Statement

A parsimonious 2-state Markov regime-switching extension of the CIR square-root term-structure model — with regime-dependent drift, mean-reversion, volatility, and market price of risk — jointly resolves three otherwise-persistent failures of single-regime CIR: (1) it matches the observed time-varying conditional volatility of US Treasury yields, (2) it matches the observed time-varying conditional correlations between yields of different maturities, and (3) it reproduces the negative Campbell-Shiller regression slopes that constitute the empirical violation of the expectations hypothesis. The estimated regimes are economically interpretable as US business-cycle states.

Evidence summary

Direct evidence comes from Bansal and Zhou (2002, Journal of Finance):

  • EMM estimation with an SNP auxiliary on US Treasury yield data identifies two regimes whose dynamics differ in mean reversion, conditional volatility, and price of risk.
  • Simulated yields from the estimated model match the unconditional first and second moments of the observed yield curve, plus the time-varying conditional second moments that single-regime CIR fails on.
  • Campbell-Shiller regressions on simulated data reproduce the empirical negative slopes, providing a no-arbitrage rationalization of the EH puzzle.

Conditions and scope

Holds only when all of the following are true:

  • Underlying short-rate process is CIR-style (square-root, non-negative, mean-reverting).
  • Markov chain has 2 states with constant transition matrix.
  • Bond pricing uses a log-linear approximation across regime trajectories (closed-form bond prices are not available globally).
  • Estimation uses EMM with a sufficiently expressive SNP auxiliary.
  • Maturity range is moderate (the paper does not separately validate very long maturities).

The claim is not asserted for: more than 2 regimes, multi-factor short-rate processes with regimes, state-dependent transition matrices, non-Treasury debt, or non-US markets.

Counter-evidence

None known within the paper’s scope. Independent confirmations of regime-switching benefits in fixed income exist (Dai-Singleton-Yang 2007, Ang-Bekaert-Wei 2008) but use somewhat different model classes; they generally agree with the directional finding that latent regimes substantially improve fit on conditional moments.

Linked ideas

(none yet)

Open questions

  • Does the resolution of EH violations carry over to richer multi-factor affine regime-switching models, or is the 2-state CIR result a coincidence of low-dimensional functional form?
  • How much of the bond pricing error in the log-linear approximation accumulates at long maturities, and does that error cancel against the regime-switching gains?
  • Can the regime mechanism be linked structurally to macro variables (output gap, inflation, monetary policy) instead of being treated as a latent chain?