Bond investors face massive uncertainty when estimating r-star, the natural real rate of return that guides monetary policy, with a confidence band of plus or minus 170 basis points, according to a new study published August 4 by the Federal Reserve Bank of New York. The research, authored by Guillaume Roussellet, explores what the term structure of interest rates reveals about r-star and how precisely investors understand it. The findings suggest that financial-based estimates of r-star come with far more uncertainty than commonly acknowledged.
The study's model, estimated on quarterly U.S. yield curve and macroeconomic data from the 1960s onward, produces 95 percent confidence bands of plus or minus 225 basis points for the nominal interest rate trend, plus or minus 125 basis points for the inflation trend, and plus or minus 80 basis points for the growth trend. At the end of the sample in 2022, investors estimated the nominal interest rate trend at 3.75 percent with a 95 percent confidence band stretching from 1.55 percent to 5.95 percent. The perceived r-star trend shows a remarkably stable path from the 1960s to 2022, ranging between 0 percent and 2.5 percent, and aligns closely with estimates from Bauer and Rudebusch's 2020 research. Even when investors have access to the full history from 1960 to 2022—eliminating real-time constraints—uncertainty bands remain as wide as plus or minus 130 basis points, reflecting persistent ambiguity surrounding r-star.
The report finds that investors rely on their subjective assessment of trend and cycle components of the short-term interest rate rather than the true states, which are unobservable to them, when pricing the term structure of interest rates. As a result, "bond yields reflect the perceived trend and cycle components and policymakers can learn from them as long as investors possess different information than the policymakers," the research explains. The study also reveals that investors' estimated r-star during the great moderation turned out lower after the fact than it appeared in real time, indicating that monetary policy was more restrictive than perceived at the time. The increase in r-star at the end of the sample proves more modest and gradual than what other financial-based estimates and term structure models suggest, casting doubt on the death of the low r-star era.
The framework assumes that aggregate macroeconomic variables are driven by long-run trends and shorter-lived cyclical movements, which can't be separated by investors in real time. Instead, based on all aggregate macroeconomic variables and some private information, investors infer a decomposition of the aggregates into perceived long- and short-run components—an imperfect decomposition that is nonetheless optimal given the information they possess. For instance, if investors observe the short-term interest rate at 5 percent, they also observe aggregate inflation and growth, along with the path that led the economy there, and infer a decomposition into 2 percent trend and 3 percent cycle. This mechanism reveals that the term structure of interest rates can only disclose the information that investors can see, not the true underlying economic states.
The yield curve can reveal valuable information about r-star as perceived by investors, even if investors lack perfect knowledge about the state of the economy in real time, the report concludes. Investors are faced with a large degree of uncertainty that doesn't disappear over time, which implies that policymakers should consider financial-based estimates of r-star with accompanying uncertainty measures. The persistent ambiguity surrounding r-star—even with decades of data—means that any single point estimate offers an incomplete picture of where the natural rate actually stands.