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 infor-mation on the shocks identified by the external instruments. In the latter case, the additional restrictions may be overidentifying and checked against the data. In a sec-ond setting, we assume that proxy variables are only ‘plausibly exogenous’. In this case, various inequality restrictions based e.g. on correlations or variance contribu-tions can be used for set-identification. This can be combined with conventional sign restrictions to further narrow down the set of admissible models. For our B-model type Proxy SVAR setup, we develop Bayesian inference and discuss the computation of Bayes factors to check overidentifying restrictions. We illustrate the usefulness of our methodology in estimating the effects of oil market and monetary policy shocks.