Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity

I study a simple, widely applicable approach to handling the initial conditions problem in dynamic, nonlinear unobserved effects models. Rather than attempting to obtain the joint distribution of all outcomes of the endogenous variables, I propose finding the distribution conditional on the initial value (and the observed history of strictly exogenous explanatory variables). The approach is flexible, and results in simple estimation strategies for at least three leading dynamic, nonlinear models: probit, Tobit, and Poisson regression. I treat the general problem of estimating average partial effects, and show that simple estimators exist for important special cases.