Binary Choice Model with Endogeneity: Identification via Heteroskedasticity

Abstract

The idea of identifying structural parameters via heteroskedasticity is explored in the context of binary choice models with an endogenous regressor. Sufficient conditions for parameter identification are derived for probit models without relying on instruments or additional restrictions. The results are extendable to other parametric binary choice models. The semi-parametric model of Manski (1975, 1985), with endogeneity, is also shown to be identifiable in the presence of heteroskedasticity. The role of heteroskedasticity in identifying and estimating structural parameters is demonstrated by Monte Carlo experiments.

Keywords: Qualitative response, Probit, Logit, Linear median regression, Endogeneity, Identification, Heteroskedasticity

JEL Classification: C25, C35, C13