Common Shocks in panels with Endogenous Regressors

This paper introduces a novel approach to study the effects of common shocks on panel data models with endogenous explanatory variables when the cross section dimension (N) is large and the time series dimension (T) is fixed: this relies on conditional strong laws of large numbers and conditional central limit theorems. These results can act as a useful reference for readers who wish to further investigate the effects of common shocks on panel data. The paper shows that the key assumption in determining consistency of the panel TSLS and LIML estimators is the independence of the factor loadings in the reduced form errors from the factor loadings in the exogenous variables and instruments conditional on the factors. We also show that these estimators have non-standard asymptotic distributions but tests on the coefficients have standard distributions under the null hypothesis provided the estimators are consistent.