Identification of SVAR Models by Combining Sign Restrictions With External Instruments

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.

Automated summary

This article discusses the combination of sign restrictions with information from external instruments to identify structural vector autoregressive (SVAR) models. The availability of valid external instruments allows for the use of sign restrictions to identify additional orthogonal shocks or to provide more precise identification of the shocks identified by the external instruments. In cases where proxy variables are plausibly exogenous, various types of inequality restrictions can be used to limit the relationship between structural shocks and the external variable, narrowing down the set of admissible models. Bayesian inference and computation of Bayes factors are conducted within a proxy-augmented SVAR, which can be used to test the validity of sign or instrumental variable (IV) restrictions. The methodology is illustrated in estimating the effects of oil supply and monetary policy shocks.