The Effect of Model-Selection Uncertainty on Error Bands for Estimated Impulse Response Functions in Vector Autoregressive Models

Model selection uncertainty adds to the variability in the coefficient estimates when small samples are used because model-selection criteria perform poorly in small samples. Previous literatures account for model-selection uncertainty to improve inference by endogenizing the lag order selection using bootstrap methods. This paper shows that all bootstrap methods fail in cases that are most common in macroeconomic applications. As the maximum eigenvalue of the vector autoregressive model gets closer to one, the bias of the impulse response estimates increases. As a result, the standard bootstrap resampling produces low interval coverage accuracy while bootstrap subsampling produces zero coverage. A proposed solution for this problem is using the first-order bias correction with bootstrap interval for impulse response estimates, which corrects for the first and second order bias of these estimators. This dramatically improves the interval coverage accuracy for impulse response estimates