The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

CHAPTER 6

Regression Models with Categorical Variables

After 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 variables 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 numerical 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 associated 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 ...