On the form of the rotation matrix in a traditional sign-identified VAR

This paper examines the implications of the form of the rotation matrix for the impulse responses in a traditional sign-identified empirical VAR. In traditional sign restrictions, the rotation matrix is generated by either Givens matrices or by the orthogonal matrix from a QR decomposition. We show that when sign restrictions are used to identify the shocks in the empirical VAR, the method used to rotate the shocks, whether it be Givens or QR, produces accepted impulse responses which are very similar and which give the same inferences. We show that this occurs because the rotation matrices implied by the accepted impulse responses are similar, due to the sign restrictions which identify the shocks. This implies that the accepted responses are influenced mainly by the rotation matrix, be it Givens or QR, and not the Cholesky factor which also influences the accepted impulse responses, and unlike the rotation matrix depends on the data.