The Federal Reserve (Fed) is tasked with maintaining price stability and achieving maximum employment. In practice, over the last decades, the Fed has sought to achieve its objectives primarily through the manipulation of a short-term interbank interest rate, the federal funds rate (FFR). At the height of the Great Recession of 2007–2009, the Fed pushed its benchmark policy rate to zero. With its principal tool unavailable, the Fed resorted to a sequence of unconventional policy actions in an attempt to provide further stimulus to the economy. These actions included large-scale asset purchases (more commonly referred to as quantitative easing, or QE) and forward guidance. These programs were viewed by most as solutions to the temporary problem of the zero lower bound (ZLB) on the short-term policy rate. Market participants never expected the ZLB to last more than a couple of years (Bauer and Rudebusch 2016; Wu and Xia 2016), but in actuality the FFR was at zero for seven years. And though the Fed began raising the FFR at the end of 2015, it has since cut it three times, and at present, the FFR sits less than 200 basis points above zero. Markets are expecting further rate cuts in the near future. A substantial body of research finds that the so-called natural rate of interest, or sometimes “r-star,” is on a continuing secular

Two novel models specify interest rates from factors other than time to demonstrate bond market expectations of riskless rates converge to the natural rate of interest. The first yield curve model is based upon risk rather than time. The riskless rate is the incremental yield for an infinitesimal amount of risk and is computed directly from bond yields. Resulting expected riskless rates are comparable to survey measures of expected short-term rates. Conversely, expected riskless rates for specific periods produce expected bond yields for those periods that also are comparable to survey expectations measures. The model produces a typical concave yield curve shape. The second model aligns with Wicksell’s original conception of a natural rate of interest as determined by productivity of real capital rather than time. The natural rate is the capital factor share of incremental growth from capital investment. The savings/consumption function is determined by equivalence between incremental capital product and forgone consumption, replacing the problematic IS equation. This proxy provides a real rate of interest consistent with short-term yields in the U.S. and other advanced economies, especially when adjusted for central bank intervention. The measure is more stable and easier to estimate than other natural rate measures. This natural rate of interest proxy provides better forecasts of riskless rates over multi-year horizons than do expectations measures. Future yield curves are