Econometric issues with Laubach and Williams estimates of the natural rate of interest

Document pages: 98 pages

Abstract: Holston, Laubach and Williams (2017) estimates of the natural rate ofinterest are driven by the downward trending behaviour of other factor $z {t}$. I show that their implementation of Stock and Watson s (1998) MedianUnbiased Estimation (MUE) to determine the size of the $ lambda {z}$ parameterwhich drives this downward trend in $z {t}$ is unsound. It cannot recover theratio of interest $ lambda {z}=a {r} sigma {z} sigma { tilde{y}}$ from MUErequired for the estimation of the full structural model. This failure is dueto an unnecessary misspecification in Holston et al. s (2017) formulation ofthe Stage 2 model. More importantly, their implementation of MUE on thismisspecified Stage 2 model spuriously amplifies the point estimate of $ lambda {z}$. Using a simulation experiment, I show that their procedure generatesexcessively large estimates of $ lambda {z}$ when applied to data generatedfrom a model where the true $ lambda {z}$ is equal to zero. Correcting themisspecification in their Stage 2 model and the implementation of MUE leads toa substantially smaller $ lambda {z}$ estimate, and with this, a more subdueddownward trending influence of other factor $z {t}$ on the natural rate.Moreover, the $ lambda {z}$ point estimate is statistically highlyinsignificant, suggesting that there is no role for other factor $z {t}$ inthis model. I also discuss various other estimation issues that arise inHolston et al. s (2017) model of the natural rate that make it unsuitable forpolicy analysis.