Shadow Rates : When the Central Bankers Hit The Bottom

A very interesting concept

Basically it determines the equivalent short rate in an economy where policy rate has hit the Zero Lower Bound (ZLB). The methodology uses a standard Gaussian affine term structure model, augment by two equations. The first one in which the ZLB is covered by modelling the short rate r as r = Max(z, s), where z is the lower bound on the short rate, and the shadow rate s. This of course non-linearize the term structure model. The second tweak is to approximate the resulting forward rates in to a closed form solution, which make the model very much tractable. 

This still requires extended Kalman filter to solve the system (becuase of the non-linearlity), and hence needs writing explicit code unfortunately. Most of the standard packages will have only linear Kalman filter implemented

Nevertheless, this is a very useful way to extract the implied short rate, as the market prices in various conventional and unconventional policy measures. The plot below cleatly shows the shadow rate effectively shadow the policy rates in a non-ZLB world. And once the policy rate hits ZLB, the shadow rates breaks free. The significant moves of the shadow rates also implies the information content which is lost in the policy rates stuck at zero

And looking at the figures it becomes explicit how the lack of ECB action has been effectively a large tightening in the Eurozone. From 2013 beginning the shadow rate for Euro area has tightened by more than 200bps. That is a LOT of tightening for an aneamic economy strucggling to find green shoots

The US case also interesting, as it shows recently the shadow rate has ventured in to further negative territory. And the UK I would have expected a bit more tightening from mid of last year than the model values suggest. I do not have any explanation for either currently. I will have a closer look as soon as I can manage to get some decent code for extended Kalman