Identification in Dynamic Models Using Sign Restrictions

35 Pages Posted: 26 Jan 2014  

Bulat Gafarov

Pennsylvania State University; National Research University Higher School of Economics

Date Written: January 12, 2014


Sign restrictions on impulse response functions are used in the literature to identify structural vector autoregressions and structural factor models. I extend the rank condition used for exclusion restrictions and provide a necessary and sufficient conditions for point identification for sign restrictions in this class of models. The necessary condition for point identification implies that as the number of sign restrictions grows a subset with sufficient number of sign restrictions becomes binding in the limit. However, one does not need to possess information about this subset to achieve point identification. So when exclusion restrictions are not justified by theory, sign restrictions can provide an alternative way to get point-identified impulse response functions. Also further, I present a closed form representation of the set of all impulse response functions satisfying a set of sign restrictions. I demonstrate that restrictions on responses to all shocks can dramatically shrink this set when compared to restrictions only on a small number of shocks.

Keywords: SVAR, SFM, point identification, sign restrictions

JEL Classification: C1, C32, C38, E47

Suggested Citation

Gafarov, Bulat, Identification in Dynamic Models Using Sign Restrictions (January 12, 2014). Available at SSRN: or

Bulat Gafarov (Contact Author)

Pennsylvania State University ( email )

524 Kern Graduate Building
University Park, PA 16802-3306
United States


National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, PA Moscow 119017


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