Problem
Nominal Treasury yields confound three economically distinct components: (i) the ex-ante real interest rate, (ii) expected inflation, and (iii) compensation for bearing inflation risk (the inflation risk premium). Without a structural identification, the level and slope of the nominal yield curve cannot be cleanly attributed to real-side economics versus inflation expectations versus risk compensation. Prior empirical work either ignored regime dynamics or imposed strong (and often inconsistent) restrictions on inflation risk premia, leaving basic questions — Is the real yield curve flat, upward, or downward sloping? How large is the inflation risk premium, and is it constant? — unresolved.
Key idea
Build a no-arbitrage three-factor term structure model in which a small number of latent factors (a real factor, an inflation factor, and a nominal short-rate factor) jointly drive both the real and the nominal yield curves, and let the parameters of the factor dynamics, market prices of risk, and inflation dynamics depend on a discrete Markov regime variable. Closed-form bond prices remain tractable: conditional on a regime path, prices are exponential-affine in the factors, and the cross-section of nominal yields plus survey inflation forecasts identify all three components — including a time-varying inflation risk premium — without requiring TIPS data.
Method
- Three-factor regime-switching state-space model. Latent factors include a real interest rate factor, an expected-inflation factor, and a third factor capturing the residual variation in nominal short rates. Factor dynamics follow a regime-switching VAR with a discrete Markov chain governing transitions.
- No-arbitrage pricing. Under the regime-switching pricing kernel, nominal bond prices are exponential-affine in the factors with regime-dependent loadings. Real bond prices are obtained by deflating with the inflation process; closed-form recursions give bond yields at all maturities.
- Identification via survey inflation forecasts. Because TIPS were unavailable for most of the sample, the model is identified by jointly fitting the cross-section of nominal Treasury yields and observed inflation, augmented with survey expectations of inflation, which discipline the expected-inflation component and separate it from the inflation risk premium.
- Estimation. Maximum likelihood with a regime-switching Kalman filter (Hamilton filter for the discrete regime; Kalman recursions for the conditional Gaussian state).
- Decomposition. Once estimated, nominal yields at every maturity are decomposed into expected real rate + expected inflation + inflation risk premium, all conditional on the inferred regime.
Results
- Real yield curve is approximately flat at ~1.3%. The model-implied ex-ante real rate term structure is essentially horizontal across maturities, with a small downward slope at long maturities.
- Nominal yield curve slope is driven by the inflation risk premium. Almost all of the upward slope in nominal yields comes from the inflation risk premium, not from rising expected real rates and not from rising expected inflation.
- Time-varying inflation risk premium. The inflation risk premium varies substantially across regimes — large and volatile in high-inflation / high-uncertainty regimes, small and stable in low-inflation regimes.
- Real rates are persistent but not as persistent as nominal rates. Real rate dynamics are dominated by the real factor, which is more mean-reverting than the inflation factor.
- Regime structure matters. A constant-parameter (no-regime) version of the model misprices long-maturity nominal bonds and produces implausibly small inflation risk premia, justifying the regime-switching extension.
Limitations
- TIPS are not directly used. Identification of the real curve relies on the joint cross-section of nominal yields and inflation expectations; the decomposition is therefore model-dependent and can be sensitive to the factor specification and the survey forecast measurement.
- Discrete regimes. Two- (or few-) state Markov chains are an approximation to a potentially smoother time-variation in inflation dynamics; the decomposition can be sensitive to the assumed number of regimes.
- Latent factors. As with most affine term structure models, the factors are statistical objects that need not map cleanly onto observable macroeconomic variables.
- Sample period. Pre-TIPS US data; the inflation risk premium estimates are identified largely from a sample dominated by the Great Inflation and its aftermath.
Open questions
- How does the decomposition change when post-TIPS data and TIPS yields are added as additional measurement equations?
- Can the latent regime be tied to identifiable monetary policy regimes (Fed chair / operating procedure / inflation target changes) rather than a purely data-driven Markov state?
- How does the time-varying inflation risk premium relate to macro variables such as the output gap, inflation uncertainty, and monetary policy stance?
My take
This is the canonical reference for a no-arbitrage, regime-switching decomposition of nominal yields into real rates + expected inflation + inflation risk premium. For the CRE asset pricing project, it is directly load-bearing in two ways: (i) the regime-switching VAR + closed-form bond pricing structure is the same architectural pattern this project uses for risk-neutral cap-rate pricing, and (ii) the empirical finding that the nominal-curve slope is dominated by the inflation risk premium tells us that asset-pricing models which collapse the inflation risk premium to zero will mis-attribute curve dynamics to real-side fundamentals. The flat real-rate finding is also a useful prior for any model that needs an exogenous real-rate process.