Models for count data with endogenous participation

We present several extensions of the Poisson and negative binomial models for count data based on the lognormal model for latent heterogeneity in the conditional means. The lognormal model provides a versatile specification that is more flexible than the familiar log gamma form, and provides a platform for several "two part" extensions that have appeared in the literature, including zero inflation, hurdle and sample selection models. We then extend these received two- part models by allowing for endogeneity of the participation equation. We conclude with a detailed application using the data employed in a recent study of the German health care system.