计量经济学练习题及参考答案.doc

第八章练习题及参考解答8.1 Sen和Srivastava（1971）在研究贫富国之间期望寿命的差异时，利用101个国家的数据，建立了如下的回归模型：(4.37) (0.857) (2.42) R2=0.752其中：X是以美元计的人均收入；Y是以年计的期望寿命；Sen和Srivastava 认为人均收入的临界值为1097美元（），若人均收入超过1097美元，则被认定为富国；若人均收入低于1097美元，被认定为贫穷国。括号内的数值为对应参数估计值的t-值。1）解释这些计算结果。2）回归方程中引入的原因是什么？如何解释这个回归解释变量？3）如何对贫穷国进行回归？又如何对富国进行回归？4）从这个回归结果中可得到的一般结论是什么？练习题8.1参考解答：1. 结果解释 依据给定的估计检验结果数据，对数人均收入对期望寿命在统计上并没有显著影响，截距和变量在统计上对期望寿命有显著影响；同时，表明贫富国之间的期望寿命存在差异。2. 回归方程中引入的原因是从截距和斜率两个方面考证收入因素对期望寿命的影响。这个回归解释变量可解释为对期望寿命的影响存在截距差异和斜率差异的共同因素。3. 对穷国进行回归时，回归模型为 对富国进行回归时，回归模型为4. 一般的结论为富国的期望寿命药高于穷国的期望寿命，并且随着收入的增加，在平均意义上，富国的期望寿命的增加变化趋势优于穷国，贫富国之间的期望寿命的确存在显著差异。8.2个人所得税起征点调整对居民消费支出会产生重要的影响。为研究个人所得税起征点调整对城镇居民个人消费支出行为的效应，收集相关的数据如表8.4和表8.5所示。 表8.4 个人所得税起征点调整情况1987年1994年2006年2008年最低的起征点400元800元1600元2000元 表8.5 城镇居民收入与消费的有关数据城镇家庭平均每人可支配收入（元）城镇家庭平均每人全年消费性支出（元）平均每户城镇家庭就业人口数（人）城镇家庭平均每一就业者负担人数（含本人）（人）1985739.1673.22.151.811986900.97992.121.819871002.1884.42.091.7919881180.211042.031.7919891373.9121121.7819901510.161278.891.981.7719911700.61453.81.961.7519922026.61671.71.951.7319932577.42110.81.921.7219943496.22851.31.881.7419954282.953537.571.871.7319964838.93919.51.861.7219975160.34185.61.831.7419985425.14331.61.81.75199958544615.91.771.7720006279.9849981.681.8620016859.65309.011.651.8820027702.86029.921.581.9220038472.26510.941.581.9120049421.67182.11.561.912005104937942.881.511.96200611759.458696.551.531.93200713785.819997.471.541.89200815780.811242.91.481.97若模型设定为：Consumet=Ct+1Incomet+2Consumet-1+3Employmentt+4Burdent+5d1t+6d2t+7d3t+8d4t+t其中Consumet表示t期城镇居民家庭人均消费支出，Incomet表示t期城镇居民家庭人均可支配收入,Employmentt表示t期城镇居民家庭平均每户就业人口, Burdent表示t期城镇居民家庭平均每一就业者负担人数，dit(i=1,2,3,4)相应的虚拟变量。1）构造用于描述个人所得税调整的虚拟变量，并简要说明其理由；2）用散点图描述两两变量之间的关系，并给出你对模型设定的结论；3）依据测算，选择你认为更能描述客观实际的模型，并简要说明其理由；4）根据分析结果，你对提高个人所得税起征点影响居民消费的有效性能得出什么结论?练习题8.2参考解答： 录入如下数据obsCONSUMEINCOMEEMPLOYMENTD1D2D3D41985673.2000739.10002.1500000.0000000.0000000.0000000.0000001986799.0000900.90002.1200000.0000000.0000000.0000000.0000001987884.40001002.1002.0900001.0000000.0000000.0000000.00000019881104.0001180.2002.0300001.0000000.0000000.0000000.00000019891211.0001373.9002.0000001.0000000.0000000.0000000.00000019901278.8901510.1601.9800001.0000000.0000000.0000000.00000019911453.8001700.6001.9600001.0000000.0000000.0000000.00000019921671.7002026.6001.9500001.0000000.0000000.0000000.00000019932110.8002577.4001.9200001.0000000.0000000.0000000.00000019942851.3003496.2001.8800001.0000001.0000000.0000000.00000019953537.5704282.9501.8700001.0000001.0000000.0000000.00000019963919.5004838.9001.8600001.0000001.0000000.0000000.00000019974185.6005160.3001.8300001.0000001.0000000.0000000.00000019984331.6005425.1001.8000001.0000001.0000000.0000000.00000019994615.9005854.0001.7700001.0000001.0000000.0000000.00000020004998.0006279.9801.6800001.0000001.0000000.0000000.00000020015309.0106859.6001.6500001.0000001.0000000.0000000.00000020026029.9207702.8001.5800001.0000001.0000000.0000000.00000020036510.9408472.2001.5800001.0000001.0000000.0000000.00000020047182.1009421.6001.5600001.0000001.0000000.0000000.00000020057942.88010493.001.5100001.0000001.0000000.0000000.00000020068696.55011759.451.5300001.0000001.0000001.0000000.00000020079997.47013785.811.5400001.0000001.0000001.0000000.000000200811242.9015780.801.4800001.0000001.0000001.0000001.000000分别作如下回归：Dependent Variable: CONSUMEMethod: Least SquaresDate: 08/24/09 Time: 13:14Sample (adjusted): 1986 2008Included observations: 23 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C744.7966378.06621.9700170.0676CONSUME(-1)0.0848730.0509071.6672210.1162INCOME0.6331180.03519817.987290.0000LOG(EMPLOYMENT)-762.9720478.5280-1.5944140.1317D137.4346050.234450.7451980.4677D2221.076538.308405.7709660.0000D3-122.049373.81439-1.6534610.1190D4-178.868865.87071-2.7154520.0160R-squared0.999861Mean dependent var4428.906Adjusted R-squared0.999796S.D. dependent var3060.917S.E. of regression43.70477Akaike info criterion10.66100Sum squared resid28651.61Schwarz criterion11.05595Log likelihood-114.6015F-statistic15413.79Durbin-Watson stat2.977604Prob(F-statistic)0.000000Dependent Variable: CONSUMEMethod: Least SquaresDate: 08/24/09 Time: 13:14Sample (adjusted): 1986 2008Included observations: 23 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C871.9310332.66272.6210670.0185CONSUME(-1)0.0835760.0501651.6660170.1152INCOME0.6299220.03444718.286760.0000LOG(EMPLOYMENT)-889.4616441.1508-2.0162300.0609D2226.036137.197916.0765790.0000D3-110.888471.26752-1.5559460.1393D4-171.692464.25105-2.6722110.0167R-squared0.999856Mean dependent var4428.906Adjusted R-squared0.999802S.D. dependent var3060.917S.E. of regression43.09316Akaike info criterion10.61040Sum squared resid29712.33Schwarz criterion10.95598Log likelihood-115.0196F-statistic18496.74Durbin-Watson stat2.787479Prob(F-statistic)0.000000Dependent Variable: CONSUMEMethod: Least SquaresDate: 08/24/09 Time: 13:15Sample (adjusted): 1986 2008Included observations: 23 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C1204.936265.10544.5451220.0003CONSUME(-1)0.0993140.0511471.9417090.0689INCOME0.5991650.02936620.403200.0000LOG(EMPLOYMENT)-1325.942354.4143-3.7412220.0016D2251.367534.815737.2199400.0000D4-141.771063.81647-2.2215430.0402R-squared0.999834Mean dependent var4428.906Adjusted R-squared0.999785S.D. dependent var3060.917S.E. of regression44.85802Akaike info criterion10.66434Sum squared resid34208.12Schwarz criterion10.96056Log likelihood-116.6399F-statistic20483.46Durbin-Watson stat2.638666Prob(F-statistic)0.000000Dependent Variable: CONSUMEMethod: Least SquaresDate: 08/24/09 Time: 13:16Sample: 1985 2008Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C1460.937233.29226.2622630.0000INCOME0.6531010.00913271.515390.0000LOG(EMPLOYMENT)-1651.937314.1501-5.2584310.0000D2277.404833.627838.2492610.0000D4-154.274266.05969-2.3353770.0306R-squared0.999810Mean dependent var4272.418Adjusted R-squared0.999769S.D. dependent var3090.239S.E. of regression46.92598Akaike info criterion10.71807Sum squared resid41838.91Schwarz criterion10.96350Log likelihood-123.6169F-statistic24931.15Durbin-Watson stat2.292463Prob(F-statistic)0.0000008.3 在统计学教材中，采用了方差分析方法分析了不同班次对劳动效率的影响，其样本数据为 表8.6 不同班次的劳动效率早班中班晚班374740355142334839335041355142365140374740试采用虚拟解释变量回归的方法对上述数据进行方差分析。练习题8.3参考解答：考虑到班次有三个属性，故在有截距项的回归方程中只能引入两个虚拟变量，按加法形式引入，模型设定形式为： 其中，为劳动效率。 在Eviews中按下列格式录入数据： obsYD1D2134.000001.0000000.000000237.000001.0000000.000000335.000001.0000000.000000433.000001.0000000.000000533.000001.0000000.000000635.000001.0000000.000000736.000001.0000000.000000849.000000.0000001.000000947.000000.0000001.0000001051.000000.0000001.0000001148.000000.0000001.0000001250.000000.0000001.0000001351.000000.0000001.0000001451.000000.0000001.0000001539.000000.0000000.0000001640.000000.0000000.0000001742.000000.0000000.0000001839.000000.0000000.0000001941.000000.0000000.0000002042.000000.0000000.0000002140.000000.0000000.000000输入命令：ls y c d1 d2，则有如下结果Dependent Variable: YMethod: Least SquaresDate: 06/29/09 Time: 16:56Sample: 1 21Included observations: 21VariableCoefficientStd. Errort-StatisticProb.C40.428570.55532972.801150.0000D1-5.7142860.785353-7.2760690.0000D29.1428570.78535311.641710.0000R-squared0.952909Mean dependent var41.57143Adjusted R-squared0.947676S.D. dependent var*6.423172S.E. of regression1.469262Akaike info criterion3.738961Sum squared resid*38.85714Schwarz criterion3.888178Log likelihood-36.25909F-statistic*182.1176Durbin-Watson stat2.331933Prob(F-statistic)0.000000表中的*号部分表示在方差分析中需要用到的数据。依据上述数据，有：， 于是方差分析的结果为方差来源离差平方和自由度方差F值组间 786.2862393.143182.118组内 38.857182.158总和 825.143208.4 Joseph Cappelleri基于1961-1966年的200只Aa级和Baa级债券的数据（截面数据和时间序列数据的合并数据），分别建立了LPM和Logit模型：LPM Logit 其中：=1债券信用等级为Aa（穆迪信用等级）=1债券信用等级为Baa（穆迪信用等级）=债券的资本化率，作为杠杆的测度（）利润率（）利润率的标准差，测度利润率的变异性总资产净值，测度规模上述模型中和事先期望为负值，而和期望为正值（为什么）。对于LPM，Cappelleri经过异方差和一阶自相关校正，得到以下结果：=0.68600.0179+0.0486+0.0572+0.3781075iSe=(0.1775)(0.0024) (0.0486) (0.0178) (0.039108)R2=0.6933对于Logit模型，Cappelleri在没有对异方差进行弥补的情形下用ML得以下结果：试解决下列问题：1）为什么要事先期望和为负值？2）在LPM中，当0是否合理？3）对LPM的估计结果应做什么样的解释？4）已知，（千元），债券晋升Aa信用等级的概率有多大？练习题8.4参考解答1）、分别是债券的资本化率和利润率的标准差的回归系数。债券的资本化率是长期债券的市值和总资本的市值的比率，若总资本的市值不变，长期债券的市值越高，即债券的资本化率越高，债券风险越高，则债券的信用等级越低，故应为负值。同样，利润率的标准差越大，表明债券的变异性越大，风险越高，则债券的信用等级越低，故应为负值。2）如上所述，是不合理的。3）经济解释：在其他条件不变的情况下，给定资本的债券化率一个水平值b，资本的债券化率每上升1%，则债券的信用等级为Aa的概率下降0.0358b%。在其他条件不变的情况下，债券的利润率每上升1%，则债券的信用等级为Aa的概率上升0.0486%。4) LPMLogit8.5 Greene在分析讲授某门经济学课程采用新的教学方法效应时，搜集了如下表所示的数据， 表8.7 采用新的教学方法讲授某门经济学课程的数据obsGRADEGPATUCEPSIobsGRADEGPATUCEPSI10.0000002.66000020.000000.000000170.0000002.75000025.000000.00000020.0000002.89000022.000000.000000180.0000002.83000019.000000.00000030.0000003.28000024.000000.000000190.0000003.12000023.000001.00000040.0000002.92000012.000000.000000201.0000003.16000025.000001.00000051.0000004.00000021.000000.000000210.0000002.06000022.000001.00000060.0000002.86000017.000000.000000221.0000003.62000028.000001.00000070.0000002.76000017.000000.000000230.0000002.89000014.000001.00000080.0000002.87000021.000000.000000240.0000003.51000026.000001.00000090.0000003.03000025.000000.000000251.0000003.54000024.000001.000000101.0000003.92000029.000000.000000261.0000002.83000027.000001.000000110.0000002.63000020.000000.000000271.0000003.39000017.000001.000000120.0000003.32000023.000000.000000280.0000002.67000024.000001.000000130.0000003.57000023.000000.000000291.0000003.65000021.000001.000000141.0000003.26000025.000000.000000301.0000004.00000023.000001.000000150.0000003.53000026.000000.000000310.0000003.10000021.000001.000000160.0000002.74000019.000000.000000321.0000002.39000019.000001.000000其中，Grade是学生在接受新教学方法（PSI，）后学习成绩是否有所提高的虚拟变量，其他变量分别为平均级点GPA，非期末考试成绩分数TUCE。试用Logit模型对此进行估计，并分析相应的边际效应。练习题8.5参考解答：在Eviews中按照给定数据进行录入，点击Quick，录入grade c gpa tuce psi，点击method，在下拉菜单中，选择binary： 并选择logit，则有：Dependent Variable: GRADEMethod: ML - Binary Logit (Quadratic hill climbing)Date: 06/29/05 Time: 17:44Sample: 1 32Included observations: 32Convergence achieved after 5 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb.C-13.021354.931324-2.6405370.0083GPA2.8261131.2629412.2377230.0252TUCE0.0951580.1415540.6722350.5014PSI2.3786881.0645642.2344240.0255Mean dependent var0.343750S.D. dependent var0.482559S.E. of regression0.384716Akaike info criterion1.055602Sum squared resid4.144171Schwarz criterion1.238819Log likelihood-12.88963Hannan-Quinn criter.1.116333Restr. log likelihood-20.59173Avg. log likelihood-0.402801LR statistic (3 df)15.40419McFadden R-squared0.374038Probability(LR stat)0.001502Obs with Dep=021Total obs32Obs with Dep=111边际效应等于其中， GPATUCEPSIMean3.11718821.937500.437500Median3.06500022.500000.000000Maximum4.00000029.000001.000000Minimum2.06000012.000000.000000Std. Dev.0.4667133.9015090.504016Skewness0.122657-0.5251100.251976Kurtosis2.5700683.0483051.063492Jarque-Bera0.3266951.4737285.338708Probability0.8492960.4786120.069297Sum99.75000702.000014.00000Sum Sq. Dev.6.752447471.87507.875000Observations3232328.6 依据下列大型超市的调查数据，分析股份制因素是否对销售规模产生影响。表8.8 某大型超市的调查数据销售规模性质销售规模性质销售规模性质销售规模性质销售规模性质1345非股份制1566非股份制2533股份制1144非股份制1461非股份制2435股份制1187非股份制1602非股份制1566股份制1433股份制1715股份制1345非股份制1839非股份制1496股份制2115非股份制1461股份制1345非股份制2218股份制1234非股份制1839股份制1639股份制2167股份制1529非股份制1345非股份制1288股份制1345非股份制1402股份制1461股份制1345非股份制1288非股份制1602非股份制2115股份制3307股份制3389股份制1345非股份制1839股份制2218股份制3833股份制981股份制1839非股份制2365非股份制3575股份制1839股份制1345非股份制2613股份制1234非股份制1972股份制1926股份制2165非股份制练习题8.6参考解答：依题意可按加法类型引入虚拟变量：其中，。键入命令 LS Y C D1，估计的回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 02/22/10 Time: 13:54Sample: 1 49I