SMALL-SAMPLE CONFIDENCE-INTERVALS FOR IMPULSE-RESPONSE FUNCTIONS

Bias-corrected bootstrap confidence intervals explicitly account for t he bias and skewness of the small-sample distribution of the impulse r esponse estimator, while retaining asymptotic validity in stationary a utoregressions. Monte Carlo simulations for a wide range of bivariate models show that in small samples bias-corrected bootstrap intervals t end to be more accurate than delta method intervals, standard bootstra p intervals, and Monte Carlo integration intervals. This conclusion ho lds for VAR models estimated in levels, as deviations from a linear ti me trend, and in first differences. It also holds for random walk proc esses and cointegrated processes estimated in levels. An empirical exa mple shows that bias-corrected bootstrap intervals may imply economic interpretations of the data that are substantively different from stan dard methods.