Refining Set-Identification in VARs through Independence
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Date
2021-10-06
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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. In this paper, 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.
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Keywords
, vector autoregression, sign restrictions, set-identification, weak identification, independent shocks, non-convex confidence set.