Estimation of limited dependent variable models with dummy endogenous regressors: Simple strategies for empirical practice

Applied economists have long struggled with the question of how to accommod ate binary endogenous regressors in models with binary and nonnegative outc omes. I argue here that much of the difficulty with limited dependent varia bles comes from a focus on structural parameters, such as index coefficient s, instead of causal effects. Once the object of estimation is taken to be the causal effect of treatment, several simple strategies are available. Th ese include conventional two-stags least squares, multiplicative models for conditional means, linear approximation of nonlinear causal models, models for distribution effects. and quantile regression with an endogenous binar y regressor. The estimation strategies discussed in the article are illustr ated by using multiple births to estimate the effect of childbearing on emp loyment status and hours of work.