Posterior Properties of Long-Run Impulse Responses

Abstract

This article describes an exact, small-sample, Bayesian analysis of impulse response functions. We show how many common priors imply that posterior densities for impulse responses at long horizons have no moments. Our results indicate that impulse responses should be assessed on the basis of their full posterior densities and that standard estimates such as posterior means, variances, or modes may be very misleading.

KEY WORDS:

• Bayesian inference
• Moment existence
• Prior sensitivity
• Shock persistence
• Time series model