Abstract

We develop methods for robust Bayesian inference in structural vector autoregressions (SVARs) where the impulse responses or forecast error variance decompositions of interest are set-identified using external instruments (or ‘proxy SVARs’). Existing Bayesian approaches to inference in proxy SVARs require researchers to specify a single prior over the model’s parameters. When parameters are set-identified, a component of the prior is never updated by the data. Giacomini and Kitagawa (2018) propose a method for robust Bayesian inference in set-identifed models that delivers inference about the identified set for the parameter of interest. We extend this approach to proxy SVARs, which allows researchers to relax potentially controversial point-identifying restrictions without having to specify an unrevisable prior. We also explore the effect of instrument strength on posterior inference. We illustrate our approach by revisiting Mertens and Ravn (2013) and relaxing the assumption that they impose to obtain point identification.

Highlights

  • Proxy structural vector autoregressions (SVARs) are an increasingly popular method for estimating the dynamic causal effects of macroeconomic shocks.1 The key identifying assumption in the proxy SVAR is that there exist one or more variables external to the SVAR – ‘proxies’ or ‘external instruments’ – that are correlated with particular structural shocks (i.e., ‘relevant’) and uncorrelated with all other structural shocks (i.e., ‘exogenous’)

  • Mertens and Ravn (2013) ( MR) develop a proxy SVAR with multiple proxies for multiple structural shocks and show that point identification of the impulse responses to these shocks requires zero restrictions on the structural parameters in addition to the zero restrictions implied by exogeneity of the proxies

  • In this paper we extend the approach of GK to set-identified proxy SVARs

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Summary

Introduction

Proxy structural vector autoregressions (SVARs) are an increasingly popular method for estimating the dynamic causal effects of macroeconomic shocks. The key identifying assumption in the proxy SVAR is that there exist one or more variables external to the SVAR – ‘proxies’ or ‘external instruments’ – that are correlated with particular structural shocks (i.e., ‘relevant’) and uncorrelated with all other structural shocks (i.e., ‘exogenous’). Bayesian inference may be appealing because it allows the researcher to use prior information about the model’s parameters and, under set identification, it may be computationally more convenient than a frequentist approach. By extending and adapting the algorithms in GK to allow for identification using proxy variables alongside standard zero and sign restrictions, we provide a general and flexible tool for empirical researchers to relax potentially controversial point-identifying restrictions without having to adopt an unrevisable prior. Using a simple analytical example, we show that our robust Bayesian procedure does not provide valid frequentist inference about the identified set under weak-proxy asymptotics, which contrasts the results in Kline and Tamer (2016) and GK.

The SVAR
Identification using proxies
Robust Bayesian inference
Frequentist validity
Strong proxies
Weak proxies
Numerical implementation
Further details about step 2
Choice of prior
Convergence issues and alternative algorithms The optimisation problem in
Point identification
Other objects of interest
Impulse responses to a unit shock
Empirical application
Findings
Conclusion
Full Text
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