Control Function Methods in Applied Econometrics

This paper provides an overview of control function (CF) methods for solving the problem of endogenous explanatory variables (EEVs) in linear and nonlinear models. CF methods often can be justified in situations where "plug-in" approaches are known to produce inconsistent estimators of parameters and partial effects. Usually, CF approaches require fewer assumptions than maximum likelihood, and CF methods are computationally simpler. The recent focus on estimating average partial effects, along with theoretical results on nonparametric identification, suggests some simple, flexible parametric CF strategies. The CF approach for handling discrete EEVs in nonlinear models is more controversial but approximate solutions are available.