Nonparametric Welfare Analysis for Discrete Choice: Levels and Differences of Individual and Social Welfare

Abstract

Empirical welfare analyses often impose stringent parametric assumptions on individuals' preferences and neglect unobserved preference heterogeneity. In this paper, we develop a framework to conduct individual and social welfare analysis for discrete choice that does not suffer from these drawbacks. We first adapt the broad class of individual welfare measures introduced by Fleurbaey ( 2009) to settings where individual choice is discrete. Allowing for unrestricted, unobserved preference heterogeneity, these measures become random variables. We then show that the distribution of these objects can be derived from choice probabilities, which can be estimated nonparametrically from cross-sectional data. In addition, we derive nonparametric results for the joint distribution of welfare and welfare differences, as well as for social welfare. The former is an important tool in determining whether those who benefit from a price change belong disproportionately to those who were initially well-off. An empirical application illustrates the methods.

Identifying the Distribution of Welfare from Discrete Choice

“…They can readily be used to set-identify the concepts that are expressed in terms of transition probabilities. In a longer version of this paper (Capéau et al, 2022), we find the identified sets for NOS measures to be small in an empirical application on female labour supply, which suggests that cross-sectional data is sufficiently rich for applied welfare analysis.…”