Question

8. Dummy variables. Interpretation and t-test of coefficients of dummy variables. Example Question: Are earnings subject to ethnic discrimination? Using the Labor Force Participation 2011 data, we run the following regression: EARNINGS = B1 + B2S + B3 EXP + B.ETHWHITE + u, where EARNINGS is the hourly earnings in dollar, S is years of schooling, EXP is total work experience, and ETHWHITE is a dummy variable which equals to 1 if the individual is white and equals to otherwise. Please use the following regression output to answer the questions. Source SS df M S Model 55993.5744 Residual | 722291.644 3 18664.5248 3591 201.139416 Number of obs - 3595 FC 3, 3591) - 92.79 Prob >F = 0.0000 R-squared - 0.0719 Adj R-squared - 0.0712 Root MSE - 14.182 Total 778285.219 3594 216.551257 EARNINGS Coef. Std. Err. t P>It! [95% Conf. Interval] SL 1.519008 EXP | .6441281 ETHWHITE 1.602015 _cons -8.570992 098555 0951886 5426891 1.782426 15.41 6.77 2.95 -4.81 0.000 0.000 0.003 0.000 1.325779 .4574989 .5380058 -12.06566 1.712238 .8307573 2.666025 -5.076324 (a) Interpret the coefficient of ETHWHITE. (b) Are earnings subject to ethnic discrimination? Perform the t test and conclude

Answer 1

(a) The coefficient of ETHWHITE is the average change in EARNINGS, if the subject is white rather than otherwise (not white). It is basically the expected/average difference in EARNINGS among white and non-white individuals.

The estimated coefficient is 1.602015 or 1.6 dollar/hour. This means that, on average, the white individual's EARNING is $1.6 more than the non-white individuals, per hour.

(b) For the null hypothesis
Ho: 34 = 0
and alternate hypothesis
HA: 840
, we have the required t-statistic as
+ se(34)
or
1.60 2015 0.5426891
or . At 5% significance level, we have the critical t as
70.975,3595 = 1.9606
. Since
t> to.975,3595
, we may reject the null and conclude that the coefficient is significant at 5% significance.

This means that the EARNINGS are indeed subjected to ethnic discrimination, as the coefficient of ETHWHITE is significant in the model. Moreover, we may say that on average, the white earns more than the non-whites according to this model.