Inference About Non-Identified SVARs

45 Pages Posted: 8 Dec 2014

See all articles by Raffaella Giacomini

Raffaella Giacomini

University College London - Department of Economics; University of California, Los Angeles - Department of Economics

Toru Kitagawa

University College London

Date Written: December 2014


We propose a method for conducting inference on impulse responses in structural vector autoregressions (SVARs) when the impulse response is not point identified because the number of equality restrictions one can credibly impose is not sufficient for point identification and/or one imposes sign restrictions. We proceed in three steps. We first define the object of interest as the identified set for a given impulse response at a given horizon and discuss how inference is simple when the identified set is convex, as one can limit attention to the set's upper and lower bounds. We then provide easily verifiable conditions on the type of equality and sign restrictions that guarantee convexity. These cover most cases of practical interest, with exceptions including sign restrictions on multiple shocks and equality restrictions that make the impulse response locally, but not globally, identified. Second, we show how to conduct inference on the identified set. We adopt a robust Bayes approach that considers the class of all possible priors for the non-identified aspects of the model and delivers a class of associated posteriors. We summarize the posterior class by reporting the "posterior mean bounds", which can be interpreted as an estimator of the identified set. We also consider a "robustified credible region" which is a measure of the posterior uncertainty about the identified set. The two intervals can be obtained using a computationally convenient numerical procedure. Third, we show that the posterior bounds converge asymptotically to the identified set if the set is convex. If the identified set is not convex, our posterior bounds can be interpreted as an estimator of the convex hull of the identified set. Finally, a useful diagnostic tool delivered by our procedure is the posterior belief about the plausibility of the imposed identifying restrictions.

Keywords: ambiguous beliefs, credible region, partial causal ordering, posterior bounds

JEL Classification: C11, C54

Suggested Citation

Giacomini, Raffaella and Kitagawa, Toru, Inference About Non-Identified SVARs (December 2014). CEPR Discussion Paper No. DP10287, Available at SSRN:

Raffaella Giacomini (Contact Author)

University College London - Department of Economics ( email )

Gower Street
London WC1E 6BT, WC1E 6BT
United Kingdom

University of California, Los Angeles - Department of Economics ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095-1361
United States

Toru Kitagawa

University College London

Gower Street
London, WC1E 6BT
United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics