With Simon (Sokbae) Lee:
Identifying Effects of Multivalued Treatments, Econometrica, November 2018.
Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently, unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity. Our results rely on two main assumptions: treatment assignment must be a measurable function of threshold-crossing rules, and enough continuous instruments must be available. We illustrate our approach for several classes of models.
From Aggregate Betting Data to Individual Risk Preferences, Econometrica, January 2019.
We show that even in the absence of data on individual decisions, the distribution of
individual attitudes towards risk can be identified from the aggregate conditions that
characterize equilibrium on markets for risky assets. Taking parimutuel horse races
as a textbook model of contingent markets, we allow for heterogeneous bettors with
very general risk preferences, including non-expected utility. Under a standard single-crossing condition on preferences, we identify the distribution of preferences among
the population of bettors and we derive testable implications. We estimate the model
on data from U.S. races. Specifications based on expected utility fit the data very poorly. Our results stress the crucial importance of nonlinear probability weighting. They also suggest that several dimensions of heterogeneity may be at work.
With Frank Wolak:
Many econometric models used in applied work integrate over unobserved heterogeneity. We show that a class of these models that includes many random coefficients demand systems can be approximated by a “small-σ” expansion that yields a linear two-stage least squares estimator. We study in detail the models of product market shares and prices popular in empirical IO. Our estimator is only approximately correct, but it performs very well in practice. It is extremely fast and easy to implement, and it is “robust” to changes in the higher moments of the distribution of the random coefficients. At the very least, it provides excellent starting values for more commonly used estimators of these models.