Identification of SVAR Models by Combining Sign Restrictions With External Instruments

ABSTRACT

We discuss combining sign restrictions with information in external instruments (proxy variables) to identify structural vector autoregressive (SVAR) models. In one setting, we assume the availability of valid external instruments. Sign restrictions may then be used to identify further orthogonal shocks, or as an additional piece of information to pin down the shocks identified by the external instruments more precisely. In a second setting, we assume that proxy variables are only “plausibly exogenous” and suggest various types of inequality restrictions to bound the relation between structural shocks and the external variable. This can be combined with conventional sign restrictions to further narrow down the set of admissible models. Within a proxy-augmented SVAR, we conduct Bayesian inference and discuss computation of Bayes factors. They can be useful to test either the sign- or IV restrictions as overidentifying. We illustrate the usefulness of our methodology in estimating the effects of oil supply and monetary policy shocks.

KEYWORDS:

• External instruments
• Proxy VAR
• Sign restrictions
• Structural vector autoregressive model

Supplementary Materials

The supplementary materials contain details and derivations related to Bayesian inference and Bayes factors (Sections A to E) as well as additional material and results associated with the empirical applications (Sections F to H).

Disclosure Statement

The authors report there are no competing interests to declare.

Acknowledgments

We are grateful to a coeditor, an associate editor, and two anonymous referees for many useful comments that helped to improve this article substantially. We also thank participants of several conferences and seminars for useful comments, and Gökhan Ider for excellent research assistance. Part of this research has been conducted when the second author was visiting Monash University, Australia. The views expressed in this article do not reflect those of the Bank of England or its committees.

Additional information

Funding

Financial support of the Graduate School of Decision Sciences (GSDS) at the University of Konstanz and the German Science Foundation (grant number: BR 2941/3-1) is gratefully acknowledged.