Correcting sample selection bias with categorical outcomes

Abstract

In this paper, I propose a method for correcting sample selection bias when the outcome of interest is categorical, such as occupational choice, health status, or field of study. Classical approaches to sample selection rely on strong parametric distributional assumptions, which may be restrictive in practice. I develop a local representation that decomposes each joint probability into marginal probabilities and a category-specific association parameter that captures how selection differentially affects each outcome. Under some exclusion restrictions, I establish nonparametric point identification of the latent categorical distribution. Building on this identification result, I introduce a semiparametric multinomial logit model with sample selection, propose a computationally tractable two-step estimator, and derive its asymptotic properties. I illustrate the method by studying the determinants of healthcare utilization in C\^ote d'Ivoire.