Different local projection (LP) estimators for structural impulse responses of proxy vector autoregressions are reviewed and compared algebraically and with respect to their small sample suitability for inference. Conditions for numerical equivalence and similarities of some estimators are...

We propose a new bootstrap for inference for impulse responses in structural vector autoregressive models identified with an external proxy variable. Simulations show that the new bootstrap provides confidence intervals for impulse responses which often have more precise coverage than and...