The Role of Initial States in Estimates of the Natural Rate of Interest

This paper provides an analysis of the relevance of initial states for the estimation of natural rates of interest. It focuses on U.S. data using an established semi-structural macroeconomic model with time-varying trends. Alternative methods for the specification of initial states are reviewed and evaluated. The results indicate that initial states can significantly impact end-of-sample estimates of the natural rate of interest, with alternative initials leading to estimates about 40 to 130 basis points lower than original estimates. Re-estimating the model with alternative initials also leads to more volatile natural rate estimates. Key dimensions of the initialization issue are discussed, including the uncertainty around initial estimates, the use of diffuse prior initials, and jointly estimated initials. An extension of the original method using an unobserved component model that makes all initial estimates data-dependent is found to provide the most robust model and state estimates relative to varying sample definitions.