VAR Inference Under Sign Restrictions

VAR Inference Under Sign Restrictions - Inference for VARs...

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Unformatted text preview: Inference for VARs Identified with Sign Restrictions Hyungsik Roger Moon University of Southern California Frank Schorfheide * University of Pennsylvania, CEPR, NBER Eleonora Granziera University of Southern California Mihye Lee University of Southern California November 3, 2009 Abstract There is a growing literature that partially identifies structural vector autoregres- sions (SVARs) by imposing sign restrictions to the responses of a subset of the en- dogenous variables to a particular structural shock (sign-restricted SVARs). To date, the methods that have been used are only justified from a Bayesian perspective. This paper develops methods of constructing error bands for impulse response functions of sign-restricted SVARs that are valid from a frequentist perspective. We also provide a comparison of frequentist and Bayesian error bands. (JEL: C1, C32) KEY WORDS: Bayesian Inference, Frequentist Inference, Partially Identified Models, Sign Restrictions, Structural VARs. * Correspondence: H.R. Moon, E. Granziera, M. Lee: Department of Economics, University of South- ern California, KAP 330C, Los Angeles, CA 90089. Email: [email protected], [email protected], mi- [email protected] F. Schorfheide, Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104. Email: [email protected] We thank Eric Renault as well as seminar par- ticipants at the 2009 Canadian Econometric Study Group Meeting and the University of Pennsylvania for helpful comments. Schorfheide gratefully acknowledges financial support from the National Science Foun- dation under Grant SES 0617803. This Version: November 3, 2009 1 1 Introduction During the three decades following Sims (1980)’s “Macroeconomics and Reality” structural vector autoregressions (SVARs) have become an important tool in empirical macroeco- nomics. They have been used for macroeconomic forecasting and policy analysis, to inves- tigate the sources of business cycle fluctuations, and to provide a benchmark against which modern dynamic macroeconomic theories can be evaluated. The most controversial step in the specification of a structural VAR is the mapping between reduced form one-step-ahead forecast errors and orthogonalized, interpretable, structural innovations. Most SVARs in the literature have been constructed by imposing sufficiently many restrictions such that the relationship between structural innovations and forecast errors is one-to-one. However, in the past decade, starting with Faust (1998), Canova and Nicolo (2002), and Uhlig (2005), empirical researchers have used more agnostic approaches that generate bounds on struc- tural impulse response functions by restricting the sign of certain responses. We will refer to this class of models as sign-restricted SVARs. They have been employed, for instance, to measure the effects of monetary policy shocks (Faust, 1998; Canova and Nicolo, 2002; Uhlig, 2005), technology shocks (Dedola and Neri, 2007; Peersman and Straub, 2009), gov-...
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VAR Inference Under Sign Restrictions - Inference for VARs...

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