On a Standard Method for Measuring the Natural Rate of Interest

Abstract

The natural rate of interest is a key latent macroeconomic variable for monetary policy, and is commonly estimated using the structural model of Holston, Laubach and Williams' (2017, HLW). This paper shows that Median Unbiased Estimation (MUE) as implemented in HLW cannot recover the signal-to-noise ratio parameter of interest, and leads to a spurious downward trend in the estimate of the natural rate. The paper provides a correction to the implementation of MUE in HLW. This correction is quantitatively important and results in substantially smaller point estimates of the signal-to-noise ratio parameter that affects the severity of the downward trend in the natural rate. For the US, the point estimate decreases from 0.040 to 0.013, and is statistically highly insignificant. For the Euro Area, the UK and Canada, the MUE point estimates are exactly zero. The resulting natural rate estimates from the corrected MUE implementation are up to 100 basis points larger than originally reported.

Keywords: Natural rate of interest, Median Unbiased Estimation, Kalman Filter, misspecified econometric models, correction to Stage 2 model.

JEL Classification: C32, E43, E52, O40