Lab Seminar: Grigory Franguridi, Nonparametric Welfare Analysis for Discrete Choice Using Convex Duality

I suggest a semi/nonparametric, computationally attractive procedure to evaluate counterfactual welfare in a general class of discrete choice models, for which a consistent estimator of in-sample conditional choice probabilities and mean utilities is available. This class includes semiparametric dynamic discrete choice models under conditional independence as in Buchholz et al. (2016) and semiparametric random utility models with additively separable heterogeneity as in Allen and Rehbeck (2019). The estimating procedure does not require any prior knowledge of the distribution of the utility shock (as in multinomial logit) or the distribution of the random coefficients (as in mixed logit); instead, the only information used in estimation is convexity of welfare as a function of mean utilities. The estimators are based on the convex dual representation of the welfare function, are nonparametrically consistent (as long as the demand can be identified) and enjoy an array of properties implied by rational behavior of the consumer. To the best of my knowledge, this is the first consistent procedure for counterfactual evaluation in the aforementioned class of discrete choice models.