On a Standard Method for Measuring the Natural Rate of Interest

I show that Holston, Laubach and Williams' (2017) implementation of Median Unbiased Estimation (MUE) cannot recover the signal-to-noise ratio of interest from their Stage 2 model. Moreover, their implementation of the structural break regressions which are used as an auxiliary model in MUE deviates from Stock and Watson's (1998) formulation. This leads to spuriously large estimates of the signal-to-noise parameter $\lambda _{z}$ and thereby an excessive downward trend in other factor $z_{t}$ and the natural rate. I provide a correction to the Stage 2 model specification and the implementation of the structural break regressions in MUE. This correction is quantitatively important. It results in substantially smaller point estimates of $\lambda _{z}$ which affects the severity of the downward trend in other factor $z_{t}$. For the US, the estimate of $\lambda _{z}$ shrinks from $0.040$ to $0.013$ and is statistically highly insignificant. For the Euro Area, the UK and Canada, the MUE point estimates of $\lambda _{z}$ are \emph{exactly} zero. Natural rate estimates from HLW's model using the correct Stage 2 MUE implementation are up to 100 basis points larger than originally computed.