Modeling Job Search and Matching with Panel Data on Vacancies and Applications

Abstract
We analyze data from a large firm that provided information on all job applications and labor market outcomes within the firm over a 5-year period. The data show that African Americans and women engage in more overt job search activity within the organization than Caucasian males, attain shorter tenure on each job, and experience slower wage growth. Furthermore, differences emerge across race and gender at each stage of the application process: African Americans are more likely to apply for positions requiring qualifications they lack, and both African Americans and women are more likely to withdraw from the application process. African Americans are also less likely to be interviewed for a position. However, conditional on being interviewed, the probability of being hired does not vary by gender or race.

To explain these empirical patterns, we develop a model of two-sided search and matching. A position becomes vacant when the current occupant of the job leaves, the manager begins a search process by advertising the position, and workers employed both inside and outside the organization apply for it. Workers choose their job search intensity by setting a threshold below which they would not accept a job offer. A committee comprising potential coworkers culls the pool of applicants; additionally, some applicants voluntarily withdraw from the process. The hiring process concludes when the firm manager fills the vacancy with one of the remaining candidates. At each stage of the process, the parties learn more about potential job match quality. Their decisions are guided by their own preferences, and the incentives of the coworkers are not necessarily aligned with those of the manager. The successful applicant accumulates experience on-the-job that increases his or her wages, as well as future employment opportunities, at a rate that depends on match quality (given job search intensity). This in turn leads to future applications and jobs in a career that eventually culminates in retirement or quitting the firm.

We focus on a steady state environment where the entry rate of workers corresponds to their exit rate. The most novel features of this model concern the equilibrium selection of the consideration set by the coworkers, a combinatorial problem of optimally choosing a group of applicants, subject to a constraint that the manager who exercises her discretion when deciding whom to hire from the group. If the manager’s objectives are not aligned well enough with the coworkers, or the additional information the manager obtains is of sufficiently low value to them, coworkers are more likely to select the minimal group size to the manager, one. Alternatively, a recursive characterization of the solution exists: when constrained to choosing a group of maximal size n, it is optimal to include everyone who would be selected if the constraint was n – 1.

To simplify the inference problem of inferring coworker preferences from observing the choice of a consideration set from a myriad of alternative sets, we exploit the inclusion property described above in estimation. Estimating the manager’s preferences from the outcomes to the discrete choice problem she solves is also nonstandard because the size of her choice set varies, generating overidentifying restrictions when the distribution of the idiosyncratic disturbances is assumed to be known. These additional restrictions are key to embedding characteristics of each potential job match, information about the applicant available to both the coworkers and manager, that is unobserved heterogeneity whose distribution we can identify and estimate. We have obtained a preliminary set of parameter estimates based on a simulated methods of moments estimator that nests the solution to the model.

Conducting counterfactuals on the model will help us understand more about how differences in race and gender are reflected in the search and matching process, and wage trajectories. For example, noting that on average females and African Americans have shorter job durations than other employees and lower wages, how would these outcomes change if committees are compelled to interview more candidates, overall, or by demographic type?

This is joint work with Rebecca Lessem.

You can sign up for this seminar by sending an email to eb-secr@ese.eur.nl.

Lunch will be provided (vegetarian option included).

About Robert Miller
Robert Miller holds the Richard M. Cyert and Morris DeGroot Professorship in Economics and Statistics, and is a Professor of Economics and Strategy at the Tepper School of Management, Carnegie Mellon University. His work on the labor market, fertility, housing, executive compensation, financial markets and auctions is widely cited. It exploits large data sets to model interactions between people as equilibrium probability distributions. Miller frequently presents his research at seminars and conferences; he mainly publishes in the top economics journals, but also in accounting and finance; he regularly gives invited lectures on his work throughout the world. Miller consults on labor issues, and he has served as an expert witness in several lawsuits. At Carnegie Mellon, Professor Miller teaches MBA courses he developed in strategic corporate management, and trade and investment strategy, along with doctoral courses in advanced econometrics.