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350 Chapter 8 Nonlinear Regression Functions

(Hint: See the discussion “Standard errors of estimated effects” on
page 310.)

c. Suppose that the variable Characters had been divided by 1000
instead of 1,000,000. How would the results in column (4) change?

8.6 Refer to Table 8.3.

a. A researcher suspects that the effect of %Eligible for subsidized lunch
has a nonlinear effect on test scores. In particular, he conjectures that
increases in this variable from 10% to 20% have little effect on test
scores but that changes from 50% to 60% have a much larger effect.

i. Describe a nonlinear specification that can be used to model this
form of nonlinearity.

ii. How would you test whether the researcher’s conjecture was better
than the linear specification in column (7) of Table 8.3?

b. A researcher suspects that the effect of income on test scores is different
in districts with small classes than in districts with large classes.

i. Describe a nonlinear specification that can be used to model this
form of nonlinearity.

ii. How would you test whether the researcher’s conjecture was better
than the linear specification in column (7) of Table 8.3?

8.7 This problem is inspired by a study of the “gender gap” in earnings in top
corporate jobs [Bertrand and Hallock (2001)]. The study compares total
compensation among top executives in a large set of U.S. public corpo-
rations in the 1990s. (Each year these publicly traded corporations must
report total compensation levels for their top five executives.)

a. Let Female be an indicator variable that is equal to 1 for females and 0
for males. A regression of the logarithm of earnings onto Female yields

ln (Earnings) = 6.48 - 0.44 Female, SER = 2.65.
(0.01) (0.05)

i. The estimated coefficient on Female is -0.44. Explain what this
value means.

ii. The SER is 2.65. Explain what this value means.

iii. Does this regression suggest that female top executives earn less
than top male executives? Explain.

iv. Does this regression suggest that there is gender discrimination?
Explain.