当长期趋势未知时：债券定价的影响（英）

N O .1 1 8 7MA R C H 2 0 2 6 Borel Ahonon|Guillaume Roussellet When Long-Run Trends Are Unknown:Bond Pricing ImplicationsBorel AhononandGuillaume RousselletFederal Reserve Bank of New York Staff Reports, no.1187March2026 Abstract We propose a macro-finance model in which inflation, growth, and the policyrate are driven byunobservable long-run trends and transitory cycles that investorsmust infer from aggregate data. Theirsubjective estimates of these trends, and theuncertainty surrounding them, are priced into the Treasuryyield curve in a tractableway through both interest rate expectations and bond risk premia. Empiricalestimatesreveal an upward smooth trend in the long-run real interest rate (r-star) until the 1980s,and JEL classification:C58, E43, E52, G12Keywords:incomplete information, interest rate stars, Bayesian learning, Treasuryyields, This paper presents preliminary findings and is being distributed to economists and other interestedreaders solely to stimulate discussion and elicit comments. The views expressed in this paper are those of 1Introduction The term structure of Treasury yields constitutes a key lens into bond investors’ informationsets and their macroeconomic and financial forecasts. Extracting this information is par-ticularly valuable for monetary policymakers, as it helps assess economic conditions andcalibrate an appropriate policy stance.Central to this calibration is the long-run neutralreal rate of interest —r-star— defined as the real interest rate consistent with a stableeconomy and a policy stance that is neither accommodative nor restrictive (Laubach and Williams 2003).Yet since r-star is inherently unobservable, policymakers must infer itfrom imperfect models and data, a challenge that Powell (2023) famously described as“navigating by the stars under cloudy skies.” The yield curve has emerged as a promising Our model is built from three successive layers. In the first layer, we specify standarddynamics of macroeconomic state variables. We consider real GDP growth, inflation, andthe nominal monetary policy rate at a quarterly frequency.The long-run trends of thesevariables are the so-calledmacroeconomic stars:they follow random walks and act asshifting endpoints à la Kozicki and Tinsley (2001), governing long-run macroeconomic The key novelty lies in the second layer, which embeds investor uncertainty about thestars directly into asset pricing. Rather than assuming investors observe trends and cyclesseparately, we assume they observe only aggregate macroeconomic variables, GDP growth, of the stars are therefore imperfect and time-varying. The private information factor, beingdirectly observable, acts as a signal about long-run conditions and allows investors to The main advantage of the framework is that the investors’ problem reduces to a directapplication of the Kalman (1960) filter, which deliverssubjectivedynamics for all the statevariables.Moving from the first to the second layer imposes two meaningful statisticalrestrictions that sharpen identification. First, the subjective state variables are driven by areduced set of shocks relative to the perfect-information benchmark, corresponding exactly Economically, the learning mechanism delivers two important theoretical predictions.First, investors’ interest rate forecast errors are serially correlated (see e.g. Pang 2025). Sec-ond, long-horizon interest rate expectations underreact to permanent shocks and overreactto transitory ones, because investors cannot perfectly identify the source of fluctuations and The third layer prices the Treasury yield curve. We show that yield movements reflectfluctuations in investors’subjectiveestimates of the stars rather than in the stars themselves.With a standard stochastic discount factor, our model preserves the tractability of Gaussianaffine term structure models (ATSMs): pricing formulas are closed-form affine functionsof the subjective states (as in Duffie and Kan 1996; Ang and Piazzesi 2003).The key Using Treasury yields from 1961 to 2022 along with a set of survey data about futureinflation, growth, and interest rates, our estimation provides four main takeaways. We firstfind that the investor’s uncertainty about the nominal interest rate trend (𝑖★𝑡), the inflation trend (𝜋★𝑡) and the GDP growth trend (𝑔★𝑡) are very large, with 95% intervals as wide asabout±225𝑏 𝑝𝑠,±125𝑏 𝑝𝑠and±80𝑏 𝑝𝑠, respectively.This leads to a large uncertaintyregarding r-star, with confidence bands of±170𝑏 𝑝𝑠. For example, in the early 2000s, the3 investor’s perceived r-star estimate is approximately at 2%, with a 95% confidence band of[0.3%,3.7%], reflecting thefuzzy blursurrounding r-star. This result confirms an intuitiveeconomic belief, but is in sharp contrast with models assuming perfect information where Second, our model reveals new historical patterns of r-star namely that it is trendingupwards during the 1960s-1970s, not downwards, contrasting both with most es