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fter reading this chapter you will understand:■ (^) What a categorical variable is.
■ (^) How to handle the inclusion of one or more categorical variables in a
regression when they are explanatory variables.
■ (^) How to test for the statistical significance of individual dummy vari-
ables in a regression and how to employ the Chow test.
■ (^) Models that can be used when the dependent variable is a categorical
variable: the linear probability model, the logit regression model, and
the probit regression model.
■ (^) The advantages and disadvantages of each type of model for dealing
with situations where the dependent variable is a categorical variable.
Categorical variables are variables that represent group membership. For
example, given a set of bonds, the credit rating is a categorical variable that
indicates to what category—AAA, AA, A, BBB, BB, and so on—each bond
belongs. A categorical variable does not have a numerical value or a numeri-
cal interpretation in itself. Thus the fact that a bond is in category AAA or
BBB does not, in itself, measure any quantitative characteristic of the bond;
though quantitative attributes such as a bond’s yield spread can be associ-
ated with each category.
Performing a regression on categorical variables does not make sense
per se. For example, it does not make sense to multiply a coefficient times
AAA or times BBB. However, in a number of cases the standard tools of
regression analysis can be applied to categorical variables after appropriate
transformations. In this chapter, we first discuss the case when categorical
variables are explanatory (independent) variables and then proceed to dis-
cuss models where categorical variables are dependent variables.
chApter
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