Federal Reserve Bank of Minneapolis Research Department Staff Report 469 Revised June 2013 Careers in Firms: Estimating a Model of Learning, Job Assignment, and Human Capital Acquisition∗ Elena Pastorino Federal Reserve Bank of Minneapolis and University of Minnesota ABSTRACT This paper develops and structurally estimates a labor market model that integrates job assignment, learning, and human capital acquisition to account for the main patterns of careers in firms. A key innovation is that the model incorporates workers’ job mobility within and between firms, and the possibility that, through job assignment, firms affect the rate at which they acquire information about workers. The model is estimated using longitudinal administrative data on managers from one U. firm in a service industry (the data of Baker, Gibbs, and Holmström (1994a,b)) and fits the data remarkably well.
The estimated model is used to assess both the direct effect of learning on wages and its indirect effect through its impact on the dynamics of job assignment. Consistent with the evidence in the literature on comparative advantage and learning, the estimated direct effect of learning on wages is found to be small. Unlike in previous work, by jointly estimating the dynamics of beliefs, jobs, and wages imposing all of the model restrictions, the impact of learning on job assignment can be uncovered and the indirect effect of learning on wages explicitly assessed. The key finding of the paper is that the indirect effect of learning on wages is substantial: overall learning accounts for one quarter of the cumulative wage growth on the job during the first seven years of tenure.
Nearly all of the remaining growth is from human capital acquisition. A related novel finding is that the experimentation component of learning is a primary determinant of the timing of promotions and wage increases. Along with persistent uncertainty about ability, experi- mentation is responsible for substantially compressing wage growth at low tenures. Keywords: Careers; Job Mobility; Experimentation; Bandit; Human Capital; Wage Growth JEL Classification: D22, D83, J24, J31, J44, J62 ∗ I am truly indebted to Ken Wolpin for his generous advice.
I benefited from numerous conversations with John Geweke and Petra Todd. Chris Ferrall, Robert Gibbons, Hiro Kasahara, Michael Keane, John Moore, and Michael Waldman have offered especially valuable comments. Finally, I thank George Baker for kindly providing me with the data and Bengt Holmström for his support of the project. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.
The literature on careers in firms studies the allocation of workers to tasks and jobs within a firm and the dynamics of wages with tenure. Observationally, workers usually advance from lower- to higher-level jobs of a firm’s hierarchy over time, wages on average increase with tenure in a firm, especially through promotions, but wage decreases are also common, mostly in response to unsuccessful performance.) Models that are qualitatively successful at explaining these patterns combine job assignment, learning, and human capital acquisition.1 One feature that has generally been missing in the literature on careers is experimentation within firms: information on worker productivity is assumed to be passively acquired independently of a worker’s job. The differential learning pos- sibilities associated with different jobs within a firm can, however, have important implications for firms’ job assignment decisions. (See Prescott and Visscher (1980) and Holmström and Tirole (1989) for early references.) Another element that the literature on careers has often ignored is worker mobility between firms and the impact of competition among firms on internal job assign- ment and compensation.
This paper is the first to provide a comprehensive examination of the empirical relevance of these models of careers, of the relative importance of their components, and of the role of these missing elements. Specifically, this paper develops and structurally estimates a model of the labor market with experimentation and turnover that integrates elements of correlated learning as in Jovanovic and Nyarko (1997), human capital acquisition as in Keane and Wolpin (1997), and careers in firms as in GW. The model is estimated using administrative data on managers from a single U. firm in a service industry (the data of Baker, Gibbs, and Holmström (1994a,b), hereafter BGH), which contain information about each manager’s yearly job assignment, salary, and performance.
A key advantage of the data is that the detailed performance information identifies the process for learning at each job in the firm. The tenure profiles of managers’ job assignments and wages separately identify the process for human capital acquisition at each job. These data allow me to estimate the informativeness of the firm’s jobs, determine the implied speed of learning at each job, and assess the contribution of learning and human capital acquisition to wage growth on the job. At the estimated parameters, the model implies that learning is a quantitatively important source of observed career paths, unlike common estimates in the literature on comparative advantage and learning, as in Gibbons, Katz, Lemieux, and Parent (2005), Lluis (2005), and Hunnes (2012).
Conceptually, these papers measure the direct and contemporaneous dependence of wages on beliefs about ability by assessing the impact of learning on the estimated effect of current characteristics of workers and jobs on current wages. This direct effect of learning on wages is estimated based on the wage process alone, instrumented to correct for the endogeneity of job assignment, and typically found to be small or insignificant or difficult to reconcile with economic intuition. In sharp contrast, 1 That learning and human capital acquisition are primary determinants of observed earnings-experience profiles has recently been argued by Rubinstein and Weiss (2007). See Bagger, Fontaine, Postel-Vinay, and Robin (2011) for a detailed assessment of the contribution of search and human capital acquisition to individual wage growth.
1 by explicitly estimating the joint dynamics of beliefs, job assignments, and wages implied by the model, here I am able to assess both the direct effect of learning on wages and its indirect effect due to its impact on the dynamics of job assignment. Intuitively, the indirect effect of learning on wages arises because learning leads managers to be more quickly promoted to higher levels of the job hierarchy over time, at which they are paid higher wages. Consistent with the literature, I find the direct effect of learning on wages to be small.2 Critically, however, I find its indirect effect to be much larger than the direct one. I estimate that learning contributes to more than one quarter of cumulative wage growth on the job during the first seven years of tenure, with the remaining growth explained by human capital acquisition.3 This finding implies a revised view of the role of learning for wages: the impact of learning on wages is substantial, but this effect is dynamic, operating indirectly though job promotions rather than through a direct static effect.
Another key finding of this paper is that the different speed of learning at different jobs, that is, the experimentation component of learning, is a primary determinant of the timing of promotions and wage increases, which leads to a compression of wages at low tenures. Without experimentation, learning would account for an even greater contribution to wage growth. In the model, production in firms is organized among distinct jobs to which workers are assigned. Initially, a worker’s ability is unobserved, but over time all firms and the worker learn about ability by observing the worker’s performance.
When employed, workers also acquire human capital, which can be task- and firm-specific to varying degrees. (See Sanders and Taber (2012) on the importance of task-specific human capital for wage growth.) Jobs differ in the output they generate and in the information they provide about ability. Hence, the speed of learning differs across jobs. As a consequence, when assigning a worker to a job, firms trade off current output against the value of information and future human capital.
Likewise, when comparing employment at different firms, workers weigh current wages against the value of information and future human capital. Thus, both firms and workers face a classic multi-armed bandit problem with dependent arms.4 I assume that in the market for managers, firms compete in jobs and wages in a Bertrand fashion. This formulation allows all firms to be heterogeneous in their technologies and thus imperfectly competitive, but it also nests GW’s framework of firms with identical technologies. Heterogeneity in technologies generates not only wage dispersion among workers at any point in time but also worker turnover over time as workers move to firms with technologies that best match their partially learned ability and acquired human capital.
With heterogeneity, equilibrium endogenously determines a flexible sharing rule of the surplus generated by a firm and a worker that does not restrict a worker to 2 By replicating the analysis of Lluis (2005) and Hunnes (2012) in my data, based on the same instrumental variable approach as in Gibbons et al. (2005), I find that the impact of learning is negligible and insignificant. These estimates, though, do not capture the total effect of learning on wages. Details are available upon request.
3 Similarly, Bagger et al. (2011) estimate that human capital acquisition accounts for 50% to 70% of the wage growth of individuals with 10 to 20 years of labor market experience. 4 Jovanovic (1979), Miller (1984), and Flinn (1986) provide influential applications of the bandit problem with independent arms to labor market and occupational turnover. 2 be paid his expected output at the employing firm.
By measuring the difference between estimated output and wages, I can then assess the degree of monopsony power of the firm in my data. The different role that wages play in my model, compared with their role in perfectly competitive models such as GW, is critical for my results. Under perfect competition among identical firms, the wage paid by a firm reflects a worker’s value to the firm. Under Bertrand competition among heterogeneous firms, the wage reflects a worker’s value to the firm’s competitors.
Hence, wages paid by the firm in my data provide direct information about the technologies of other firms in the labor market. As a result, certain interpretable reduced-form parameters of other firms can be recovered just by estimating the wage process at this one firm. These parameters can then be used to assess the degree of transferability of unobserved ability and acquired human capital between firms. The main intuition for the identification of the model is that performance data identify the process for learning independently of the process for human capital acquisition.
Job transitions within the firm identify the process for output and human capital acquisition at the firm. In particular, differences in the hazard rate of promotion across tenures and levels identify the degree of task generality of the human capital acquired at a level or with overall tenure in the firm. Finally, wages identify the degree of generality of unobserved ability and acquired human capital across firms. I estimate the model by nonparametric maximum likelihood using eight years of observations on ten cohorts of managers entering into the firm between 1970 and 1979, imposing all of the theory’s restrictions.
The estimated model successfully captures the time profile of job-to-job transitions within the firm and separations from the firm, as well as the distribution of wages and performance at the main job levels in each tenure. The estimates of the model’s parameters imply several key features of the process of information acquisition at the firm. First, initial uncertainty at the time of a manager’s entry into the firm proves to be substantial: over half of the managers in my data have initial priors (that their ability is high rather than low) close to 0. Second, initial priors about ability are highly heterogeneous across managers, implying a significant dispersion of information at the time of hiring.
Third, learning is gradual: more than 15 years of high performance are necessary for the average prior about a manager’s ability being high to reach 0.
