132 The Basics of financial economeTrics
The Chow test has the value 14.73. The F-statistics and the Chow test suggest
that there is indeed a regime shift and that the spread regressions at the two
different dates are different. Again, the use of dummy variables has greatly
improved the goodness-of-fit of the regression, even after compensating for
the increase in the number of parameters. The residuals of the model with
dummy variable D2 are shown in the last column of Table 6.2.
Illustration: testing the Mutual Fund characteristic lines in different Market
environments In the previous chapter, we calculated the characteristic line of
two large-cap mutual funds. Let’s now perform a simple application of the
use of dummy variables by determining if the slope (beta) of the two mutual
funds is different in a rising stock market (“up market”) and a declining
stock market (“down market”). To test this, we can write the following
multiple regression model:
yit = αi + β 1 ixt + β 2 i(Dtxt) + eit
where Dt is the dummy variable that can take on a value of 1 or 0. We will let
Dt = 1 if period t is classified as an up market
Dt = 0 if period t is classified as a down marketThe coefficient for the dummy variable is β 2 i. If that coefficient is statis-
tically significant, then for the mutual fund:
In an up market: βi = β 1 i + β 2 i
In a down market: βi = β 1 iIf β 2 i is not statistically significant, then there is no difference in βi for up
and down markets.
In our illustration, we have to define what we mean by an up and a
down market. We will define an up market precisely as one where the aver-
age excess return (market return over the risk-free rate or (rM – rft)) for the
prior three months is greater than zero. Then
Dt=1 if the average (rMt – rft) for the prior three months > 0
Dt=0 otherwiseThe regressor will then beDtxt=xt if (rM – rft) for the prior three months > 0
Dtxt=0 otherwise