Structural multi-equation macroeconomic models: complete versus limited-information identification-robust estimation and fit

Abstract

We propose two system-based identification-robust methods for structural models including DSGEs that are valid whether identification is weak or strong, and whether identification is theory-intrinsic and/or data specific. The first one is a full-information method, which relies on restrictions strong enough to allow the existence of a rational-expectations solution, while the second one is a limited-information approach that relies on weaker assumptions even though it remains system-based. We apply the proposed methods to a standard New Keynesian model for the U.S. We impose and relax a unique rational expectation solution, maintaining similar lagrestrictions on regression disturbances in both cases. In the latter case, we also compare singleequation to multi-equation estimation and fit. We find that when a unique stable equilibrium is imposed to complete the model, it is rejected by the data. In contrast, limited-information multiequation inference produces informative results - that cannot be reached via single-equation methods - regarding the importance of forward-looking behavior in the NKPC, and precise conclusions on the feedback coefficients in the reaction function which are not at odds with the Taylor principle.