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##### Subject 9. Using Dummy Variables in Regressions
Some observed phenomena are qualitative rather than quantitative and thus cannot be measured on a continuous scale. For example, an individual's income might depend on whether the person possesses a college degree. Dummy variables are specially constructed variables that indicate the presence or absence of some characteristics. They assume a value of 1 or 0, depending upon whether a certain characteristic is present.

Suppose the salaries of employees at a particular research institute depend on seniority (or number of years employed at the institute), whether the employee has a Ph. D. degree, and other random factors.

Suppose we express the relationship between the variables in terms of the following multiple regression model:

E(Yt | Xt, Zt) = β0 + β1Xt + β2Zt

where

• Y = salary in dollars
• X = years in seniority
• Z = 1 if individual has a Ph. D, or 0 if individual does not have a Ph.D.

Suppose the t-th individual has seniority of Xt years and does not have a Ph.D. Thus, the variable Z assumes the value 0. The expected salary would be E(Yt | Xt, Zt = 0) = β0 + β1Xt.

A person who has a Ph.D and the same seniority of Xt years would have an expected salary of E(Yt | Xt, Zt = 1) = β0 + β1Xt + β2.

Suppose β0 is \$15,000, β1 is \$1,000, and β2 is \$2,500. The expected salary of a non-Ph.D. with Xt years of seniority would be E(Yt | Xt, Zt = 0) = 15000 + 1000Xt. The constant β0 = \$15,000 represents the starting salary, and the coefficient β1 = \$1,000 represents the annual salary increment.

The expected salary of a Ph.D. with Xt years of seniority would be E(Yt | Xt, Zt = 1) = 15000 + 1000Xt + 2500. The coefficient β2 = \$2,500 represents the effect of having the Ph.D as opposed to not having the Ph.D and indicates that a person who has a Ph.D. earns, on the average, \$2,500 more per year than a person with the same seniority who does not have a Ph.D. Thus testing the hypothesis that β2 = 0 is equivalent to testing the hypothesis that there is no difference between the salaries of Ph.D.'s and the salaries of non-Ph.D.'s.

Learning Outcome Statements

j. formulate and interpret a multiple regression, including qualitative independent variables;

CFA® 2023 Level I Curriculum, Volume 1, Module 2

User Comment
turtle nice ilustration, but seniority in Ph.D. should also add to wages increase :-)
katybo n-1 dummy variables for n categories, if not, you can't estimate regression.
brave1986 eally good illustration