Dynamic Identification Using System Projections and Instrumental Variables

We propose System Projections with Instrumental Variables (SP-IV) to estimate dynamic structural relationships. SP-IV replaces lag sequences of instruments in traditional IV with lead sequences of endogenous variables. SP-IV allows the inclusion of controls to weaken exogeneity requirements, can be more efficient than IV with lags, and allows identification over many time horizons without creating many-weak-instruments problems. SP-IV also enables the estimation of structural relationships across impulse responses obtained from local projections or vector autoregressions. We provide a bias-based test for instrument strength, and inference procedures under strong and weak identification. SP-IV outperforms competing estimators of the Phillips Curve parameters in simulations. We estimate the Phillips Curve implied by the main business cycle shock of Angeletos et al. (2020), and find evidence for forward-looking behavior. The data is consistent with weak but also relatively strong cyclical connections between inflation and unemployment