Applying Indicator Variables
In this section a number of examples will be given about estimation and interpretation of regressions that include indicator variables.
Consider the simple wage equation
wage = ві + e2educ + S1black + S2 female
+Y(female x black) + e
where black and female are indicator variables. Taking the expected value of ln(wage) reveals each of the cases considered in the regression
в1 + e2educ White, Males
в1 + Si + e2educ Black, Males
в1 + S2 + e2educ White, Females
в1 + Si + S2 + y + e2educ Black, Females
The reference group is the one where all indicator variables are zero, i. e., white males. The parameter S1 measures the effect of being black, relative to the reference group; S2 measures the effect of being female relative to the reference group, and y measures the effect of being both black and female.
The model is estimated using the cps4~small. gdt data which is from 2008. The results appear below:
Model 3: OLS, using observations 11000
Dependent variable: wage
Coefficient 
Std. Error 
tratio 
pvalue 

const 
5.28116 
1.90047 
2.7789 
0.0056 
educ 
2.07039 
0.134878 
15.3501 
0.0000 
black 
4.16908 
1.77471 
2.3492 
0.0190 
female 
4.78461 
0.773414 
6.1863 
0.0000 
blk_fem 
3.84429 
2.32765 
1.6516 
0.0989 
Mean dependent var 20.61566 S. D. dependent var 12.83472
Sum squared resid 130194.7 S. E. of regression 11.43892
R2 0.208858 Adjusted R2 0.205677
F(4,995) 65.66879 Pvalue(F) 2.53e49
Loglikelihood 3853.454 Akaike criterion 7716.908
Schwarz criterion 7741.447 HannanQuinn 7726.234
Holding the years of schooling constant, black males earn $4.17/hour less than white males. For the same schooling, white females earn $4.78 less, and black females earn $5.15 less. The coefficient on the interaction term is not significant at the 5% level however.
A joint test of the hypothesis that S1 = S2 = y = 0 is performed via the script
1 open "@gretldirdatapoecps4_small. gdt"
2 series blk_fem = black*female
3 ols wage const educ black female blk_fem
4 restrict
5 b[3]=0
6 b[4]=0
7 b[5]=0
8 end restrict and the result is
Restriction set 1: b[black] = 0 2: b[female] = 0 3: b[blk_fem] = 0
Test statistic: F(3, 995) = 14.2059, with pvalue = 4.53097e009 Restricted estimates:
Standard error of the regression = 11.6638 
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