Partial observability in bivariate probit models

Abstract

This study investigates random utility models in which the observed binary outcome does not reflect the binary choice of a single decision-maker, but rather the joint unobserved binary choices of two decision-makers. Under the usual normality assumptions, the model that arises for the observed binary outcome is not a univariate probit model, but rather a bivariate probit model in which only one of the four possible outcomes is observed. Estimation and identification issues are discussed, and the implications for sample selectivity problems are noted.