Return to equations (13.59) and (13.60).

(a) Test whether or not the three slopes in equation (13.59) are statistically significant. What do these tests indicate about the effect of being a black woman on expected earnings?

(b) Test whether or not the three slopes in equation (13.60) are statistically significant. What do these tests indicate about the effect of being a black woman on expected earnings?

(c) For the regression of equation (13.60), the F-statistic for the test of the joint null hypothesis Hâ•›0 : β2 + β3 = 0 is .08. The degrees of freedom are 1 and 179,545. Using table A.3, interpret the results of this test. What does this test indicate about the effect of being a black woman on expected earnings?

(d) In equation (12.30), note 10 of chapter 12, and exercise 12.12, we assert that any F-test with a single degree of freedom in the numerator can be reformulated as a t-test. Consider the population relationship

where x1i is a dummy variable identifying women, x2i is a dummy variable identifying black men, and x3i is a dummy variable identifying black women. Compare the expected values of earnings for nonblack men, nonblack women, black men, and black women to those of equations (13.53)
through (13.56). Explain why this specification is equivalent to that of equation (13.48), where x1i is a dummy variable identifying women and x2i is a dummy variable identifying blacks.

(e) The sample regression that corresponds to the population relationship of part

d, calculated with the sample of equation (13.60), is

How do the effects for females, black males, and black females compare in the two regressions? Are they statistically significant? Interpret them.
In this equation, what is the statistical test for the null hypothesis that �expected earnings are the same for black and nonblack females? What is the outcome of this test?
(fâ•›) In both equations (13.59) and (13.60), women and black men have large negative slopes. This suggests the null hypothesis that their expected earnings might differ from those of males by the same amount, Hâ•›0 : β1 = β2. The F-statistic for the test of this null hypothesis in equation (13.59) is .55 with 1 and 996 degrees of freedom. For equation (13.60), it is 66.46 with 1 and 179,545 degrees of freedom. What can we conclude regarding this hypothesis?
(g) The F-tests of part f have only 1 degree of freedom in the numerator.
How would we specify a regression in order to test the null hypothesis with a t-statistic?

Transcribed Image Text:

y =+ B +2x2 +3x3; +