Yield-Curve Recession Prediction Probit Model

What this research found

An inverted Treasury yield curve is one of the most durable warning signs of a US recession, but commentators and Federal Reserve researchers disagree about which version of the curve to watch. K-Dense staged a head-to-head test of the 10-year-minus-3-month spread against the popular 10-year-minus-2-year spread, fitting the classic Estrella-Mishkin probit specification to monthly data through 1999 and then freezing the coefficients to forecast the 2000-2023 period. The short-end spread discriminated recession months slightly better, with an area under the ROC curve of 0.778 against 0.762, though a bootstrap that accounts for the clustered nature of recessions shows the gap is not statistically distinguishable from zero.

• On the common held-out window of 288 months from 2000 to 2023, the 10-year-minus-3-month spread reached an area under the ROC curve of 0.778 versus 0.762 for the 10-year-minus-2-year spread. Both are far above the 0.5 chance level.
• That ranking is not statistically decisive. A moving-block bootstrap with 12-month blocks put the short-end spread ahead in 76% of resamples but returned a bootstrap standard error of about 0.033, a 95% confidence interval of -0.046 to 0.083, and a two-sided p-value of roughly 0.62.
• Better in-sample fit did not mean better forecasts. The 10-year-minus-2-year model attained the higher McFadden pseudo R-squared of 0.342 against 0.266, yet lost the out-of-sample comparison; its advantage reflects a shorter 1976-onward sample that excludes the volatile 1959-1975 period.
• In both models a flatter curve raises modelled recession risk with the expected sign. A one-percentage-point fall in the spread lifts the probit index by 0.744 for the short-end measure and 1.296 for the 2-year measure, each significant at the 1% level.
• The two models read December 2023 very differently. With spreads of -1.22 and -0.44 percentage points, they implied a 66.8% versus a 32.9% probability of recession by December 2024. No recession began in 2024, so both point signals were false positives at that horizon.
• Neither model anticipated the February-April 2020 downturn, which was triggered by a public-health shock rather than the monetary and financial dynamics the yield curve summarizes.

How it was done

Monthly series were downloaded programmatically from the Federal Reserve Economic Data repository: the 10-year and 2-year Treasury constant-maturity yields, the 3-month bill rate, and the National Bureau of Economic Research recession indicator. The forecasting target was the recession indicator shifted twelve months back, so each month's spread predicts recession status a year later. Each spread entered a univariate probit model estimated by maximum likelihood over the longest window its data allowed ending in December 1999 — 492 months from 1959 for the short-end spread, 283 months from 1976 for the 2-year spread. Those coefficients were then frozen and used to generate predicted probabilities across 2000 to 2023, compared by area under the ROC curve, with the difference tested by a moving-block bootstrap of roughly 5,000 resamples to respect the serial dependence created by overlapping labelling windows.

Data sources

• Federal Reserve Economic Data — GS10, TB3MS, GS2 constant-maturity Treasury yields and the NBER-based USREC recession indicator, monthly 1959-01 to 2023-12
• Estrella & Mishkin, Review of Economics and Statistics 80:45 (1998) — the probit specification replicated here
• Estrella & Hardouvelis, Journal of Finance 46:555 (1991)
• Engstrom & Sharpe, Federal Reserve FEDS 2018-055 — the case for short-end-anchored spreads
• Bauer & Mertens, Federal Reserve Bank of San Francisco Economic Letter 2018-07
• Wright, Federal Reserve FEDS 2006-07 — adding the policy-rate level to the probit