Asymptotic Distributions of Impulse Response Functions in Short Panel Vector Autoregressions

Abstract

This paper establishes the limiting distributions of orthogonalized and nonorthogonalized impulse response functions in panel vector autoregressions with a fixed time dimension. The autoregressive parameters are estimated using the GMM estimators based on the first differenced equations and the error variance is estimated using an extended analysis-of-variance type estimator. We find that the GMM estimator of the autoregressive coefficients depends on the estimator of error variance, even in large samples with a large cross sectional dimension. The asymptotic dependence leads to additional terms in the asymptotic variance of the orthogonalized impulse response function that are not present in the time series literature. Simulation results show that the asymptotic distribution of the orthogonalized impulse response function that takes the dependence into account is more accurate than the one that does not.