Joint Confidence Sets for Structural Impulse Responses

Atsushi Inoue and Lutz Kilian

No 1401, Departmental Working Papers from Southern Methodist University, Department of Economics

Abstract: Many users of structural VAR models are primarily interested in learning about the shape of structural impulse response functions. This requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint inference is complicated by the fact that the joint distribution of structural impulse response becomes degenerate when the number of structural impulse responses of interest exceeds the number of model parameters, as is often the case in applied work. This degeneracy may be overcome by transforming the estimator appropriately. We show that the joint Wald test is invariant to this transformation and converges to a nonstandard distribution, which can be approximated by the bootstrap, allowing the construction of asymptotically valid joint confidence sets for any subset of structural impulse responses, regardless of whether the joint distribution of the structural impulse responses is degenerate or not. We demonstrate by simulation the coverage accuracy of these sets in finite samples under realistic conditions. We make the case for representing these joint confidence sets in the form of "shotgun plots" rather than joint confidence bands for impulse response functions. Several empirical examples demonstrate that this approach not only conveys the same information as confidence bands about the statistical significance of response functions, but provides economically relevant additional information about the shape of response functions that is lost when reducing the joint confidence set to two-dimensional bands

Keywords: Confidence Bands; Simultaneous Inference; Singular Covariance Matrix. (search for similar items in EconPapers)
JEL-codes: C32 C52 C53 (search for similar items in EconPapers)
Date: 2014-02
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Joint confidence sets for structural impulse responses (2016)
Working Paper: Joint Confidence Sets for Structural Impulse Responses (2016)
Working Paper: Joint Confidence Sets for Structural Impulse Responses (2014)
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