會計研究實證模型

Chapter 7Multiple Regression Analysis with Qualitative Information265

(iv)Bad on the equation in part (iii),can women realistically get enough

years of college so that their earnings catch up to tho of men? Explain.

C7.1U the data in for this exerci.

(i)Add the variables mothcoll and fathcoll to the equation estimated in (7.6)

and report the results in the usual form. What happens to the estimated

effect of PC ownership? Is PC still statistically significant?

(ii)Test for joint significance of mothcoll and fathcoll in the equation from

part (i) and be sure to report the p-value.

(iii)Add hsGPAto the model from part (i) and decide whether this gener-

2

alization is needed.

C7.2U the data in W for this exerci.

(i)Estimate the model

log(wage) ?educ ?exper ?tenure ?married

????

0 1234

?

?

?

south ?black ?urban ?u

??

?

567

and report the results in the usual form. Holding other factors fixed,what

is the approximate difference in monthly salary between blacks and non-

blacks? Is this difference statistically significant?

(ii)Add the variables experand tenureto the equation and show that they

2 2

are jointly insignificant at even the 20% level.

(iii)Extend the original model to allow the return to education to

dependon race and test whether the return to education does depend

on race.

(iv)Again,start with the original model,but now allow wages to differ

across four groups of people:married and black,married and nonblack,

single and black,and single and nonblack. What is the estimated wage

differential between married blacks and married nonblacks?

C7.3A model that allows major league baball player salary to differ by position is

log(salary) ?years ?gamesyr ?bavg ?hrunsyr

????

rbisyr ?runsyr ?fldperc ?allstar

0 1 234

?

?

???

?

?

5678

?frstba ?scndba ?thrdba shrtstop

?

?

9101112

???

?

?

13

catcher ?u,

where outfield is the ba group.

(i)State the null hypothesis that,controlling for other factors,catchers and

outfielders earn,on average,the same amount. Test this hypothesis using

the data in and comment on the size of the estimated salary

differential.

(ii)State and test the null hypothesis that there is no difference in average

salary across positions,once other factors have been controlled for.

266Part 1Regression Analysis with Cross-Sectional Data

(iii)Are the results from parts (i) and (ii) consistent? If not,explain what is

happening.

C7.4U the data in for this exerci.

(i)Consider the equation

colgpa ?hsize ?hsizehsperc ?sat

???

0 1234

??

?

??

2

?female athlete ?u,

?

?

56

where colgpa is cumulative college grade point average,hsize is size

of high school graduating class,in hundreds,hsperc is academic per-

centile in graduating class,sat is combined SAT score,female is a

binary gender variable,and athlete is a binary variable,which is one

for student-athletes. What are your expectations for the coefficients in

this equation? Which ones are you unsure about?

(ii)Estimate the equation in part (i) and report the results in the usual form.

What is the estimated GPA differential between athletes and nonath-

letes? Is it statistically significant?

(iii)Drop sat from the model and reestimate the equation. Now,what is the

estimated effect of being an athlete? Discuss why the estimate is differ-

ent than that obtained in part (ii).

(iv)In the model from part (i),allow the effect of being an athlete to differ

by gender and test the null hypothesis that there is no ceteris paribus dif-

ference between women athletes and women nonathletes.

(v)Does the effect of sat on colgpa differ by gender? Justify your answer.

C7.5In Problem 4.2,we added the return on the firm’s stock,ros,to a model explain-

ing CEO salary; ros turned out to be insignificant. Now,define a dummy variable,rosneg,

which is equal to one if ros ?0 and equal to zero if ros ?0. U to

estimate the model

log(salary) ?log(sales) ?roe ?rosneg ?u.

???

0 123

?

?

Discuss the interpretation and statistical significance of .

?

?

3

C7.6U the data in for this exerci. The equation of interest is

sleep ?totwrk ?educ ?age ?ageyngkid ?u.

????

0 12345

??

??

2

(i)Estimate this equation parately for men and women and report the

results in the usual form. Are there notable differences in the two esti-

mated equations?

(ii)Compute the Chow test for equality of the parameters in the sleep equa-

tion for men and women. U the form of the test that adds male and the

interaction terms maleиtotwrk,…,maleиyngkid and us the full t of

obrvations. What are the relevant df for the test? Should you reject the

null at the 5% level?

(iii)Now,allow for a different intercept for males and females and determine

whether the interaction terms involving maleare jointly significant.