Impulse response confidence intervals for persistent data: What have we learned?

This paper provides a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that the methods proposed in Kilian [1999. Finite-sample properties of percentile and percentile-t bootstrap confidence intervals for impulse responses. Review of Economics and Statistics 81(4), 652-660], Wright [2000. Confidence intervals for univariate impulse responses with a near unit root. Journal of Business and Economic Statistics 18(3), 368-373], Gospodinov [2004. Asymptotic confidence intervals for impulse responses of near-integrated processes. Econometrics Journal 7(2), 505-527] and Pesavento and Rossi [2005. Small sample confidence intervals for multivariate IRFs at long horizons. Journal of Applied Econometrics, forthcoming] have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkle's [1987. Vector autoregression and reality. Journal of Business and Economic Statistics 5, 437-442] bootstrap, Andrews and Chen [1994. Approximately median-unbiased estimation of autoregressive models. Journal of Business and Economic Statistics 12(2), 187-204] and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.