April 7 2022, 5pm Paris time / 11am NY time
(University of Chicago Booth School of Business)
Price Discovery in Waiting Lists:
A Connection to Stochastic Gradient Descent (joint with Itai Ashlagi, Pengyu Qian and Amin Saberi)
Abstract: Waiting lists offer agents a choice among types of items and associated non-monetary prices given by required waiting times. These non-monetary prices are endogenously determined by a simple tâtonnement-like price discovery process: an item’s price increases when an agent queues for it, and decreases when an item arrives and a queuing agent is assigned. By drawing a connection between price adjustments in waiting lists and the stochastic gradient descent optimization algorithm, we show that the waiting list mechanism achieves the optimal allocative efficiency minus a loss due to price fluctuations that is bounded by the granularity of price changes. We further consider a price discovery process inspired by the waiting list mechanism and show that this sim- ple price discovery process performs well if the granularity of price changes is chosen to appropriately trade-off the speed of price adaptation and loss from price fluctuations.
March 31 2022, 5pm Paris time / 11am NY time
A Task-Based Theory of Occupations with Multidimensional Heterogeneity
Abstract: I develop an assignment model of occupations with multidimensional heterogeneity in production tasks and worker skills. Tasks are distributed continuously in the skill space, whereas workers have a discrete distribution with a finite number of types. Occupations arise endogenously as bundles of tasks optimally assigned to a type of worker. The model allows us to study how occupations respond to changes in the economic environment, making it useful for analyzing the implications of automation, skill-biased technical change, offshoring, and workers’ training. I characterize how wages, the marginal product of workers, the substitutability between worker types, and the labor share depend on the assignment of tasks to workers. I introduce automation as a choice of the optimal size and location of a mass of identical robots in the task space. Automation displaces workers by replacing them in the performance of tasks. This generates a cascading effect on other workers as the boundaries of occupations are redrawn.
February 17 2022, 5pm Paris time / 11am NY time
(University of Michigan)
Matching for causal effects via multimarginal optimal transport (joint with Yuliang Xu)
Abstract: Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge in these settings stems from the often high-dimensional structure of the problem. Many methods have been introduced to deal with this challenge, with different advantages and drawbacks in computational and statistical performance and interpretability. Moreover, the methodological focus has been on matching two samples in binary treatment scenarios, but a dedicated method that can optimally balance samples across multiple treatments has so far been unavailable. This article introduces a natural optimal matching method based on entropy-regularized multimarginal optimal transport that possesses many useful properties to address these challenges. It provides interpretable weights of matched individuals that converge at the parametric rate to the optimal weights in the population, can be efficiently implemented via the classical iterative proportional fitting procedure, and can even match several treatment arms simultaneously. It also possesses demonstrably excellent finite sample properties.
January 6 2022, 5pm Paris time / 11am NY time
Education Expansion, Sorting, and the Decreasing Education Wage Premium
(job market paper)
Abstract: This paper studies the interplay between worker supply and firm demand, and their effect on sorting and wages in the labor market. I build a model of one-to-many matching with multidimensional types in which several workers are employed by a single firm. Matching is dictated by worker preferences, their relative productivity in the firm, and substitution patterns with other workers. Using tools from the optimal transport literature, I solve the model and structurally estimate it on Portuguese matched employer-employee data. The Portuguese labor market is characterized by an increase in the relative supply of high school graduates, an increasingly unbalanced distribution of high school graduates versus non-graduates across industries, and a decreasing high school wage premium between 1987 and 2017. Counterfactual exercises suggest that both changes in worker preferences and the increasing relative productivity of high school graduates over non-graduates act as a mitigating force on the decreasing high school wage premium, but do not fully compensate for high school graduates’ rise in relative supply.
December 2 2021, 5pm Paris time / 11am NY time
Sorting with Team Formation
(with Aleh Tsyvinski and Alexander P. Zimin)
Abstract: We fully solve an assignment problem with heterogeneous firms and multiple heterogeneous workers whose skills are imperfect substitutes, that is, when production is submodular. We show that sorting is neither positive nor negative and is characterized sufficiently by two regions. In the first region, mediocre firms sort with mediocre workers and coworkers such that output losses are equal across all these pairings (complete mixing). In the second region, high skill workers sort with a low skill coworker and a high productivity firm, while high productivity firms employ a low skill worker and a high skill coworker (pairwise countermonotonicity). The equilibrium assignment is also necessarily characterized by product countermonotonicity, meaning that sorting is negative for each dimension of heterogeneity with the product of heterogeneity in the other dimensions. The equilibrium assignment as well as wages and firm values are completely characterized in closed form. We illustrate our theory with an application to show that our model is consistent with the observed dispersion of earnings within and across U.S. firms. Our counterfactual analysis gives evidence that the change in the firm project distribution between 1981 and 2013 has a larger effect on the observed change in earnings dispersion than the change in the worker skill distribution.
September 23 2021, 1pm Paris time / 7am NY time
Duality and Estimation of Undiscounted Markov Decision Processes
Abstract: This paper studies estimation of undiscounted Markov decision processes (MDPs). Exploiting convex analytic methods, it argues that undiscounted MDPs can be treated as static discrete choice models over state-action frequencies, leveraging this idea to derive a conjugate duality framework for studying this type of models. It then exploits this framework to draw implications in several dimensions. First, it characterizes the empirical content of undiscounted MDPs, analyzing how exclusion or parametric restrictions can produce identification of agents’ payoffs, and providing an axiomatic characterization of the undiscounted dynamic logit model; second, it proves convergence of simple inversion algorithms based on progressive Tâtonnements, and investigates novel estimation strategies based on these. Finally, it shows that the dual framework extends to models with persistent fixed effects and to models where certain actions or states are unobserved.