Two-part models are robust to endogenous selection

This note shows that the two-part model (TPM) can be used to estimate conditional and populationaveraged effects of exogenous covariates when there is endogenous selection between the two parts. Much like estimating an average treatment effect on the treated, the TPM estimator only needs estimates of parameters that are recoverable from the observable data to estimate covariate effects. The TPM estimator is consistent for the counter factual of interest when selection between the parts is endogenous because the unobservable parameter is multiplied by zero.