A Window into Bond Investors’ Uncertainty About R‑Star

Monetary policymakers scrutinize the term structure of sovereign bond yields to glean insights into market participants' expectations regarding future monetary policy, inflation, and economic activity. A significant focus lies on the natural real rate of return, or "r-star," which serves as a benchmark for monetary policy decisions.

Recent research questions the extent of information investors possess and their precision in understanding r-star. This article, based on a recent Staff Report, delves into what the bond yield term structure can disclose about r-star and investors' perception of it.

The study utilizes a bond pricing framework that acknowledges the presence of incomplete information. It is presumed that aggregate macroeconomic variables are influenced by long-term trends and short-lived cyclical fluctuations, the latter of which remain undisclosed to investors at the time. Consequently, investors infer a decomposition of these aggregates into perceived long- and short-run components, based on all available macroeconomic data and private information.

For instance, if investors observe a short-term interest rate of 5 percent, alongside inflation and growth metrics, coupled with the historical economic trajectory, they may infer a separation into a 2 percent trend and a 3 percent cycle. However, this decomposition is imperfect, as true economic conditions may deviate from investors' beliefs, yet it remains optimal given their available information.

The framework indicates that when assessing the term structure of interest rates, investors primarily consider their subjective interpretation of the trend and cycle components of the short-term interest rate, rather than the actual, unobservable states. Consequently, bond yields encapsulate the perceived trend and cycle components, allowing policymakers to glean information about investors' perspectives, provided the information differs from policymakers' own knowledge. In essence, the bond yield term structure can only reveal the information accessible to investors.

The empirical analysis employing a realistic bond pricing model reveals several critical insights. Observations of three macroeconomic variables—interest rates, inflation, and growth—are utilized, but their decomposition into short- and long-run components is not accessible to investors. Drawing upon macrofinance literature, a finance-based measure of r-star is defined as the difference between the nominal interest rate trend and the inflation trend.

Furthermore, it is assumed that investors possess private information regarding the economy's long-term trajectory, denoted by an unobservable factor by econometricians. By analyzing quarterly yield curve data and macroeconomic statistics from the United States spanning the 1960s, the model uncovers several noteworthy points.

Firstly, investors perceive the trends in interest rates, inflation, and growth as sluggishly evolving, yet exhibit considerable uncertainty. The estimated 95 percent confidence bands for the nominal interest rate trend (i-star) range from ±225 basis points, for inflation (pi-star) from ±125 basis points, and for growth (growth trend) from ±80 basis points.

By the conclusion of the dataset in 2022, investors estimated i-star at 3.75 percent, with a confidence band spanning [1.55 percent, 5.95 percent]. This underscores the substantial uncertainty involved in estimating the fundamental drivers of the economy.

Subsequent examination focuses on investors' expectations of r-star, represented by the spread between i-star and pi-star. The perceived r-star trend, depicted in gold in the accompanying chart, exhibits a remarkably stable trajectory from the 1960s to 2022, fluctuating between 0 percent and 2.5 percent. The estimates align with those of Bauer and Rudebusch (2020), who also utilize yield curve data.

Nevertheless, the trend estimates derived from this study are smoother and less volatile compared to those produced by Laubach and Williams (2003), accessible on the New York Fed's website (represented in blue in the chart). However, estimates of investors' 95 percent confidence bands for r-star at ±170 basis points reveal that Laubach and Williams' r-star remains within these bounds from the 1970s onward, indicating low volatility in their estimates.

The study also quantifies investors' real-time estimates of perceived r-star, emphasizing that these assessments are based solely on information available up to a specific point in time. Consequently, these estimates are compared to alternative real-time estimations. Due to the inherent uncertainties faced by investors, the increase in r-star at the end of the dataset is more gradual and subdued than suggested by other financial-based models or term structure models.

This finding calls into question the notion that the era of low r-star rates is a thing of the past. Lastly, the analysis incorporates the computation of two-sided investors' r-star estimates, illustrated in green in the chart. Two observations emerge: first, the uncertainty bands remain considerable, reinforcing the theme of investor uncertainty; second, the perceived r-star trend presents a stable path without significant fluctuations over the analyzed period, further corroborating the findings.