Dynamic effects of persistent shocks

We show that several shocks identified without restrictions from a model, and frequently used in the empirical literature, display some persistence. We demonstrate that the two leading methods to recover impulse responses to shocks (moving average representations and local projections) treat persistence differently, hence identifying different objects. In particular, standard local projections identify responses that include an effect due to the persistence of the shock, while moving average representations implicitly account for it. We propose methods to re-establish the equivalence between local projections and moving average representations. In particular, the inclusion of leads of the shock in local projections allows to control for its persistence and renders the resulting responses equivalent to those associated to counterfactual non-serially correlated shocks. We apply this method to well-known empirical work on fiscal and monetary policy and find that accounting for persistence has a sizable impact on the estimates of dynamic effects.