Identification and inference with ranking restrictions

We propose to add ranking restrictions on impulse-responses to sign restrictions to narrow the identified set in vector autoregressions (VARs). Ranking restrictions come from micro data on heterogeneous industries in VARs, bounds on elasticities, or restrictions on dynamics. Using both a fully Bayesian conditional uniform prior and prior-robust inference, we show that these restrictions help to identify productivity news shocks in the data. In the prior-robust paradigm, ranking restrictions, but not sign restrictions alone, imply that news shocks raise output temporarily, but significantly. This holds both in an application with rankings in the form of heterogeneity restrictions and in another applications with slope restrictions as rankings. Ranking restrictions also narrow bounds on variance decompositions. For example, the bound of the contribution of news shocks to the forecast error variance of output narrows by about 30 pp at the one-year horizon. While misspecification can be a concern with added restrictions, they are consistent with the data in our applications.