Fixed-Effects Dynamic Panel Models, a Factor Analytical Method


  • Jushan Bai

    1. Dept. of Economics, Columbia University, New York, NY 10012, U.S.A. and CEMA, Central University of Finance and Economics, Beijing, China;
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    • The author thanks a co-editor and three anonymous referees for constructive comments, and Marcelo Moreira for useful discussions. He also thanks seminar participants at Rutgers University, Michigan State University, and Columbia Econometrics Colloquium for helpful comments. Partial results of this paper were also presented at the 10th World Congress of the Econometric Society, Shanghai, China and the Asian Meetings of Econometric Society, Seoul, Korea, both as paired-invited talks, and at the 16th African Econometric Society meetings, Nairobi, Kenya, as a keynote talk. Financial support from the NSF (Grant SES-0962410) is acknowledged.


We consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions: individual fixed-effects and time fixed-effects, as well as incidental parameters in the variances. We adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves. In the presence of cross-sectional heteroskedasticity, the factor method estimates the average of the cross-sectional variances instead of the individual variances. The method thereby eliminates the incidental-parameter problem in the means and in the variances over the cross-sectional dimension. We further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental-parameter bias even when T and N are comparable. Moreover, efficient and robust estimation is obtained by jointly estimating heteroskedasticities.