Reporting point estimates and error bands for structural vector autoregressions that are only set identified is a very common practice. However, unless the researcher is persuaded on the basis of prior information that some parameter values are more plausible than others, this common practice has no formal justification. When the role and reliability of prior information is defended, Bayesian posterior probabilities can be used to form an inference that incorporates doubts about the identifying assumptions. We illustrate how prior information can be used about both structural coefficients and the impacts of shocks, and propose a new distribution, which we call the asymmetric t distribution, for incorporating prior beliefs about the signs of equilibrium impacts in a nondogmatic way. We apply these methods to a three-variable macroeconomic model and conclude that monetary policy shocks were not the major driver of output, inflation, or interest rates during the Great Moderation.
structural vector autoregressions set identification monetary policy impulse-response functions historical decompositions model uncertainty informative priors