Dynamic Identification Using System Projections and Instrumental Variables
Abstract: We propose System Projections on Instrumental Variables (SP-IV) to estimate dynamic structural relationships using impulse responses obtained from local projections or vector autoregressions. SP-IV replaces lag sequences of instruments in traditional IV with lead sequences of endogenous variables. By allowing the inclusion of lagged variables as controls, SP-IV weakens exogeneity requirements and can improve efficiency and effective instrument strength relative to 2SLS. We provide inference procedures under strong and weak identification, and show that SP-IV outperforms conventional IV estimators of Phillips Curve parameters in simulations. We estimate the Phillips Curve implied by the main business cycle shock of Angeletos et al. (2020), and find that the impulse response estimates are consistent with weak but also relatively strong cyclical connections between inflation and unemployment.