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Exercises 351

b. Two new variables, the market value of the firm (a measure of firm
size, in millions of dollars) and stock return (a measure of firm
performance, in percentage points), are added to the regression:

ln(Earnings) = 3.86 - 0.28 Female + 0.37ln(MarketValue) + 0.004 Return,

(0.03) (0.04) (0.004) (0.003)

n = 46,670, R 2 = 0.345.

i. The coefficient on ln(MarketValue) is 0.37. Explain what this
value means.

ii. The coefficient on Female is now -0.28. Explain why it has
changed from the regression in (a).

c. Are large firms more likely than small firms to have female top exec-
utives? Explain.

8.8 X is a continuous variable that takes on values between 5 and 100. Z is a binary
variable. Sketch the following regression functions (with values of X between
5 and 100 on the horizontal axis and values of Yn on the vertical axis):

a. Yn = 2.0 + 3.0 * ln(X).
b. Yn = 2.0 - 3.0 * ln(X).
c. i. Yn = 2.0 + 3.0 * ln(X) + 4.0Z, with Z = 1.
ii. Same as (i), but with Z = 0.

d. i. Yn = 2.0 + 3.0 * ln(X) + 4.0Z - 1.0 * Z * ln(X), with Z = 1.
ii. Same as (i), but with Z = 0.
e. Yn = 1.0 + 125.0X - 0.01X2.

8.9 Explain how you would use Approach #2 from Section 7.3 to calculate the
confidence interval discussed below Equation (8.8). [Hint: This requires
estimating a new regression using a different definition of the regressors
and the dependent variable. See Exercise (7.9).]

8.10 Consider the regression model Yi = b0 + b1X1i + b2X2i + b3(X1i * X2i) +
ui. Use Key Concept 8.1 to show:

a. ∆Y> ∆X1 = b1 + b3X2 (effect of change in X1, holding X2 constant).
b. ∆Y> ∆X2 = b2 + b3X1 (effect of change in X2, holding X1 constant).
c. If X1 changes by ∆X1 and X2 changes by ∆X2, then ∆Y =

(b1 + b3X2)∆X1 + (b2 + b3X1)∆X2 + b3∆X1∆X2.
8.11 Derive the expressions for the elasticities given in Appendix 8.2 for the

linear and log-log models. (Hint: For the log-log model, assume that u