Asymptotic Distributions of Impulse Response Functions in Short Panel Vector Autoregressions

This paper establishes the asymptotic distributions of the impulse response functions in panel vector autoregressions with a \u85xed time dimension. It also proves the asymptotic validity of a bootstrap approximation to their sampling distributions. The autoregressive parameters are estimated using the GMM estimators based on the \u85rst di¤erenced equations and the error variance is estimated using an extended analysis-of-variance type estimator. Contrary to the time series setting, we \u85nd that the GMM estimator of the autoregressive coe ¢ cients is not asymptotically independent of the error variance estimator. The asymptotic dependence calls for variance correction for the orthogonalized impulse response functions. Simulation results show that the variance correction improves the coverage accuracy of both the asymptotic con\u85dence band and the studentized bootstrap con\u85dence band for the orthogonalized impulse response functions