计量经济学作业HW6

Homework6for Econometrics(due June5,2013)Spring2013Instructor:Jihai YuTA:Kunyuan Qiao1.Let inlf(“in the labor force”)be a binary variable indicating labor force participation by a married womanduring1975:inlf1if the woman reports working for a wage outside the home at some point during the year,and zero otherwise.We assume that labor force participation depends on other sources of income,including husband’s earnings(nwifeinc,measured in thousands of dollars),years of education(educ),past years oflabor market experience(exper),age,number of children less than six years old(kidslt6),and number ofkids between6and18years of age(kidsge6).Using the data in MROZ.RAW from Mroz(1987),we estimatethe following linear probability model,where428of the753women in the sample report being in the laborforce at some point during1975:d inlf=0:586 0:0034nwifeinc+0:38educ+0:039exper 0:0006exper2 0:16age 0:262kidslt6+0:13kidsge6:(0:154)(0.0014)(0.007)(0.006)(0.00018)(0.002)(0.034)(0.0132) n=753;R2=0:264Suppose that we de…ne outlf to be one if the woman is out of the labor force,and zero otherwise.(i)If we regress outlf on all of the independent variables in the above equation,what will happen to the intercept and slope estimates?(Hint:inlf=11-outlf.Plug this into the population equation and rearrange.) (ii)What will happen to the standard errors on the intercept and slope estimates?(iii)What will happen to the R-squared?2.Which of the following are consequences of heteroskedasticity?(i)The OLS estimators,^ j,are inconsistent.(ii)The usual F statistic no longer has an F distribution.(iii)The OLS estimators are no longer BLUE.3.The variable smokes is a binary variable equal to one if a person smokes,and zero ing thedata in SMOKE.RAW,we estimate a linear probability model for smokes:\smokes=0:656 0:069log(cigpric)+0:012log(income) 0:029educ(0:855)(0.204)(0.026)(0.006)[0:856][0.207][0.026][0.006]+0:02age 0:00026age2 0:101restaurn 0:026white:(0:006)(0.00006)(0.039)(0.052)[0:005][0.00006][0.038][0.050]n=807;R2=0:062The variable white equals one if the respondent is white,and zero otherwise;the other independent variables are de…ned in Example8.7.Both the usual and heteroskedasticityrobust standard errors are reported.(i)Are there any important di¤erences between the two sets of standard errors?(ii)Holding other factors…xed,if education increases by four years,what happens to the estimated probability of smoking?(iii)At what point does another year of age reduce the probability of smoking?(iv)Interpret the coe¢cient on the binary variable restaurn(a dummy variable equal to one if the person lives in a state with restaurant smoking restrictions).(v)Person number206in the data set has the following characteristics:cigpric67.44,income6,500,educ 16,age77,restaurn0,white0,and pute the predicted probability of smoking for this person and comment on the result.e the data in LOANAPP.RAW for this exercise.The binary variable to be explained is approve,which is equal to one if a mortgage loan to an individual was approved.The key explanatory variable is white,a dummy variable equal to one if the applicant was white.The other applicants in the data set are black and Hispanic.To test for discrimination in the mortgage loan market,a linear probability model can be used:approve= 0+ 1while+other factors(i)If there is discrimination against minorities,and the appropriate factors have been controlled for, what is the sign of1?(ii)Regress approve on white and report the results in the usual form.Interpret the coe¢cient on white. Is it statistically signi…cant?Is it practically large?(iii)As controls,add the variables hrat,obrat,loanprc,unem,male,married,dep,sch,cosign,chist, pubrec,mortlat1,mortlat2,and vr.What happens to the coe¢cient on white?Is there still evidence of discrimination against nonwhites?(iv)Now,allow the e¤ect of race to interact with the variable measuring other obligations as a percentage of income(obrat).Is the interaction term signi…cant?(v)Using the model from part(iv),what is the e¤ect of being white on the probability of approval when obrat32,which is roughly the mean value in the sample?Obtain a95%con…dence interval for this e¤ect.e VOTE1.RAW for this exercise.(i)Estimate a model with voteA as the dependent variable and prtystrA,democA,log(expendA),and log(expendB)as independent variables.Obtain the OLS residuals,^u i,and regress these on all of the independent variables.Explain why you obtain R2=0.(ii)Now,compute the Breusch-Pagan test for e the F statistic version and report the p-value.(iii)Compute the special case of the White test for heteroskedasticity,again using the F statistic form. How strong is the evidence for heteroskedasticity now?e the data in LOANAPP.RAW for this exercise.(i)Estimate the equation in part(iii)of Problem4,computing the heteroskedasticity-robust standard pare the95%con…dence interval on white with the nonrobust con…dence interval.(ii)Obtain the…tted values from the regression in part(i).Are any of them less than zero?Are any of them greater than one?What does this mean about applying weighted least squares?。