Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

Abstract

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.

Publication
Journal of Economic Dynamics and Control, 31 (7), pp. 2398-2412

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