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

98 Pages Posted: 24 Mar 2020 Last revised: 3 Aug 2021

Date Written: July 28, 2021


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 the signal-to-noise parameter λ(z) which controls the severity of the 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 a misspecification in Holston et al.’s (2017) Stage 2 model. Moreover, their implementation of MUE on this misspecified Stage 2 model spuriously amplifies the point estimate of λ(z). Using a simulation experiment, I show that their procedure leads to 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 results in 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 outlines various other issues with Holston et al.’s (2017) model of the natural rate that make it unsuitable for policy analysis.

Keywords: Natural Rate of Interest, Median Unbiased Estimation, Kalman Filter, Spuri- Ous Relations, Mis-specified Econometric Models.

JEL Classification: C32, E43, E52, O40.

Suggested Citation

Buncic, Daniel, Econometric Issues with Laubach and Williams’ Estimates of the Natural Rate of Interest (July 28, 2021). Available at SSRN: or

Daniel Buncic (Contact Author)

Stockholm Business School ( email )

Stockholm University


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