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Economics 209
Regression Extensions: Dummy Variables
A dummy variable is a variable which takes on the value 1 or 0 depending upon the answer to a yes or no question. For example, a dummy variable might take on the value 1 if male and 0 if female, or 1 if republican and 0 otherwise or 1 if Jewish and 0 otherwise or 1 if the year was 1980 or later and 0 otherwise.
Example I. , Where MALE= 1 if the person is male, and 0 if
the person is female. This generates two equations one for females and one for males.
A test of the hypothesis is a test of the hypothesis that the wage equation is the same for
men and women.
Example II. Where D is a variable which takes on
the value 1 if the year is 1975 or greater and 0 otherwise. If the coefficient of D is positive it would indicate that the velocity function shifted upward in 1975.
Example III.
Where C = 1 if Christian, 0 otherwise; J = 1 if Jewish, 0 otherwise. Note that in this case there are three categories of persons Christian, Jewish, and all others. The last three equations are respectively the wage equations for all others, Christians, and Jewish. A test of the hypothesis is a test of
the hypothesis that there is no discrimination by religious group. (Note: There are three categories but we only define two dummies. Why. Note also that it would be inappropriate to define a variable R = 0 if other, 1 if Christian, 2 if Jewish.)
Example IV: Interaction Terms. Suppose we define the variable EDM to be the product of ED and
MALE. Then we estimate the equation: If the
coefficient of EDM is positive it means that an additional year of education adds more to a man’s wage than to a woman’s wage. There are two wage equations :
The first is the wage equation for women, the second is the wage equation for men. The hypothesis
is the hypothesis that there is no discrimination against or in favor of men.
Example 5. Define JMALE = J times MALE.
This equation suggests that there might be discrimination in favor of or against males and Jewish
persons. and are respectively the effect on wages of being male and the effect on wages of being
Jewish. It may be that the effect of being both male and Jewish is different than the sum of the individual
effects. captures this effect. It is the effect on wages of being both Jewish and male. If is
different than zero it means the discrimination against Jewish persons is different for men than it is for women or conversely that the discrimination against men is different for Jewish persons than it is for non-Jewish persons.
Example VI: The velocity equation again. Define D as in example 2 and define DINT = the product of D and INTEREST
This equation allows for the possibility that both the slope and intercept changed in 1975. A test of the
hypothesis (using an F-test) is a test of the hypothesis that there was no change in
the velocity function in 1975. This is known as test of structural stability ( A similar test for structural stability is known as the Chow Test. The F-test using dummy variables described here is a simpler and
more informative way to accomplish the same thing.) The test of is equivalent to
running separate regressions for the years before 1975 and 1975 and after and comparing the results. You will recognize that example IV above also is equivalent to comparing two separate regressions, a wage equation for men and a wage equation for women.
Example VII : Suppose we redefine the variable ED in the following way. A set of new variables E1, E2, E3 is defined as follows: E1 = 1 if the person is a high school graduate, 0 otherwise; E2 = 1 if the person is a college graduate, 0 otherwise; E3 = 1 if the person has an advanced degree, 0 otherwise. We then estimate the wage equation
This wage equation has distinct steps at various levels. The wage for a non-high school graduate is ,
for a high school graduate without a college degree wage = and so forth. It is important when
you are using a model that you are clear on the meaning of the variables. If , for example, E2 = 1 implies that E1 =1 also the results will be interpreted differently than if E2 = 1 implies that E1 = 0.
Example VIII. Dummy variables can also we use to model equations with kinks and discontinuities. For example suppose you are investigating a function with a bend at x = x*. Define a dummy variable
D =0 if then estimate the equation.
Example IX: Seasonal factors. Dummy variables can be used to take account of seasonal factors. For example a demand function might look like this
where D1, D2,D3 are dummies for spring, summer, and fall. (Note that one category, winter is left out)
