The role of Career Choice in Understanding Job Mobility Ronni Pavan∗ Department of Economics, University of Rochester Harkness Hall, Rochester NY, 14627 e-mail:
[email protected] First Draft: April 2004 This Draft: July 2007
Abstract This paper presents a simple model that explains how the likelihood of job changes and their complexity changes over a worker’s career, and the empirical work presented here uses the life cycle patterns of mobility and their complexity to infer the relative importance ∗
I thank Nathaniel Baum-Snow, Jeffrey Campbell, Lars Hansen, Mario Macis, Natalia Ramondo, Alejandro Rodriguez, Robert Shimer and especially Derek Neal for helpful comments and discussions. I also thank participants of the Micro Lunch at the Federal Reserve of Chicago, of the Workshop in Empirical Economics at the University of Chicago and of the Villa Mondragone Workshop in Economic Theory and Econometrics. All remaining errors are my own.
1
of firm-specific versus career-specific concerns as determinants of mobility decisions. The estimates of the model indicate that the contemporaneous presence of two quality matches, one career-specific and one firm-specific, is necessary to understand the patterns of the data. The model performs much better than alternative models that are not characterized by a two-dimensional search process. I compare the welfare losses due to workers’ displacement predicted by the baseline model and by a model with only firm-specific matches and I find that they are around 30% smaller in the baseline model.
2
1
Introduction
An earlier literature documented important facts about patterns of job mobility. It is well understood that worker mobility between firms declines with experience, and that conditional to experience, workers mobility declines with firm seniority. However, a more recent literature explores the fact that the types of job changes that workers make also change as they gain more experience.1 For example, the percentage of job changes that involve significant changes of tasks is lower among workers with more labor market experience. This suggests that the preferences of individuals are not only related to the quality of the matches they have with their employers but also to the quality of the matches they have with the type of job they perform. This paper presents a simple model that explains how the likelihood of job changes and their complexity changes over a worker’s career, and the empirical work presented here uses the life cycle patterns of mobility and their complexity to infer the relative importance of firm-specific versus career-specific concerns as determinants of mobility decisions. In the model presented here, workers’ utility depends on career-specific and firm-specific matches. The matches are pure experience goods, and therefore they are observed only once the agent has chosen to work in a specific career or firm. A key characteristic of the model is that the matches evolve stochastically over time and their evolution helps generate the pattern of job mobility that is observed in 1
See for example Miller (1984), McCall (1990) and Neal (1999). Parnes (1954) is an earlier example.
3
the data. The two types of matches are characterized by different degrees of transferability. While a worker is always replacing the firm-specific match after a change of employer, he is replacing the career-specific match only if the new job is in a different career. The goal of this paper is to show that a simple search model where search is two-dimensional (workers are searching both for a good career and for a good employer) implies some restrictions on how job mobility changes over the life of an individual that are remarkably similar to patterns that are found in the data. These patterns would be extremely difficult to reproduce in a model without both firm and career matches. I estimate the parameters of the model using the Efficient Method of Moments (EMM). I use data on career and job durations to identify the parameters of the stochastic processes that govern the evolutions of the career and firm specific matches. Even though the model is very simple, it is able to capture remarkably well many important features of the data related to job duration and mobility patterns. It is important to note that I do not examine wages in this paper. If I included wages, I would have to explicitly model the relationship between wages and quality matches, and I would have to explicitly differentiate the role of monetary and non-monetary components. Instead, the quality matches in this paper are meant to capture both effects. Adding a richer matching structure would be extremely interesting but it would be computationally difficult to handle.2 2
In Pavan (2005), I do not include non-monetary components and I interpret the
4
It is clear that an important part of the empirical analysis is the choice of an empirical definition of career. The first solution that comes to mind is to use occupations as proxies for careers. This would not be ideal in the context of this paper. In my model, a worker changes career because he does not have a good match with it. A fraction of occupational changes that we observe in the data are related to promotions and would not satisfy this condition. I see occupational changes that are due to promotions as advancements in the same career and they are not modelled in this paper. In order to avoid the confusion between promotions and career changes, in my definition, I link a career change to a change of both occupation and industry. This choice is determined by the fact that a promotion is likely to imply a change in occupation but it is not likely to imply a change of industry - a salesman in a shoe store is likely to become a sales manager in the shoe industry much more than in any other industry. In the paper, I present a detailed discussion on the empirical definition of career change. I find that the parameters of the processes that govern the evolution of the two matches are economically important and similar in magnitudes. This result suggests that both types of matches play a substantial role in determining job mobility decisions. Using the estimates of the structural parameters, I compute several sets of counter-factual probabilities of job mobility decisions, conditional on tenure in the career and tenure in the firm. matches as productivities, using wages as noisy measures of them. This assumption limits the understanding of job mobility patterns.
5
I show that the model is indeed able to capture many dimensions of the observed pattern of job mobility. I also show that simplified versions of the model, which include either only the firm specific match or only the career specific match, perform much worse than the richer model. In the data, the probability of changing career when changing employer is greatly reduced by the fact that a worker has already experienced an employer change within the same career. One very intuitive explanation is that workers that have changed employer but decided to stay in the same career have revealed that they are satisfied with their careers. This might not be true for workers who have not changed job within the same career yet. This important feature of the data is well captured by my model and it would be very hard to capture in a model where workers are not searching for both a good career and a good employer. Workers find it optimal to discover what they do well in life before searching for where to do it and labor economists should not think of a matching process of only firms and workers, because it is key to consider also careers. This will give a richer understanding in terms of wage growth, worker displacement and optimal training programs. One advantage of estimating structural parameters is that it provides a framework for evaluating policy and welfare implications. I compute the welfare losses of displaced workers implied by the model. Welfare losses are around 30% smaller in the full model than in a model with only firm specific matches. Quite intuitively, if we do not include career matches in the model, we over-estimate the impact of components that are not transferable across 6
jobs. This welfare calculation contains information about both the pecuniary and non-pecuniary losses suffered at the time of displacement. In another experiment, I use the two-match model to see how large the welfare losses are if a displaced worker does not have the possibility to find another job in the same career. Forcing the worker to change career when displaced on average nearly doubles his welfare losses. Thus, the closure of a single plant has very different welfare implications for its workers than the closure of a whole sector of the economy. This, for example, would justify a structure of unemployment benefit that is more generous in situations where a whole sector is hit by a negative shock, rather than just a single plant. The model I develop and estimate in this paper is an extension of Neal’s (1999) model. In his model, the firm-specific and career-specific matches are constant over time. That assumption allows him to solve explicitly for the optimal policy, but also implies that if a worker stays in a firm or in a career for more than one period, he will never change again. In the same paper, Neal shows that the data gives evidence of the presence of career specific matches. Other papers have analyzed the impact of occupation-specific matches on workers’ behavior, though they focus on different aspects of the problem. Miller (1984) shows that young workers are more likely to try risky but rewarding occupations. Unfortunately, in his model the information received about one job does not give any new information about different jobs in the same occupation. McCall’s (1990) also explores occupation and firm specific match components. He shows empirically and theoretically that at a given 7
tenure in the firm, the probability of changing jobs is negatively related to the tenure in the occupation. A recent related paper is Sullivan (2005). In his model, a worker is characterized by a vector of occupational specific monetary and non-monetary returns. These values are known ex ante and the worker is allowed to search for the best employer. As the value of the occupational specific matches is known, the worker is not searching for the best career but selects at each period the occupation with the highest return. His model is able to explain why workers switch from different occupations in different parts of their lives but it is not suited to explain the patterns mentioned above. Section II presents the theoretical model. Section III contains a detailed description of the data, and the discussion of the empirical definition of career. Section IV contains the structural estimation of the model. Section V shows the comparison of the true data with the simulated data of my model and of the models with only one match. In section VI, I present some welfare analysis. In section VII, I show that observed heterogeneity could affect the results and should be addressed in future research. In section VIII, I present my concluding remarks.
2
The Model
A worker-employer relationship is characterized by two match qualities. One match quality (θit ) is specific to the career and the other (εiτ ) is specific to
8
the firm. The index t corresponds to the time spent in the same career by worker i, while the index τ is the time spent with the same employer. These match qualities are initially drawn from known normal distributions: ¡ ¡ ¢ ¢ θi1 ∼ N μθi , σ 2θ , εi1 ∼ N μεi , σ 2ε The unconditional means of these distributions is free to vary across workers. The matches follow a random walk:
θit = θit−1 + uθit , and εiτ = εit−1 + uεiτ The innovations come from known distributions: uθit ∼ N (0, η 2θ ) , and uεiτ ∼ N (0, η 2ε ). I assume that all distributions are independent of each other. The choice of normality is not crucial for the model and could be relaxed, but the choice of a distribution is needed to simulate the model. The worker derives utility from the match qualities. I assume that the utility function is linear in the value of the matches. He discounts the utility at a constant rate β, and he lives forever. In any given period he can decide to change employer or to change career. I assume that if the worker changes career he changes employer as well. I therefore rule out changes of career within the same employer. Following Parnes (1954), I define a "simple change" as a change of employer within the same career, and "complex change" a change of career and therefore of employer as well. In any period the worker could separate exogenously from his employer with probability p. 9
An exogenous separation could be caused, for example, by a plant closure. I also assume that the worker pays a search cost C every time he changes employer. At this point, I suppress the individual index i and the time indices t and τ for clarity. This is possible because tenure in the career and tenure in the firm are not state variables. The recursive problem can be written as:
V (θ, ε) = θ + ε + β {(1 − p) VNS (θ, ε) + pVS (θ)} Where VNS is the expected value of the next period if the exogenous separation does not occur, and VS is the expected value if the separation occurs. They are defined as follow3 :
VNS (θ, ε) = max {E [V (θ0 , ε0 ) |nc, θ, ε] , E [V (θ0 , ε0 ) |sc, θ] − C, E [V (θ0 , ε0 ) |cc] − C} VS (θ) = max {E [V (θ0 , ε0 ) |sc, θ] , E [V (θ0 , ε0 ) |cc]} − C where nc indicates that no employer change has occurred, sc indicates 3
The conditional expectation operators are defined as follows: µ 0 ¶ µ 0 ¶ ¡ 0 0¢ 1 θ −θ ε −ε φ φ dθ0 dε0 V θ ,ε ηθ ηε ηθ ηε µ 0 ¶ µ 0¶ Z Z £ ¡ 0 0¢ ¤ ¡ 0 0¢ 1 θ −θ ε E V θ , ε |sc, θ = φ φ dθ0 dε0 V θ ,ε ηθ σε ηθ σε µ 0¶ µ 0¶ Z Z £ ¡ 0 0¢ ¤ ¡ 0 0¢ 1 θ ε E V θ , ε |cc = φ φ dθ0 dε0 V θ ,ε σθ σε σθ σε
£ ¡ ¢ ¤ E V θ0 , ε0 |nc, θ, ε =
Z Z
10
that a simple change occurred and cc that a complex change occurred. Once a change occurs, the relevant match is drawn from an unconditional distribution. The timing is the following. At the beginning of each period a worker enjoys his matches. At the end of the period, before making any decision, the worker can be exogenously separated from his employer. If the worker is exogenously separated, his expected value for the next period is VS (θ) because he has lost the firm specific match ε. If he is not exogenously separated from his employer, the workers’ expected value is VNS (θ, ε). After observing if he did or did not receive the exogenous separation, the worker makes his job mobility decision. He then chooses the option that maximizes his lifetime utility. In one case (VNS (θ, ε)), he can choose to 1) stay with the current employer, 2) change employer within the same career or 3) change career. In the other case (VS (θ)), he can only decide whether to stay in the same career or not. Notice that every time the worker changes career or employer, he draws a new match from an unconditional distribution that does not vary with time or experience. In particular, this implies that all careers are ex-ante identical. This symmetry, although very convenient, is violated in the data where some careers are more likely to be chosen among young workers. In Miller’s model (1984), the worker is drawing a firm-specific match from distributions that are occupation specific. His estimates imply that young workers are more likely to try riskier occupations. This aspect is not addressed in this paper. This simple model delivers a very intuitive optimal policy for the worker. 11
If we define t0 and τ 0 the next period tenures in the firm and in the career, the policy can be written as: ⎧ ⎪ ⎪ (1, 1) if θ < θ∗ and ε < ε∗ (θ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ or exogenous separation occurs and θ < θ∗ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ (t + 1, 1) if θ ≥ θ∗ and ε < ε∗ (θ) 0 0 (t , τ ) = ⎪ ⎪ or exogenous separation occurs and θ ≥ θ∗ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ (t + 1, τ + 1) if ε ≥ ε∗ (θ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ and exogenous separation does not occur
The steps to derive the policy are reported in the appendix, where I also show that if θ < θ∗ , then
∂ε∗ (θ) ∂θ
< 0. A graphical example of the policy
function is reported in figure 1. The interpretation is straightforward. Poor career and employer matches induce the worker to change career. If the employer match is relatively high, 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 simple change. If both matches are high the worker is happy to keep working in the same firm.
12
3
The Data
3.1
The definition of career
The key concept needed for the empirical analysis is the empirical definition of career change. Following the literature4 , I use the US Census classification codes for industry and occupations. The first natural proxy for a career change could be the change of an occupational code. I decided not to implement this definition for the following reason. It is clear that some occupational changes are not related to bad quality matches but quite the opposite. It would be difficult to consider a promotion as a career change. In my opinion, a promotion can be seen as an occupational change along the same career path. This feature is not considered in my model. At this point, I could link all occupations that are likely to be in the same career path, but this would be extremely complicated and not free of arbitrary interpretations. I consider an alternative, and much simpler to implement, solution. In my definition, a career change implies a change of occupation and a change of industry. If a salesman in a shoe store is promoted to sales manager with a different employer, this position is very likely to be in the shoe industry. This definition of career change might still be controversial: a bus driver that becomes an engineer for a firm that produces trains would not be considered as a career change, while it should be. Nevertheless, the inclusion of this type 4
See Miller (1984), McCall (1990), Neal (1995-1999), Parent(2000), Kambourov and Manovskii (2005).
13
of errors seems of little practical consequence, in particular if compared with the gain of better selecting promotions. Using only occupations to define a career would not change drastically the job mobility patterns. More in details, my strategy to identify career changes is the following. I group 3-digit occupation codes in 50 groups and the 3-digit industry codes in 36 groups. A career change is a job change that involves a change of both occupation and industry codes. The reason for linking a change of career to a change of job is also practical. As reported in the next subsection, I estimate the model using data from the National Longitudinal Survey of Youth (NLSY). In the data set, we observe many intra-job changes of industry and occupation codes. Many times a change for A to B is followed by a change From B to A. As Neal (1999) argues, most of these changes are coding errors. I perform an extra step to reduce the probability of coding errors. I record all the occupational and industry codes used for each job and, at the time of an employer change, I compare all the codes used for the two adjacent spells. A worker changes career if all the occupation and industry codes used to describe the old job are different from all the occupation and industry codes used to describe the new job. This method may understate the number of career changes for the following reason. Codes introduced by mistakes could match codes of the next job (that otherwise would be classified as part of a different career). As a result, I could erroneously classify some complex changes as simple changes. Nevertheless, this approach minimizes the numbers of career changes due to coding errors. As I consider 50 occupational 14
codes and 36 industry groups, the latter aspect is likely to be far more important. After performing this step, the pattern observed becomes clearer; I interpret this as evidence of the reduced presence of measurement errors.5
3.2
The procedure followed to select the final data set
I use the National Longitudinal Survey of Youth to estimate the model. The first survey was conducted in 1979. It contains people who were born between 1957 and 1964; therefore the individuals entered in the sample with age between 14 and 22. I use data from 14 survey years, 1979-1992.6 In particular I use the NLSY Work History file that contains information about respondents’ weekly activities. For each week the data provides information about the employment status of the respondents. The file contains also yearly information about up to 5 jobs for each individual. This allows me to create variables such as tenure in the firm and tenure in the career. I consider only the representative sub sample of males that contains 3003 individuals. In order to prepare the data for the analysis, I have to deal with several problems: unemployment spells, missing occupation and industry codes, missing information, temporary changes of jobs (A to B to A) and so on. Here below, I report the steps I followed to construct the final version of the 5 I tried several alternative definitions of career change using the US Census classification codes. My preferred definition is also the one that produces the sharpest results in terms of observed patterns of job mobility even though they all are qualitatively similar. The results are available upon request. 6 The NLSY contains data till 2002. I decided not to use the whole sample to reduce the computational burden of the estimation. This choice is also due to the fact that in 1993 the method to record occupational codes changed in the NLSY.
15
data. In a first step, I transform the weekly data into monthly data. In each month, I select the job with the highest number of hours worked per week. I choose months as unit of time in order to be able to compare the data to the previous literature on job mobility, even though the final data set used for the estimation will have a different unit of time, as discussed later. I delete 68 individuals because their work histories do not offer any information for periods longer than 9 months, even if they are associated with a full-time job. I delete 83 individuals because they did not report their weekly activities for a period longer than 9 months. These two steps reduce the number of workers to 2849. In order to focus on mobility from the time workers first make a primary commitment to the labor market, I limit the sample to individuals who make their first long-term transition from non-work to work during the sample period. I define a worker in the labor force when he works at least 9 months for at least 30 hours per week over the last year. I delete 549 workers because they were already working full time at the beginning of the sample and 128 individuals because they never worked full time during the sampling period. At this point the sample counts 2172 individuals. I only consider jobs that involve at least 30 hours a week of work; 5.71% of the observations are deleted because they do not satisfy this restriction. I observe 10830 job changes. A more careful inspection shows that 819 job changes imply a return to an old job. In my model the worker’s decision 16
process is a renewal process and therefore it is not possible to return to a previous job. Even if I allow a worker to go back to a previous job, it would never be optimal to do so. Therefore my model is not rich enough to capture this feature of the data and including this information would overstate the number of job changes. In the vast majority of the cases, a worker returns to an old job after a very short period, for example less than three months. A worker can hold more jobs at the same time and this may sometimes produce "fake" job mobility, as jobs switch between primary and secondary over time. Other job changes could be due to temporary layoffs, seasonal jobs or also coding errors and they should be removed in order not to produce spurious results. Only in very few cases, workers go back to a previous job after a long period of time. I decided to operate as follows. If after returning to an old job, the employment spell that follows is shorter than the period that the worker spent working for the interim employer, I delete the last spell. If this period is longer, I delete the observations that separate the two spells of the same job. This reduces the number of job changes to 9376. I delete 30 workers because they held jobs that have missing information about their industry or occupation and lasted more than 6 months. Short spelled jobs often do not report occupational and industry codes, in particular jobs that last less than 9 weeks. I delete the observations with missing codes relative to those short spelled jobs (2044 observations). At this point I observe 8033 job changes and 3415 (42.5%) career changes. This number is smaller than the percentage found by Neal (55.5%) for many reasons. He compares the 17
adjacent occupational codes and the first industry codes used to describe the two subsequent jobs. He is implicitly assuming that there are no coding errors in the first observation for the industry or in the first and last observations for the occupation and therefore, he might be overstating career mobility. Another explanation is that I use wider occupational groups and more narrow industry groups.7 After merging the data with demographic information, I delete 3 individuals because they never reported their educational level. My final monthly data set counts 2139 individuals. In order to reduce the computational time needed to estimate the structural parameters, I group the data in semi-annual observations. For each period of six months, I select the job that has been worked for the longest period. This data set involves 7488 job changes and among them 3382 career changes (45.1%). The clear drawback of using biannual data is that I am under-reporting short spelled jobs. Table 1 reports some summary statistics.
4
Estimating the Model
4.1
About the Identification of the Structural Parameters
The model is characterized by the following parameter vector: 7
I reproduced all the tables presented by Neal (1999 but see errata in 2004) using my definition, and I find even stronger evidence of the presence of a career specific match than I would using his definition. These tables are not reported but are available upon request.
18
¡ ¢ ϕ0 = μθ , με , σ 2θ , σ 2ε , η 2θ , η 2ε , p, C, β
In this paper, I use only data on the durations of career and job spells. As in a standard probit, if I multiply a worker’s payoffs by a constant or if I add a constant to all of them, I do not change the ordering of the preferences and therefore I do not affect the observations. This implies that I need some normalizations. I choose to set μθ = 0, με = 0 for all individuals and σ 2θ = 1. In order to reduce the complexity of the estimation, I also choose to calibrate the parameters p and β using values commonly used in the literature. To explore the consequences of this decision I perform some sensitivity tests8 . Hence, the parameter vector I am going to estimate is ϕ = (σ 2ε , η 2θ , η 2ε , C).
4.2
The Method
I use the Efficient Method of Moments (Gallant and Tauchen 1996, Gourieroux, Monfort and Renault 1993, Gourieroux and Monfort 1996) to estimate the structural model. The idea of simulation based techniques is to choose the structural parameters that are able to generate synthetic data with similar properties to the real data. These properties are described in the "auxiliary model". Hence, an auxiliary model should provide a good description of the data. In particular, the parameters of the auxiliary model should be able to capture all the important features that the structural model is meant to 8
The main results do not vary substantially when we vary the value of the calibrated parameters. See table 3.
19
describe. As you can see in Gourieroux and Monfort (1996) and Gourieroux Monfort and Renault (1993), this estimator is consistent and asymptotically normal. This procedure also gives a specification test that follows a χ2 distribution asymptotically with dim (δ) − dim (ϕ) degrees of freedom, where δ is the vector of parameters of the auxiliary model. The auxiliary model has to provide a good statistical description of the data. I use a multinomial logit where the multiple choices are: not changing job, changing job within the same career, changing career. A well established fact is that the goodness of the estimates depends on the choice of the auxiliary model.9 To address this concern, I estimate four specifications of the multinomial logit model. The regressors I chose for every model are related to the tenures in the career and in the firm, because these variables are endogenously related to the structural parameters of the model. In the first specification, I include variables as tenure in the career and in the firm, tenures squared, experience, having already experienced one, two or more simple changes and dummies for the first periods in the career or in the firm, for a total of 22 regressors. For the other specifications, I include piecewise constant terms as explanatory variables to capture the variation in the probabilities across the two tenures.10 The second, the third and the fourth specification differ in the choice and number of these dummy variables. The 9
See Gourieroux, Monfort and Renault (1993). An example of regressor is δ ij = 1 if Ai−1 < τ ≤ Ai and Bj−1 < c ≤ Bj where τ I J is tenure in the firm, c is tenure in the career, {Ai }i=1 and {Bj }j=1 are two sequences of non-negative increasing numbers. 10
20
second specification contains 14 regressors, the third 32 and the fourth 72. The fourth specification provides a better description of the data because more informative regressors are included. The estimates of the auxiliary models are available upon request.
4.3
The Estimation Results
For any given vector of the structural parameters, I compute a numerical approximation of the value function and I use the implied policy function to simulate the data. I approximate the state variables — the career and the firm specific matches — with grids of n = 51 values each and I approximate the law of motion of the matches using a first order Markov Chain, as in Tauchen (1984). In the data, each worker is observed for a certain number of time periods and this number varies across workers. In order to reduce the distortions that might be generated by this feature, I simulate synthetic data that maintain the characteristics of the original data set. Each step of the estimation uses s = 200 simulations of the same size of the real data (the total number of observation is therefore s multiplied the number of observations contained in the original data set). The unit of time of one observation is six months. I choose such a time interval to reduce the computational time needed to estimate the model. I set the discount factor β = 0.975 and the exogenous probability of separation p = 0.015. These values imply an annual discount factor equal to 0.95 and an annual exogenous probability of
21
separation of 3%.11 The search algorithm I use is the method of simulated annealing combined with the Nelder-Mead simplex method. In table 2, I report the estimates of the structural parameters for the four specifications of the auxiliary model. The first, third and fourth specifications of the auxiliary model yield very similar estimates of the structural parameters. It is worth noting that the second specification has only 10 degrees of freedom and it is therefore the less likely to give precise estimates. This suggests that the results are pretty robust across specifications, and therefore not too sensitive to the choice of the auxiliary model. I choose the fourth specification as baseline for the remaining of the paper. The standard deviation of the initial draw is around 17% higher for the firm specific match (σε ) in the most flexible specification. The difference between the standard deviations of the innovations of the two matches is not significant (η ε and η θ ). The value of the search cost C indicates that after the first period in a new career the value of the sum of the matches is lower than the search cost with probability equal to 95%. Changing job is a costly experience. As we normalized the unconditional means of the matches to be equal to zero, the sum of the matches is to be interpreted as the sum of the ex-post rents generated by the matches. All the parameters are significant at 1% level of confidence. The estimates clearly indicates that both matches 11
The value of the exogenous probability of separation is close to the one estimated by Nagipal (2003).
22
are important to describe job mobility decisions of workers. I investigate the robustness of the results varying the magnitudes of the calibrated parameters. I estimate the fourth specification setting the annual discount factor equal to 0.9 and 0.99, and setting the annual probability of separation equal to 1% and 5%.
The results are reported in table 3. As
you can see, a higher β implies a slightly higher search cost C. The other parameters do not change sensibly when we vary the value of the calibrated parameters. Varying the exogenous probability of separation p has the same small effect on the estimates, but a bigger effect on the χ2 statistic.12
5
Evaluating the Performance of the Model
Looking at the specification test that is reported in the last line of table 2, you can notice that the structural model is always rejected. This rejection means that the estimates of the auxiliary model obtained using the synthetic data are statistically different from the estimates obtained using the real data. Is the model failing to describe important features that we observe in the data, or is the rejection coming from a statistical difference between parameters that are nevertheless similar? In order to answer the question, I use the data to calculate three sets of probabilities that are key in describing 12 I perform two extra robustness checks. In the first test, I include the parameter p in the estimation. The estimated value of p is close to an annual 4.8% and the other parameter estimates are very close to the estimates of the baseline model. In the second test, I included a drift in the evolution of the matches. The career-specific drift is positive while the firm-specific drift is negative but much smaller in magnitude. The χ2 statistic improves sensibly. See table 11.
23
the empirical facts. These are the probability of a job change, either simple or complex, the probability of a complex change and the probability of a complex change given that a change is observed. I compute each probability conditional on the career and firm tenure for the first five years (15 cells). I then simulate data using the estimates for the fourth specification and I calculate the same probabilities. The results are reported in tables 4 to 6 and are discussed below. A crucial point that this paper wants to underline is the importance of the contemporaneous existence of both matches and their interactions. Most of the previous literature on job mobility concentrates on models with only firm specific characteristics. Is such a model able to reproduce the pattern above? On the other extreme, a part of the recent literature on the specificity of human capital (industry specific or occupation specific) suggests that the firm specific human capital is not important for workers.13 Is a model with only career specific human capital able to explain the complexity of job mobility? In the appendix, I develop two alternative models. In the first alternative model, the relationship between a worker and a job is characterized only by a firm-specific match, and changes of career are exogenous. In the second alternative model, such relationship is characterized only by a career-specific match, and within career changes of employer are exogenous. I estimates both models and, using the estimates of the structural parameters, I compute the same three sets of probability mentioned above. The structural estimates 13
See for example Neal (1995) or Kambourov and Manovskii (2002).
24
are shown in table 7.14 The results are reported in tables 4 to 6 and are discussed next. The probability of a job change - Table 4 reports the probability of a job change, either simple or complex (see also figure 2). In the data (upper left), the probability declines with firm tenure, given career tenure and with career tenure conditional on firm tenure, even though the magnitude is smaller. The model (upper right) captures very well the decline in both dimension. The decline with career tenure, given firm tenure, is slightly sharper than in the real data. Bold numbers are not statistically different from the ones constructed with real data. Nearly all probabilities are not statistically different from the real ones. The model with only the firm specific match (lower left) predicts a decline with firm tenure while the probability of a job change is unaffected by the tenure in the career. The decline with firm tenure is too sharp and, as a result, nearly all probabilities are statistically different from the real ones. The model that includes only the career-specific match (lower right) predicts a too sharp decline with career tenure while firm tenure has a negligible effect on the probabilities. Also in this case, nearly all probabilities are statistically different from the real probabilities. The probability of a complex change - Table 5 reports the probabilities of a complex change, that is a change of firm and career (see also figure 3). The diagonal terms have a very different meaning from the off-diagonal 14
Note also that the χ2 statistics are four/five times bigger than in the original model.
25
terms. The workers in the diagonal never experienced a simple change, that is a change of firm within the same career. Workers off the diagonal did experience it, and therefore are more likely to have found a good career match. It is not surprising that the diagonal probabilities are in general much higher, in particular when tenure is not high. These probabilities declines with career tenure and they show a jump after the first simple change. The diagonal probabilities decline very sharply. The model captures very well all these feature. The model with only the firm specific match does not predict a jump when leaving the diagonal. The absence of the off-diagonal jump is particularly interesting, because it is a clear consequence of the two-dimensional search process of workers. The model with only the career specific match performs much better. Notice, though, that even in this case there is no evidence of an off-diagonal jump in the probabilities. The probability of a complex change given that a job change occurred Table 6 reports the probability of a complex change given that a job change occurred (see also figure 4). As in the previous set of probabilities, the diagonal terms have a particular meaning. Also in this case, we observe a big difference between workers who already experienced a simple change and workers who did not. Given the tenure in the firm, who has already experienced a simple change has a probability of leaving the career when changing job around 50% lower than who has not experienced it. The probabilities in the diagonal are declining sharply while the pattern of the probabilities 26
given career tenure, but off the diagonal, is not clear. The model is able to reproduce the big drop in the probability of leaving the career after experiencing a simple change. The decline in the diagonal terms is not as steep as in the real data. Given career tenure, the probabilities are increasing with firm tenure, while there was no clear path in the real data. Conditioning on firm tenure, there is a decline with career tenure like in the real probabilities. By construction, the model with only firm specific matches predicts that the probability is not affected by the tenure variables. The model with only career specific match works better than the previous, but it does not predict a jump off the diagonal.
6
Some Welfare Analysis
The model presented in this paper provides a valid framework to analyze welfare losses of displaced workers. The literature that addresses this issue evaluates welfare losses from the reduction in wages that displaced workers suffer. A wage approach is not able to capture the importance of nonpecuniary components of the loss. This model incorporates all aspects of the loss, pecuniary and non pecuniary. The under-identification of the parameter vector limits the type of information one can retrieve from the model. Nevertheless, I can identify the expected percentage of lifetime utility due to rents, defined as the difference between the value of a match and its unconditional mean, that is lost at the time of displacement. The losses are defined
27
as follow:
loss (θ, ε) =
max {V1 (θ, ε) , V2 (θ) , V3 } − max {V2 (θ) , V3 } max {V1 (θ, ε) , V2 (θ) , V3 }
where V1 (θ, ε) is the value function associated with staying in the firm, V2 (θ) is the value function associated with a simple change and V3 is the value function associated with a complex change. The value functions are interpreted as lifetime utility due to rents because we normalized the unconditional averages of the matches to be equal to zero. In appendix D, I provide the exact analytical expression of this statistic and I show its identification. These statistics are invariant to linear transformations of the utility function, which is the standard requirement in an expected utility framework. In order to calculate the statistic above, I simulate a large number of observations and, using the simulated values of the matches, I compute the value function for each worker at each period. Finally, I compute the averages of the implied individual losses, conditioning on the relevant variables. In the second column of table 8, I show how this percentage varies with experience. The welfare loss is relatively low after the first year, around 3%, but it grows fast and after 4 years reaches nearly 8%. After 10 year, the loss is around 10%. In the first column, I report the losses predicted by a model with only firm-specific matches. The losses are 25% higher in the first period, and they become 50% higher after 10 years. In the third column, I compute the welfare losses that a worker would
28
experience if, after displacement, he did not have the possibility of finding a new job in the same career. The losses are nearly twice as big and they are also sensibly bigger than the losses produced by the model with only firm specific matches. This last column provides very interesting results, underlying the difference between a normal plant closure and a major structural change in the economy. In this second case, certain careers may disappear and the welfare losses of workers may be much higher. For instance, as a policy maker is normally able to distinguish the two cases, an optimal unemployment insurance could take this difference into account. In table 9 and 10, I perform similar experiments, conditioning both on experience and tenure in the firm. I choose to condition on these two variables because in many data sets the tenure in the career is not available. In table 9, I compare the baseline model to the model with only firm matches. If tenure in the firm is less or equal to one year, the two models give very similar welfare losses, around 4%. The two models imply very different losses with higher levels of tenure. When both tenure and experience are high, the loss can be as big as 12% for the two-match model and nearly 20% for the onematch model. In table 10, I compare the losses implied by baseline model in the case the worker has or has not the possibility of finding a new job in the same career. The differences between the two situations are bigger when tenure in the firm is low but experience is high (they are nearly three times as big). In this case, the worker is more likely to have found a good career match but not a good firm match. The difference between the two types 29
of displacement reaches the minimum when tenure in the firm is very high. Here, the second model predicts losses that are "only" 55% higher and are around 19% in absolute value. This is due to the fact that, when tenure is high, also the firm match is likely to be a good match.
7
Extensions: Observed ex-ante Heterogeneity
In my model, every agent is characterized by the same parameters. In a more general set-up, ex-ante different people might be characterized by different structural parameters. Leaving to future research the role of unobserved exante heterogeneity, I study here how some observed variables affect workers’ behavior. In particular, I investigate the effect of schooling and race. The results are reported in table 12. I first select only workers that have a college degree. Due to limited number of individual, 581, I decided to use the second specification for the auxiliary model15 . The firm-specific standard errors are higher than using the whole sample, and the standard error of the careerspecific innovation is lower. This could mean that schooled workers have better information about their careers and therefore most of the variation in the attractiveness of their jobs comes from firm specific components. Also the search cost is higher, indicating that educated workers change job less 15
Some of the dummies of the fourth specification were not identified because of the small sample.
30
frequently. I then estimate the model for workers that do not get a college degree. As expected, the career specific components are more volatile and the search cost is lower. In the last estimation, I exclude blacks and college graduated from the sample. The results are very similar to the previous ones. The career specific variances are slightly higher but the differences are not statistically significant. This might depend on the limited number of observations for black workers, given that my data set have only 231 black workers without college degree.
8
Conclusions
In this paper I develop a model that aims to explain the patterns of job mobility in relation to workers’ career choices. Each worker-job relationship is characterized by a time-varying career-specific match and a time-varying firm-specific match. These matches evolve as random walks. I estimate the structural parameters of the model using Efficient Method of Moments. In order to test how the results vary with the choice of the auxiliary model, I estimate the model using different specifications of multinomial logits where the choices are: to change career, to change firm within the same career and to keep the job. To evaluate the performance of the model, I compute three set of probabilities conditional on career and firm tenure. These are the probability of a job change, the probability of a complex change and the probability of a complex change given that a job change occurs. The
31
simulated probabilities resemble the real probabilities. In order to show that the key aspect of this result is the existence of both types of matches, I develop and estimate a model with only firm specific matches and a model with only career specific matches. The simulated probabilities of these two models are not able to capture the patterns of the real probabilities. Some calculations show that welfare losses at the time of displacement grow rapidly with experience. A model with only firm specific matches would overstate the losses by around 30%. These losses can be much higher, between 55 and 170%, if a worker does not have the possibility of finding a new job within the same career. A structural change in the economy is likely to cause higher individual welfare losses that a simple plant closure. Future research should address the issue of ex-ante heterogeneity. In a preliminary study I find that firm specific components are relatively more important than career specific components for college graduates. A natural explanation for this fact could be that college graduates have better information about their available careers.
32
References [1] Altonji, G., R. Shakotko (1987). "Do Wages Raise with Seniority?." The Review of Economic Studies 54-3:437-59. [2] Flinn, C.J. (1986). "Wages and Job Mobility of Young Workers". The Journal of Political Economy 94-3. [3] Gourieroux, C., A. Monfort and E. Renault (1993). "Indirect Inference." Journal of Applied Econometrics 8: S85-S118. [4] Gallant, R., G. Tauchen (1996). "Which Moments to Match?" Econometric Theory 12:657-81. [5] Gibbons, R., L.F. Katz, T. Lemieux, and D. Parent (2002). "Comparative advantage,learning, and sectorial wage discrimination." NBER Working Paper 8889. [6] Gourieroux, C., A. Monfort (1996). Simulation-Based Econometric Methods. Oxford University Press. [7] Harber, H. (1994). "The Analysis of Interfirm Worker Mobility. " Journal of Labour Economics 12-4: 554-93. [8] Jovanovic, B. (1979). "Job Matching and the Theory of Turnover”, The Journal of Political Economy 87: 972-90. [9] Judd K.L. (1999). Numerical Methods in Economics. The MIT Press.
33
[10] Kambourov, G., I. Manovskii (2002). "Occupational Specificity of Human Capital", Working Paper. [11] McCall, B. (1990). "Occupational Matching: A Test of Sorts." The Journal of Political Economy 98: 45-69. [12] Miller, R. (1984). "Job matching and Occupational Choice." The Journal of Political Economy 92 : 1086-120. [13] Nagypal, E. (2003). "Learning by Doing Versus Learning About Match Quality: Can We Tell Them Apart?." Northwestern University, Department of Economic, Working Paper. [14] Neal, D. (1995). "Industry-Specific Human Capital: Evidence from Displaced Workers." Journal of Labor Economics 13: 653-77. [15] Neal, D. (1999). "The Complexity of Job Mobility among Young Men." Journal of Labour Economics 17-2: 237-61. [16] Neal, D. (2004). "Erratum." Journal of Labour Economics 22-2: 523-24. [17] Parent, D. (2000). "Industry-Specific Capital and the Wage Profile: Evidence from the National Longitudinal Survey of Youth and the Panel Study of Income Dynamics." Journal of Labour Economics 18-2: 306-23. [18] Sullivan, P. (2005). "A Dynamic Analysis of Educational Attainment, Occupational Choice, and Job Search." Working Paper.
34
[19] Tauchen, G.E. (1984). "Finite State Markov Chain Approximations to Univariate and Vector Autoregressions." Working Papers in Economics 84-09, Department of Economics, Duke University. [20] Topel, R., M. Wald (1988). "Job Mobility and The Career of Young Men." Quarterly journal of Economics 107: 439-79. [21] Topel, R. (1991). "Specific Capital, Mobility, and Wages: Wages Raise with Job Seniority." The Journal of Political Economy 99-1:145-76.
35
A
Appendix
A.1
Derivation of the policy function
Consider VF (θ). The second term in the max operator is constant, while the first term is continuous and increasing in θ16 , because θ affects the conditional distribution of θ0 . Therefore, there is a θ∗ such that E [V (θ0 , ε0 ) |sc, θ∗ ] = E [V (θ0 , ε0 ) |cc]. We can write: ⎧ ⎪ ⎨ E [V (θ0 , ε0 ) |sc, θ] M (θ) = ⎪ ⎩ E [V (θ0 , ε0 ) |cc]
if θ ≥ θ∗ if θ < θ∗
VF (θ) = M (θ) − C
Consider now VNF (θ, ε). Using the previous result we can rewrite VNF (θ, ε) as follow:
VN F (θ, ε) = max {E [V (θ0 , ε0 ) |nc, θ, ε] , M (θ) − C} Then, using the fact that the value function is continuous and increasing 16
Existence and continuity of the value function can be easily shown if the support of the distributions is bounded or the utility function is bounded. We can think at it as an aproximation of the normal distribution where the tail is truncated at a very high, in absolute value, number. The value function is increasing in the 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.
36
in the value of both matches, there will exist a unique ε∗ (θ) such that: ⎧ ⎪ ⎨ E [V (θ0 , ε0 ) |nc, θ, ε] if ε ≥ ε∗ (θ) VN F (θ, ε) = ⎪ ⎩ M (θ) − C if ε < ε∗ (θ)
If ε = ε∗ (θ) and θ < θ∗ we can write:
E [V (θ0 , ε0 ) |nc, θ, ε∗ (θ)] = E [V (θ0 , ε0 ) |cc] Using the implicit function theorem and assuming, without loss of generality, that the unconditional mean of the matches is non negative: h ³ 0 ´ i 0 0 θ −θ ∗ E V (θ |nc, θ, ε , ε ) × (θ) 2 ∂ε (θ) η ³ θ ´ i <0 =− h 0 ∂θ ∗ (θ) |nc, θ, ε E V (θ0 , ε0 ) × εη−ε 2 ∗
ε
A.2
Alternative Models
Only Firm Specific Match - The relationship between a worker and a firm is described by a match that evolves as a random walk: ¡ ¡ ¢ ¢ εi1 ∼ N μεi , σ 2ε , εit = εit−1 + uεit , uεit ∼ N 0, η 2ε where t is tenure in the firm. The utility of the worker is linear in the value of the match. The recursive problem can be written as:
V (ε) = ε+β {(1 − p) max {E [V (ε0 ) |nc, ε] , E [V (ε0 ) |jc] − C} + p (E [V (ε0 ) |jc] − C)} 37
where jc indicates a job change, p is the exogenous probability of separation and the expectations are defined as usual. If the worker does not suffer the exogenous separation he can decide to stay with the current employer or to change employer. The optimal policy of the worker is t0 = 1 if ε < ε∗ or exogenous separation occurs, t0 = t + 1 if ε ≥ ε∗ and exogenous separation / does not occur. The tenure in the career τ evolves as follows: if t0 = t + 1, then τ 0 = τ +1. If t0 = 1, then τ 0 = τ +1 with probability 1−pc , τ 0 = 1 otherwise. The parameter pc is the exogenous probability of changing career when a change occurs. As for the baseline model, I set β = 0.975 and p = 0.015. I also normalize με = 0 and σ ε = 1. I estimate with the same EMM procedure the parameter vector Ωf = (η ε , C, pc ). I use the fourth specification of the auxiliary model. The results are reported in table 7. Notice that the χ2 test statistic is nearly 5 times bigger than the χ2 test statistic of the baseline model. Only Career Specific Match - The relationship between a worker and a career is described by a match that evolves as a random walk: ¡ ¡ ¢ ¢ θi1 ∼ N μiθ , σ 2θ , θit = θit−1 + uθit , uθit ∼ N 0, η 2θ where τ is tenure in the career. The utility of the worker is linear in the value of the match. The value function is:
V (θ) = θ + β max {E [V (θ0 ) |nc, θ] , E [V (θ0 ) |cc] − C}
38
and the expectations are defined as usual. The worker can decide to either stay with the current career or change career. The optimal policy of the worker is: t0 = 1 if θ < θ∗ , t0 = t + 1 if θ ≥ θ∗ . The tenure in the firm τ evolves as follow: if t0 = 1, then τ 0 = 1. if t0 = t + 1, then τ 0 = τ + 1 with probability 1 − pf − p, τ 0 = 1 otherwise. To maintain the comparability with the other two models, I still include the parameter p. Notice that the exogenous separation is the only reason to change employer within the same career. I set β = 0.975 and p = 0.015 and normalize μθ = 0 and σ θ = 1. I estimate with the usual EMM procedure the parameter vector Ωc = (η θ , C, pf ). I use the fourth specification of the auxiliary model. The results are reported in table 7. The χ2 test statistic is 4 times bigger than the χ2 test statistic of my model and it is considerably smaller than the test statistic of the model with only the firm specific match.
A.3
Welfare Calculation
Consider the lifetime utility of the worker W (θ, ε/Ω ) for a given pair (θ, ε), where the complete parameter vector is Ω = (μθ , με , σ 2θ , σ 2ε , η 2θ , η 2ε , p, C, β). As I stated in the paper, this is not identified. It can be shown that the following relation holds:
W (dθ + kθ, dε + kε|Ω0 ) =
dθ + dε + kW (θ, ε|Ω ) 1−β
where Ω0 = (dθ + μθ , dε + με , kσ 2θ , kσ 2ε , kη 2θ , kη 2ε , p, kC, β). I need to nor39
malize the unconditional means and a variance (I choose σ θ ). ˜ 0 = (μθ , με , σ 2 , σ 2ε , η 2 , η 2ε , p, σ θ C, β) Consider now the two parameter vectors Ω θ θ ´ ³ 2 η2 η2 σ ˜ = 0, 0, 1, ε2 , θ2 , ε2 , p, C2 , β . Notice that the two vectors cannot be and Ω σ σ σ σ θ
θ
θ
θ
identified in the data. Define the following:
V1 = = V2 = =
³ ´ EW μθ + σ θ θ, με + σ θ ε|Ω˜ 0 ,μθ +σθ θ−1 ,με +σθ ε−1 ´ ³ μθ + με + σ θ EW θ, ε|Ω,θ ˜ −1 ,ε−1 1−β ´ ³ E1 W μθ + σ θ θ, με + σ θ ε|Ω˜ 0 ,μθ +σθ θ−1 − σ θ C ´ ³ μθ + με + σ θ E1 W θ, ε|Ω,θ ˜ −1 − σ θ C 1−β
V3 = E11 W (μθ + σ θ θ, με + σ θ ε|Ω˜ 0 ) − σ θ C μθ + με + σ θ E11 W (θ, ε|Ω˜ ) − σ θ C 1−β ³ ´ = EW θ, ε|Ω,θ ˜ −1 ,ε−1 ´ ³ = E1 W θ, ε|Ω,θ ˜ −1 − C
= V˜1 V˜2
V˜3 = E11 W (θ, ε|Ω˜ ) − C
Because of the under-identification of the model, the two sets of value functions V˜1 , V˜2 and V˜3 and V1 , V2 and V3 cannot be told apart. Using the property above, I can show that the statistic used in the welfare calculation would be the same for both sets of value functions and therefore it is identified
40
by the data: o n o n ˜1 , V˜2, V˜3 − max V˜2, V˜3 max V max {V1, V2, V3 } − max {V2, V3 } n o =E E θ +με max {V1, V2, V3 } − μ1−β max V˜1 , V˜2, V˜3 This statistic represents the percentage of lifetime utility due to rents (the part of the matches that is above the unconditional mean) that is lost when a worker is displaced. Column 2 of table 8 reports this statistic when the operator E is conditional on experience. In column 3, I report the following statistic:
o n max V˜1 , V˜2, V˜3 − max V˜3 o n E ˜ ˜ ˜ max V1 , V2, V3
This represents the percentage loss when the worker is forced to change career too. In column 1, I report the percentage loss for the model with only the firm specific match. It is computed similarly. In table 9 and 10, I report the 3 statistics conditional on both experience and tenure in the firm.
41
B
Tables and Figures Figure 1
STAY
ε*(θ)
FIRM MATCH
ε CHANGE CAREER
CHANGE FIRM
θ*
CAREER MATCH θ
Table 1: Summary Statistics Variables Number of workers
2139
Number of observations (worker/period) Number of observations per worker
40443 18.9
Change of job Change of career
19.5% 8.8%
Change of career given change of job Average employer spell (in years)
45.1% 2.1
Average career spell (in years)
3.7
Average number of jobs per worker Average number of careers per worker Black
4.5 2.6 12.2%
College or more
27.1%
Note: This data set is obtained using NLSY. I select only full time male workers. The unit of time six months. A career change is roughly defined as a change of employer, occupation and industry.
42
Table 2: Estimation Results Parameters (σθ=1) Specification 1 Specification 2 Specification 3 Specification 4 1.12***
1.29***
1.15***
1.17***
(0.046)
(0.072)
(0.013)
(0.022)
1.55***
2.11***
1.52***
1.50***
(0.115)
(0.144)
(0.060)
(0.058)
ηε
1.51***
4.07***
1.58***
1.63***
(0.055)
(0.418)
(0.049)
(0.042)
C
2.53***
1.62***
2.51***
2.55***
(0.128)
(0.164)
(0.306)
(0.050)
σε ηθ
Degrees of Fredoom χ2
18
10
28
68
206.29
55.92
197.41
225.51
Note: the numbers in parenthesis are the standard errors. The data set used for the estimation of the structural parameters is obtained using NLSY. Only full time male workers are selected. The unit of time six months. In this estimation, I set p=0.015 (3% yearly) and β=0.975 (0.95 yearly). The last row contains the statistics associated with the specification test. Each column contains the estimates for a different specification of the auxiliary model. I use specification 4 as baseline. *=significant at 10% level. **=significant at 5% level. ***=significant at 1% level.
Parameters
Table 3: Robustness Checks β =0.9 p =0.03 β2=0.99 p2=0.03 β2=0.95 p2=0.01 2
2
β2=0.9 p2=0.05
1.13***
1.22***
1.17***
1.17***
(0.015)
(0.027)
(0.027)
(0.015)
1.52***
1.50***
1.50***
1.53***
(0.061)
(0.069)
(0.051)
(0.052)
ηε
1.58***
1.70***
1.74***
1.49***
(0.040)
(0.045)
(0.066)
(0.044)
C
2.31***
2.73***
2.34***
2.76***
(0.074)
(0.071)
(0.083)
(0.131)
σε ηθ
D. of F. χ2
68
68
68
68
226.22
225.71
271.05
216.1
Note: the numbers in parenthesis are the standard errors. The data set used for the estimation of the structural parameters is obtained using NLSY. Only full time male workers are selected. The unit of time six months. In the first two columns, I explore the effect of changing the calibration value of the discount factor β on the estimates of the structural parameters. In the last two columns, I explore the effect of varying the calibrated value of the probability of an exogenous separation. *=significant at 10% level. **=significant at 5% level. ***=significant at 1% level.
43
Years
Real Data
Simulated Data
Tenure in the firm
Tenure in the firm
1
2
3
4
1
28.94
2
29.24 22.85
3
26.39 20.32 13.09
4
24.12 20.65 14.34 10.53 21.15 17.33 13.77 9.12
5
Tenure in the career
Tenure in the career
Table 4: Probability of a job change (either complex or simple)
5
9.27
Years
1
2
25.59 20.98
3
23.51 18.12 13.24
4
22.62 17.31 12.21 21.88 16.72 11.76
5
1
25.22
2
25.55 16.47
3
25.61 16.06 10.06
4
25.5 15.47 25.02 15.91
5
9.76 9.81
5
9.83 9.35
7.69
Tenure in the firm
3
4
7.42 7.25
Tenure in the career
Tenure in the career
2
4
Only Career Specific Match
Tenure in the firm 1
3
29.63
Only Firm Specific Match Years
2
1
5
6.01
Years
1
2
1
26.26
2
21.03 20.96
3
4
5
17.6 17.51 17.44
3
16.14 15.64 15.67 15.72 15.18 14.98 14.63 14.69 14.58
4 5
Note: The tables above contain the empirical probabilities of observing a job change conditional on tenure in the firm and tenure in the career. The data set used for the first quadrant is obtained using NLSY. Only full time male workers are selected. The data used for the second quadrant is obtained simulating the structural model with career and firm specific matches. The third and fourth quadrants use data simulated by the models with only firm-specific or only career-specific matches, alternatively. The bold numbers in the last three quadrants indicate that the percentages are not statistically different from the percentages reported in the first one. Figure 2: Probability of a Job Change 35%
30%
Real Probabilities if career tenure <=2 years
Probabilities
25%
Simulated Probabilities if career tenure <=2 years
20% Simulated Probabilities if career tenure >5 years
15%
Real Probabilities if career tenure >5 years
10%
5%
0% 0
1
2
3
4
5
6
7
8
9
Tenure in the Firm in years
44
10
11
12
13
14
15
Years
Real Data
Simulated Data
Tenure in the firm
Tenure in the firm
1
2
3
4
Tenure in the career
Tenure in the career
Table 5: Probability of career change
5
18.1
1
9 12.24
2 3
8.9
6.49
5.52
4
6.17 5.18
5.04 4.38
4.1 4.68
5
4.33 1.18
2.92
Years
1
1
9.82 11.54
3
6.18
6.71
6.72
4
4.62 3.57
4.92 3.74
4.52 3.54
5
1
11.29
2
11.32
7.35
3
11.39
7.05
5
4.76 3.52
3.59
4
5
Tenure in the firm
3
4
Tenure in the career
Tenure in the career
2
4
Only Career Specific Match
Tenure in the firm 1
3
2
Only Firm Specific Match Years
2
18.68
5
4.48
Years
1
1
2
3
18.21
2
12.2 12.05
3
8.27
8.05
7.96
11.36 6.97 4.31 3.28 4 6.51 5.94 5.84 5.91 5 5 5.24 5.02 4.71 4.72 4.68 11.2 7.12 4.36 3.14 2.66 Note: The tables above contain the empirical probabilities of observing a career change conditional on the tenure in the firm and the tenure in the career. The data set used for the first quadrant is obtained using NLSY. Only full time male workers are selected. The data used for the second quadrant is obtained simulating the structural model with career and firm specific matches. The third and fourth quadrants use data simulated by the models with only firm-specific or career-specific matches, alternatively. The bold numbers in the last three quadrants indicate that the percentages are not statistically different from the percentages reported in the first one. 4
Figure 3: Probability of a complex change 20% Simulated probability of a complex change if tenure in career <=2 years
18% 16% 14%
Real probability of a complex change if tenure in career <=2 years
Probability
12% 10% 8% 6%
Simulated probability of a complex change if tenure in career >5 years
Real probability of a complex change if tenure in career >5 years
4% 2% 0% 0
1
2
3
4
5
6
7
8
Tenure in firm in years
45
9
10
11
12
13
14
15
Years
Real Data
Simulated Data
Tenure in the firm
Tenure in the firm
1
2
3
4
5
1
62.54
2
30.77 53.58
3
33.73 31.93 42.18
4
25.57 24.41 28.57 41.09 24.49 25.3 33.96 12.9 31.54
5
Tenure in the career
Tenure in the career
Table 6: Probability of career change given that a job change occurs
Years
1
3
38.37 54.99
3
26.28
4
20.41 28.45 36.97 48.41 16.29 22.39 30.06 37.63 46.68
5
37 50.74
Tenure in the firm 4
5
1
44.78
2
44.29 44.63
3
44.48 43.91 44.56
4
44.55 45.06 44.15 44.22 44.76 44.78 44.47 43.33 44.35
5
5
Only Career Specific Match
Tenure in the career
Tenure in the career
2
4
2
Tenure in the firm 1
3
63.03
Only Firm Specific Match Years
2
1
Years
1
2
3
4
5
1
69.34
2
58.01 57.48
3
46.99 45.99 45.65
4
40.36 37.99 37.28 37.6 34.54 33.54 32.18 32.15 32.14
5
Note: The tables above contain the empirical probabilities of observing a change of career given that a job change occurs. The probabilities are conditional on tenure in the firm and tenure in the career. The data set used for the first quadrant is obtained using NLSY. Only full time male workers are selected. The data used for the second quadrant is obtained simulating the structural model with career and firm specific matches. The third and fourth quadrants use data simulated by the models with only firmspecific or career-specific matches, alternatively. The bold numbers in the last three quadrants indicate that the percentages are not statistically different from the percentages reported in the first one.
Figure 4: Probability of a complex change given a job change 70% 65% Real probability of a complex change if no simple changes previously experienced
60%
Simulated probability of a complex change if no simple changes previously experienced
55%
Probability
50% Simulated probability of a complex change if has previously experienced a simple change
45% 40%
Real probability of a complex change if has previously experienced a simple change
35% 30% 25% 20% 0
1
2
3
Tenure in career in years
46
4
5
Table 7: Estimation of Alternative Models Parameters (σθ=1) Only Firm Specific Match Only Career Specific Match 0.45***
pc
-
(0.008) pf
-
0.10***
ηθ
-
1.09***
ηε
1.88***
(0.002) (0.030) -
(0.063) C Degrees of Fredoom χ2
0.93***
3.86***
(0.030)
(0.099)
68
68
1108.51
937.23
Note: the numbers in parenthesis are the standard errors. The data set used for the estimation of the structural parameters is obtained using NLSY. Only full time male workers are selected. The unit of time six months. In this estimation, I set p=0.015 (3% yearly), β=0.975 (0.95 yearly). The fourth specification of the auxiliary model is used. I report the structural estimates for a model with only firm-specific matches in the first column, and for a model with only career-specific matches in the second column. The details on the specifications of the two models are in the appendix. *=significant at 10% level. **=significant at 5% level. ***=significant at 1% level.
Table 8: Simulated implied welfare losses at the time of displacement Experience
Loss at Displacement
Loss at Displacement if
in years
Only Firm Match
Firm and Career Match
1
4.07%
3.27%
Career shuts down 6.31%
2
7.83%
5.51%
10.47%
3
10.10%
6.89%
12.86%
4
11.51%
7.74%
14.29%
5
12.58%
8.39%
15.36%
6
13.25%
8.79%
16.02%
7
13.74%
9.08%
16.48%
8
13.99%
9.24%
16.70%
9
14.12%
9.33%
16.81%
10 14.04% 9.26% 16.64% Note: This table reports the extected percentage of lifetime utility due to rents that is lost at the time of displacement. In the model, displacement occurs when the worker is hit by an exogenous separation. In order to calculate these percentages, I simulate data using the estimated structural model. The simulated sample is 100 times bigger that the real data set. For each worker at each time period, I simulate the value of each one of his options: 1) staying in the current job, 2) changing employer and career and 3) changing employer but not career. In the first column, I report the losses implied by the model with only firm specific matches. In the second column, I report the losses implied by the baseline model with career and firm specific matches. In the third column, I report the losses implied by the baseline model, if the worker did not have the option of finding a new job in the same career if exogenously separated. The expected losses are conditional on the years of labor market experience.
47
Exp.
Table 9: Simulated implied welfare losses. Comparison between models Tenure in the Firm
(years)
1
1
3.3%
2
3.8% 7.3%
Baseline model
4.2% 10.7%
Only Firm Match
2
3
4
5
6
7
8
9
10
4.1%
3
4.0% 7.8%
9.9%
4.3% 10.9% 14.7%
4
4.2% 8.0%
10.2% 11.1%
4.2% 10.8% 14.6% 16.8%
5
4.3% 8.1%
10.4% 11.4% 11.9%
4.2% 10.8% 14.6% 16.9% 18.3%
6
4.3% 8.1%
10.4% 11.5% 11.9% 12.2%
4.1% 10.6% 14.5% 16.6% 18.0% 19.1%
7
4.4% 8.2%
10.4% 11.5% 12.1% 12.3% 12.3%
4.1% 10.6% 14.3% 16.5% 17.9% 18.8% 19.6%
8
4.3% 8.1%
10.3% 11.5% 12.0% 12.4% 12.4% 12.3%
4.0% 10.3% 14.1% 16.2% 17.5% 18.6% 19.2% 19.8%
9
4.3% 8.0%
10.3% 11.4% 12.0% 12.3% 12.4% 12.4% 12.2%
3.9% 10.1% 13.8% 15.9% 17.2% 18.2% 18.8% 19.4% 19.8%
10
4.2% 7.8%
10.0% 11.2% 11.7% 12.1% 12.1% 12.1% 12.2% 11.9%
3.8% 9.8% 13.2% 15.3% 16.7% 17.6% 18.2% 18.8% 19.3% 19.5% Note: This table reports the extected percentage of lifetime utility due to rents that is lost at the time of displacement. In the model, displacement occurs when the worker is hit by an exogenous separation. In order to calculate these percentages, I simulate data using the estimated structural model. The simulated sample is 100 times bigger that the real data set. For each worker at each time period, I simulate the value of each one of his options: 1) staying in the current job, 2) changing employer and career and 3) changing employer but not career. The expected losses are conditional on the years of labor market experience and on the tenure in the firm. Tenure in the career is not generally available in most data sets. In each cell, I compare the losses implied by the baseline model (first number in the cell) to the losses implied by the model with only firm-specific matches (second number in the cell).
48
Table 10: Welfare losses. Comparison between plant closure and structural change Exp. Tenure in the Firm (years)
1
1
3.3%
2
3.8%
2
3
4
5
6
7
8
9
10
6.3% 7.3%
Baseline model
8.4% 12.6%
3
4.0%
7.8%
Career Shuts down 9.9%
9.6% 14.1% 16.1%
4
4.2%
8.0%
10.2% 11.1%
10.3% 14.9% 17.1% 17.7%
5
4.3%
8.1%
10.4% 11.4% 11.9%
10.9% 15.4% 17.8% 18.6% 18.7%
6
4.3%
8.1%
10.4% 11.5% 11.9% 12.2%
11.2% 15.8% 18.1% 19.1% 19.1% 19.1%
7
4.4%
8.2%
10.4% 11.5% 12.1% 12.3% 12.3%
11.5% 16.0% 18.3% 19.2% 19.6% 19.5% 19.2%
8
4.3%
8.1%
10.3% 11.5% 12.0% 12.4% 12.4% 12.3%
11.6% 16.0% 18.3% 19.4% 19.6% 19.8% 19.5% 19.0%
9
4.3%
8.0%
10.3% 11.4% 12.0% 12.3% 12.4% 12.4% 12.2%
11.6% 16.0% 18.3% 19.3% 19.7% 19.8% 19.6% 19.5% 18.9%
10
4.2%
7.8%
10.0% 11.2% 11.7% 12.1% 12.1% 12.1% 12.2% 11.9%
11.4% 15.6% 18.1% 19.1% 19.2% 19.5% 19.3% 19.1% 19.2% 18.5% Note: This table reports the extected percentage of lifetime utility due to rents that is lost at the time of displacement. In the model, displacement occurs when the worker is hit by an exogenous separation. In order to calculate these percentages, I simulate data using the estimated structural model. The simulated sample is 100 times bigger that the real data set. For each worker at each time period, I simulate the value of each one of his options: 1) staying in the current job, 2) changing employer and career and 3) changing employer but not career. The expected losses are conditional on the years of labor market experience and on the tenure in the firm. Tenure in the career is not generally available in most data sets. In each cell, I compare the losses at the time of displacement implied by the baseline model (first number in the cell) to the losses implied by the baseline model if the worker did not have the possibility of finding a new job in the same career (second number in the cell).
49
Table 11: Other Robustness Checks Parameters Estimation of p Including Drifts σε ηθ
1.16***
0.93***
(0.012)
(0.002)
1.54***
1.65***
(0.056)
(0.057)
ηε
1.49***
1.12***
(0.051)
(0.034)
C
2.75***
2.40***
(0.128)
(0.079)
0.024***
-
p
(0.003) μθ
-
0.096***
με
-
-0.03***
(0.011) (0.007) D. of F. χ2
68
68
215.65
183.61
Note: the numbers in parenthesis are the standard errors. The data set used for the estimation of the structural parameters is obtained using NLSY. In the first column, the parameter p is estimated jointly with the other parameters. In the second column, two drifts are included in the specifications of the law of motion of the two matches. ***=significant at 1% level.
Table 12: Estimation Results with Observed Heterogeneity College No College No CollegeParameters All the Sample σε
1.17*** (0.022)
(0.011)
(0.014)
(0.016)
ηθ
1.50***
1.03***
1.60***
1.62***
(0.058)
(0.023)
(0.069)
(0.065)
1.63***
3.13***
1.39***
1.38***
(0.042)
(0.038)
(0.002)
(0.056)
2.55***
6.58***
2.10***
2.08***
(0.050)
(0.155)
(0.084)
(0.149)
68
18
68
68
225.51
92.93
171.28
161.75
ηε C D. of F. χ2
2.14***
1.04***
1.04***
Note: the numbers in parenthesis are the standard errors. The data set used for the estimation of the structural parameters is obtained using NLSY. When estimating the parameter estimates for the college graduate, I use the second specification of the auxiliary model because of the small sample size. In all other cases, I use specification 4. *=significant at 10% level. **=significant at 5% level. ***=significant at 1% level.
50
