60 The Basics of financial economeTrics
zero-coupon securities and coupon securities. Securities issued with one year
or less to maturity are called Treasury bills; they are issued as zero-coupon
instruments. Treasury securities with more than one year to maturity are
issued as coupon-bearing securities. Treasury securities from more than one
year up to 10 years of maturity are called Treasury notes; Treasury securities
with a maturity in excess of 10 years are called Treasury bonds. The U.S.
Treasury auctions securities of specified maturities on a regular calendar
basis. The Treasury currently issues 30-year Treasury bonds but had stopped
issuance of them from October 2001 to January 2006.
An important Treasury note is the 10-year Treasury note. In this illus-
tration, we try to forecast this rate based on two independent variables sug-
gested by economic theory. A well-known theory of interest rates, known as
the Fisher equation, is that the interest rate in any economy consists of two
components. The first is the expected rate of inflation. The second is the real
rate of interest. We use regression analysis to produce a model to forecast
the yield on the 10-year Treasury note (simply, the 10-year Treasury yield)—
the dependent variable—and the expected rate of inflation (simply, expected
inflation) and the real rate of interest (simply, real rate).
The 10-year Treasury yield is observable, but we need a proxy for the
two independent variables (i.e., the expected rate of inflation and the real
rate of interest) because they are not observable at the time of the forecast.
Keep in mind that since we are forecasting, we do not use as our indepen-
dent variable information that is unavailable at the time of the forecast.
Consequently, we need a proxy available at the time of the forecast.
The inflation rate is available from the U.S. Department of Commerce.
However, we need a proxy for expected inflation. We can use some type
of average of past inflation as a proxy. In our model, we use a five-year
moving average. There are more sophisticated methodologies for calculat-
ing expected inflation, but the five-year moving average is sufficient for our
illustration.^13 For the real rate, we use the rate on three-month certificates
of deposit (CDs). Again, we use a five-year moving average.
The monthly data for the three variables from November 1965 to
December 2005 (482 observations) are provided in Table 3.5. The regres-
sion results are reported in Table 3.6. As can be seen, the regression coef-
ficients of both independent variables are positive (as would be predicted by
economic theory) and highly significant. The R^2 and adjusted R^2 are 0.90
and 0.83, respectively. The ANOVA table is also shown as part of Table 3.6.
The results suggest a good fit for forecasting the 10-year rate.
(^13) For example, one can use an exponential smoothing of actual inflation, a meth-
odology used by the Organisation for Economic Co-operation and Development
(OECD).