Homework5for Econometrics
(due May22,2013)
Spring2013
Instructor:Jihai Yu
TA:Kunyuan Qiao
1.Using the data in RDCHEM.RAW,the following equation was obtained by OLS:
\
rdintens=2:613+0:00030sales 0:0000000070sales2
(0:429)(0:00014)(0:0000000037)
n=32;R2=0:1484
(i)At what point does the marginal e¤ect of sales on rdintens become negative?
(ii)Would you keep the quadratic term in the model?Explain.
(iii)De…ne salesbil as sales measured in billions of dollars:salesbil sales/1,000.
Rewrite the estimated equation with salesbil and salesbil2as the independent variables.Be sure to report standard errors and the R-squared.
[Hint:Note that salesbil2=sales2=(1000)2]
(iv)For the purpo of reporting the results,which equation do you prefer?
2.The following model allows the return to education to depend upon the total amount of both parents’education,called pareduc:
log(wage)= 0+ 1educ+ 2edu pareduc+ 3exper+ 4tenure+u:
(i)Show that,in decimal form,the return to another year of education in this model is
log(wage)= educ= 1+ 2pareduc:霸道
What sign do you expect for 2?Why?
量纲分析法
(ii)Using the data in WAGE2.RAW,the estimated equation is
\
log(wage)=5:65+0:047educ+0:00078edu pareduc+0:019exper+0:010tenure:
(0:13)(0.010)(0.00021)(0.004)(0.003)
n=722;R2=0:169
(Only722obrvations contain full information on parents’education.)Interpret the coe¢cient on the interaction term.It might help to choo two speci…c values for pareduc—for example,pareduc=32if both parents have a college education,or pareduc=24if both parents have a high school education—and to compare the estimated return to educ.考试的英语
(iii)When pareduc is added as a parate variable to the equation,we get:
\
log(wage)=4:94+0:097educ+0:033paredu 0:0016edu pareduc+0:020exper+0:010tenure: (0:38)(0.027)(0.017)(0.012)(0.004)(0.003)鸭的英语
n=722;R2=0:174
Does the estimated return to education now depend positively on parent education?Test the null hypothesis that the return to education does not depend on parent education.
3.Suppo we want to estimate the e¤ects of alcohol consumption(alcohol)on college grade point average (colGPA).In addition to collecting information on grade point averages and alcohol usage,we also obtain attendance information(say,percentage of lectures attended,called attend).A standardized test score(say, SAT)and high school GPA(hsGPA)are also available.
(i)Should we include attend along with alcohol as explanatory variables in a multiple regression model? (Think about how you would interpret alcohol.)
(ii)Should SAT and hsGPA be included as explanatory variables?Explain.
4.Using the data in SLEEP7
5.RAW(e also Problem3.3),we obtain the estimated equation
[
sleep=3840:43 0:163totwrk 11:71educ 8:70age+0:128age2+87:75male:
(235:11)(0.018)(5.86)(11.21)(0.134)(34.33)
明视距离n=706;R2=0:123; R2=0:117
The variable sleep is total minutes per week spent sleeping at night,totwrk is total weekly minutes spent working,educ and age are measured in years,and male is a gender dummy.
(i)All other factors being equal,is there evidence that men sleep more than women?How strong is the evidence?
日历带农历
(ii)Is there a statistically signi…cant tradeo¤between working and sleeping?What is the estimated tradeo¤?
(iii)What other regression do you need to run to test the null hypothesis that,holding other factors …xed,age has no e¤ect on sleeping
5.Consider a model where the return to education depends upon the amount of work experience(and vice versa):
wage= 0+ 1educ+ 2exper+ 3educ exper+u.
(i)Show that the return to another year of education(in decimal form),holding exper…xed,is 1+ 31exper.
(ii)State the null hypothesis that the return to education does not depend on the level of exper.What do you think is the appropriate alternative?
(iii)U the data in WAGE2.RAW to test the null hypothesis in(ii)against your stated alternative.
(iv)Let 1denote the return to education(in decimal form),when exper=10: 1= 1+10 3.Obtain ^
and a95%con…dence interval for 1.(Hint:Write 1= 1 10 3and plug this into the equation;then 1
rearrange.This gives the regression for obtaining the con…dence interval for 1.)
考试检讨6.U the data in WAGE2.RAW for this exerci.
(i)Estimate the model
log(wage)= 0+ 1educ+ 2exper+ 3tenure+ 4married+ 5black+ 6south+ 7urban+u.
and report the results in the usual form.Holding other factors…xed,what is the approximate di¤erence in monthly salary between blacks and nonblacks?Is this di¤erence statistically signi…cant?
(ii)Add the variables exper2and tenure2to the equation and show that they are jointly insigni…cant at even the20%level.
(iii)Extend the original model to allow the return to education to depend on race and test whether the return to education does depend on race.
(iv)Again,start with the original model,but now allow wages to di¤er across four groups of people: married and black,married and nonblack,single and black,and single and nonblack.What is the estimated wage di¤erential between married blacks and married nonblacks?
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