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.
Inoue, Atsushi, Guido M. Kuersteiner, and Oscar Jorda. 2023. “Significance Bands for Local Projections,” Federal Reserve Bank of San Francisco Working Paper 2023-15. Available at https://doi.org/10.24148/wp2023-15