欧洲央行-宏观金融收益率曲线模型中自然利率的估计（英）

Working Paper Series Estimating the natural rate of interest in a macro-finance yield curve model Claus Brand, Gavin Goy, Wolfgang Lemke Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. No 3160 AbstractUsing a novel macro-finance model we infer jointly the equilibrium real interest rate r∗t ,trend inflation, interest rate expectations, and bond risk premia for the United States. In themodel r∗t plays a dual macro-finance role: as the benchmark real interest rate that closes theoutput gap and as the time-varying long-run real interest rate that determines the level ofthe yield curve. Our estimated r∗t declines over the last decade, with estimation uncertaintybeing relatively contained. We show that both macro and financial information is importantto infer r∗t . Accounting for the secular decline in interest rates renders term premia morestable than those based on stationary yield curve models.A previous version of this paper by the same authors entitled “Natural rate chimera andbond pricing reality” has been published as ECB Working Paper No 2612.Keywords: Equilibrium real rate, natural interest rate, arbitrage-free Nelson-Siegel term struc-ture model, term premia, Bayesian estimation.JEL Classification: E43, C32, E52, C11, G12.ECB Working Paper Series No 31601Non-technical summaryWe introduce a novel macro-finance model that addresses the “natural rate puzzle”, a dis-connect in the literature whereby macroeconomic and finance perspectives yield inconsistentestimates of the natural real rate of interest. From a macroeconomic standpoint, the naturalrate of interest r∗t is the real interest rate consistent with the economy operating at its potentialand thereby constitutes an indicator for monetary policy, while in asset pricing, r∗t serves as ananchor for interest rate expectations in the long run. We propose an integrated approach wherer∗t fulfills both roles simultaneously.To integrate the macroeconomic and the financial perspective, our model features two keycomponents: (1) a “macro module” that links r∗t to output growth trends and a non-growthcomponent, while modeling inflation expectations and the output gap dynamics through the IScurve and Phillips curve; and (2) an arbitrage-free affine Nelson-Siegel (AFNS) term structuremodel, where the equilibrium nominal short-term rate i∗t = r∗t +π∗t anchors the yield curve. Themodel is estimated using U.S. data (1961–2019) using Bayesian methods.Our findings can be summarized as follows:We identify a trend in r∗t that is distinct from established approaches that suggests a steadydecline. The model identifies a rise and fall in r∗t over six decades, with lower levels in the 1960s,1970s, and post-Global Financial Crisis. This behavior arises because the model endogenizesthe real rate, making the real rate gap stationary, in contrast to models treating the real rateas