当长期趋势未知时：债券定价的影响

Borel Ahonon|Guillaume Roussellet When Long-Run Trends Are Unknown:Bond Pricing ImplicationsBorel AhononandGuillaume Roussellet Federal Reserve Bank of New York Staff Reports, no.1187March2026https://doi.org/10.59576/sr.1187 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,andlarge investor uncertainty with confidence bands on as wide as 3.4 percentagepoints, contrasting with thevolatile rate implied by perfect information models. JEL classification:C58, E43, E52, G12Keywords:incomplete information, interest rate stars, Bayesian learning, Treasuryyields,investor’s uncertainty Roussellet: Federal Reserve Bank of New York (email:guillaume.roussellet@ny.frb.org).Ahonon:McGill University(email:borel.ahonon@mail.mcgill.ca).The authors thankPaul Beaumont, RichardCrump, Basile Dubois, Bruno Feunou, Jean-SébastienFontaine, Anne Lundgard Hansen, ThomasMertens, Emanuel Mönch, Mikkel Plagborg-Moller, and theparticipantsofthe Chicago Fed conferenceon inflation, the brownbag seminar at McGill University, and atthe New York Federal Reserve lunchseminar. 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 ofthe author(s) and do not necessarily reflect theposition of the Federal Reserve Bank of New York or theFederal Reserve System. Any errors or omissions are the responsibility of the author(s). 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 andWilliams 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 promisingsource of information (Bauer and Rudebusch 2020), but how precisely it can be inferredremains contested.1Yield-curve-based estimates may convey a false sense of precision:they typically assume that bond market investors perfectly observe r-star.We propose a newmodel that quantifies how much can be inferred about r-star from the Treasury yield curvewhen bond investors, like policymakers and economists alike, face fundamental uncertaintyabout its true level. 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 macroeconomicforecasts. In the context of the model, r-star is the long-run trend of the real interest rate,the difference between the nominal rate trend and the inflation trend. Cyclical components,by contrast, evolve according to a stationary VAR(1) process whose shocks dissipate in thelong run. 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,inflation, the policy rate, and a private information factor whose shocks are correlatedwith those driving the long-run trends.They perform Bayesian learning each quarter todecompose macroeconomic aggregates into trend and cycle components. Their estimates 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 topotentially know more than the econometrician. 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 dri