We develop a linear GMM estimator of the discrete-time mixed proportional hazard (MPH) model of duration with an arbitrary distribution of unobserved heterogeneity. We allow for competing risks, observable characteristics, and censoring. We prove our estimator is consistent and apply it to the duration of price spells. We find substantial unobserved heterogeneity with economically meaningful implications for the response of output to a monetary policy shock in a model with time-dependent pricing rules and for the degree of state dependence in a model of price plans.

We survey the literature on search-theoretic models of the labor market. We show how this approach addresses many issues, including the following: Why do workers sometimes choose to remain unemployed? What determines the lengths of employment and unemployment spells? How can there simultaneously exist unemployed workers and unfilled vacancies? What determines aggregate unemployment and vacancies? How can homogeneous workers earn different wages? What are the tradeoffs firms face from different wages? How do wages and turnover interact? What determines efficient turnover? We discuss various modeling choices concerning wage determination and the meeting process, including recent models of directed search.

We study a model of over-the-counter trading in which ex ante identical traders invest in a contact technology and participate in bilateral trade. We show that a rich market structure emerges both in equilibrium and in an optimal allocation. There is continuous heterogeneity in market access under weak regularity conditions. If the cost per contact is constant, heterogeneity is governed by a power law and there are middlemen, market participants with unboundedly high contact rates who account for a positive fraction of meetings. Externalities lead to overinvestment in equilibrium, and policies that reduce investment in the contact technology can improve welfare. We relate our findings to important features of real-world trading networks.

For an incompatible patient–donor pair, kidney exchanges often forbid receipt-before-donation (the patient receives a kidney before the donor donates) and donation-before-receipt, causing a double-coincidence-of-wants problem. We study an algorithm, the Unpaired kidney exchange algorithm, which eliminates this problem. In a dynamic matching model, we show that the waiting time of patients under Unpaired is close to optimal and substantially shorter than under widely used algorithms. Using a rich administrative dataset from France, we show that Unpaired achieves a match rate of 63% and an average waiting time of 176 days for transplanted patients. The (infeasible) optimal algorithm is only slightly better (64% and 144 days); widely used algorithms deliver less than 40% match rate and at least 232 days waiting times. We discuss a range of solutions that can address the potential practical incentive challenges of Unpaired. In particular, we extend our analysis to an environment where a deceased donor waitlist can be integrated to improve the performance of algorithms. We show that our theoretical and empirical comparisons continue to hold. Finally, based on these analyses, we propose a practical version of the Unpaired algorithm.