Dynamic Models of Reputation and Competition in Job-Market Matching

A fundamental decision faced by a firm hiring employees - and a familiar one to anyone who has dealt with the academic job market, for example - is deciding what caliber of candidates to pursue. Should the firm try to increase its reputation by making offers to higher-quality candidates, despite the risk that the candidates might reject the offers and leave the firm empty-handed? Or should it concentrate on weaker candidates who are more likely to accept the offer? The question acquires an added level of complexity once we take into account the effect one hiring cycle has on the next: hiring better employees in the current cycle increases the firm's reputation, which in turn increases its attractiveness for higher-quality candidates in the next hiring cycle. These considerations introduce an interesting temporal dynamic aspect to the rich line of research on matching models for job markets, in which long-range planning and evolving reputational effects enter into the strategic decisions made by competing firms. We develop a model based on two competing firms to try capturing as cleanly as possible the elements that we believe constitute the strategic tension at the core of the problem: the trade-off between short-term recruiting success and long-range reputation-building; the inefficiency that results from underemployment of people who are not ranked highest; and the influence of earlier accidental outcomes on long-term reputations. Our model exhibits all these phenomena in a stylized setting, governed by a parameter q that captures the difference in strength between the two top candidates in each hiring cycle. We show that when q is relatively low the efficiency of the job market is improved by long-range reputational effects, but when q is relatively high, taking future reputations into account can sometimes reduce the efficiency

The Secretary Problem with Independent Sampling

In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of maximum value. The most classic version of the problem is that in which the elements arrive in random order and their values are arbitrary. However, by varying the available information, new interesting problems arise. Also the case in which the arrival order is adversarial instead of random leads to interesting variants that have been considered in the literature. In this paper we study both the random order and adversarial order secretary problems with an additional twist. The values are arbitrary, but before starting the online sequence we independently sample each element with a fixed probability $p$. The sampled elements become our information or history set and the game is played over the remaining elements. We call these problems the random order secretary problem with $p$-sampling (ROS$p$ for short) and the adversarial order secretary problem with $p$-sampling (AOS$p$ for short). Our main result is to obtain best possible algorithms for both problems and all values of $p$. As $p$ grows to 1 the obtained guarantees converge to the optimal guarantees in the full information case. In the adversarial order setting, the best possible algorithm turns out to be a simple fixed threshold algorithm in which the optimal threshold is a function of $p$ only. In the random order setting we prove that the best possible algorithm is characterized by a fixed sequence of time thresholds, dictating at which point in time we should start accepting a value that is both a maximum of the online sequence and has a given ranking within the sampled elements.Comment: 41 pages, 2 figures, shorter version published in proceedings of SODA2

An Examination into Teacher Hiring: Preferences, Efficiency, Stability, and Student Outcomes

This dissertation studies teacher hiring practices, an avenue to potentially raise teacher quality which has not been studied extensively. I analyze three aspects of the teacher hiring process, which, if improved, could promote education quality: the principal hiring decision, the teacher application decision, and the effects of information on teacher behavior and market outcomes in the teacher labor market. The first two are empirical studies utilizing administrative data from an urban school district, and the last is a laboratory experiment. Education is a labor focused enterprise where outcomes are largely determined by teacher quality, so hiring the most productive teachers is paramount. Hiring is even more important given that teaching is a high-turnover profession, thus hiring occurs frequently. I first compare the elements of a teacher’s application that predict principal hiring decisions to those predicting teacher performance and retention outcomes. Similar to other recent work, I find disparities between the two sets of predictors. I utilize additional methods to study the relation of the size and quality of the applicant pool, as well as how those factors relate to the quality of the selected candidate. The results indicate that the applicant pools do not systematically vary by school characteristics in an obvious manner. Also, while the quality of the candidate pool may influence principal hiring decisions, it is not the dominate factor. Given that teaching sorting across schools occurs in the new-teacher labor market (Sass, et al. 2012) and in post-hire differential patterns of teacher mobility,[1] which in turn create disparities in access to effective teachers, it is important to understand the mechanisms that lead to teacher sorting across schools. In chapter 2, I study how teacher application behavior reveals teacher preferences over schools. The preferences can lead to differences in application pools, thereby affecting principals’ ability to hire quality candidates. I find that the application decisions of new-to-the-district candidates may be affected by accountability pressures or the resource level in high-needs schools, but current teachers’ revealed preferences agree with those previously found in the research literature. It has also been found that a teacher’s compatibility with a school can affect their ability to improve student outcomes and their own satisfaction (which decreases mobility, thereby increasing experience and decreasing turnover costs). In my third chapter, I use a laboratory experiment to examine teacher and school behavior and their effects on outcomes in a controlled setting while varying the preference structure of the market and the information agents have on competitors’ actions. I find that information on competitor behavior affects signaling behavior and the market efficiency and payoffs, but that these effects are dependent on the preference structure. I also find that the preference structure affects the stability of the matches. [1] Darling-Hammond, 2001; Viadero, 2002; Gordon & Maxey, 2000; Goldhaber et al., 2007; Feng & Sass, 201

Secretary problems with competing employers

Abstract. In many decentralized labor markets, job candidates are offered positions at very early stages in the hiring process. It has been argued that these early offers are an effect of the competition between employers for the best candidate. This work studies the timing of offers in a theoretical model based on the classical secretary problem. We consider a secretary problem with multiple employers and study the equilibria of the induced game. Our results confirm the observation of early offers in labor markets: for several classes of strategies based on optimal stopping theory, as the number of employers grows, the timing of the earliest offer decreases.