计量经济学作业HW4

Homework4for Econometrics
(due May8,2013)
Spring2013
Instructor:Jihai Yu
TA:Kunyuan Qiao
1.(i)In the simple regression model
price= 0+ 1assess+u;
the assessment is rational if 1=1and 0=0.The estimated equation is
[
price= 14:47+0:976assess
(16:27)(0.049)
n=88;SSR=165644:51;R2=0:820
First,test the hypothesis that H0: 0=0against the two-sided alternative.Then,test H0: 1=1 against the two-sided alternative.What do you conclude?
(ii)To test the joint hypothesis that 1=1and 0=0,we need the SSR in the restricted model.This amounts to computing P n i=1(price i assess i)2,where n=88,since the residuals in the restricted model are just price i assess i.(No estimation is needed for the restricted model because both parameters are speci…ed under H0.)This turns out to yield SSR=209448:99.Carry out the F test for the joint hypothesis.
(iii)Now,test H0: 2= 3= 4=0in the model
price= 0+ 1assess+ 2lotsize+ 3sqrft+ 4bdrms+u.
The R-squared from estimating this model using the same88houses is0.829.
(iv)If the variance of price changes with assess,lotsize,sqrft,or bdrms,what can you say about the F test from part(iii)?
2.We estimated the equation
[
sleep=3638:25 0:148totwork 11:13educ+2:20age
(112:28)(0.017)(5.88)(1.45)
n=706;R2=0:113
where we now report standard errors along with the estimates.
(i)Is either educ or age individually signi…cant at the5%level against a two-sided alternative?Show your work.
(ii)Dropping educ and age from the equation gives
[
sleep=3586:38 0:151totwork
(38:91)(0.017)
n=706;R2=0:103
Are educ and age jointly signi…cant in the original equation at the5%level?Justify your answer.
(iii)Does including educ and age in the model greatly a¤ect the estimated tradeo¤between sleeping and working?
(iv)Suppose that the sleep equation contains heteroskedasticity.What does this mean about the tests computed in parts(i)and(ii)?
3.For the above regression equation,the sample size is T=100.We expect that the…rst60periods follows
y= 0+ 1x1+ 2x2+ 3x3+u,
while the second40periods follows
y= 0+ 1x1+ 4x2+ 5x3+u.
That is,there is a structural change between this two samples.
Construct an F test for the null hypothesis that" 2= 4and 3= 5".
4.In the simple regression model under MLR.1through MLR.4,we argued that the slope estimator,^ 1,is consistent for ing^ 0= y ^ 1 x1,show that plim^ 0= 0.
[You need to use the consistency of^ 1and the law of large numbers,along with the fact that 0= E(y) 1E(x1).]
e the data in DISCRIM.DTA to answer this question.
(i)Use OLS to estimate the model
log(psoda)= 0+ 1prpblk+ 2log(income)e+ 3prppov+u.
and report the results in the usual form.Is^ 1statistically di¤erent from zero at the5%level against a two-sided alternative?What about at the1%level?
(ii)What is the correlation between log(income)and prppov?Is each variable statistically signi…cant in any case?Report the two-sided p-values.
(iii)To the regression in part(i),add the variable log(hseval).Interpret its coe¢cient and report the two-sided p-value for H0: log(hseval)=0.
(iv)In the regression in part(iii),what happens to the individual statistical signi…cance of log(income) and prppov?Are these variables jointly signi…cant?(Compute a p-value.)What do you make of your answers?
(v)Given the results of the previous regressions,which one would you report as most reliable in deter-mining whether the racial makeup of a zip code in‡uences local fast-food prices?
e the data in WAGE1.DTA for this exercise.
(i)Estimate the equation
wage= 0+ 1educ+ 2exper+ 3tenure+u.
Save the residuals and plot a histogram.
(ii)Repeat part(i),but with log(wage)as the dependent variable.
(iii)Would you say that Assumption MLR.6is closer to being satis…ed for the level-level model or the log-level model?。