Wu-Xia Shadow Federal Funds Rate
The Federal Open Market Committee has targeted the federal funds rate between 0 and 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 characlterize 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.
As long as the FOMC maintains the target range for the federal funds rate at 0 to 1/4 percent, we will generally try and update the Wu-Xia shadow federal funds rate on the day of, or the business day after, the Federal Reserve Board of Governors first releases the Gurkaynak, Sack, and Wright (GSW) daily yield curve estimates for the last business day of the previous month. The Board typically releases the GSW data weekly on Tuesdays for the period up to the Friday of the previous week.
April 8, 2022, note: As the Federal Open Market Committee (FOMC) raised the target range for the federal funds rate from 0 to 0.25 percent to 0.25 to 0.50 percent on March 16, we have suspended updates to the Wu-Xia shadow rate. When the target range is above 0 to 0.25 percent, the shadow rate is generally close to the effective fed funds rate. Updates to the shadow rate will be suspended as long as the target range for the fed funds rate remains above 0 to 0.25 percent.
The Wu-Xia shadow federal funds rate stood at 0.21 percent on February 28. 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)
- Documentation for Leo Krippner estimates of shadow short rate