On different approaches to obtaining partial effects in binary response models with endogenous regressors

- We study partial effects in binary response models.
- Our interest is in models with endogenous explanatory variables.
- The average structural function is superior to the average index function.
- Our conclusions hold for linear models and probit models.

We compare three different approaches to obtaining partial effects in binary response models. Among the three approaches, we maintain that the average structural function (ASF) due to Blundell and Powell (2003, 2004) defines the marginal effect of primary interest, for it is based on the unconditional marginal distribution of the structural error. Analytical examples are provided to show that the average index function (AIF) proposed recently by Lewbel, Dong, and Yang (2012), suffers from essentially the same shortcomings as the propensity score as a basis for defining average partial effects.