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Significance Bands for Local Projections

Author

Listed:
  • Atsushi Inoue
  • Òscar Jordà
  • Guido M. Kuersteiner

Abstract

An impulse response function describes the dynamic evolution of an outcome variable following a stimulus or treatment. A common hypothesis of interest is whether the treatment affects the outcome. We show that this hypothesis is best assessed using significance bands rather than relying on commonly displayed confidence bands. Under the null hypothesis, we show that significance bands are trivial to construct with standard statistical software using the LM principle, and should be reported as a matter of routine when displaying impulse responses graphically.

Suggested Citation

  • Atsushi Inoue & Òscar Jordà & Guido M. Kuersteiner, 2023. "Significance Bands for Local Projections," Working Paper Series 2023-15, Federal Reserve Bank of San Francisco.
    • Handle: RePEc:fip:fedfwp:96372
    DOI: 10.24148/wp2023-15
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    References listed on IDEAS

    as
    1. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
    2. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    3. James H. Stock & Mark W. Watson, 2018. "Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments," Economic Journal, Royal Economic Society, vol. 128(610), pages 917-948, May.
    4. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    5. Christina D. Romer & David H. Romer, 2004. "A New Measure of Monetary Shocks: Derivation and Implications," American Economic Review, American Economic Association, vol. 94(4), pages 1055-1084, September.
    6. Òscar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
    7. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
    8. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2019. "Simultaneous confidence bands: Theory, implementation, and an application to SVARs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 1-17, January.
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    More about this item

    Keywords

    local projections; impulse responses; instrumental variables; Wild Bootstrap;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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