I am grateful to a co-editor and four anonymous referees for their constructive comments, which led to a much improved presentation. I am also grateful for comments and suggestions from seminar participants at the University of Pennsylvania, Rice, MIT/Harvard, Columbia Econometrics Colloquium, New York Econometrics Camp (Saratoga Springs), Syracuse, Malinvaud Seminar (Paris), European Central Bank/Center for Financial Studies Joint Workshop, Cambridge University, London School of Economics, Econometric Society European Summer Meetings (Vienna), Quantitative Finance and Econometrics at Stern, and the Federal Reserve Bank of Atlanta. This work is supported in part by NSF Grants SES-0551275 and SES-0424540.
Panel Data Models With Interactive Fixed Effects
Article first published online: 21 JUL 2009
© 2009 The Econometric Society
Volume 77, Issue 4, pages 1229–1279, July 2009
How to Cite
Bai, J. (2009), Panel Data Models With Interactive Fixed Effects. Econometrica, 77: 1229–1279. doi: 10.3982/ECTA6135
- Issue published online: 21 JUL 2009
- Article first published online: 21 JUL 2009
- Manuscript received October, 2005; final revision received January, 2009.
- Additive effects;
- interactive effects;
- factor error structure;
- bias-corrected estimator;
- Hausman tests;
- time-invariant regressors;
- common regressors
This paper considers large N and large T panel data models with unobservable multiple interactive effects, which are correlated with the regressors. In earnings studies, for example, workers' motivation, persistence, and diligence combined to influence the earnings in addition to the usual argument of innate ability. In macroeconomics, interactive effects represent unobservable common shocks and their heterogeneous impacts on cross sections. We consider identification, consistency, and the limiting distribution of the interactive-effects estimator. Under both large N and large T, the estimator is shown to be consistent, which is valid in the presence of correlations and heteroskedasticities of unknown form in both dimensions. We also derive the constrained estimator and its limiting distribution, imposing additivity coupled with interactive effects. The problem of testing additive versus interactive effects is also studied. In addition, we consider identification and estimation of models in the presence of a grand mean, time-invariant regressors, and common regressors. Given identification, the rate of convergence and limiting results continue to hold.