Estimating Causal Effects in Binary Response Models with Binary Endogenous Explanatory Variables - A Comparison of Possible Estimators

This paper reviews and compares different estimators used in the past to estimate a binary response model (BRM) with a binary endogenous explanatory variable (EEV) to give practical insights to applied econometricians. It also gives a guidance how the average structural function (ASF) can be used in such a setting to estimate average partial effects (APEs). In total, the (relative) performance of six different linear parametric, non-linear parametric as well as non-linear semi-parametric estimators is compared in specific scenarios like the prevalence of weak instruments. A simulation study shows that the non-linear parametric estimator dominates in a majority of scenarios even when the corresponding parametric assumptions are not fullfilled. Moreover, while the semi-parametric non-linear estimator might be seen as a suitable alternative for estimating coefficients, it suffers from weaknesses in estimating partial effects. These insights are confirmed by an empirical illustration of the individual decision to supply labor.