论文标题
Laubach和Williams对自然利率的估计的计量经济学问题
Econometric issues with Laubach and Williams' estimates of the natural rate of interest
论文作者
论文摘要
Holston，Laubach and Williams（2017）自然利率的估计是由“其他因素” $ z_ {t} $的向下趋势行为驱动的。我表明，他们对股票和沃森（1998）的实施实施了中值无偏见的估计（MUE），以确定$λ_{z} $参数的大小，该估计的大小不符合$ z_ {t} $的下降趋势。它无法恢复利益的比率$λ_{z} = a_ {r}σ_{z}/σ_ {\ tilde {y}} $从估计完整结构模型所需的mue中。这种失败是由于Holston等人（2017）对第2阶段模型的表述中的“不必要”错误指定。更重要的是，他们在此误指出的阶段2模型上的实现微微地放大了$λ_{z} $的点估计值。使用仿真实验，我表明他们的过程在从模型生成的数据应用于TRUE $λ_{Z} $等于零的模型中生成的数据时会产生过多的$λ_{Z} $的估计。在其2阶段模型中纠正错误指定和MUE的实现会导致$λ_{z} $估计值较小，因此，“其他因素” $ z_ {t} $对自然率的“其他因素” $ z_ {t}的下降趋势影响更大。此外，$λ_{z} $点估计在统计上是无关紧要的，这表明该模型中的“其他因素” $ z_ {t} $没有作用。我还讨论了Holston等人（2017）自然率模型中出现的其他各种估计问题，使其不适合政策分析。
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 $λ_{z}$ parameter which drives this downward trend in $z_{t}$ is unsound. It cannot recover the ratio of interest $λ_{z}=a_{r}σ_{z}/σ_{\tilde{y}}$ from MUE required for the estimation of the full structural model. This failure is due to an 'unnecessary' misspecification in Holston et al.'s (2017) formulation of the Stage 2 model. More importantly, 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 generates excessively large estimates of $λ_{z}$ when applied to data generated from a model where the true $λ_{z}$ is equal to zero. Correcting the misspecification in their Stage 2 model and the implementation of MUE leads to a substantially smaller $λ_{z}$ estimate, and with this, a more subdued downward trending influence of 'other factor' $z_{t}$ on the natural rate. Moreover, the $λ_{z}$ point estimate is statistically highly insignificant, suggesting that there is no role for 'other factor' $z_{t}$ in this model. I also discuss various other estimation issues that arise in Holston et al.'s (2017) model of the natural rate that make it unsuitable for policy analysis.
