基于调查的利率转移终点动态期限结构模型

A Survey-Based Shifting-EndpointDynamic Term Structure Modelof Interest Rates Working Paper 2025-03 August 2025 A Survey-Based Shifting-Endpoint Dynamic TermStructure Model of Interest Rates Michael McGrane* Abstract In this paper, I present a dynamic term structure model of interest rates that fea-tures a shifting endpoint and incorporates survey forecasts of interest rates to sharpenthe model’s implied forecasts and estimate trend interest rates. I present a new esti-mate of trend interest rates from the model as well as the model’s estimates of termpremiums. I conduct an out-of-sample forecast analysis with the model and find thatit significantly outperforms a standard dynamic term structure model with no shiftingendpoint and only slightly underperforms a random walk model. JEL Classification:E43, E47, G12 1Introduction Dynamic term structure models (DTSMs) are models of interest rates across the yield curvethat describe how interest rates change over time. Specifically, yields are modeled as a func-tion of “factors” (typically some linear combination of yields or macroeconomic variables),and those factors follow a stochastic process in the model. By specifying how those factorsevolve over time, yields can be projected by mapping those factors into yields. The mostcommonly used class of DTSMs specifies yields as an affine function of the factors (Duffieand Kan 1996). That class of models excludes arbitrage opportunities by specifying (eitherexplicitly or implicitly) the market price of risk as a function of the factors. That requirementensures that portfolios of bonds cannot be constructed that earn positive returns without apositive net investment and without taking any risk. Although DTSMs have become ubiquitous in the finance literature and are extensivelyused to price fixed-income derivatives, evidence on their forecast performance of interest ratesis mixed (Duffee 2002). Specifically, it has proved notoriously difficult to outperform a naiverandom walk forecast of interest rates, in which interest rates in the future are projectedto be what they are today (Gamber 2017). One likely culprit for that underperformance isestimation bias in time-series models, which can lead to underestimation of the persistenceof time-series processes (Kendall 1954, Marriott and Pope 1954). For example, least squaresestimates of autoregressive and vector autoregressive processes estimated using post–WorldWar II macroeconomic data suffer from significant bias, which will produce forecasts thatmean revert faster than the true data-generating process (see, among others, Andrews 1993and Kilian 1998). In the context of DTSMs estimated with least squares or maximum like-lihood, that bias will substantially affect forecasts of interest rates from DTSMs (Bauer etal. 2012). One potential solution to that issue involves incorporating shifting endpoints (which canbe thought of as time-varying trends) into models of inflation and interest rates (Kozickiand Tinsley 2001 and van Dijk et al. 2014). In models with shifting endpoints, interest rates,inflation, or both are stationary around a slow-moving trend that is allowed to vary over time. That allows shifting-endpoint models to incorporate the fact that inflation expectationshave fallen considerably since the 1980s as the Federal Reserve has moved toward inflationtargeting, and that equilibrium real interest rates have likely fallen considerably since the1990s (see, among others, Holston et al. 2017 and Del Negro et al. 2017). Another solution involves incorporating external information into the DTSM—for exam-ple, using interest rate forecasts from surveys of forecasters (Kim and Orphanides 2012).That helps by disciplining the model’s implied forecast to be close to forecasts from sur-veys, which alleviates the tendency of standard estimation procedures to underestimate thepersistence of time-series data.1 In this paper, I combine those two approaches of modeling a shifting endpoint and in-corporating information from survey forecasts into an otherwise standard DTSM of interestrates. The model has a structure similar to that of the observed-shifting-endpoint model ofBauer and Rudebusch (2020), but rather than providing the DTSM with an external es-timate of the time-varying trend of the short-term interest rate, I provide the model withboth short-term and long-term survey forecasts of interest rates to pin down the estimatedtrend. In this model, yields are a function of the first three principal components of interestrates. Those principal components are decomposed into trend and cycle components, withthe cycle components evolving according to a stationary vector autoregression (VAR) whilethe trend components are linear functions of the trend short-term interest rate, which isassumed to follow a random walk. In the model, the trend interest rate is what the interest rate would be if the cyclecomponent of the interest rate were equal to zero. Because the trend interest