Estimation and Inference under Weak Identi…cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function

The reaction coefficients of expected inflations and output gaps in the forecast-based monetary policy reaction function may be merely weakly …identified when the smoothing coefficient is close to unity and the nominal interest rates are highly persistent. In this paper we modify the method of Andrews and Cheng (2012, Econometrica)on inference under weak / semi-strong identification to accommodate the persistence issue. Our modification involves the employment of asymptotic theories for near unit root processes and novel drifting sequence approaches. Large sample properties with a desired smooth transition with respect to the true values of parameters are developed for the nonlinear least squares (NLS) estimator and its corresponding t / Wald statistics of a general class of models. Despite the not-consistent-estimability, the conservative confidence sets of weakly-identified parameters of interest can be obtained by inverting the t / Wald tests. We show that the null-imposed least-favorable confidence sets will have correct asymptotic sizes, and the projection-based method may lead to asymptotic over-coverage. Our empirical application suggests that the NLS estimates for the reaction coefficients in U.S.Âs forecast-based monetary policy reaction function for 1987:3Â2007:4 are not accurate sufficiently to rule out the possibility of indeterminacy.