Many industries, including the NFL with the Rooney Rule and law firms with the Mansfield Rule, have adopted interview-stage diversity interventions requiring a minimum representation of disadvantaged groups in the interview set. However, the effectiveness of such policies remains inconclusive. In light of this, we develop a framework of a two-stage hiring process, where rational firms, with limited interview and hiring capacities, aim to maximize the match value of their hires. The labor market consists of two equally sized social groups, m and w, with identical ex-post match value distributions. Match values are revealed only post-interview, while interview decisions rely on partially informative pre-interview scores. Pre-interview scores are more informative for group m, while interviews reveal more for group w; as a result, if firms could interview all candidates, both groups would be equally hired. However, due to limited interview capacity and information asymmetry, we show that requiring equal representation in the interview stage does not translate into equal representation in the hiring outcome, even though interviews are more informative for group w. In certain regimes, with or without intervention, a firm may interview more group w candidates but still hire fewer. At an individual level, we show that strong candidates from both groups benefit from the intervention as the candidate-level competition weakens. For borderline candidates, only group w candidates gain at the expense of group w. To understand the impact of non-universal interview-stage interventions on the market, we study a model with two vertically differentiated firms, where only the top firm adopts the intervention. We characterize the unique equilibrium and demonstrate potentially negative effects: we show that in certain regimes the lower firm hires fewer group w candidates due to increased firm-level competition for them, and further find examples where overall fewer group w candidates are hired across the market. At an individual level, while superstar candidates in both groups benefit, surprisingly the impact on borderline candidates may reverse: the lower firm may replace borderline group w candidates with borderline group m candidates in its interview set, effectively reducing the chance of those borderline group w candidates being hired. Overall, our findings highlight challenges in diversifying the labor market at early hiring stages due to information asymmetry, filtering, and competition. Beyond our context, our natural framework of a market with two-stage hiring may be of independent interest.

Motivated by our collaboration with a major refugee resettlement agency in the U.S., we study a dynamic matching problem where each new arrival (a refugee case) must be matched immediately and irrevocably to one of the static resources (a location with a fixed annual quota). In addition to consuming the static resource, each case requires post-allocation services from a server, such as a translator. Given the uncertainty in service time, a server may not be available at a given time, thus we refer to it as a dynamic resource. Upon matching, the case will wait to avail service in a first-come-first-serve manner. Bursty matching to a location may result in undesirable congestion at its corresponding server. Consequently, the central planner (the agency) faces a dynamic matching problem with an objective that combines the matching reward (captured by pair-specific employment outcomes) with the cost for congestion for dynamic resources and over-allocation for the static ones. Motivated by the observed fluctuations in the composition of refugee pools across the years, we aim to design algorithms that do not rely on distributional knowledge. We develop learning-based algorithms that are asymptotically optimal in certain regimes, easy to interpret, and computationally fast. Our design is based on learning the dual variables of the underlying optimization problem; however, the main challenge lies in the time-varying nature of the dual variables associated with dynamic resources. Our theoretical development brings together techniques from Lyapunov analysis, adversarial online learning, and stochastic optimization. On the application side, when tested on real data from our partner agency, our method outperforms existing ones, making it a viable candidate for replacing the current practice upon experimentation.