Transformed Estimation for Panel Interactive Effects Models

Abstract

We propose a transformed estimator for the slope coefficients of panel models with interactive effects. The transformed estimation method does not require the prior knowledge of the dimension of factor structure. It is consistent and asymptotically normally distributed under fairly general conditions when N is fixed and $T\to \infty$ or T is fixed and $N\to \infty ,$ or when both N and T are large and $\frac{N}{T}\to a\ne 0<\infty .$ Moreover, because the transformation is equivalent to aggregating cross-sectional units or time units before implementing the least-square method over time or across cross-sectional units, it can bypass the issues arising from heteroscedasticity across cross-sectional units or serial correlations over time in the idiosyncratic errors. Furthermore, in the case that the idiosyncratic errors are independent over time, there is no asymptotic bias even the explanatory variables contain lagged dependent variables when $\frac{N}{T}\to a<\infty$ as $T\to \infty .$ Extensive Monte Carlo simulations are also conducted to examine the finite sample performance of the transformed estimation method.

Keywords:

• Eigenvalue
• Eigenvector
• Panel interactive effects models
• Transformed estimation

Acknowledgments

We thank to the editor, the associate editor, three referees for helpful comments and Whitney Newey and Martin Weidner for helpful discussions.

Additional information

Funding

Partial research was supported by China (NSF #71631004 and #72033008) to the first author is also gratefully acknowledged.