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 parameter λ(z) which drives this downward trend in z(t) is unsound. It cannot recover the ratio of interest λ(z) = a_r*σ(z)/σ(˜y) from MUE because of an 'unnecessary' misspecification in Holston et al.'s (2017) Stage 2 model. Moreover, their implementation of MUE on this 'unnecessarily' misspecified Stage 2 model spuriously amplifies the point estimate of λ(z). Using a simulation experiment, I show that their procedure generates excessively large estimates of λ(z) when applied to data generated from a model where the true λ(z) is zero. Correcting the misspecification in their Stage 2 model and the implementation of MUE leads to a substantially smaller (and highly insignificant) λ(z) point estimate, and thereby a more subdued downward trend in 'other factor' z(t) and the natural rate. The paper also discusses various other issues with Holston et al.'s (2017) model of the natural rate that make it unsuitable for policy analysis.