Dynamic effects of persistent shocks

We provide evidence that many narrative shocks used by prominent literature display some persistence. We show that the two leading methods to estimate impulse responses to an independently identified shock (local projections and distributed lag models) treat persistence differently, hence identifying different objects. We propose corrections to re-establish the equivalence between local projections and distributed lag models, providing applied researchers with methods and guidance to estimate their desired object of interest. We apply these methods to well-known empirical work and find that how persistence is treated has a sizable impact on the estimates of dynamic effects.