Replication — the yield curve predicts recessions (Estrella-Mishkin 1998)¶

Of all the leading indicators macroeconomists track, the slope of the Treasury yield curve is the most famous: when the curve inverts — short-term rates rise above long-term rates — a recession has tended to follow within a year or so. Estrella & Mishkin (1998) put a number on it with a probit, and it has held up across the cycles since.

This reproduces the core result with tsecon.recession_probit, estimated from a committed FRED snapshot (retrieved 2026-07-18) — it runs fully offline — and recovers the canonical numbers.

.venv/bin/python docs/examples/replication_yield_curve_recession.py

The three FRED series — GS10 (10-year Treasury), TB3MS (3-month bill), and USREC (the NBER recession indicator) — are aligned into one monthly panel committed at fixtures/yield_curve_recession.csv, so this runs fully offline (tsecon ships no data loaders). The term spread is GS10 − TB3MS.

The result¶

A probit of the recession indicator twelve months ahead on the current term spread, monthly, 1953–2026 (867 observations after the 12-month lead). The estimand is the 12-month-ahead probability — the chance the economy is in recession in month t+12, not at some point during the intervening year:

Probit:  P(recession at t+12) = Φ(b0 + b1 · term_spread)

  b0 (const)   = -0.6421
  b1 (spread)  = -0.5833   (z = -9.62)
  McFadden R²  =  0.187

The signature finding is the sign and significance of b1: strongly negative, z ≈ -10. One honest caveat on that z-statistic: these are i.i.d. maximum-likelihood standard errors, and recession months are strongly serially dependent, so z ≈ -10 overstates the precision — the sign and economic magnitude are the robust part. The shipped route to modelling that dependence is the Kauppi-Saikkonen dynamic probit (dynamic=True, below). A flatter or inverted curve raises the recession probability. Reading it as probabilities:

term spread	P(recession in month t+12)
+3.0 pp (steep)	0.8%
+1.0 pp	11%
0.0 pp (flat)	26%
−1.0 pp (inverted)	48%

A steeply upward-sloping curve implies a near-zero probability of being in recession a year later; a one-percentage-point inversion implies close to a coin flip. This is the "inverted yield curve" signal that appears in the financial press every cycle — here it is estimated from scratch in a dozen lines.

How it is built¶

import csv, numpy as np, tsecon

# read the committed monthly panel: date, gs10, tb3ms, usrec
rows = [r for r in csv.reader(open("fixtures/yield_curve_recession.csv"))
        if r and not r[0].startswith("#")][1:]
spread    = np.array([float(r[1]) - float(r[2]) for r in rows])   # GS10 - TB3MS
recession = np.array([float(r[3]) for r in rows])

lead = 12
y = recession[lead:]                              # recession at t+12
X = np.column_stack([np.ones(len(y)), spread[:-lead]])   # explicit intercept
fit = tsecon.recession_probit(y, X, link="probit")
fit["params"]        # [b0, b1]
fit["pseudo_r2"]     # McFadden
fit["probabilities"] # fitted P(recession) for every month

Two modelling notes the recession model card makes: the design must carry an explicit intercept column, and recession_probit also fits the Kauppi-Saikkonen dynamic probit (an autoregressive recession index) via dynamic=True — a natural extension when recession states are persistent month to month.

What this is, and is not¶

This reproduces the shape of the Estrella-Mishkin result — a term-spread probit with a strongly significant negative slope and a pseudo-R² of the same order — on current data. It is not their exact vintage, sample window, or spread definition (they examine several horizons and financial variables). The point being replicated is the economic one: the curve's slope is a genuine, strong, out-of-model predictor of recessions, and recession_probit recovers it.

The result is guarded offline in CI: test_replication_yield_curve.py re-runs the estimation against a committed snapshot of the FRED panel (fixtures/yield_curve_recession.csv) and asserts the coefficient stays significantly negative, so this page cannot quietly go stale.

Data. Federal Reserve Bank of St. Louis (FRED), series GS10, TB3MS, USREC — public data, redistributed with attribution.

Reference. Estrella, A. & Mishkin, F. S. (1998), "Predicting U.S. Recessions: Financial Variables as Leading Indicators," Review of Economics and Statistics 80(1):45-61.