Nonparametric identification in nonseparable panel data models with generalized fixed effects

This paper is concerned with extending the familiar notion of fixed effects to nonlinear setups with infinite dimensional unobservables like preferences. The main result is that a generalized version of differencing identifies local average structural derivatives (LASDs) in very general nonseparable models, while allowing for arbitrary dependence between the persistent unobservables and the regressors of interest, even if there are only two time periods. These quantities specialize to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects. We extend the basic framework to include time trends and dynamics in the regressors, and we show how distributional effects as well as average effects are identified. In addition, we show how to handle endogeneity in the transitory component. Finally, we adapt our results to the semiparametric binary choice model with interaction between observables and persistent unobservables, and we establish that average structural marginal probabilities are iden-tified. We conclude this paper by applying the last result to a real-world data example. Using the PSID, we analyze the way in which the lending restrictions for mortgages ease