Back to Feedback: Dynamics and Heterogeneity in Panel Data

TL;DR

This paper reviews methods for panel data analysis that relax strict exogeneity assumptions, allowing for feedback and heterogeneity, thus broadening the applicability of econometric models.

Contribution

It provides a comprehensive review of recent developments in panel data methods that accommodate sequential exogeneity and heterogeneity, including nonlinear and network models.

Findings

Classical linear models with constant coefficients are extended to allow heterogeneity.

Recent methods enable sequential exogeneity in nonlinear panel data models.

Potential extensions to network data are discussed.

Abstract

Many popular estimation methods in panel data rely on the assumption that the covariates of interest are strictly exogenous. However, this assumption is empirically restrictive in a wide range of settings. In this paper I argue that credible empirical work requires meaningfully relaxing strict exogeneity assumptions. Econometricians have developed methods that allow for sequential exogeneity, which in contrast with strict exogeneity allows for the presence of feedback from past outcomes to future covariates or treatments. I review some of the classic work on linear models with constant coefficients, and then describe some approaches that allow for coefficient heterogeneity in models with feedback. Finally, in the last two parts of the paper I review recent work that allows for sequential exogeneity in nonlinear panel data models, and mention possible extensions to network settings.