Control Function Methods in Applied Econometrics

TLDR

Control function methods address endogeneity in linear and nonlinear models by offering consistent estimators when plug‑in approaches fail, requiring fewer assumptions than maximum likelihood, and providing computationally simpler, flexible strategies for estimating average partial effects, though their application to discrete endogenous variables remains more controversial. The paper reviews control function methods for handling endogenous explanatory variables in linear and nonlinear models, highlighting flexible parametric strategies for estimating average partial effects. It surveys control function techniques that transform models with endogenous regressors into estimable forms, reducing bias while maintaining computational simplicity.

Abstract

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.