Exclusion bias in sample-selection model estimators

Exclusion restrictions are routinely used in sample-selection models with "selection" and "outcome" equations. A false restriction, however, can cause an "exclusion bias" for the outcome equation estimator. In this paper, the specific form of the exclusion bias is derived for various sample-selection model estimators. Furthermore, it is shown that the outcome equation parameters for regressors with zero coefficients in the selection equation are immune to exclusion bias if only one regressor is excluded. Exclusion bias, or a lack thereof, is verified through a simulation study with the regressors taken from Mroz (1987).