Wu-Xia Shadow Federal Funds Rate
The Federal Open Market Committee has targeted the federal funds rate between 0 to ¼ percent from December 16, 2008, to December 15, 2015, and, subsequently, since March 15, 2020. In these "zero lower bound" environments, a number of researchers have used shadow rate models to characterize the term structure of interest rates (Kim and Singleton  and Bauer and Rudebusch ) or quantify the stance of monetary policy (Bullard  and Krippner ). This web page hosts estimates from the Wu and Xia (2016) model of the shadow rate.
Latest update — June 3, 2020
The Wu-Xia shadow federal funds rate stood at 0.48 percent on May 29. The rate is constructed with underlying input data for Gurkaynak, Sack, and Wright yield curve estimates.
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 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.
- The Shadow Knows (the Fed Funds Rate) (macroblog)
- What Is the Stance of Monetary Policy? (macroblog)
- Shadow Interest Rates and the Stance of U.S. Monetary Policy (St. Louis Fed)
- Summarizing Monetary Policy (Econbrowser)