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(1/T), nor from bias terms that are of order O(1/N). Therefore, it can operate under substantially weaker restrictions compared to existing large T procedures. Two alternative GMM estimators are analysed; one makes use of a fixed number of ``averaged estimating equations'' a 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 goes to infinity for any value of T. Low-level conditions that ensure local and global identification in this setup are examined using several examples.