An incidental parameters free inference approach for panels with common shocks

This paper develops a novel Method of Moments approach for panel data models with endogenous regressors and unobserved common factors. The proposed approach does not require estimating explicitly a large number of parameters in either time-series or cross-sectional dimension, T and N respectively. Hence, it is free from the incidental parameter problem. In particular, the proposed approach does not suffer from “Nickell bias” of order O(T⁻¹), nor from bias terms that are of order O(N⁻¹). Therefore, it can operate under substantially weaker restrictions compared to existing large T procedures. Two alternative GMM estimators are analyzed; one makes use of a fixed number of “averaged estimating equations” à la Anderson and Hsiao (1982), whereas the other one makes use of “stacked estimating equations”, the total number of which increases at the rate of O(T). It is demonstrated that both estimators are consistent and asymptotically mixed-normal as N→∞ for any value of T. Low-level conditions that ensure local and global identification in this setup are examined using several examples.