Career Choice and Wage Growth Ronni Pavan University of Rochester First Draft: November 2004 This Draft: January 2011

Abstract In this paper, I present structural estimates of a search model that ‡exibly incorporates general human capital accumulation along with career and …rm choice, where a career is empirically identi…ed as a combination of industry and occupation. I use these estimates to empirically distinguish between the relative importance of various factors for generating wage growth over the lifecycle. Evidence presented in the paper highlights the importance of considering the two-stage search process that originates from the model. In particular, I demonstrate that previous IV methods dramatically underestimate the importance of …rm speci…c matches for wage growth.

1

Introduction

A large body of empirical literature demonstrates that real wages grow over the working life of individuals. Two broad mechanisms have been proposed to explain this pattern in the data. First, workers may accumulate general and …rm speci…c human capital that enhances their productivity over time.1 Second, over the course of their working life workers may select into …rms where they I would speci…cally like to thank Derek Neal for his help on this project. I would also like to thank Nathaniel Baum-snow, Lars Hansen, Uta Schoenberg, Robert Shimer, Robert Topel, Gauhar Turmuhambetova and seminar participants at the University of Chicago, the University of Texas in Austin, the University of Minnesota, MIT, the University of Wisconsin in Madison, the University of Rochester, Arizona State University, the University of Western Ontario and the University of California in Santa Cruz, for helpful comments and discussions. All remaining errors are my own. Contact the author at [email protected] 1 See for example Becker (1962), Oi (1962), Mincer (1974) or Mortensen (1978) for explanations of how accumulation of …rm speci…c or general human capital causes wage growth. Other theoretical models provide similar empirical predictions: deferred compensation in Laezar (1979) or Viscusi (1980), insurance motives in Freeman (1977) and Harris and Holmstrom (1982), adverse selection in Salop and Salop (1976), Nickell (1976) and Guasch and Weiss (1982). See Topel (1991) or Altonji and Shakotko (1987) for an empirical investigation.

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are more productive or better matched.2 Despite the presence of an extensive empirical literature on this topic dating back to Topel & Ward (1992), there is little consensus on the relative importance of di¤erent factors that a¤ect wage growth over the life-cycle. Recent literature notes that …rm switches may or may not imply changes in tasks and that this distinction has important economic consequences.3 Building on Miller (1984) and McCall’s (1990) incorporation of occupational choice in this framework, Neal (1999) argues that one important aspect of this selection process is the sequential choice of career and then …rm. Using a constructed instrumental variables method developed by Altonji and Shakotko (1987), Parent (2000) and Kambourov and Manovskii (2009) …nd that the returns to industry or occupational experience are large, around 10 and 20% in ten years, but they also …nd that the returns to …rm tenure are either negligible or negative.4 In this paper, I present structural estimates from a search model that ‡exibly incorporates general human capital accumulation along with career and …rm choice, where career is empirically identi…ed as a combination of industry and occupation. In the model, wages depend on career speci…c and …rm speci…c matches in addition to other factors, such as individual heterogeneity, labor market experience and schooling. In each period, workers can choose to stay at their current …rm, or draw a new …rm speci…c match by changing employers or change careers by drawing both new career and …rm speci…c matches. Matches that survive evolve over time following a stochastic law of motion that depends on the individual characteristics of the worker. The model provides the intuitive prediction that a worker will choose to discard low matches, or matches that deteriorate a lot over time. I use these model estimates to empirically distinguish between the relative importance of various factors for generating wage growth over the lifecycle. In particular, I calculate the implied returns to tenure in the career and tenure in the …rm. I …nd that on average 10 years of career tenure increase log wages by approximately 0.2 points for workers with some college education (0.11 for workers with at most a high school degree). Contrary to existing estimates in the literature, I …nd the wage e¤ect of 10 years of …rm tenure to be positive and around 0.05. Additionally, in the spirit of Topel and Ward (1992), I use the estimates to isolate the contribution of sorting into better careers and employers on wage growth. I calculate that the search process for a good career accounts for an average increase of 0.05 in log wages during the …rst decade of work, while searching for a good employer accounts for an increase of 0.12. 2 For

example, Johnson (1978) and Jovanovic (1979). In Zhang (2007), job mobility gives potential employers information about workers’productivity. See Topel and Ward (1992) for an empirical analysis. 3 See Gibbons et al. (2005), Miller (1984), McCall (1990) and Neal (1999) for job mobility implications, Neal (1995), Parent (2000), Kambourov and Manovskii (2009), Gathmann and Schoenberg (2010) for wage growth implications. 4 Empirical studies that have not included occupation or industry experience have found a larger and positive impact of …rm seniority. Topel …nds a return to …rm tenure of 25% in ten years while Altonji and Shakotko …nd a return of around 6%.

2

The evidence I present below highlights the importance of considering the two-stage search process that originates from the model. In particular, I demonstrate that the IV method employed by Parent (2000) and Kambourov and Manovskii (2009) dramatically underestimates the importance of …rm speci…c matches for wage growth because the underlying model cannot control for the dynamic selection of a two-dimensional search process. Indeed, using their method I …nd a large negative implied estimate for the …rm speci…c component of wage growth. An additional concern ignored by much of the existing empirical literature on wage growth is the importance of heterogeneity. In my model, realizations from the process of human capital accumulation vary across individuals. This is an important extension because both in the data and the model, wage growth pro…les and job mobility are closely related. This feature of the model relates to the literature that distinguishes between ex-ante and ex-post returns to treatments, underscoring the importance of heterogeneity in responses (for example Heckman and Vytlacil (2005) or Heckman and Navarro (2007)). As an example, I …nd that the average ex-ante return to career tenure for workers with at least some college is 50% smaller than the average ex-post return.5 The di¤erence is even more striking in the case of workers with at most a high school degree, for whom the average ex-ante return to career tenure is close to zero while the ex-post increase in log wages due to career experience is around 0.11. An important feature of this paper is the de…nition of career. In the empirical work, I de…ne a career as a combination of 3-digit occupation and industry codes, meaning that a worker changes career when he changes both occupation and industry. Contrary to much of the existing literature, this empirical strategy does not de…ne promotions as career changes and helps reduce the impact of coding errors.6 The model is estimated by full maximum likelihood. One essential component for tractable estimation of the model is my treatment of …rm speci…c and the career speci…c matches as latent variables, following the non-Gaussian state space model approach of Kitagawa (1987). The non-Gaussian feature is a direct consequence of the fact that workers reject bad match o¤ers, generating truncations at the lower end of match distributions. At each step, the likelihood is obtained by integrating over the distributions of these latent matches. The distribution of the latent variables is updated at each period using Bayes’rule. This procedure is similar to methods used by Abbring and Campbell (2003) and Fernandez-Villaverde and Rubio-Ramirez (2007). This paper is organized as follows. Section 2 discusses the data. In section 3, I present the model. In section 4, I derive the likelihood function for the model. In section 5, I present the estimation results and the wage growth decompositions. The …nal section concludes the paper. 5 Ex-ante returns are the returns that the agents expect from a career spell at the beginning of this career, while the ex-post returns are the actual realizations. 6 Neal (1999) uses a similar de…nition. In his paper, a worker changes career if the new job involves both a new 1-digit industry code and a new 3-digit occupational code.

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2

Data

I use data from the National Longitudinal Survey of Youth 1979 (NLSY79) for the analysis. This data set includes information on weekly employment status for a sample of individuals born between 1957 and 1964. I use reported weekly employment histories to construct annual information on employment transitions and wages for main jobs. I de…ne a person’s main job as the job in which he works the most hours in each week and the most weeks in each year. Limitations in wage information dictate that I restrict my analysis to one observation per person per year. The sample includes 3003 males from the representative NLSY79 subsample. In order to allow the model in the next section to fully capture patterns in the data, I exclude 604 individuals whose initial labor market attachment is not observed. Following Farber and Gibbons (1996), I also exclude 123 individuals who worked less than 1200 hours for two consecutive years while being employed in a job of at least 30 hours per week.7 The few full-time workers who go back to school full-time after relatively short periods of work are included after their re-entry into the labor market. I drop 47 more workers because they spend two years or more in the military service. If they stay in the army for a shorter period, I delete only the corresponding yearly observations. I exclude 79 workers because they have a weak attachment to the labor force.8 I omit another 80 workers because they did not report important information like the census code for their industry or occupation.9 Seven workers are eliminated because of missing demographic or schooling information. Wages are measured using the usual rate of pay at the time of the interview, with the implicit assumption that this is representative of the average wage received during that year. Wages are de‡ated using a CPI de‡ator. 28% of the wage observations are missing. This is partly due to the fact that since 1993 the NLSY79 has continuous information about employment status but wages are recorded only once every two years. Prior to 1993, the percentage of missing wages is 13%.10 I also consider the ten highest and ten lowest wage observations as missing.11 I drop observations for high school dropouts who are 7 In their paper, they include a person in the sample if he has worked at least 26 weeks in a job with 30 hours for at least three years. The regression analysis presented in this section does not change much when this alternative de…nition is used. 8 If a person drops out of the labor force for only one year, I delete that observation. If he drops out for more than one year after spending at least ten years in the labor market, I delete that observation and all the subsequent observations (0.7% of the observations). A worker is dropped completely from the sample only if he drops out of the labor force for more than a year after fewer than ten years in the labor market. 9 Using a variable that links each job across di¤erent interviews, I impute the missing industry and occupation codes whenever possible. 1 0 I include in the data set only one wage for each survey period. After 1993, the sampling period spans two years and I observe two wages only for those workers who have changed jobs. Unfortunately this event is clearly not random and I therefore exclude the …rst wage from the …nal data set. 1 1 Following Bollinger and Chandra (2005), I chose a very mild trimming strategy that does not have an impact on the regression coe¢ cients presented in this section.

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less than 16 years old, high school graduates who are less than 18 years old, and college graduates who are less than 21 years old. At this point, my sample consists of 2063 workers and 33617 observations, where 24% of the observations are job changes. In the next subsection, I discuss in greater detail the empirical de…nition of career change. Table 1 presents some summary statistics.

2.1

Empirical De…nition of Career

I wish to empirically capture career changes which can be said to occur when workers join new jobs where the skills required are substantially di¤erent from those used in their old jobs. Following the literature, I rely on occupational and industry codes from the Census to build a career index. A career change occurs if an individual changes 3-digit industry, 3-digit occupation and job. As discussed in Neal (1999), there are a host of di¢ culties in de…ning career changes as changes in industry or occupation code alone. The probability that the occupational code changes from one year to another, even if the worker is working for the same …rm, is 42%. In addition, 36% of individuals report di¤erent industry codes in adjacent periods while working for the same …rm. The probability that both codes change is 17%. As noted by Neal (1999) many of these changes are cycles between two values, from occupation A to occupation B and then back to occupation A. The frequency of these events is an indicator that they are most likely the consequence of coding errors.12 After cleaning the data of these cycles, we still observe within-…rm occupation changes for 16% of observations, within-…rm industry changes for 13% of observations and within…rm changes in both for 5% of observations. These within-…rm changes of codes could be the result of promotions, coding errors, or real changes in tasks. Given that it would be impossible to distinguish real changes of careers from other explanations like promotions, I do not treat these dual code changes as career changes. Following the literature, I focus on de…nitions of career changes that also involve a change of employer.13 The empirical de…nition of career has a marked e¤ect on the number of career transitions measured in the data. To demonstrate this, I build career changes using four di¤erent de…nitions. The benchmark de…nition of career change utilizes both 3-digit industry and occupations codes. Consider a job change that happens between t and t + 1. The benchmark de…nition of career change classi…es this change as a career change if all industry and occupation codes used to describe the old job in both t and t 1 are di¤erent from all industry and occupation codes used to describe the new job in t + 1 and t + 2.14 Using information from t 1 and t + 2 as well helps reducing the impact of misclassi…cation. The second de…nition uses both occupation and industry codes 1 2 Kambourov and Manovskii (2009) …nd that occupational mobility in the PSID is two times smaller using the 1999 Retrospective Occupation-Industry Supplemental Data Files rather than the originally released occupation-industry codes. This di¤erence is attributed to coding errors. 1 3 This procedure is also adopted by Neal (1999), Parent (2000) and Kambourov and Manovskii (2009). 1 4 If the old or new job last only one year, I only consider the available information.

5

as well, but compares only the codes utilized in t and t + 1. In the third de…nition I only compare occupation codes between t and t + 1, while in the fourth de…nition I compare industry codes. Table 2 provides summary statistics given these di¤erent de…nitions of career. It shows that the benchmark career de…nition implies the smallest number of career changes among the four analyzed. The fraction of observations with a career change is 58% relative to 62%, 69% and 78% for the remaining de…nitions respectively. Not reported, the benchmark career de…nition is also the one associated with the highest R2 in a Mincer style OLS regression that controls for experience, tenure in the …rm and tenure in the career, plus other standard covariates. Interestingly, the returns to career tenure implied by the coe¢ cients of such OLS regressions do not change much across speci…cations, in particular when comparing the …rst three de…nitions.15 Figure 1 presents an example that provides additional evidence supporting the simultaneous consideration of industry and occupation codes for de…ning careers. The individual in the example works for three years as a clerk in a department store or mail order establishment. In the fourth year he becomes an administrator in a di¤erent …rm, but in the same industry. Using my preferred de…nition, this job change is coded as a within-career change. Using only occupation to de…ne career, this episode would be coded as a career change. This type of transition does not typically happen due to a bad career speci…c match nor does it typically imply a drastic change in tasks. Recognizing that each empirical de…nition of career change has its limitations, I stipulate that my baseline de…nition is the best choice for the empirical analysis of this paper given the data available.

2.2

Existing IV Estimates of the Importance of Career speci…c Human Capital

Before going into the details of the model, I present here IV estimates of the returns to career experience and …rm tenure that have been proposed in the previous literature. The goal of this section is to show that some of the results produced by the standard approach are di¢ cult to reconcile with standard theory. I show that these results do not vary much across the previously discussed de…nitions of career change and I …nally argue that they are likely to be generated by the restrictive assumptions necessary in order for the IV method to yield consistent estimates. In the next section, it will then be clear that my model does not su¤er such limitations. Parent (2000) and Kambourov and Manovskii (2009) use an instrumental variable approach to estimate the return to career experience and …rm tenure.16 1 5 These

results are available upon request. a less related work, Neal (1995) uses evidence from the Displaced Worker Survey. Unfortunately, it is not possible to measure career experience or actual labor market experience in this data set. 1 6 In

6

They assume that the econometric model that determines wages is: ln wicf t =

1 + 2 f tenif t + 3 ctenict + 4 eit + 5 OJif t + i + ic + if +"icf t ;

(1)

where ln wicf t is the real hourly log wage of person i working for …rm f and career c in period t. OJ is a dummy variable that equals one if the individual is not in the …rst year with the current employer, f tenif t is tenure in the …rm, ctenict is tenure in the career and eit is total labor market experience.17 Of particular note is that in this model, the returns to career tenure, …rm tenure and experience are common across all agents. In general, because better matches are likely to last longer, we expect the OLS estimates of career and …rm tenure e¤ects 2 and 3 to be upward biased. This bias arises because there is a positive correlation between the tenure and experience variables and …rm and career …xed e¤ects. Parent (2000) and Kambourov and Manovskii (2009) use a variant of the AltonjiShakotko (1987) instrumental variables method to estimate the parameters. In particular, they instrument for the tenure variables with their deviations from spell-speci…c sample means.18 These instruments are uncorrelated with their corresponding …xed e¤ects by construction. Parent runs this IV regression using the NLSY79 and the Panel Study of Income Dynamics (PSID), while Kambourov and Manovskii use only the PSID. Parent identi…es changes in career as changes of employer and industry (both 3-digit and 1-digit) while Kambourov and Manovskii identify career changes as changes in employer and occupation. In table 3, I compare their results with 3digit codes and continuous spells.19 The two papers …nd a similar level of implied growth attributable to ten years of career tenure. They also …nd similar results for the return to …rm tenure when they use the same data set. However, Parent …nds a very speci…c unexpected result when using the NLSY79. According to his estimates, ten years in the same …rm reduces log wage by about 0.09.20 Using my data set, I estimate a set of similar regressions and …nd very similar estimates. In table 4, I report the implied returns for the four de…nitions of career change obtained using this IV estimator.21 Notice that, in line with the IV literature, ten years in the same career increase log wages by 0.10 to 0.15 points, depending on the de…nition of career change used. As expected, the 1 7 Following

the literature, in all regressions I include the squared term for …rm tenure and both the squared and cubit term for career tenure and labor market experience. Variables like schooling, race and dummies for 1-digit occupation and industry codes are also included in the wage equation. 1 8 For example if X is the variable, and t is calendar time, the IV is X X . As an t t example, if the worker experiences a spell that lasts for three periods, then Xt = 1; Xt+1 = 2 and Xt+2 = 3 . In this case X = 1+2+3 = 2 and the IV takes the values f 1; 0; 1g. The 3 instrumented variables are the tenure in the career, the tenure in the …rm, the labor market experience and the dummy variable OJ. 1 9 In a continuous spell, the tenure in an industry or occupation starts from zero even if the worker has already worked there in the past. 2 0 This number is around -0.075 using 1-digit industry codes. When using non-continuous spells, it is between -0.03/-0.05. Unfortunately, the standard deviations cannot be calculated. 2 1 The standard errors are calculated using the robust (sandwich) estimator and are reported under the estimates. In the regressions, I include schooling, race, and dummies for one-digit industries and occupations.

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benchmark de…nition of career tenure displays the highest return. The return to …rm tenure after ten years is always large and negative, between -0.07 and -0.09, consistent with the estimates of Parent (2000), using the NLSY79. The four di¤erent de…nitions of career changes imply di¤erent estimates but the impact of di¤erent de…nitions of career change is not very large. When we split the sample into workers with at most a high school degree and workers with at least some college (table 5) some interesting patterns emerge. Workers with at most a high school degree are characterized by small returns to …rm and career tenure that are not statistically di¤erent form zero. Workers with at least some college education, on the other hand, display large and negative returns to …rm tenure and large and positive returns to tenure in the career. In the last two columns of table 5, I report the results obtained without the inclusion of the occupation and industry dummies. There are two reasons for doing so. First, it is not clear that these dummies should be included. The choice of industries and occupations is endogenous and treating them as exogenous components might produce misleading results. Second, the model presented in the next section will not be able to deal with ex-ante di¤erences between occupations or industries and therefore this last set of results will provide a natural point of comparison. The main di¤erence, when the industry and occupation dummies are excluded, is that the return to career tenure is smaller, while the return to experience is larger than in the previous case. This is due to the fact that on average workers move towards better paid occupations during their working life. Also, standard errors are generally smaller since fewer parameters are estimated and the conditional variation in the right-hand side variables is larger. Some of these empirical results are at odds with predictions of standard theory and common sense. The theoretical literature on the e¤ects of tenure predicts that, everything else equal, wages increase with tenure, or at least do not decrease. Even though it is clearly possible to write down a theory that could allow also for a negative e¤ect, we must wonder whether this result is due to the modeling assumptions and estimation techniques that have been used. In particular, the underlying econometric model assumes that the matchspeci…c growth is homogeneous across workers and the probability of leaving a career or …rm depends on the time-invariant match but not on the wage growth experienced. In the real world, it could be the case that workers who decide to leave a job or a career have experienced a di¤erent return to tenure than workers who decide to remain in that job or in that career. Light and McGarry (1998) present evidence, for example, of the fact that wage growth and job mobility are intrinsically related. If this is the case the interpretation of the estimated returns is di¢ cult. Heckman and Vytlacil (2005) discuss the use of IV techniques in models with heterogeneous returns and show that IV can be even more biased than OLS when the assumption of homogenous responses is misspeci…ed. This arises when the treatment, in this case a change of …rm or career, is at least partially induced by the unobserved heterogeneous return, in this case the returns to career or …rm tenure. Another concern with the IV approach is that in order to produce consistent 8

estimates, the instruments described above need to be uncorrelated with all …xed e¤ects, not only with the corresponding …xed e¤ects. The IV approach breaks down if, for example, career tenure is correlated with the …rm speci…c component of the wage. Kambourov and Manovskii (2009) are aware that their estimation strategy might su¤er from this endogeneity problem, but they argue that such a correlation is not likely to be strong. The evidence provided in Neal (1999) and Pavan (2010) goes against their argument, …nding strong evidence of a twostage search process, in which workers tend to choose …rst a career and then a …rm, creating a positive correlation that would bias the IV estimates. This concern is consistent with the fact that estimates of the return to …rm tenure are more negative in the NLSY79 than in the PSID. The NLSY79 contains younger workers and therefore individuals who are more likely to still be looking for a suitable career. As a consequence, the correlations that may cause the IV estimates to be biased are likely to be stronger in the NLSY79 than in the PSID. In the next section I present a model that allows for heterogeneous returns and incorporates a two-stage search process. After estimating the parameters of the model I am able to, among other things, produce unbiased estimates of the returns to tenure and experience and compare them with the ones produced by the IV literature.

3 3.1

The Model The Matches and Their Evolution

At each point in time a worker’s wage is in‡uenced by three factors: he c

"t

= general human capital, = career speci…c human capital, = …rm speci…c human capital,

where he is the worker’s general human capital after e years in the labor market, c is the worker’s career speci…c human capital after c years of experience in that career and "t is the worker’s …rm speci…c human capital after t years of tenure in the …rm. Every worker is characterized by an initial level of general human capital h1 . Every time the worker changes career, he draws a new career speci…c match 1 and a new …rm speci…c match "1 .22 Every time the worker changes employer within the same career, he draws a new …rm speci…c match. All random variables come from independent, known normal distributions:23 2 2 I assume that a worker cannot change careers without changing employers. See the data section for a discussion on this assumption. 2 3 Because I cannot separately identify the unconditional means of three random variables, I assume that initial draw of the career spec…c and …rm speci…c human capital have zero mean.

9

h1

2 h1 ; h 2

N

N 0;

1

"1

N 0;

;

;

2 "

(2)

:

I assume that c and "t follow a random walk process with drift and normally distributed innovations, and that he grows deterministically:24 he c

"t

= h (e; h1 ) ; = + 1 h1 =

"

+

2

h1

h1 h1

+

c 1

+ "t

1

+u

c

where u

+ u"t where u"

N 0; N 0;

2 2 "

;

(3)

:

All random variables are perfectly observed by the agents. The assumption of normality is convenient for deriving the analytical expression of the likelihood function but it is not necessary.25 General human capital increases with experience at di¤erent rates depending on its initial level h1 . The matches, c and "t , which represent the human capital of a worker in a particular career or in a particular …rm, grow stochastically over time. Their evolution is heterogenous across workers for two reasons. First, the drifts of both stochastic processes, which represent the average gains from staying one additional year in the same career or …rm, are functions of the initial level of human capital. This level of ex-ante heterogeneity represents the “type” of the worker. It implies that di¤erent types of workers experience di¤erent pro…les in terms of accumulation of general, …rm speci…c and career speci…c human capital.26 Second, di¤erent workers experience di¤erent realizations of the shocks to these random variables, c t fu n gn=1 and fu"n gn=1 . This re‡ects an important departure from previous literature which imposed homogeneous returns. The assumption of stochasticity in the evolution of the matches is consistent with the empirical …nding that wage changes in‡uence the job mobility behavior of workers (as found, for example by Light and McGarry (1998)).

3.2

The Wage

The worker is paid his marginal productivity, and the worker’s productivity is the exponential value of the three human capital’s measures:27 wect = e

Xe +he +

2 4 Topel

c +"t

;

and Wald (1992), among others, argue that the stochastic process of within-job wages is well approximated by the sum of a random walk and a transitory shock. 2 5 In order to show the existence of the value function, I will need to assume that these random variables are truncated, even though I can set the truncation points at an arbitrary large (in absolute value) but …nite value. 2 6 The closest example of model that allows for this level of ex-ante heterogeneity is Guvenen (2007), where individuals are allowed to have heterogeneous pro…les in wages. 2 7 Given the data used for the estimation of this model, it is not possible to understand if the variation of the …rm speci…c component of the wages is driven by …rm speci…c match productivities, …rm speci…c human capital or other reasons that are pointed out by the literature (insurance motives, incentive structures, etc.).

10

where Xe is a vector of dummies that includes race and years of schooling completed after e years of experience. Schooling is assumed to be exogenous, but I will estimate the model separately for workers with at most a high school degree and workers with at least some college education. Taking logs: ln wect = Xe + he +

c

+ "t :

(4)

The econometrician observes ln wect ve

=

ln wect + ve ; N 0; 2v ;

(5)

where ve is an i:i:d: measurement error.28

3.3

The Recursive Problem

The worker cares about earnings and leisure.29 I assume that the utility function is logarithmic in earnings and separable with respect to leisure. The current utility is given by:30 ~ U

= ln (we He ) Ke (He ) = ln e Xe +he + = Xe + he + + " + ln He Ke (He ) ;

+"

He

Ke (He )

(6)

where He is the number of hours worked in a given year and Ke (He ) is an increasing and convex di¤erentiable function of He . In this model, the number of hours worked in a given year is a static decision because it does not interact with the job mobility behavior of a worker. As a result the optimal amount of hours worked He will only be a function of a worker’s labor market experience and can be derived from the …rst order condition: 1 = Ke0 (He ) : He This assumption, although restrictive, will help to reduce the number of state variables in the value function and make the estimation computationally less intensive. The …rm speci…c and the career speci…c matches are assumed to be experience goods. This means that the worker will not be able to observe the new potential matches unless he decides to change employer or career. I assume 2 8 It is only for practical reasons that I assume that this idiosyncratic shock is meaurement error. The reservation rule that the worker will follow or the derivation of the likelihood function would not be a¤ected if I instead assume that this shock is part of the wage received by the worker. 2 9 An underlying assumption of the model is that the worker cannot borrow, save or buy insurance. 3 0 For simplicity, I suppress the index relative to tenure in the career and tenure in the …rm. Given that the evolution of the career-speci…c and …rm-speci…c human capital does not depend on the tenure variables, they will not be state variables.

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that in every period he receives one job o¤er in a di¤erent career and one job o¤er in the same career. This implies that there is no unemployment and that the worker will always accept one job o¤er if he decides to leave his current employer. I also assume that the worker can be separated exogenously from his employer with probability pf . If this happens, then with probability pc , he will not be able to continue working in the same career. These exogenous probabilities of separation from a …rm or a career capture job mobility decisions that are induced by non-monetary reasons, or by any other reason that is exogenous to the model.31 At this stage the state variables of the model are the initial level of human capital h1 , labor market experience e, the career speci…c human capital , the …rm speci…c human capital ", and the controls Xe . These variables de…ne the value function of a worker V~ (h1 ; e; ; "; Xe ). The sequential problem can be written as: V~ (h1 ; e; ; "; Xe )

= he + + " + ln He Ke (He ) + Xe + + pf V~S (h1 ; e + 1; ; Xe+1 ) + + (1 pf ) V~N S (h1 ; e + 1; ; "; Xe+1 ) :

(7)

The functions V~S and V~N S are de…ned as follows:32 V~S (h1 ; e + 1; ; Xe+1 )

=

(1

pc )

(8)

E V~ h1 ; e + 1; ; "1 ; Xe+1 Cf max ~ E V (h1 ; e + 1; 1 ; "1 ; Xe+1 ) Cc n o +pc E V~ (h1 ; e + 1; 1 ; "1 ; Xe+1 ) Cc : 0

+

8 <

9 E " V~ h1 ; e + 1; 0 ; "0 ; Xe+1 = V~N S (h1 ; e + 1; ; "; Xe+1 ) = max ; (9) E V~ h1 ; e + 1; 0 ; "1 ; Xe+1 Cf : ; E V~ (h1 ; e + 1; 1 ; "1 ; Xe+1 ) Cc

The components Cf and Cc are the search costs associated with a …rm switch or career switch, respectively. Although I do not model unemployment, these components help capture the welfare e¤ects associated with the unemployment spell that often accompanies a job change. If a worker does not separate exogenously from his employer (VN S ), he has three options. He can: 1) stay in the same …rm, and enjoy a value E " V~ h1 ; e + 1; 0 ; "0 ; Xe+1 where 0 and "0 are the next period values of the career speci…c and …rm speci…c human capitals; 2) change …rm in the same career, and receive a value E V~ h1 ; e + 1; 0 ; "1 ; Xe+1 where "1 is the new …rm speci…c match drawn from 3 1 The exogenous separations are needed to match mobility data without compromising wage dynamics. 3 2 The conditional expectation operators are de…ned as follows: Z Z Z Z Z Z E "= V~ dF 0 j dF"0 j" ; E = V~ dF 0 j dF"1 ; E = V~ dF 1 dF"1

12

the unconditional distribution by the worker; 3) change career, and get a value E V~ (h1 ; e + 1; 1 ; "1 ; Xe+1 ). If a worker exogenously separates from the employer (VS ) but not from the career, he has the choice of …nding a new job in the same career or changing careers. If a worker separates exogenously from the employer and the career (with probability equal to pc pf ), he has no options but to …nd a new career. Workers are not allowed to leave the labor force. The modeling choices that I make allow me to simplify the problem and greatly reduce the number of state variables that in‡uence workers’ decisions. In particular, the assumptions of a logarithmic utility function and log-linearity of earnings allow me to decompose the value function into two additive terms: V~ (h1 ; e; ; "; Xe ) = W (h1 ; e; Xe ) + V (h1 ; ; ") : Hence, the relevant part of the problem can be written as: V (h1 ; ; ") = + " +

fpf VS (h1 ; ) + (1

pf ) VN S (h1 ; ; ")g

(10)

where VN S (h1 ; ; ")

=

max

VS (h1 ; )

=

(1

E " V h1 ; 0 ; " 0 ; E " V h1 ; 0 ; " 1 EV (h1 ; 1 ; "1 ) Cc pc ) max

+pc fEV (h1 ;

E V h1 ; 0 ; " 1 EV (h1 ; 1 ; "1 ) 1 ; "1 )

Cf ; Cc

Cf ;

; (11)

+

Cc g :

Proposition 1 There exists a function (h1 ) and a function " (h1 ; ) such that: 8 career change: (1; 1) if < (h1 ) ; " < " (h1 ; ) > > > > or exogenous …rm separation occurs and < (h1 ) > > > > or exogenous career separation occurs < within career …rm change: (c + 1; 1) if (h1 ) ; " < " (h1 ; ) (c0 ; t0 ) = > > or exogenous …rm separation occurs and (h1 ) > > > > no change: (c + 1; t + 1) if " " (h ; ) > 1 > : and no exogenous separation occurs

where t0 and c0 are next period’s tenures in the …rm and in the career. If (h1 ) it can be shown that @" @(h1 ; ) < 0: Proof. See appendix.

<

Figure 2 presents a graphical representation of the policy function for a reasonable vector of parameters and for a given value of h1 . Poor career and employer matches together induce the worker to change his career. If the employer match is relatively high, then the worker might decide to keep the job, even if the career match is relatively low. A high career match and a low employer match push the worker towards a change of employer within the same career. If both matches are high, the worker will try to keep the job.

13

One appealing feature of this model is the low dimensionality of the state space.33 This makes it easy to solve numerically and then use in the estimation procedure. On the other hand, some assumptions of the model imply very severe empirical restrictions. Here I discuss these issues further. For example, I assume that hours worked are independent of the search process. This assumption would be rejected in the data and should be addressed more carefully in future research. Nevertheless, there is no reason to believe that this simpli…cation might distort the results in a particular way. I also assume that, conditioning on the value of past career and …rm matches, the stochastic processes that generate wage growth do not depend on the level of experience or tenure. Only general human capital is allowed to grow at di¤erent rates for di¤erent experience levels. Clearly, it would be interesting to assume instead that the drifts of the random walks describing the evolution of the career speci…c and …rm speci…c matches depend on tenure in the …rm and tenure in the career, but given the already high level of computational intensity, this feature is not implemented. Notice, though, that my model predicts that the expected value of the surviving matches is a concave function of the "age" of the match. Assume for a moment that the drifts are positive. The probability that a shock causes the match to fall below its threshold value for a job change declines over time. This is the direct consequence of the fact that the positive drifts make match qualities grow. A corollary of this fact is that the distribution of shocks for those matches that survived is less "truncated" when matches are "old". Therefore, the expected value of the shock conditional on surviving is higher for young matches (because they are more likely to be truncated), generating a concave pattern in the evolution of the matches. An interesting extension to this type of characterization of human capital has recently been completed by Gathmann and Schoenberg (2010), Poletaev and Robinson (2008) and Yamaguchi (2010). They show that in reality workers perform more tasks than are usually captured by the three types of human capital assumed by most of the literature. Instead of assuming that all career speci…c human capital is lost when a worker changes career, they show that the magnitude of this loss is proportional to the distance between the old and the new career. There is no unemployment in this model. Workers can always …nd a new job in the same career or in a new career at each period. Although this assumption is not realistic, I believe that it does not compromise our understanding of the wage growth pro…les. The search costs Cf and Cc can capture the loss in utility 3 3 Recently Yamaguchi (2010) has extended the model presented in this paper by introducing more state variables, but restricting the match values to be constant within a spell. As a consequence his extension does not allow him to di¤erentiate between ex-ante and expost returns. As we will see, this is an important feature of this model. Sullivan (2010) also estimates a dynamic model of occupational choice, in which workers chose between …ve occupations. However workers in his model do not search for a career because they already know how productive they are in each one of them. James (2010) does not include a …rm speci…c match in his model but allows for correlation across di¤erent careers. He addresses the curse of dimensionality by adopting an estimation method that does not require solving the model, using a version of the procedure developed Arcidiacono and Miller (2010).

14

associated with the fact that workers who quit their job might not be able to …nd another job for a certain amount of time. Although I estimate the model separately by education level, one extension of the model would be to endogenize schooling decisions. This extension would increase the dimensionality of the state space but would allow us to understand whether the di¤erences that we observe across educational levels are caused by the schooling decision or are the result of sorting. Do di¤erent types of workers choose di¤erent levels of schooling or do workers become di¤erent after making di¤erent schooling decisions? Answering such a question can be important in terms of policy since any policy that impacts the search process can potentially generate a change in schooling decisions. In my model, workers cannot observe the quality of a match before accepting a job. This is an extreme version of learning about match quality, as in Jovanovic (1979), where the worker learns perfectly about the match during the …rst period. This di¤erentiates my model from a traditional on-the-job search model (for example Burdett (1978)), where workers are able to observe the wages that they would earn with their potential employers before accepting the job. In this type of model, workers would only accept jobs whose matches o¤ered a better option value than the current one. In my model, however, workers may end up accepting jobs characterized by matches implying lower option values. This assumption implies that only those workers with low matches endogenously decide to change employers or careers, whereas in an on-the-job search model some workers with already good matches might change jobs if better o¤ers came along. One likely consequence is that the model might …nd it di¢ cult to explain some job mobility decisions and therefore the probability of an exogenous separation will be biased upwards. In my opinion, this is a very restrictive assumption and should be relaxed in future research. Altonji and Shakotko (1987) present a discussion of the possible biases introduced by this simpli…cation and they argue that this could result in a downward bias in the estimated return to …rm tenure.

4 4.1

The Estimation The Likelihood Function

The model is characterized by two state variables that are both hidden and persistent. It cannot be estimated using standard techniques for structural, dynamic discrete choice models that incorporate Rust’s (1987) conditionalindependence assumption because the hidden state variables display persistence even after conditioning on the worker’s observed choice. My strategy for calculating maximum likelihood estimates is an extension of Abbring and Campbell (2003). This method of estimating the likelihood function follows the nonGaussian state-space approach of Kitagawa (1987). The computation of the likelihood is nontrivial because the model involves repeated selection on the basis of the persistent latent state variables, namely career speci…c and …rm

15

speci…c matches. The mechanics of this procedure are simple. First, for each parameter vector I numerically solve for the reservation rule. After observing the …rst-period wage and mobility decisions, I calculate the conditional distribution of the latent variables given those observations. I can derive the likelihood contribution of the second period conditional on the …rst-period matches. I then integrate those matches out using the conditional distribution just calculated. After observing the second-period wage and job mobility decision, I update the distribution of the matches using Bayes’rule. I repeat the process until the end of the career spell. After each change of career, the distribution of the matches starts from the unconditional distribution. Two recent papers on the estimation of models with unobserved states that are correlated over time are worth mentioning. Fernandez-Villaverde and RubioRamirez (2007) uses a similar procedure to decompose the likelihood function. Instead of using numerical integration like in this paper, they calculate integrals using particle …ltering. Norets (2009) allows serially correlated unobserved state variables, and estimates the model through Bayesian Markov Chain Monte Carlo. I;E The data that I use to estimate the model can be written as fYie gi=1;e=1 E

where i is the individual and e is labor market experience; YiE = fYie ge=1 is the history of one individual. A single data point is composed of a pair Yie = (ln wie ; JMie ), where ln wie is the log wage, if observed, and JMie is the job mobility decision. JMe can be a career change (cc), a job change (jc) or no change (nc). For expositional ease, I assume that all objects are indexed by i and all densities are conditional on Xe . I also de…ne the relevant labor market history up to e years of experience Y e = fYe 1 ; Ye g if JMe 1 = jc or JMe 1 = nc and Y e = fYe g if JMe 1 = cc. Note that the history cancels out every time that a career change occurs. The contribution of each individual to the likelihood function can be written as: ln L Y E j

= ln

Z Y E

e=1

fe Ye jY e

1

; h1

1 h

h1

h1

dh1 ;

(12)

h

where fe Ye jY e 1 ; h1 is the distribution of an observation with a given history and conditional on the individual speci…c e¤ect h1 ; and is the vector of parameters. Before each calculation of the likelihood function, I numerically solve for the value function and calculate the two-dimensional reservation rule (" (h1 ; ) ; (h1 )) associated with the parameter vector. These functions will be then used to calculate the contributions to the likelihood function. 4.1.1

The …rst period after a career change

After a career change, the distribution of Ye conditional on the individual e¤ect does not depend on the past: fe Ye jY e 1 ; h1 = fe (Ye jh1 ) if JMe 1 = cc: Using Bayes’rule I can write:

16

fe (Ye jh1 )

= fe ((ln we ; JMe ) jh1 ) = fwe (ln we jh1 ) fJM e (JMe j ln we ; h1 ) :

(13)

The JMe variable can indicate three possible behaviors: JMe = cc, a career change, JMe = jc, a job change within career and JMe = nc, no change. The worker’s choice depends on the reservation rule (" (h1 ; ) ; (h1 )). Suppose for example that Ye = (ln we ; nc). Then: fe (ln we ; ncjh1 ) = f (he + 1 + "1 + ve jh1 ) p

=

1 2

(1

+

2 "

pf )

1

+ Z

2 v

(14)

Pr (ncjh1 ; ln we ) ! ln we h (e; h1 ) p 2+ 2+ 2 " v

E ( 1 j ln we h (e; h1 )) 1 1 std ( 1 j ln we h1 ) std ( 1 j ln we h (e; h1 )) " (h1 ; 1 ) E ("1 j ln we h (e; h1 ) 1) d 1: std ("1 j ln we h (e; h1 ) ) 1

The …rst part of the expression in the density function is the distribution of the wage conditional on h1 , while the second part is the probability that the …rm speci…c match is higher than " (h1 ; 1 ) and that no exogenous separation occurs, conditional on h1 and ln we . Thanks to the properties of normal distributions, the conditional distributions of 1 and "1 are still normal and the conditional means and standard deviations are easy to derive. At this point we are implicitly assuming that the wage ln we is observed. As noted in the discussion of the data, wages are often missing. Assuming that the probability of not observing a wage is exogenous to the model, it is easy to extend the current derivation of the likelihood function to include this feature. I then use Bayes’ rule to calculate the distribution of the matches, given Ye and h1 . The joint distribution of the matches, after a new wage is observed and the worker has decided to stay in the same …rm, can be written as: f

1 ;"1 jY1 ;h1

( 1 ; "1 )

= f ( 1 ; "1 jh1 ; ln we ; nc) =

=

f ( 1 ; "1 ; ncjh1 ; ln we ) P (ncjh1 ; ln we ) f ( 1 ; "1 jh1 ; ln we ) 1 ("1 > " (h1 ; Pr ("1 > " (h1 ; 1 ) jh1 ; ln we )

(15)

1 ))

;

where every component of the right-hand side is simple to compute or has already been computed in the previous steps. The distribution of the matches after the …rst period is just a truncated bivariate normal. The reservation rule

17

implied by the model yields the truncation. The formulae for the case of a career change or a …rm change can be derived similarly.34 4.1.2

The other periods

If a worker does not change career, i.e. JMe 1 6= cc, the distribution in period e depends on the previous period matches c 1 and "t 1 . Assume for the moment that we know the joint distribution of those matches, f c 1 ;"t 1 jY e 1 ;h1 . The contribution to the likelihood function can be written as:

fe Ye jY e

1

; h1 =

Z Z

fe Ye jY e

1

; h1 ;

c 1 ; "t 1

f

1 ;"t

c

1 jY

e

1 ;h

1

d

c 1 d"t 1 ;

(16) where fe Ye jY e 1 ; h1 ; c 1 ; "t 1 is the distribution of Ye given history and (h1 ; c 1 ; "t 1 ). This last distribution can be decomposed as follows: fe Ye jY e

1

; h1 ;

c 1 ; "t 1

= fwe ln we jY e

1

fJM e JMe jY

; h1 ;

e 1

c 1 ; "t 1

; h1 ;

(17)

c 1 ; "t 1 ; ln we

:

The term fwe ln we jY e 1 ; h1 ; c 1 ; "t 1 is a normal p:d:f with conditional mean he + + 1 h1 + c 1 + " + 2 h1 + "t 1 and conditional variance 2 + 2 2 (h1 )) " + v . The worker’s choice depends on the reservation rule (" (h1 ; ) ; and the distribution of c and "t given (ln we ; h1 ; c 1 ; "t 1 ). The conditional distribution for JMe = nc if t > 1 is: fJM e ncjY e Z = (1 pf )

1

; h1 ;

c 1 ; "t 1 ; ln we

1 std ( c jh1; ln we ; c 1 ; "t 1 ) E ( c jh1; ln we ; c 1 ; "t 1 ) c std ( c jh1; ln we ; c 1 ; "t 1 ) " (h1 ; c ) E ("t jh1; ln we ; c 1 ; "t 1 ; 1 std ("t jh1; ln we ; c 1 ; "t 1 ; c )

(18)

c)

d c;

that is the probability that "t " (h1 ; c ) and no exogenous separation occurs given (ln we ; c 1 ; "t 1 ). Again, thanks to normality, the conditional distributions of the matches are still normally distributed, and the mean and variances can be easily derived using linear projection. The last step shows how to update the distribution of the matches, f c ;"t jY e ; given that we know f c 1 ;"t 1 jY e 1 . I use Bayes’rule to rewrite the density in a more appropriate form. If JMe = nc and t > 1; then the distribution of the 3 4 All

derivations are available upon request.

18

matches is: f

c ;"t jY

e ;h

1

( c ; "t )

= f =

c ; "t jY

f

e 1

; h1 ; ln we ; nc

(19)

e 1

; h1 c ; "t ; ln we ; ncjY : f (ln we ; ncjY e 1 ; h1 )

The denominator has already been calculated while the numerator is derived as follows: f

c ; "t ; Ye jY

e 1

; h1

= f

c ; "t ; ln we ; ncjY

e 1

; h1

(20) e 1

= f (ncj c ; "t ; h1 ) f c ; "t ; ln we jY ; h1 = (1 pf ) 1 ("t > " (h1 ; c )) Z Z 1 std ( c jh1; ln we ; c 1 ; "t 1 ) E ( c jh1; ln we ; c 1 ; "t 1 ) c std ( c jh1; ln we ; c 1 ; "t 1 ) 1 std ("t jh1; ln we ; c 1 ; "t 1 ; c ) "t E ("t jh1; ln we ; c 1 ; "t 1 ; c ) std ("t jh1; ln we ; c 1 ; "t 1 ; c ) he

ln we f

c

1 ;"t

1 jY

e

1 ;h

1

d

h p1 1 2+

c 1 2 "

+

"

p

1 2

+

2 "

2 h1

2 v

c 1 d"t 1 :

At this point we have the tools to compute the contribution to the likelihood function given the distribution of the latent variables, and we have a rule for updating that distribution. Starting from the …rst period in a career, we can implement this method recursively to compute the likelihood function.

5

The Estimation Results

In order to calculate the likelihood function, I approximate the integrals with quadrature methods. I use the Gauss-Legendre quadrature rule for the …rm and career matches and the Gauss-Hermite for the individual-speci…c component. With each calculation of the likelihood function, I solve the model numerically, and I approximate the policy function " ( ) with two low-order polynomial functions.35 In order to …nd the parameter vector that maximizes the likelihood function, I use the Nelder-Mead (1965) algorithm which is a widely used gradient-free minimization algorithm. The standard errors are calculated numerically, using the outer-product of the gradient. In the next table, I show 3 5 One

for <

and one for

.

19

+ "t

2 v 1

!

the estimation results using the baseline de…nition of career change. I set the discount factor to 0.95.36 I choose a ‡exible speci…cation for the function describing the evolution of general human capital.37 The results are reported in table 6. The average drifts of the two matches ( and " ) are positive for both samples but the average drift for career speci…c human capital is not statistically signi…cant for workers with at most a high school diploma while it is signi…cant and ten times larger for workers with some college. The drift for the …rm speci…c human capital " has the same magnitude in both samples but it is signi…cant only for workers with at most a high school diploma. Interestingly, high skilled workers (workers characterized by a larger amount of initial unobserved general human capital h1 ) have a faster ex-ante accumulation of both general and career speci…c human capital, as indicated by the positive estimates of the parameter 1 and 4 . The accumulation of …rm speci…c human capital is faster only for high skilled workers with at most a high school degree, as indicated by the estimates of 2 . The standard deviation of the initial value of the …rm speci…c human capital " is large compared to the other components. The standard deviation of the innovation to this value, " , is …ve times smaller. The standard deviation of the initial value of the career speci…c human capital is twice as small as the standard deviation of the relative innovation, . From this I conclude that there is a lot of uncertainty with respect to the initial match with a …rm. The same is not true for careers, at least when compared with the uncertainty on the amount of career speci…c human capital that the worker will be able to accumulate. As anticipated, the exogenous probability of separation (pf ) is very large, around 20.6% for workers with at most a high school degree and 17.8% for workers with at least some college, implying that a large share of the separations cannot be explained by the model. Although this is clearly a failure for the model, we will see that the endogenous separations generated by the model are enough to capture many dimensions of the data and invalidate the instrumental variable approach presented in section 2.38 Although the estimates di¤er between education levels, most of these differences do not seem extremely pronounced with the exception of the career speci…c drift. Workers with at most a high school diploma have a much lower expected return from spending more time in the same career than workers who 3 6 There

is a large body of literature on the estimation of the discount factor. See for example Gourinchas and Parker (2002) who …nd numbers very close to the one I chose. Results are robust even when a of 0.975 is used. 3 7 The estimated speci…cation for the h is h (e; h ) = h + 2 3 h1 e 1 1 1e + 2e + 3e + 4 e + 5 e2 : 3 8 This feature is quite common in structural estimation. Dynamic models are simpli…ed versions of very complicated processes that real workers experience. Structural works typically use an i:i:d shock to the utility function, often from an extreme value distribution, to capture patterns that cannot be explained by those models. The standard deviation of those shocks is often very large. Just to give an example Sullivan (2010) estimates a standard error of around 4 for the utility shock (see table 6 panel A: scale parameter = 3.29 for an extreme value distribution). This is large if compared with the measurement error of the wage which is around 0.3.

20

have at least some college education. An interesting interpretation of this result is that individuals undertake an important investment by going to college. The knowledge that they accumulate while in college is not completely general (think about di¤erent majors) but it is also a type of knowledge that typically can be applied to a large set of jobs. Similarly, it is likely that their investment leads them towards developing skills that may further facilitate the acquisition of career speci…c human capital once in the labor market. To understand the extent to which this model is able to reproduce the wage growth pro…les and job-mobility patterns in the data, I simulate a data set 10 times the size of the original. A comparison of a few summary statistics is reported in table 7. Although the job mobility rates and the wage growth pro…les between the real and the simulated data are very similar, it is possible to see that the model underestimates the wage pro…les within the same employment spell.39 These di¤erences are most likely due to the fact that the model captures job mobility patterns only partially, and does not replicate the behavior of workers with higher tenure very well. Given this issue, it is reasonable to wonder whether the model is able to replicate the interactions between di¤erent dimensions of job mobility and wage growth. In table 8, I present simple statistics generated by probit and OLS regressions. The probit regressions describe the probability of changing jobs within the same career (panel A) or the probability of changing career (panel B). The OLS regression of panel C describes the increase in log wage of a worker as a function of his labor market history. Although the results derived from the simulated data are not identical to those derived using the real data, it is striking how close the two sets of estimates are given the simplicity of the model. Nevertheless the model fails to capture some dimensions of the data. Controlling for tenure in the career and tenure in the …rm, the probability of changing careers is negatively correlated with tenure in the …rm in the NLSY79, while it is positively correlated in the simulated data. In the model, having high …rm tenure conditional on tenure in the career means that the worker is less likely to have a good career speci…c match compared to another worker with lower tenure. This also implies that in the event of a separation, a worker will probably choose to separate from his career as well. The pattern is di¤erent from the data where separation rates decline more sharply. This disparity is due to the fact that in my model tenure in the …rm and experience are not state variables. This particular feature of the data could therefore easily be captured by allowing, for example, the moving cost or the exogenous probability of separation be a function of tenures and experience. Looking at panel C, we can see that the model predicts that the wage growth has a small positive correlation with tenure in the …rm conditional on tenure in the career, experience and wages, while the data does not display a clear pattern. This small di¤erence may be explained by the fact that in the model the drifts of the matches do not depend on tenure. These results show that the model can reproduce not only the observed wagegrowth pro…les but also the patterns that arise from job-mobility decisions. This 3 9 The average growth in the simulated data is the sum of the growths due to the three unobserved components and the growth due to changes in schooling levels, which is a minor component but statistically di¤erent from zero.

21

implies that the high probability of exogenous separation does not compromise the results. Moreover if mobility were completely random, an IV estimator on this generated data would give similar results to an OLS estimator and this is not the case. In section 5.2, I show that the IV estimates are unable to capture the true returns, which, in the case of the generated data, are known to the econometrician.

5.1

Wage Decompositions

The main goal of this paper is to quantify and describe the level of transferability of human capital, that is, how much of the observed wage growth is due to the accumulation of …rm speci…c or career speci…c skills, and how much is due to the process of selecting good careers and good employer matches. As there is no simple statistic that provides this information, I present three basic decompositions. In the …rst decomposition, I calculate the average contributions to the increase in log wages for workers who have been with the same employer and in the same career for a certain number of years. This decomposition provides the main estimates of the return to …rm tenure. Next, I calculate the determinants of the increase in log wages during a career spell, letting workers sort into better …rm speci…c matches. This decomposition provides the main estimates of the return to career tenure. Finally, I decompose the components of the increase in log wages in the …rst years of labor market experience. This decomposition provides the main estimates of the importance of the search processes. My strategy for disentangling the components is as follows: I simulate a large number of observations and then calculate the average increase in log wages for the relevant workers in the relevant time period. Simultaneously, I save the values of the …rm speci…c and career speci…c matches. Log wage changes can be decomposed into seven di¤erent categories. We can have wage growth because the worker has a new …rm or career match, or due to the accumulation of general human capital, or from greater amounts of …rm speci…c or career speci…c human capital. These last two components can be further divided: wage growth can occur due to the deterministic drift of the speci…c match or it can be due to the realization of the permanent shock to the match. The deterministic component identi…es the ex-ante return to tenure while the sum of the deterministic and the stochastic component identi…es the ex-post return to tenure: ln w(e+1)c0 t0

ln wect

= =

(he+1 he ) + c0 + "t0 "t ; (21) c 0 (he+1 he ) + [ h" + u"t ] 1 (t = t + 1) + + [ h + u c ] 1 (c0 = c + 1) + 0 +( 1 "t ) 1 (t0 = 1) : c ) 1 (c = 1) + ("1

In the next exercises, I decompose workers’log wage pro…les by looking at the accumulated values of the above components, conditional on di¤erent events. In order to take into account that we are using estimated parameters and not the true ones, I also indicate in the tables whether each number is statistically

22

di¤erent from zero.40 5.1.1

First decomposition: wage growth components along a …rm spell

I compute the contributions to wage growth from the career speci…c and …rm speci…c matches for workers who have stayed …ve or ten years in the same career working for the same employer. This exercise provides the main estimates of the returns to …rm-tenure. Using the procedure described above, I calculate the implied average returns and report them in table 9. As we have seen in table 7, the model underestimates the average increase in log wages after 10 years for both samples. The model predicts that the return to …rm tenure is positive and statistically signi…cant although the magnitude is not very large, around 0.05 in ten years. There is a striking di¤erence between ex-ante and ex-post returns. The ex-ante returns, which is the deterministic component of the growth in "t , is only a third of the ex-post return and it is statistically signi…cant only for workers with at most a high school diploma. The return to career tenure is negligible for workers with at most a high school degree, while it is quite large for workers with at least some college. For them the ex-ante return is around 0.09 in ten years while the ex-post return is around 0.10. In the case of workers with at most a high school diploma, a fourth of the total wage growth after ten years in the same …rm is due to …rm speci…c components, while only 7% of the increase in log wages is due to career speci…c components. The remainder is due to the accumulation of general human capital. In the case of workers with at least some college, 16% of the total increase after ten years is due to …rm speci…c factors and 30% is due to career speci…c factors. It is worth noting that although less educated workers are characterized by a ‡atter pro…le, this can be almost entirely explained by the smaller accumulation of career speci…c human capital. This is consistent with the discussion of the di¤erences in the estimates of the structural parameters between the two groups. 5.1.2

Second decomposition: wage growth components along a career spell

In this exercise, I analyze the determinants of wage growth during a worker’s career spell. This exercise provides the main estimates of the returns to career tenure. Furthermore, I compute the impact of the second stage of the search process, which is the process of selecting a good employer within the same career. The results are shown in table 10. The average log wage increase from accumulation of career speci…c human capital is around 0.11 in 10 years for a worker with at most a high school degree, while it is around 0.20 for a worker with at least some college. Although previous studies do not di¤erentiate by 4 0 Using the estimated asymptotic covariance matrix of the structural parameters, I simulate many draws (500) of the parameter vector, simulate data for each of the draws and calculate the statistics of the table. I then use the distribution of these statistics to derive their statistical signi…cance.

23

schooling levels, these estimates are in line with the results in the literature. The increase from …rm speci…c human capital is larger than in the previous exercise, around 0.07 or 0.08. The accumulation of career speci…c human capital accounts for 35% of the total increase for workers with at most a high school degree and more than 40% for workers with at least some college, while the impact of the …rm speci…c human capital is around 20% for both groups. Also in the second decomposition, more than half of the di¤erence in the pro…les between the two education groups can be explained by the smaller accumulation of career speci…c human capital of workers with at most a high school degree. Again there is a large di¤erence between ex-ante and ex-post returns. Nearly all the career speci…c wage growth for workers with at most a high school degree is due to selection, while the ex-ante return to career tenure is half the size of the ex-post return for workers with at least some college. It should also be noted that nearly all the wage growth due to …rm speci…c human capital comes from the search for a good employer within the same career. 5.1.3

Third decomposition: the …rst years of working life

This wage decomposition follows Topel and Ward (1992) to some extent. They study the relationship between high wage growth and high job turnover in the …rst years in the labor market. They …nd that in the …rst ten years, a worker holds on average seven jobs and his wage grows by 66%. They also calculate that one third of wage growth is due to "job shopping". Using the structure implied by my model, I can also study a worker who is not only shopping for the best employer but is also looking for the best type of job, or career. As a …rst step, in table 11, I replicate some of the results of Topel and Ward. The numbers are not directly comparable to theirs due to the di¤erent structure of the sample. Their data set uses wage data collected from 1957 to 1972 and they do not observe schooling levels or labor supply within a quarter.41 Nevertheless many patterns look similar. Topel and Ward …nd that wage gains from job changes account for 40% of total growth.42 In my sample, wage gains after a job change account for 55% of total growth for workers with at most a high school degree and 45% for workers with at least some college education. Gains from a simple job change (change of employer within the same career) and gains from a complex job change (change of employer and career) are similar in magnitudes. The model does a good job in replicating these statistics, even though it overstates the impact of complex changes. Although very informative, this decomposition cannot tell us the relative importance of …rm speci…c human capital or career speci…c human capital. Using the same approach that I used in the previous decomposition, I disentangle the components of the average increase in log wages and present them in table 12. From this analysis, it emerges that …rm speci…c factors account for an increase of around 0.13 points after 10 years of experience, which is around 35% of the total increase for workers with at most a high school degree and 28% for workers with at least some college. Nearly all 4 1 They 4 2 See

use the LEED, longitudinal employee-employer data. row 3 and 5 of table 7 in Topel and Ward (1992).

24

of this is due to changes of employer. The contribution of career speci…c human capital is around 0.05 points for workers with at most a high school degree and 0.12 for workers with at least some college. While in the case of less educated workers nearly all of this gain is due to the search process, more than 60% of this contribution is due to the accumulation of career speci…c human capital in the case of workers with at least some college education. It is remarkable that even in this case, most components are very similar across di¤erent education levels, with the exception of the accumulation of career speci…c human capital. Topel and Ward note that this "try and try again" process is the principal method by which workers can improve their positions, because workers do not have detailed information about the nature of the job or their abilities. Looking at the results presented in this paper, we can understand better the potential impact of policies that facilitate or reduce labor mobility. For example, an increase in labor protection would also have the e¤ect of increasing hiring costs for a …rm and ultimately reduce workers’mobility. The allocational e¢ ciency of an economy might be reduced by such a policy, preventing workers from …nding their best possible match. Also, training programs that make heavy investments in career speci…c human capital before workers have had time to select a suitable career might prove less bene…cial than expected. For example, this is the case for the German apprenticeship system, as noted by Neal (1999).43

5.2

The IV Estimation Strategy

In section 2, we saw that the return to …rm tenure obtained by the Altonji and Shakotko IV estimation strategy is negative and quite large, in particular for workers with at least some college education. However, my model estimates indicate that the accumulation of …rm speci…c human capital is responsible for an increase in log wages of around 0.05 in the …rst ten years in a …rm. How can the two results be reconciled? As already discussed in section 2, there are reasons to believe that the proposed IV strategy may su¤er from a serious bias, particularly in a data set like the NLSY where young workers are still shopping for a good career. Although my structural estimates strongly rely on the nature of the model, they have the merit of controlling for the search process of young workers. As a test for the quality of the IV procedure, I perform the following exercise. Taking the data simulated from my model, I use the same IV procedure I have applied to the real data and I check whether the IV estimates are close to the structural estimates presented in tables 9, 10 and 12. In table 13, we can see that the IV estimates obtained from the simulated data are very close to the IV estimates obtained with the real data. A closer look shows that these estimates are remarkably close for workers with at least some college education while for workers with at most a high school diploma the model tends to underestimate the return to …rm tenure and overestimate the return to career tenure although the di¤erences are not statistically di¤erent from zero. More importantly, the IV estimates on the simulated data display negative returns to …rm tenure while 4 3 See

Harho¤ and Kane (1997) for a description of the system.

25

from the previous section we know that the correctly measured returns are positive. It can be concluded that the IV procedure previously used in the literature can potentially lead to seriously biased estimates. In this context, structural models can be very useful because they directly model those features of the data that generate the biases of IV estimates.

6

Conclusions

In this paper, I estimate a dynamic discrete choice model in which workers simultaneously search for a good career and a good employer. I then use the estimates to decompose overall wage growth into several components. Literature going back to Burdett (1978) and Jovanovic (1979) has recognized the importance of …rm speci…c human capital and job search to explain wage dispersion, wage dynamics and job mobility. However, considerably less e¤ort has been dedicated to understanding the level of transferability of human capital across di¤erent jobs. For example, a job change that involves a change of industry or occupation has di¤erent characteristics from a job change within the same line of work. This paper provides an empirical strategy to identify the importance of di¤erent types of human capital that does not su¤er from the limitations of the previous IV literature. Although this paper represents an important step that provides signi…cant information for understanding the welfare consequences of displacement or the impact of policies that in‡uence labor mobility, much needs to be done in future research. In particular, I believe that future data sets must be constructed to provide more information on the tasks and skills that workers utilize in their jobs. Only using more detailed information can we hope to break into the black box of what a career is and greatly expand our understanding of the nature of human capital.

26

References [1] Abbring, Jaap H., and Je¤rey Campbell. 2003. A Structural Empirical Model of Firm Growth, Learning, and Survival. Working Paper no. 781. Institute for the Study of Labor (IZA). Altonji, Joseph G., and Shakotko, Robert A. 1987. Do Wages Rise with Job Seniority? Review of Economic Studies, 54 no. 3:437-59. Arcidiacono, Peter and Robert Miller. 2010. CCP Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity. Unpublished manuscript, Department of Economics, Duke University, Durham. Becker, Gary. 1962. Investment in Human Capital: A Theoretical Analysis. Journal of Political Economy, 70 no. 1:1-13. Bollinger, Christopher R. and Amitabh Chandra. 2005. Iatrogenic Speci…cation Error: A Cautionary Tale of Cleaning Data. Journal of Labor Economics, 23 no. 2:235-258. Burdett, Kenneth. 1978. A Theory of Employee Job Search and Quit Rates. American Economics Review, 68 no. 1:212-220. Farber, Henry S. and Robert Gibbons. 1996. Learning and Wage Dynamics. Quarterly Journal of Economics, 111 no. 4:1007-10047. Fernandez-Villaverde, Jesus and Juan F. Rubio-Ramirez. 2007. Estimating Macroeconomic Models: A Likelihood Approach. Review of Economic Studies, 74 no. 4:1059-1087. Freeman, Smith. 1977. Wage Trends as Performance Displays Productive Potential: A Model and Application to Academic Early Retirement. Bell Journal of Economics, 8 no. 2:419-443. Gathmann Christina and Uta Schoenberg. 2010. How General is Human Capital? A Task-Based Approach. Journal of Labor Economics, 28 no. 1:1-49. Gibbons, Robert, Lawrence F. Katz, Thomas Lemieux, and Daniel Parent (2005). "Comparative Advantage, Learning, and Sectoral Wage Determination." Journal of Labor Economics, 23 no. 4:681-724. Gourinchas, Pierre-Olivier and Jonathan A. Parker. 2002. Consumption Over the Life Cycle. Econometrica, 70 no. 1:47-89. Guasch, Luis J. and Weiss Andrew. 1982. An Equilibrium Analysis of WageProductivity Gaps. Review of Economic Studies, 49 no. 4:485-97. Guvenen, Fatih. 2007. Learning Your Earning: Are Labor Income Shocks Really Very Persistent? American Economic Review, 97 no. 3:687-712. Harho¤, Dietmar and Thomas J. Kane. 1997. Financing Apprenticeship Training: Evidence from Germany. Journal of Population Economics 10, no. 2:171-196.

27

Harris, Milton and Bengt Holmstrom. 1982. A Theory of Wage Dynamics. Review of Economic Studies, 49 no. 3:315-333. Heckman, James J. and Salvador Navarro. 2007. Dynamic Discrete Choice and Dynamic Treatment E¤ects. Journal of Econometrics, 136 no. 2:341396. Heckman, James J. and Edward Vytlacil. 2005. Structural Equations, Treatment E¤ects and Econometric Policy Evaluation. Econometrica, 73 no. 2:669-738. James, Jonathan. 2010. Ability Matching and Occupational Choice. Unpublished manuscript, Department of Economics, Duke University, Durham. Jovanovic, Boyan. 1979. Job Matching and the Theory of Turnover. The Journal of Political Economy, 87 no. 5:972-990. Johnson, William R. 1978. A Theory of Job Shopping. Quarterly journal of Economics, 92 no. 2:261-78. Kambourov, Gueorgui and Iourii Manovskii. 2009. Occupational Speci…city of Human Capital. International Economic Review, 50 no. 1:63-115. Kitagawa, Genshiro. 1987. Non-Gaussian State-Space Modeling of Nonstationary Time Series. Journal of the American Statistical Association, 82 no. 4:1032-1063. Lazear, Edward P. 1979. Why is there Mandatory Retirement. Journal of Political Economy, 87 no. 6:1261-1284. Light, Audrey and Kathleen McGarry. 1998. Job Change Patterns and the Wages of Young Men. The Review of Economics and Statistics, 80 no. 2:276-286. McCall, Brian P. 1990. Occupational Matching: A Test of Sorts. The Journal of Political Economy, 98 no. 1:45-69. Mincer, Jacob. 1974. Schooling, Experience and Earnings. New York: Columbia University Press. Miller, Robert. 1984. Job matching and Occupational Choice. The Journal of Political Economy, 92 no. 6:1086-1120. Mortensen, Dale T. 1978. Speci…c Capital and Labor Turnover. Bell Journal of Economics, 9 no. 2:572-586. Neal, Derek. 1995. Industry-Speci…c Human Capital: Evidence from Displaced Workers. Journal of Labor Economics, 13 no. 4:653-77. Neal, Derek. 1999. The Complexity of Job Mobility among Young Men. Journal of Labor Economics ,17 no. 2:237-61. Nelder, John and Roger Mead. 1965. A simplex method for function minimization. Computer Journal, 7 no.4:308–313. Nickell, Stephen J. 1976. Wage Structures and Quit Rates. International Economic Review, 17 no. 1:191-203. 28

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29

A A.1

Appendix Proof of proposition 1.

Existence and continuity of the value function can be easily shown if the supports of the distributions are bounded.44 As mentioned in section 3, this can be achieved by assuming that all distributions are truncated normals, setting the truncation at a very large but …nite value. The value function is increasing in both arguments. Intuitively, if we raise the value of one match we also raise the value of the conditional mean of the match in the next period in the case the worker keeps it, and hence we raise the value of the function. I now prove the existence of a reservation strategy for the worker. Consider VS . Conditional on h1 , the second term in the max operator is constant, while the …rst term is continuous and increasing in . Therefore there exists a function RR (h1 ) such that V h1 ; 0 ; "1 dF"1 dF 0 j (h1 ) Cf = EV (h1 1 ; "1 ) Cc . This function represents the reservation strategy of the worker. If (h1 ) a worker separated from his employer will chose to keep working in the same career. If < (h1 ) the opposite is true. Consider now VN S . Using the previous result, de…ne: N (h1 ; ) =

E V h1 ; 0 ; " 1 EV (h1 ; 1 ; "1 )

if if

Cf Cc

<

(h1 ) :: (h1 )

We can then rewrite VN S as follow: VN S = max E " V h1 ; 0 ; "0 ; N (h1 ; ) : Then, using the fact that the function is continuous and increasing in ", there will exist a unique function " (h1 ; ) such that: VN S =

E " V h1 ; 0 ; "0 if " " (h1 ; ) : N (h1 ; ) if " < " (h1 ; )

If " " (h1 ; ) the worker keeps working with the same employer. If " < " (h1 ; ) the worker will change employer. If (h1 ) he will look for an employer in the same career, while if < (h1 ) he will also change career. Using the implicit function theorem we can …nd that @" @(h1 ; ) < 0 in the case < (h1 ). If " = " (h1 ; ) and < (h1 ) we can write: E " V h1 ; 0 ; "0 = EV (h1 ; Using the implicit function theorem we get: h E V h1 ; 0 ; " 0 " @" (h1 ; ) h = @ E V h ; 0 ; "0 "

1

1 ; "1 )

Cc :

0

1 h1 2

"0

"

2 h1 2 "

"

i

i < 0;

because both the numerator and the denominator can be shown to be positive. 4 4 See

for example Stokey, Lucas and Prescott (1989).

30

B

Figures and Tables 6.8 Year 1: Generic Clerk Year 2: Stock Handler Year 3: Generic Clerk In Department and Mail Order Establishment 6.6 Administrator - Same Industry

Salesman in Shoe Store

Log-Wage

6.4

6.2

6

Career Change 5.8 Within Career Change

5.6 1

2

3

4

5

6

Experience

Figure 1: An Example of Career Mobility.

STAY

ε*(θ)

FIRM MATCH

ε Change Career and Firm

Change Firm Keep Career

θ*

CAREER MATCH θ

Figure 2: The Policy Function

31

7

8

Variable Number of Observations Number of Individuals Average Years of Schooling per Individual Percentage of Job Changes Average Duration of an Individual Spell Median Duration of an Individual Spell Average Duration of a Job Spell Median Duration of a Job Spell Average Log- Wage Increases 5 Years of Experience 10 Years of Experience 5 Years of Tenure in the Firm 10 Years of Tenure in the Firm

Table 1: Summary Statistics All Sample At Most High School 33617 17105 2063 1008 13.2 11.2 24.4% 26.4% 16.3 17.0 17 18 3.3 3.1 2 2

0.26 0.44 0.18 0.34

0.22 0.35 0.15 0.26

At Least Some College 16512 1055 15.3 22.3% 15.7 16 3.5 2

0.30 0.52 0.21 0.43

Note: These statistics are calculated using the representative sub-sample of the NLSY79 WorkHistory File. For a description of the sample selection see section 2. The unit of time is a year.