Term-premium decomposition and the ACM framework

Under the expectations hypothesis, a long-term yield equals the average of expected future short rates plus a term premium — the compensation investors demand for bearing duration risk. The Adrian-Crump-Moench (2013) affine term-structure model decomposes nominal Treasury yields into these two components using five pricing factors extracted from principal components of the yield curve. Per the NY Fed's published series, the 10-year ACM term premium has oscillated between roughly −100 bp and +400 bp over the post-1990 sample, and was deeply negative (around −60 bp) during much of the 2019-2023 episode — implying that the observed curve inversion overstated the expected-policy-path component of the signal.

This matters for interpreting current readings: an inverted curve driven primarily by a compressed term premium (e.g. heavy duration demand from pension liability matching, foreign reserve managers, or QE residuals) carries different macro information than one driven by expected aggressive easing. Practitioners commonly cross-check the model-implied risk-neutral 1Y-forward-in-9Y rate against the ACM expected component to gauge which channel dominates.

NSS calibration philosophy: fixed-lambda vs free-lambda

Nelson-Siegel-Svensson (Svensson, 1994) extends the original Nelson-Siegel (1987) form with a second curvature hump, governed by decay parameters λ₁ and λ₂. Two estimation philosophies dominate practice. The Bundesbank/ECB convention jointly optimises all six parameters (4 betas + 2 lambdas) per cross-section, which produces tight in-sample fits at the cost of unstable lambda trajectories that can hop discontinuously day to day, complicating time-series inference on factor loadings. The BIS/Fed convention fixes lambdas at sensible values (we use λ₁ = 1.5y, λ₂ = 5.0y) and estimates betas by OLS, sacrificing a few basis points of fit for parameter stability and cleaner level/slope/curvature factor interpretation. Diebold-Li (2006) further demonstrate that fixed-lambda Nelson-Siegel admits a state-space VAR(1) representation of the betas, enabling Kalman-filter forecasting that free-lambda fits cannot easily support.

Estrella-Mishkin probit: calibration caveats outside the US sample

The NY Fed probit, P(recession) = Φ(−0.5333 − 0.6629 × spread_3m10y), was estimated by Estrella and Mishkin (1998) on US monthly data from 1959-1995 using NBER recession dating as the binary outcome. Out-of-sample applications inherit three caveats. First, the slope coefficient embeds the historical correlation between US term premia and US business cycles — economies with structurally different demographic, fiscal, or financial-architecture profiles (Japan's chronic ZLB regime, India's higher equilibrium real rate, China's administered curve) violate the i.i.d. assumption on which the maximum-likelihood estimates rely. Second, "recession" is a US-NBER construct; equivalents like the CEPR Euro Area Business Cycle Dating Committee chronology produce different probit estimates when re-fit locally (Moneta, 2005, finds materially lower curve predictive power for the euro area pre-2008). Third, the probit is silent on the term-premium component of the spread, so easing global term premia (Bauer-Rudebusch, 2020) mechanically push probabilities higher without any change in actual expected policy.

Why 3m10y is more theoretically grounded than 2s10s

The 3m10y spread anchors the short leg to the current policy rate (the 3-month bill arbitrages directly against the IORB/repo cash rate), making the spread a clean read on the gap between today's policy stance and the market's long-run nominal anchor. The 2s10s, by contrast, places both legs inside the term structure, so a 2s10s move can reflect changes in expected policy 6-24 months out without saying anything about current restrictiveness. Estrella-Hardouvelis (1991) and the subsequent literature consistently find 3m10y outperforms 2s10s in out-of-sample recession AUC, and the NY Fed's published series uses 3m10y for that reason. The 2s10s retains pedagogical and trading appeal — it is harder to manipulate via short-end forward guidance — but for probit-style probability work the 3m10y is the canonical input.