Identification and inference with ranking restrictions

Abstract

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.

A new algorithm for structural restrictions in Bayesian vector autoregressions

“…3 If desired, several other restrictions can be incorporated in a straightforward way, such as ranking restrictions (Amir- Ahmadi and Drautzburg, 2021), restrictions on elasticities, or other restrictions on magnitudes of shocks. For example, if for shock j variable i should react with a larger magnitude than variable k, then we get the restriction Λ ij > Λ kj which is fairly simple to incorporate within an MCMC sampling setting.…”

Advances in Using Vector Autoregressions to Estimate Structural Magnitudes

“…A much better algorithm in settings like this is the direct sampling approach proposed by Amir-Ahmadi and Drautzburg (2021). This imposes all the sign restrictions before drawing a candidate for Q instead of generating unrestricted values of Q and then discarding millions of draws.…”

Robust Bayesian Analysis for Econometrics

“…However, since the algorithm requires checking s n−f −1 combinations of restrictions, the algorithm may become slow or infeasible when there is a large number of sign restrictions. 7 A third approach to checking whether the identified set is empty is the 'Chebyshev criterion' proposed in Amir-Ahmadi and Drautzburg (2021). This algorithm is applicable when there are sign restrictions that constrain a single column of Q and there are no zero restrictions.…”