A procedure for combining zero and sign restrictions in a VAR-identification scheme

In this paper we describe a procedure for implementing zero restrictions within the context of a sign restrictions identification scheme for VARs. The procedure introduces an additional step into the algorithm outlined in Fry and Pagan (2011) and Rubio-Ramirez et al. (2006) for implementing sign restrictions. This extra step involves rotating a candidate identification matrix using Givens rotation matrices to introduce zero restrictions. We then check whether the elements of the candidate matrix satisfy the sign restrictions as usual. We illustrate how our procedure works by generating artificial data from the theoretical model of An and Schorfheide (2007), which implies certain restrictions on the impact of its structural shocks on the model's endogenous variables. We exploit our knowledge of that pattern to identify structural shocks from the reduced-form errors of a VAR estimated on the simulated data.