Statement
In a discrete-time Gaussian no-arbitrage DTSM applied to US Treasury yields,
allowing the Markov-chain transition matrix to depend smoothly on the underlying
factors — Π = Π(X_t) rather than Π = const — produces a statistically and
economically significant improvement in fit relative to the otherwise identical
constant-Π baseline, as measured by likelihood, out-of-sample yield prediction,
and consistency of estimated regimes with identifiable monetary policy episodes.
Evidence summary
DSY 2007 estimate the constant-Π and state-dependent-Π versions of the same
two-regime Gaussian DTSM on monthly US Treasury zero-coupon yields and compare
them on (a) in-sample likelihood ratio, (b) out-of-sample yield-prediction RMSE,
and (c) interpretability of the smoothed regime probabilities relative to
identified historical monetary policy episodes (Volcker disinflation, post-Volcker
Greenspan period). The state-dependent-Π model wins on all three. Crucially,
the parameters of Π(X_t) (the slope coefficients on X_t in the
multinomial-logit transition function) are statistically distinguishable from
zero, so the improvement is not an unidentified-overparametrization artifact.
Conditions and scope
The claim is established for:
- Gaussian-affine factor dynamics (no stochastic volatility within a regime);
- US Treasury yields, monthly frequency, sample bracketing the Volcker episode;
M = 2regimes;- Logistic / multinomial-logit parametrization of
Π(X_t); - Closed-form-affine bond pricing via a log-linear approximation of
log Π^Q(X_t)aroundE[X_t].
The claim has not been established for:
- Compound (multiple independent binary sub-chain) Markov structures;
- Non-Gaussian (CIR / square-root) factor dynamics;
- Non-Treasury asset classes (corporate bonds, mortgages, commercial real estate cap rates);
- Settings where the regime path has to be sampled by particle filter rather
than Hamilton-filtered analytically (the closed-form
Π^Qrecursion is what makes Hamilton filtering work); - More than 2 regimes per chain.
Counter-evidence
None recorded yet in this wiki. Earlier constant-Π DTSMs (Bansal–Zhou 2002,
Ang–Bekaert–Wei 2008) do not directly contradict the claim — they simply do not
allow Π to be state-dependent, so they cannot test it. A potential
counter-finding would be a regime-switching DTSM that incorporates
state-dependent transitions but fails to improve fit on yields data; none is
recorded here.
Linked ideas
(none yet)
Open questions
- Does the improvement carry over to commercial real estate cap rates, where hold periods are much longer and regime-shift risk should plausibly be more important?
- Does the improvement survive when the regime structure is decomposed into multiple independent binary sub-chains rather than a single multi-state chain?
- How sensitive is the improvement to the log-linear approximation of
log Π^Q(X_t)used to keep bond prices closed-form-affine?