An Estimator for Some Binary-Outcome Selection Models Without Exclusion Restrictions

This article provides a new maximum-likelihood estimator forselection models with dichotomous dependent variables when identicalfactors affect the selection equation and the equation of interest.Such situations arise naturally in game-theoretic models whereselection is typically nonrandom and identical explanatory variablesinfluence all decisions under investigation. When identicalexplanatory variables influence selection and a subsequent outcomeof interest, the commonly used Heckman-type estimators identifyfrom distributional assumptions about the residuals alone. Whenits own identifying assumption is reasonable, the new estimatorallows the researcher to avoid the painful choice between identifyingfrom distributional assumptions alone and adding a theoreticallyunjustified variable to the selection equation in a mistakenattempt to "boost" identification. The article uses Monte Carlomethods to compare the small-sample properties of the estimatorwith those of the Heckman-type estimator and ordinary probit.