Identifying Policy Causal Effects from Rule Changes

Recent applied work has used interacted local projections to study how the propagation of macroeconomic shocks changes with the policy regime. We characterize the estimand of such strategies and relate it to the policy shock literature. Our main result is a set of conditions on the regressors and underlying data-generating process under which those two approaches are equivalent in the nature of their estimand, with both identifying slices of the same space of policy dynamic causal effects. Since policy is inherently high-dimensional, however, the two approaches generically recover different slices of that space. For example, for monetary policy, standard shocks tend to deliver the effects of transitory policy rate changes, while looking across policy regimes instead isolates gradual, more forward guidance-like policy treatments.