Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/128451 
Year of Publication: 
2016
Series/Report no.: 
CESifo Working Paper No. 5746
Publisher: 
Center for Economic Studies and ifo Institute (CESifo), Munich
Abstract: 
Many questions of economic interest in structural VAR analysis involve estimates of multiple impulse response functions. Other questions relate to the shape of a given impulse response function. Answering these questions 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 the structural impulse response estimators 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 propose to represent the 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 may be used to provide economically relevant additional information about the shape of and comovement across response functions that is lost when reducing the joint confidence set to two-dimensional bands.
Subjects: 
joint inference
shotgun plots
confidence bands
impulse response shapes
bootstrap
degenerate limiting distribution
JEL: 
C32
C52
C53
Document Type: 
Working Paper
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