Wu-Xia Shadow Federal Funds Rate

Updated 5/5/2015

Since December 2008 the federal funds rate has been in the 0 to 1/4 percent range targeted by the Federal Open Market Committee. In this "zero lower bound" environment, a number of researchers have used shadow rate models to characterize the term structure of interest rates (Kim and Singleton (2012) and Bauer and Rudebusch (2013)) or quantify the stance of monetary policy (Bullard (2012) and Krippner (2013)). This web page hosts estimates from the Wu and Xia (2014) model of the shadow rate. Unlike the observed short-term interest rate, the shadow rate—first introduced by Fischer Black (1995)—is not bounded below by 0 percent. Whenever the Wu-Xia shadow rate is above 1/4 percent, it is exactly equal to the model implied one-month interest rate by construction.

The input data for the Cynthia Wu and Fan Dora Xia model are one-month forward rates beginning n years hence. Wu and Xia use forward rates corresponding to n = 1/4, 1/2, 1, 2, 5, 7, and 10 years. These forward rates are constructed with end-of-month Nelson-Siegel-Svensson yield curve parameters from the Gurkaynak, Sack, and Wright (2006) dataset. The full details of the Wu and Xia model are described in their accompanying working paper. In short, the shadow rate is assumed to be a linear function of three latent variables called factors, which follow a VAR(1) process. The latent factors and the shadow rate are estimated with the extended Kalman filter.