Econometric Issues with Laubach and Williams’ Estimates of the Natural Rate of Interest

Holston, Laubach and Williams' (2017) estimates of the natural rate of interest are driven by the downward trending behaviour of `other factor' $z_{t}$. I show that their implementation of Stock and Watson's (1998) Median Unbiased Estimation (MUE) to determine the size of $\lambda_{z}$ is unsound. It cannot recover the ratio of interest $\lambda _{z}=a_{r}\sigma _{z}/\sigma _{\tilde{y}}$ from MUE required for the estimation of the full structural model. This failure is due to their Stage 2 model being incorrectly specified. More importantly, the MUE procedure that they implement spuriously amplifies the estimate of $\lambda _{z}$. Using a simulation experiment, I show that their MUE procedure generates excessively large estimates of $\lambda _{z}$ when applied to data simulated from a model where the true $\lambda _{z}$ is equal to zero. Correcting their Stage 2 MUE procedure leads to a substantially smaller estimate of $\lambda _{z}$, and a more subdued downward trending influence of `other factor' $z_{t}$ on the natural rate. This correction is quantitatively important. With everything else remaining the same in the model, the natural rate of interest is estimated to be 1.5% at the end of 2019:Q2; that is, three times the 0.5% estimate obtained from Holston et al.'s (2017) original Stage 2 MUE implementation. I also discuss various other issues that arise in their model of the natural rate that make it unsuitable for policy analysis.