A Three-Factor Econometric Model of the U.S. Term Structure
Eli M. Remolona
Bank for International Settlements (BIS) - Monetary and Economic Department
FRB of New York Staff Report No. 19
We estimate a three-factor model to fit both the time-series dynamics and cross-sectional shapes of the U.S. term structure. In the model, three unobserved factors drive a discrete-time stochastic discount process, with one factor reverting to a fixed mean and a second factor reverting to a third factor. To exploit the conditional density of yields, we estimate the model with a Kalman filter, a procedure that also allows us to use data for six maturities without making special assumptions about measurement errors. The estimated model reproduces the basic shapes of the average term structure, including the hump in the yield curve and the flat slope of the volatility curve. A likelihood ratio test favors the model over a nested two-factor model. Another likelihood ratio test, however, rejects the no-arbitrage restrictions the model imposes on the estimates. An analysis of the measurement errors suggests that the three factors still fail to capture enough of the comovement and persistence of yields.
Number of Pages in PDF File: 54
Keywords: term structure, pricing kernel, affine yields, mean reversion, time-varying mean, Kalman filter
JEL Classification: E43, G12, G13
Date posted: November 17, 2006
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