Let us consider some of the most important stylized facts and the ability of our model to replicate
them, in principle:
(1) The average yield curve is increasing and concave. In our framework, the average yield
curve is the yield curve corresponding to the average values of β1t, β2t and β3t. It is
certainly possible in principle that it may be increasing and concave.
(2) The yield curve assumes a variety of shapes through time, including upward sloping,
downward sloping, humped, and inverted humped. The yield curve in our framework
can assume all of those shapes. Whether and how often it does depends upon the
variation in β1t, β2t and β3t.
(3) Yield dynamics are persistent, and spread dynamics are much less persistent. Persistent
yield dynamics would correspond to strong persistence of β1t, and less persistent spread
dynamics would correspond to weaker persistence of β2t.
(4) The short end of the yield curve is more volatile than the long end. In our framework, this is
reflected in factor loadings: the short end depends positively on both β1t and β2t,
whereas the long end depends only on β1t.
(5) Long rates are more persistent than short rates. In our framework, long rates depend only on
β1t. If β1t is the most persistent factor, then long rates will be more persistent than short
rates.
Overall, it seems clear that our framework is consistent, at least in principle, with many of the key
stylized facts of yield curve behavior. Whether principle accords with practice is an empirical matter, to
which we now turn.
3. Modeling and Forecasting the Term Structure II: Empirics
In this section, we estimate and assess the fit of the three-factor model in a time series of cross
sections, after which we model and forecast the extracted level, slope and curvature components. We
begin by introducing the data.
The Data
We use end-of-month price quotes (bid-ask average) for U.S. Treasuries, from January 1985
through December 2000, taken from the CRSP government bonds files. CRSP filters the data,
eliminating bonds with option features (callable and flower bonds), and bonds with special liquidity
problems (notes and bonds with less than one year to maturity, and bills with less than one month to
maturity), and then converts the filtered bond prices to unsmoothed Fama-Bliss (1987) forward rates.
Then, using programs and CRSP data kndly supplied by Rob Bliss, we convert the unsmoothed