The Computation of Opportunity Costs in Polytomous Choice Models with Selectivity

Abstract

This article provides general formulas for the computation of opportunity costs (or forgone earnings) of unchosen alternatives in sample selection models with binary or polytomous choices. With observed choice probabilities and outcomes of chosen alternatives, the opportunity costs of unchosen alternatives can be evaluated. The derived formulas for the general model involve only single integrals. For the probability indexed sample selection models with conditional logit choice probabilities, which include the polytomous choice model of Lee [1983], the formulas have simple closed form expressions. These formulas are useful for empirical studies.