Identifying modern macro equations with old shocks

Despite decades of research, the consistent estimation of structural forward-looking macroeconomic equations remains a formidable empirical challenge because of pervasive endogeneity issues. Prominent cases—the estimation of Phillips curves, Euler equations, or monetary policy rules—have typically relied on using predetermined variables as instruments, with mixed success. In this work, we propose a new approach that consists in using sequences of independently identified structural shocks as instrumental variables. Our approach is robust to weak instruments and is valid regardless of the shocks’ variance contribution. We estimate a Phillips curve using monetary shocks as instruments and find that conventional methods substantially underestimate the slope of the Phillips curve.