An incidental parameters free inference approach for panels with common shocks

Abstract

This paper develops a novel Method of Moments approach for panel data models withendogenous regressors and unobserved common factors. The proposed approach doesnot require estimating explicitly a large number of parameters in either time-series orcross-sectional dimension,T and N respectively. Hence, it is free from the incidental parameter problem. In particular, the proposed approach does not suffer from ‘‘Nickellbias" 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 largeT 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 onemakes use of ‘‘stacked estimating equations", the total number of which increases at therate 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 example