Inference for VARs Identified with Sign Restrictions

TL;DR

This paper develops a frequentist method for constructing confidence bands for impulse responses in sign-restricted SVARs, addressing limitations of Bayesian approaches and providing a comparison through empirical analysis.

Contribution

It introduces a moment-inequality framework for inference in sign-restricted SVARs, enabling valid frequentist confidence bands for impulse responses.

Findings

Frequentist confidence bands can be wider than Bayesian ones.

The proposed method is valid and provides an alternative to Bayesian inference.

Empirical application demonstrates differences between frequentist and Bayesian bands.

Abstract

There is a fast growing literature that set-identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign-restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign-restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for sign-restricted SVARs within a moment-inequality framework. In particular, it develops methods of constructing confidence bands for impulse response functions of sign-restricted SVARs that are valid from a frequentist perspective. The paper also provides a comparison of frequentist and Bayesian coverage bands in the context of an empirical application - the former can be substantially wider than the latter.