Estimation and Inference under Weak Identification and Persistence in Dynamic Nonlinear Regression

Abstract

The reaction coefficients in the forecast-based monetary policy reaction function are only weakly identified when the smoothing coefficient for the nominal interest rate is close to unity. This situation also causes the nominal interest rate to be highly persistent. Inference based on the standard strong identification assumption and recently developed identification robust procedures based on stationarity fail in this setting, and we propose modifications. In particular, based on nonlinear least squares (NLS) estimation, we develop valid confidence sets for reaction coefficients that are robust to a wide range of the smoothing coefficient, including close and distant neighborhoods of unity. Allowing for both potential weak identification and a nearly unit root constitutes the novelty of the suggested procedure. Our empirical application using recently available real-time data suggests that, whether the estimates are accurate enough to rule out the possibility of indeterminacy in US monetary policy depends on forecast horizons of expected inflations and output gaps used in the model.