European Central Bank working paper proposes macro‑finance yield curve model to estimate US r-star and term premia

The European Central Bank published a Working Paper presenting an integrated macro-finance yield curve model that jointly estimates the equilibrium real interest rate (r*), trend inflation, interest rate expectations and bond risk premia for the United States using Bayesian methods and data from 1961 to 2019. The paper aims to reconcile differences between macroeconomic and asset-pricing approaches by modelling r* both as the real rate consistent with closing the output gap and as the time-varying long-run real rate anchoring the yield curve. The authors find r* exhibits a rise-and-fall pattern over six decades and a steep decline after the Global Financial Crisis, with lower levels in the 1960s and 1970s and post-crisis than in established semi-structural estimates. Longer-maturity real rate gaps (around ten years) are preferred to short-term gaps for explaining output gaps, and the model delivers comparatively narrow uncertainty bands for r* (90% bands below 3 percentage points). By allowing for a stochastic trend in equilibrium rates within an arbitrage-free affine Nelson-Siegel term structure framework, the resulting term premia are more cyclical and do not show the persistent downward trend implied by stationary yield curve models, with reported robustness to alternative specifications including a shadow-rate adjustment for the zero-lower-bound period. The paper notes possible extensions including the incorporation of inflation-linked bonds and the effects of central bank asset purchase programmes.