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Joint Confidence Sets for Structural Impulse Responses

Author

Listed:
  • Kilian, Lutz
  • Inoue, Atsushi
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.

Suggested Citation

  • Kilian, Lutz & Inoue, Atsushi, 2014. "Joint Confidence Sets for Structural Impulse Responses," CEPR Discussion Papers 9892, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:9892
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Bootstrap; Confidence regions; Degenerate limiting distribution; Impulse response shapes; Joint inference; Shotgun plots;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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