year. I aggregate employed weeks and divide by total weeks for each calendar year. Labor Market Entry Labor market entry is difficult to define because working while enrolled in school is very common. My definition of labor market entry date follows that of Altonji and Pierret (2001): the month and year of the respondent s most recent enrollment in school at the first interview when the respondent is not currently enrolled. Labor Market Experience Labor market experience is calculated as total years worked since entering the labor market. Since I know the exact year of labor market entrance, I can compute actual labor market experience rather than potential experience (age - years of education - 6). Education I use the highest grade completed when each individual enters the labor market. In the data, this variable varies over time because some individuals go back to school later in life. However, I focus on the initial impact of education on employment, so the highest grade completed when entering the labor market is used. AFQT Score The AFQT provides a summary measure of basic literacy and numeric skills. 7 The AFQT test score is generally viewed as a good indicator of workers overall cognitive abilities, although it is of course a somewhat noisy signal of these. AFQT scores have a positive correlation with the age and schooling levels of agents at the time they took the test. For age, the causality runs in one direction, from age to AFQT (old agents have high test scores). Due to the large age dispersion in the sample, I adjust test scores for the respondents age when they took test. The relationship between AFQT and education is more complicated than that between AFQT and age. The correlation between the highest grade completed and 7 I use the 1989 version of the AFQT, which is a composite score of tests on paragraph comprehension, arithmetic reasoning, word knowledge, and numerical operations. 8

9 AFQT scores is Unlike with age, the causality can run in both directions. For example, college students are more likely to get better test scores than high school students. At the same time, high test score students are more likely to go to college. Therefore, controlling for education can understate the ability of individuals who go to college with high test scores. However, if I do not control for education, then I overstate the ability of individuals who attended college but still have low test scores. In my empirical analysis, I want to separate the effect of education and ability on employment cyclicality. However, the results might be different when I use the test score that is adjusted education level or not. Therefore, I perform several robustness checks using differently adjusted AFQT scores. My baseline analysis holds for (conventional) adjusted AFQT scores based only on age. Then I run a robustness test with AFQT scores conditioning on age and education. A second robustness check is done with a restricted sample. I restrict the sample to those whose age was between 14 and 18 in No member of this sub-sample had been to college in 1980, so there is no education effect on AFQT score. Other Control Variables A race dummy, 3 occupation dummies, and 5 industry dummies are included in my regression analysis. There are some individuals who have multiple jobs or who change jobs within a year. Hence, I define the main job in each year for each individual as the job with the most weeks worked. Main occupation and industry are assigned for the main job. I use the 1970 census code for occupation and industry and group them into 3 and 5 categories, respectively. 8 Filtering Method In order to perform a business cycle analysis, aggregate employment and the individual employment rate need to be filtered to remove the trends in the series. I use a quartic time trend as a filtering method. Moreover, the trend can be affected by common characteristics, such as education or experience, across each agent. In order to take this into account, I also include time interaction with the race dummy, experience, education and adjusted AFQT score in the filter. 8 In 1993, NLSY79 only provides 1980 census code instead of 1970 census code. I use 1980 census code to group occupation and industry into in

10 3 Empirical Analysis In this section, I empirically analyze individual employment cyclicality across ability. A baseline regression examines individual employment elasticity relative to aggregate employment, in terms of AFQT scores, highest grade completed in the first year of labor market experience, and average wage. I then decompose these factors over the labor market experience and investigate how they evolve differently for workers with different ability levels. In the empirical analysis, I use adjusted AFQT score and highest grade completed. First, the adjusted AFQT score is standardized to match a mean of zero and a standard deviation of one. I also subtract 12 years of schooling, so that a value of zero for my schooling variable corresponds to high school completion. Therefore, the benchmark individual in the empirical analysis is a person with an AFQT score of zero and a high school diploma (12 years of schooling). All coefficients can therefore be interpreted in terms of how much more (or less) response is expected relative to the benchmark individual. The following components are commonly used throughout the empirical analysis: aggregate male employment rate from the BLS; race; a cubic in experience; 5 industry dummies; 3 occupation dummies; and schooling years and AFQT score. I also include a quartic time trend and the interaction between the time trend and the AFQT, the highest grade completed, race dummy, and experience. 3.1 Baseline Analysis Let y i,t be the log employment rate for individual i at time t. y i,t = β 0 cyc t + β 1 (cyc t exp i,t ) + β 2 (cyc t adj.hgc i ) + β 3 (cyc t adj.afqt i ) + α 1 T t + α 2 X i,t + u i,t (1) I call this my baseline regression, where cyc t is the log aggregate employment rate from the Bureau of Labor Statistics (BLS), T t captures any trends through the filter and X i,t is a vector of controls listed above. β 0 captures the employment cyclicality of an individual who has AFQT score equal to the population mean, 12 years of schooling, and zero labor market experience. The employment cyclicality for individuals who deviate from the benchmark can 10

11 be expressed as β 0 plus an appropriate sum of other βs. Suppose the aggregate employment rate falls by 1 percent. First, the benchmark individual s employment rate falls β 0 percent. Consider an agent with a college degree and a mean AFQT score. This agent experiences (β 0 + β 2 4years) percentage point drop in his employment rate given the same experience level. An individual with the same schooling level but an AFQT score 1 standard deviation higher has a (β 0 + β 3 1s.d.) percent change in his employment rate. The OLS regression results from the baseline analysis are presented in Table 2. Table 2: Employment Rate Cyclicality (1) (2) (3) (4) (5) cyc (0.2390) (0.2520) (0.2395) (0.2524) (0.2613) cyc (0.0194) (0.0197) (0.0195) (0.0197) (0.0197) cyc. adj. hgc (0.0540) (0.0574) (0.0574) cyc. adj. AFQT (0.0797) (0.0916) (0.0918) cyc. log avg. wage (0.0181) Observations Notes: The dependent variable is the log individual employment rate, which is defined as weeks worked divided by 52 weeks. The cyclical measure, cyc, is the (annual) male employment rate from the BLS. All equations control for observables using a race dummy, a cubic in experience, 5 industry dummies, and 3 occupation dummies. I use a quartic time trend and quartic time trend interacted with the AFQT, the highest grade complete, race dummy, and experience are used as filters. Wage is deflated using the CPI. I compute average wages for each individual and take the log. The White/Huber standard errors in parenthesis control for correlation at the individual level over time. p < 0.05, p < 0.01 Columns (1) and (2) illustrate that more experienced and educated workers have less 11

12 procyclical employment. These results agree with the previous literature such as Gomme et al. (2005) or Keane and Prasad (1993). In column (3), I introduce AFQT scores without controlling for education. An individual with an AFQT score 1 standard deviation above the mean experiences a 0.75 percent drop in his employment rate when the aggregate employment rate falls 1 percent. Column (4) is the main empirical finding in this paper. I include both schooling and AFQT scores. First, high AFQT score workers have a less procyclical employment rate even conditioning on schooling and experience. However, the coefficient for the highest grade completed changes dramatically from column (2) to column (4); the point estimate falls 96% and becomes no longer significant. Since the highest grade completed variable is highly correlated with AFQT scores, I can interpret this result as measuring that AFQT scores as a proxy for ability are superior to the highest grade completed. Therefore, when I introduce the AFQT score, the highest grade measure loses its explanatory power. Now, suppose AFQT is a proxy for a fixed unobserved market productivity. If I include a variable that measures productivity with less error than the AFQT, AFQT scores will be washed out, just like schooling was. In the last column, I introduce the average log wages for each individual. Wages directly reflect a worker s productivity in the labor market. Hence, if the AFQT is simply a proxy for market productivity, the estimate of β 3 may change a lot. However, column (5) shows that the AFQT score still survives when controlling for average log wages. Therefore, AFQT is not a proxy for unobserved market productivity but is a proxy for ability. In order to investigate the role of ability as captured by AFQT scores, I decompose this AFQT effect over experience. Before I move on to the experience decomposition analysis, I briefly discuss the baseline results without controlling for occupation and industry. In my baseline regression, I control for individual occupation and industry in each year. The empirical results show that the AFQT proxy for ability affects employment cyclicality even within same occupation and industry. However, there is also some possibility that workers with high ability may sort into some sectors which are less vulnerable over the business cycle. In the Appendix B, I present empirical results using the same specification as my baseline model without controlling for occupation and industry. 9 High AFQT score workers have a much less procyclical employment rate when 9 The experience decomposition results without controlling for occupation and industry are also presented 12

13 occupation and industry are not controlled for. The results suggest that the sorting effect exists. 3.2 Decomposition Over the Experience Profile Now, I decompose the effects of schooling and AFQT on the cyclicality of employment by looking at how these effects change as workers gain experience. y i,t = β 0 cyc t + β 1 (cyc t exp i,t ) + (β 21 + β 22 )(cyc t adj.hgc i ) + (β 31 + β 32 exp)(cyc t adj.afqt i ) + α 1 T t + α 2 X i,t + u i,t (2) β 2 and β 3 from the baseline regression are separated into two parts: an initial part and changes across experience. β 21 and β 31 indicate the effect of years of schooling and AFQT scores on the employment rate in the initial period. β 22 and β 32 are the marginal effect of each variable as an individual accumulates 1 year of labor market experience. Depending on the sign of β 22 or β 32, the schooling or AFQT effects can increase or decrease over the experience profile. Table 3 reports the results of the experience decomposition. in the Appendix B. 13

14 Table 3: Employment Rate Cyclicality over Experience (1) (2) (3) (4) cyc (0.2524) (0.2616) (0.2616) (0.2711) cyc (0.0197) (0.0201) (0.0201) (0.0386) cyc. adj. hgc (0.0574) (0.0608) (0.0609) (0.0610) cyc. adj. AFQT (0.0916) (0.0914) (0.1024) (0.1022) cyc. adj. hgc (0.0024) (0.0024) (0.0027) cyc. adj. AFQT (0.0002) (0.0002) cyc. log avg. wage (0.0213) cyc. log avg. wage (0.0118) Observations Notes: The dependent variable is the log individual employment rate, which is defined as weeks worked divided by 52 weeks. The cyclical measure, cyc, is the (annual) male employment rate from the BLS. All equations control for observables using a race dummy, a cubic in experience, 5 industry dummies, and 3 occupation dummies. I use a quartic time trend and quartic time trend interacted with the AFQT, the highest grade complete, race dummy, and experience are used as filters. Wage is deflated using the CPI. I compute average wages for each individual and take the log. Column (1) is from column (5) in Table 2. From columns (2) to (4), I introduce experience to the cycle interacting with other variables. The White/Huber standard errors in parenthesis control for correlation at the individual level over time. p < 0.05, p <

15 Column (1) repeats column (4) from Table 2 for comparison. From columns (2) to (4), I sequentially introduce 3 interaction terms for highest grade completed, AFQT, and average log wage. Column (3) displays the second empirical finding. First, schooling effects in the first period of labor market experience, β 21, change dramatically. In the initial period, individuals with more education have a less procyclical employment rate. For instance, college graduates employment rate drops only 18% relative to the drop in high school graduates employment rate when the aggregate employment rate decreases one percentage point. 10 However, as an individual accumulates labor market experience, the college degree effect decreases (β 22 > 0). A similar situation appears with respect to the AFQT (β 32 > 0). High AFQT score workers have a less procyclical employment rate initially but the effect of AFQT scores on employment cyclicality diminishes with experience. However, the main difference between schooling and the AFQT is how fast the effect of each on employment cyclicality decreases with experience. 0 Figure 1: Schooling and AFQT Effect over Experience Schooling and AFQT effect over experience Schooling AFQT Schooling years AFQT experience Figure 1 shows the employment gap between the benchmark individual 11 and otherwise 10 When the aggregate employment rate falls 1 percent, the employment rate of high school graduates falls 1.5 percent and that of college graduates 1.22(= ). Thus, college graduates experience only 18% employment rate drop compared to high school graduates. 11 Recall that the benchmark individual has 12 years of schooling (high school graduates) and average AFQT 15

16 identical agents with different years of schooling or different AFQT scores when aggregate employment falls 1 percent. The blue line is the employment gap between high school and college graduates who have an average AFQT score. The red line shows the employment gap between average AFQT score workers and one standard deviation above average AFQT score workers, but all workers have 12 years of schooling. The response to one percent drop in aggregate employment rate, college graduates employment drop less than high school graduates when they first enter the labor market. Similarly, high AFQT score workers experience smaller declines in the employment than average AFQT score workers. Moreover, the contribution of schooling or AFQT score to the employment gap decreases with additional experience. However, the education effect decreases much faster than the AFQT effect. After 15 years of labor market experience, a college degree has no impact on the cyclical behavior of employment. However, a significant difference between a worker with a high test score and one with an average test score still exists even after 20 years of experience. Even though schooling and AFQT effects on employment decrease over the life-cycle, schooling effects disappear much faster than AFQT effects. 3.3 Robustness From the two previous regression results, I document that high AFQT score agents have less procyclical employment rates even after conditioning on experience, education and average wages. Highly educated workers have less procyclical employment rates but once I control for AFQT scores, this schooling effect shrinks dramatically. Both effects decrease with additional labor market experience; however, the schooling effect vanishes much faster than the AFQT effect. In order to confirm the AFQT effect on the cyclicality of employment, I perform two sets of robustness checks. I first control for unobserved fixed components simply by using a fixed effect specification rather than an OLS, I find that there is no statistical difference between OLS and fixed effect results. The second robustness check is related to the AFQT adjustment. As shown, years of schooling and AFQT scores are highly correlated. Unlike age, the causality between schooling and AFQT scores goes in both directions. Also, the NLSY79 sample has a substantial amount score. 16

17 of dispersion in schooling. In the benchmark regressions, I use AFQT scores only to control for age. Hence, the first robustness check in the second set obtained by using the AFQT scores conditioning on both age and education in Most importantly, I control for whether the individual has a college degree. As a second robustness check, I use only a sub-sample of the original sample by restricting attention to individuals whose ages were between ages 14 and 18 in This sub-sample consists of individuals who had not attended college by 1980, and therefore had not attended college before taking the AFQT. Hence, in this sample there is no issue with sample selection. Table 4 and 5 show the robustness results for the baseline and the experience decomposition specifications, respectively. All results confirm that the AFQT effect on cyclical employment is robust. 17

18 Table 4: Robustness: Employment Cyclicality BASE FE AGE & EDU in 79 cyc (0.2524) (0.2195) (0.2520) (0.2860) cyc (0.0197) (0.0167) (0.0197) (0.0223) cyc. adj. hgc (0.0574) (0.0515) (0.0551) (0.0704) cyc. adj. AFQT (0.0916) (0.0827) (0.0818) (0.1018) Observations Notes: Column (1) is the baseline analysis, which is the same as column (4) of Table 2. Fixed effect is included in column (2). In column (3), I run the same OLS regression as in the baseline model, adjusting the AFQT score conditional on age and education in Column (4) also uses the same specification as the baseline model but using a restricted sample, ages 14 to 18 in All regressions use the same cyclical measure, the male employment rate from the BLS. I use a quartic time trend and quartic time trend interacted with the AFQT, the highest grade complete, race dummy, and experience are used as filters. Note that fixed variables, such as highest grade completed and the race dummy, are automatically dropped in the fixed effect analysis. The White/Huber standard errors in parenthesis control for correlation at the individual level over time. p < 0.05, p <

19 Table 5: Robustness: Employment Cyclicality over Experience BASE FE AGE & EDU in 79 cyc (0.2616) (0.2318) (0.2613) (0.3020) cyc (0.0201) (0.0173) (0.0201) (0.0232) cyc. adj. hgc (0.0609) (0.0831) (0.0589) (0.0795) cyc. adj. AFQT (0.1024) (0.0924) (0.0879) (0.1161) cyc. adj. hgc (0.0024) (0.0055) (0.0024) (0.0040) cyc. adj. AFQT (0.0002) (0.0002) (0.0002) (0.0003) Observations Notes: Column (1) is the experience decomposition analysis, which is the same as in column (3) of Table 3. The fixed effect analysis is shown in column (2). In column (3), I run same the OLS regression as in the experience decomposition model, with AFQT score conditioning on age and college degree in The last column also uses the same specification as in the experience decomposition model but using the restricted sample, ages 14 to 18 in All regressions use the same cyclical measure, the male employment rate from the BLS. I use a quartic time trend and quartic time trend interacted with the AFQT, the highest grade complete, race dummy, and experience are used as filters. Note that the fixed variables, such as highest grade completed and race dummy, are automatically dropped in the fixed effect analysis. The White/Hurber standard errors in parenthesis control for correlation at the individual level over time. p < 0.05, p <

20 4 Model A life-cycle model with human capital accumulation through learning-by-doing is developed in this section. I introduce heterogeneous learning ability. Specifically, high ability workers are capable of learning more, and thus accumulate more human capital, during any given period of employment. 4.1 Setup All risk neutral agents have J periods in their working lifetime. In every period, each individual decides whether to work or not. Depending on his working decision, he builds a different amount of human capital in each period. Timing At the beginning of the period, aggregate productivity, z, is realized and all agents enter the period with human capital, h. After drawing idiosyncratic productivity, x, each individual decides whether to work or not in this period. When an agent decides to work, he can accumulate human capital; the amount of human capital accumulation depends on his learning ability. In the next period, the process is repeated starting from the agent s new level of human capital. Firms There is a representative firm, which uses labor as its only input to operate the production technology, which is linear in aggregate productivity and labor, Y t = z t L t. (3) (4) Hence, the marginal productivity of labor is z t and the wage per efficiency unit turns out to be z t in equilibrium. Labor Income Individual labor income is the product of 3 components: the wage per efficiency unit of labor, w, individual human capital level, h, and idiosyncratic productivity, x. Given the production technology, the efficiency wage is the same as aggregate productivity. Labor income is defined as W = zh exp(x) where x i.i.d. N(0, σx). 2 (5) Each individual compares the value of his potential labor income and the value of not supplying labor, b, and makes a labor market participation decision. 20

21 4.2 Human Capital Production The human capital production function is; ln h j+1 = A 0 + α(η)1 E + γ ln h j given h 0 where 1 E is an indicator function that returns 1 if employed and 0 otherwise, and η indexes learning ability, which differs across agents. An employed individual accumulates exp(α(η)) amount of human capital at the end of the period. I assume α (η) > 0, so high ability workers can accumulate more human capital when working. Although I use a learning-by-doing human capital production function, the Ben-Porath (1967) human capital function is also widely used in the human capital literature (Andolfatto et al. (2000) and Huggett et al. (2006)). The main difference between these formulations is the relation between market work and human capital production. In learning-by-doing, working and producing human capital are complementary. However, in Ben-Porath, these two factors are substitutable. I can write the production function as a Ben-Porath s model style function by switching 1 E to (1 1 E ). Education is exogenously given and initial human capital, h 0, is determined by education. The remaining key parameter is γ, which is assumed to be between zero and one. (1 γ) is the depreciation rate of previous human capital. γ is therefore related to the speed of convergence across workers with the same learning ability but different levels of human capital. As γ gets close to zero, previously accumulated human capital stock has less impact on current human capital. So all agents converge to the their own steady-state human capital 12 more rapidly. Steady-state human capital depends on a worker s learning ability but not on education (that is, the initial level of human capital). 12 If an agents provide his labor all the time, the steady-state human capital is h ss = exp(a 0 + α(η)) 1 1 γ. 21

22 4.3 Worker s Problem Agents have five dimensions of heterogeneity: experience, j, current human capital, h, ability, η, initial human capital, h 0, and idiosyncratic productivity, x. 13 An employed worker receives labor income, W, and accumulates human capital depending on his ability, η. function for employed workers is V E j (z, h; η, h 0 ) = zh exp(x) + βev j+1 (z, h E, x ) zh exp(x) if j < J if j = J The value (6) where h E = exp(a 0 + α(η))h γ. (7) A non-employed worker s value function is b + βev Vj U j+1 (z, h U (z, h; η, h 0 ) =, x ) b such that if j < J if j = J (8) h U = exp(a 0 )h γ. (9) Since the agent only lives for J periods, there is no future value added in the last working period. The important difference between the value functions of employed and non-employed workers appears in (7) and (9), the laws of motion for next period human capital, h. Employed workers accumulate exp(α(η)) human capital more than non-employed workers. Since the value function is a non-decreasing function in human capital, the future expected utility for employed workers is higher than for the non-employed. work: Each individual compares his value of working and not-working and decides whether to V j (z, h; η, h 0 ) = max {Vj E (z, h; η, h 0 ), Vj U (z, h; η, h 0 )}. (10) This working decision generates a cutoff value, x, in idiosyncratic productivity. The cutoff value depends on aggregate productivity, current human capital and the difference in terms of 13 Since x is i.i.d. over time, x is not treated as a state variable in the value function. However, z is assumed to follow an AR(1) process, so it is a state variable. 22

23 expected utility between employment and non-employment. However, the difference generated by future human capital is gone in the last period, J. ( ) ln b x zh j(z, h; η, h 0 ) = + β zh (EV j+1(z, h U ) EV j+1(z, h E )) ( ) ln b zh if j < J if j = J (11) I define the individual employment rate as the probability of working at a given level of human capital and aggregate productivity. ( x ) j (z, h; η, h 0 ) E j (z, h; η, h 0 ) = 1 Φ σ x (12) where Φ( ) is the CDF of the standard normal distribution. Note that there is a negative relationship between the cutoff value and the employment rate. For instance, a high cutoff value produces a low employment rate. 4.4 Discussion The main features of the model are all summarized in the cutoff value of idiosyncratic productivity, (11). There is no future effect in the last period, so I focus on j < J. This equation can be decomposed into a static effect (S.E.) and a dynamic effect (D.E.) on the employment rate as Without Aggregate Shocks Static Effect = b zh Dynamic Effect = β zh (EV j+1(z, h U) EV j+1 (z, h E)). First, I characterize the cutoff value without aggregate fluctuations. The static effect depends on the leisure value from non-employment, b, and current human capital, h. An individual with high h has a low x and a high employment rate. Since human capital increases with experience, x decreases over the life-cycle, as documented in the literature (Gomme et al., 2005). Also, the static effect matches an empirical fact that college graduates have a higher employment rate than high school graduates when entering the labor market. In the model, education determines initial human capital, h 0, so college graduates enter the labor market with a higher h 0 than high school graduates. Hence, college graduates have a lower x conditioning on other characteristics. 23

24 The dynamic effect is generated by learning-by-doing in the human capital production function. Suppose there is no learning-by-doing and human capital evolves independently of employment status. Then h E = h U and the expected value from employment and nonemployment are equal. The dynamic effect disappears and x is only governed by the static effect. Otherwise, due to learning-by-doing, h E is greater than h U and the expected value function is increasing in h. Hence, the dynamic effect is always negative. This negative sign drives x down and increases the employment rate. The magnitude of this dynamic effect is governed by two factors: learning ability and current human capital. A high η generates a wider gap between h E and h U, so the size of the dynamic effect increases with ability. However, a high h shrinks the dynamic effect because future gains from human capital accumulation are small. In sum, the dynamic effect is negative and the size of the dynamic effect increases with learning ability but decreases with current human capital. Since x is the sum of both effects, it is important to determine the size of each. If the dynamic effect is much larger than the static effect, working is more valuable than not working. In this situation, all agents want to be employed regardless of ability or current human capital. 14 over the life-cycle. Therefore, the magnitudes of those effects are important in driving employment With Aggregate Shocks I now introduce aggregate fluctuations into the economy. Both the static and the dynamic effects are affected by aggregate productivity. The static effect rises when z is low. In recessions, because of low aggregate productivity, labor income falls and all agents have less incentive to provide labor services. Consequently, the static effect moves counter-cyclically and the employment rate is procyclical in z. However, the dynamic effect moves in exactly the opposite direction. There is no uncertainty in human capital production, so the return to working is higher in low aggregate productivity states. 15 This dynamic effect pushes all agents to work during recessions. Note that the dynamic effect is stronger for high η and low h workers. However, as before, x is the sum of the static effect and dynamic effects. 14 Ben-Porath production generates contrasting results. When working and accumulating human capital are substitutable and the dynamic effect dominates the static effect, all agents want to accumulate human capital. A zero employment rate results. 15 For simplicity, assume the aggregate shock is i.i.d. The expected value of working and not working is independent of current aggregate productivity. Therefore, the expected gain from working is constant. This expected gain is relatively higher in recessions than in booms because current labor income is low. 24

25 We know that the aggregate employment rate is procyclical. This fact implies that the static effect has to be larger than the dynamic effect. It is also consistent with the life-cycle pattern of cyclical employment. Gomme et al. (2005) document that young workers have a more volatile employment rate than prime age workers. If the dynamic effect is larger than the static effect, young workers will have a less volatile employment rate over the business cycle. 5 Calibration and Steady-State Analysis This section describes the calibration of the model. I calibrate the model in the steady state to match log wages and employment profiles over experience in the NLSY79. Then I introduce an aggregate shock, z, to evaluate the business cycle performance of the model. In calibration, I focus on high school graduates (with 12 years of schooling) and college graduates (with 16 years of schooling).i divide each education group by AFQT score into three equal-sized groups, Low, Medium and High. This yields a total of 6 sub-groups and each individual in the model belongs to one of these sub-groups. I compute the average AFQT scores for each sub-group and assign this average scores to all individuals in each subgroup. Log wage profiles and employment rate profiles for each sub-group are also computed from the data. I simulate the model and generate log wage and employment profiles in order to calibrate parameters to match both of these moments. The discount factor, β, is set to match a 4% annual interest rate. 5.1 Adjusting for the College Premium The rise in skill premiums, especially in the early 1980s, is a well-documented fact (Autor et al., 2008; Katz and Murphy, 1992), and various theories have been put forward to explain it. Autor et al. (1998) rely on skill-biased technological change to rationalize an increasing skill premium. Krusell et al. (2000) and Castro and Coen-Pirani (2008) show that capital-skill complementarity can account for almost all of the growth in the skill premium. All of these papers explain the rise in skill premiums from the demand side. However, my model is based on a labor supply mechanism and does not have any features to capture an increasing skill premium. Hence, I adjust the individual wage series to remove this trend. Note that since I only consider college and high school graduates who are male in the model and the data, I 25