Local projections identify the same policy counterfactuals as empirical and structural models

Abstract

We study policy counterfactuals that impose path restrictions on a policy instrument over a finite window. Under a sequential intervention design, we define two counterfactual objects, policy-peg impulse responses and policy-path effects, and we provide a novel local projection identification method. Under policy invariance and a linear moving average envelope, the local projection estimands coincide with the counterfactual outcomes implied by empirical vector autoregressions and linearized forward looking structural models, and the counterfactual outcomes are fully characterized by the relevant impulse responses. We also provide local projection identification of both counterfactual objects under an one-shot intervention design. In the empirical applications, we quantify the propagation of an oil-supply news shock under interest-rate pegs and study alternative liftoff paths during the post-pandemic tightening episode.