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Title: Refining set-identification in VARs through independence Authors:  Thorsten Drautzburg - Federal Reserve Bank of Philadelphia (United States) [presenting]
Jonathan Wright - Johns Hopkins University (United States)
Abstract: Identification in VARs has traditionally mainly relied on second moments. Some researchers have considered using higher moments as well, but there are concerns about the strength of the identification obtained in this way. We propose refining existing identification schemes by augmenting sign restrictions with a requirement that rules out shocks whose higher moments significantly depart from independence. This approach does not assume that higher moments help with identification; it is robust to weak identification. In simulations, we show that it controls coverage well, in contrast to approaches that assume that the higher moments deliver point-identification. However, it requires large sample sizes and/or considerable non-normality to reduce the width of confidence intervals by much. We consider some empirical applications. We find that it can reject many possible rotations. The resulting confidence sets for impulse responses may be non-convex, corresponding to disjoint parts of the space of rotation matrices. We show that, in this case, augmenting sign and magnitude restrictions with an independence requirement can yield bigger gains.