中级计量经济学 作业四

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1、中级计量经济学作业四（DueJanuary5，2015）(共120分)1.(2’×5=10’)根据20世纪70年代早期101个国家以美元计人均收入（x）和预期寿命（y）的数据，Sen和Srivastava得到如下回归结果yˆ=−2.40+9.39lnx−3.36[D(lnx−7)]iiii2se=(4.73)(0.859)(2.42)R=0.752其中，如果lnxi>7,Di=1，否则Di=0。注：当lnxi=7时，x=1097美元（近似）。（a）以对数形式引入收入变量的原因是什么？（b）你如何解释lnxi的系数9.39？（c）引入回归元Di(lnxi-7)的理由是什么？你又如何解释这个

2、回归元的系数-3.36？（d）假定穷国与富国之间的分界线为人均收入1097美元，你如何推导出收入低于1097美元国家的回归线和收入高于1097美元国家的回归线？（e）你从回归结果中能得出什么一般结论？2.(5’×2=10’)设时间序列｛Xt｝是由X୲ൌδ଴൅δଵt൅ε୲生成的，如果ε୲是一个零均值，同方差，序列不相关的白噪声，请问：（a）Xt是平稳时间序列吗？为什么？（b）Xt–E(Xt)是平稳时间序列吗？为什么？3.(5’×4=20’)Fromthehouseholdbudgetsurveyof1980oftheDutchCentralBureauofStatistics,J.S.Cr

3、amerobtainedthefollowinglogitmodelbasedonasampleof2820households.(Theresultsgivenherearebasedonthemethodofmaximumlikelihoodandareafterthethirditeration.)Thepurposeofthelogitmodelwastodeterminecarownershipasafunctionof(logarithmof)income.Carownershipwasabinaryvariable:Y=1ifahouseholdownsacar,zeroo

4、therwise.L෠୧ൌെ2.77231 ൅ 0.347582lnIncomet=(−3.35)(4.05)2χ(1df)=16.681(pvalue=0.0000)2whereL෠୧=estimatedlogitandwherelnIncomeisthelogarithmofincome.Theχmeasuresthegoodnessoffitofthemodel.(a)Interprettheestimatedlogitmodel.(b)Fromtheestimatedlogitmodel,howwouldyouobtaintheexpressionfortheprobabilit

5、yofcarownership?(c)Whatistheprobabilitythatahouseholdwithanincomeof20,000willownacar?Andatanincomelevelof25,000?Whatistherateofchangeofprobabilityattheincomelevelof20,000?(d)Commentonthestatisticalsignificanceoftheestimatedlogitmodel.第1页共4页4.(5’)Letgradbeadummyvariableforwhetherastudent-athleteat

6、alargeuniversitygraduatesinfiveyears.LethsGPAandSATbehighschoolgradepointaverageandSATscore,respectively.Letstudybethenumberofhoursspentperweekinanorganizedstudyhall.Supposethat,usingdataon420student-athletes,thefollowinglogitmodelisobtained:P෡ሺgradൌ1

7、hsGPA,SAT,studyሻൌΛሺെ1.17൅.24hsGPA൅.00058SAT൅.

8、073studyሻwhereΛሺzሻൌexp ሺzሻ/ሾ1൅expሺzሻሿisthelogitfunction.HoldinghsGPAfixedat3.0andSATfixedat1,200,computetheestimateddifferenceinthegraduationprobabilityforsomeonewhospent10hoursperweekinstudyhallandsomeonewhospent5hour