Learning, Equilibrium Trend, Cycle, and Spread in Bond Yields

Given that the stochastic discount factor (SDF) from any equilibrium model has direct implications for yield curves, the historical dynamics of the US Treasury yield curve should tell us what a good SDF should look like from a historical perspective. Some key features in the US Treasury bond yields—the trends in the long-term yields, business-cycle movements in the short-term yields and level shifts in the yield spreads—pose serious challenges to existing equilibrium asset pricing models.

The stationarity assumption, which implies short rates are stationary, makes it hard for standard models to generate the hump-shaped trend in US Treasury yields and match the unconditional volatility in the data. The standard inflation-risk-premium approach for an upward-sloping yield curve cannot explain the level shifts and business-cycle movements in the yield spreads. An important but often overlooked puzzle—the less-frequent inverted yield curves (and less-frequent recessions) after the 1990s—remains unsolved.

I present a new equilibrium model to explain these key features. The trend is generated by learning from the stable components in GDP growth and inflation, which share similar patterns to the neutral rate of interest (R-star) and trend inflation (Pi-star) estimates in the literature. Cyclical movements in the yields and spreads are mainly driven by learning from the transitory components in GDP growth and inflation. The less-frequent inverted yield curves after the 1990s are due to the recent secular stagnation and procyclical inflation expectations.