Local Projections When IVs are Correlated with Multiple Shocks

Abstract: Local-projection instrumental-variable (LP-IV) methods typically assume that an instrument is correlated with a single structural shock. We study the empirically relevant case in which an IV loads on multiple shocks, as in narrative tax instruments and high-frequency monetary surprises. In this setting, the usual impact normalization becomes a matrix normalization, so conventional LP-IV identifies only rotation-mixtures of structural impulse responses. Additional instruments do not by themselves resolve this indeterminacy, because the impact matrix and dynamic responses remain jointly unidentified up to rotation. We restore identification using Rigobon (2003)-type regime-dependent heteroskedasticity and estimate the structural dynamic responses by local projections. The method preserves the noninvertibility robustness of IV-based identification (Plagborg-Møller and Wolf, 2021). We apply it to the monetary-policy and central-bank-information shocks of Jarociński and Karadi (2020) and to the tax multipliers of Mertens and Ravn (2013).