Small sample confidence intervals for multivariate impulse response functions at long horizons

Existing methods for constructing confidence bands for multivariate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this paper is to propose a simple method for constructing confidence bands for impulse response functions that are robust to the presence of highly persistent processes. We do so by using alternative approximations based on local-to-unity asymptotic theory and by allowing the lead time of the impulse response function to be a fixed fraction of the sample size. Monte Carlo simulations, in which this method is compared with those existing in the literature, show that our method has good coverage properties. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. An example to the analysis of nominal versus real sources of fluctuations in real and nominal exchange rates is discussed