计量经济学作业.doc

XY8055100658570110801207911584130981409512590907510574160110150113165125145108180115225140200120240145185130220152210144245175260180190135205140265178270191230137250189第一次作业第一题：下列数据中，X表示家庭收入，Y表示家庭支出，请对如下数据运用戈德菲尔德-匡特检验。第二题：X代表职工的工龄，Y代表薪水。要求：1. 通过散点图或残差图对样本进行初步观察。2. 对可能存在的问题进行检验。3. 采取措施消除问题。4. 写出最终表达式。XY0.5690002.5705004.5740506.5826008.59143910.58312712.58470014.58260116.59328618.59040020.598200231000002699662301160123485200第一题：步骤：（1） 、将样本数据排序，分组，剔除中间样本 ，然后做OLS回归 第一组： 8055857090751006510574110801158412079125901309814095Dependent Variable: YMethod: Least SquaresDate: 04/18/11 Time: 08:52Sample: 1 11Included observations: 11Y=C(1)+C(2)*XCoefficientStd. Errort-StatisticProb.C(1)12.5369510.538701.1896100.2646C(2)0.6059110.0952716.3598670.0001R-squared0.817990Mean dependent var78.63636Adjusted R-squared0.797767S.D. dependent var12.87069S.E. of regression5.787989Akaike info criterion6.512413Sum squared resid301.5074Schwarz criterion6.584757Log likelihood-33.81827Hannan-Quinn criter.6.466810F-statistic40.44791Durbin-Watson stat2.272765Prob(F-statistic)0.000131第二组：205140210144220152225140230137240145245175250189260180265178Dependent Variable: YMethod: Least SquaresDate: 04/18/11 Time: 08:54Sample: 1 11Included observations: 11Y=C(1)+C(2)*XCoefficientStd. Errort-StatisticProb.C(1)-36.6018740.67131-0.8999430.3916C(2)0.8296260.1700964.8774050.0009R-squared0.725518Mean dependent var161.0000Adjusted R-squared0.695020S.D. dependent var21.48022S.E. of regression11.86244Akaike info criterion7.947598Sum squared resid1266.458Schwarz criterion8.019942Log likelihood-41.71179Hannan-Quinn criter.7.901995F-statistic23.78908Durbin-Watson stat1.178680Prob(F-statistic)0.000875（2）： F=1266.458/301.5074=4.2004给定a=5%查表，得临界值： F0.05(9,9)=2.97判断F大于F0.05(9,9)否定两组子样本方差相同的假设，从而该总体随机项存在异方差性。第二题：做散点图：Dependent Variable: YMethod: Least SquaresDate: 04/18/11 Time: 09:04Sample: 1 24Included observations: 24Y=C(1)+C(2)*XCoefficientStd. Errort-StatisticProb.C(1)-84.2480311.17191-7.5410600.0000C(2)7.7836110.62113412.531290.0000R-squared0.877118Mean dependent var51.27438Adjusted R-squared0.871532S.D. dependent var38.30328S.E. of regression13.72881Akaike info criterion8.156526Sum squared resid4146.567Schwarz criterion8.254697Log likelihood-95.87831Hannan-Quinn criter.8.182571F-statistic157.0333Durbin-Watson stat0.602173Prob(F-statistic)0.000000由散点图可看出，该样本可能存在异方差性。作G-Q检验：将大样本分为两个小样本， 第二次上机步骤：先对全样本作整体回归：Dependent Variable: YMethod: Least SquaresDate: 04/18/11 Time: 09:04Sample: 1 24Included observations: 24Y=C(1)+C(2)*XCoefficientStd. Errort-StatisticProb.C(1)-84.2480311.17191-7.5410600.0000C(2)7.7836110.62113412.531290.0000R-squared0.877118Mean dependent var51.27438Adjusted R-squared0.871532S.D. dependent var38.30328S.E. of regression13.72881Akaike info criterion8.156526Sum squared resid4146.567Schwarz criterion8.254697Log likelihood-95.87831Hannan-Quinn criter.8.182571F-statistic157.0333Durbin-Watson stat0.602173Prob(F-statistic)0.000000将样本分组，分别作OLS回归，YX15.8710.817.7311.919.0413.121.6114.917.212.518.8513.716.7111.314.8110.419.0214.220.5515.224.2917.124.3816.9第一组：Dependent Variable: YMethod: Least SquaresDate: 04/18/11 Time: 08:42Sample: 1 12Included observations: 12Y=C(1)+C(2)*XCoefficientStd. Errort-StatisticProb.C(1)1.1498011.2470100.9220460.3782C(2)1.3349530.09122414.633830.0000R-squared0.955387Mean dependent var19.17167Adjusted R-squared0.950926S.D. dependent var3.063924S.E. of regression0.678744Akaike info criterion2.213866Sum squared resid4.606933Schwarz criterion2.294684Log likelihood-11.28320Hannan-Quinn criter.2.183944F-statistic214.1491Durbin-Watson stat1.237672Prob(F-statistic)0.000000第二组：27.817.243.0118.4665.6519.967.0520.388.2521.578.1520.991.48522.11110.323.8105.3323.189.9919.2119.2425.1114.2724.3Dependent Variable: YMethod: Least SquaresDate: 04/18/11 Time: 08:44Sample: 1 12Included observations: 12Y=C(1)+C(2)*XCoefficientStd. Errort-StatisticProb.C(1)-147.585028.43609-5.1900610.0004C(2)10.831851.3256228.1711470.0000R-squared0.869737Mean dependent var83.37708Adjusted R-squared0.856710S.D. dependent var28.45566S.E. of regression10.77149Akaike info criterion7.742695Sum squared resid1160.250Schwarz criterion7.823513Log likelihood-44.45617Hannan-Quinn criter.7.712773F-statistic66.76765Durbin-Watson stat1.798463Prob(F-statistic)0.000010RSS(R)=4146.567RSS(U)=RSS1+RSS2=4.606933+1160.250 =1164.856933 (4146.567-1164.856933)/12 F= = 4.2662035 1164.856933/(24-2*2)给定显著性水平5%，F0.05(12,20)=2.28F所以，不显著，拒绝原假设。第三次作业步骤：对整体样本作OLS回归：Dependent Variable: YMethod: Least SquaresDate: 04/25/11 Time: 08:27Sample: 1 30Included observations: 30Y=C(1)+C(2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5CoefficientStd. Errort-StatisticProb.C(1)15.3836914.017301.0974790.2833C(2)0.0207520.0128651.6131100.1198C(3)-0.0021780.133207-0.0163490.9871C(4)0.0343380.0135352.5370080.0181C(5)-0.0037900.004617-0.8209530.4198C(6)0.0117740.3982550.0295650.9767R-squared0.949200Mean dependent var45.63967Adjusted R-squared0.938616S.D. dependent var21.74352S.E. of regression5.387113Akaike info criterion6.382753Sum squared resid696.5037Schwarz criterion6.662992Log likelihood-89.74129Hannan-Quinn criter.6.472404F-statistic89.68776Durbin-Watson stat0.983723Prob(F-statistic)0.000000用软件得到参差序列：Last updated: 04/25/11 - 08:32Modified: 1 30 / makeresid-2.387916742786327-3.626222161418159-6.831392318290824-2.9562125828705524.0820951169858878.7055956662165242.933711819027032-1.3743818562942562.8555907084027792.5120149260854350.9061041373137081.2181295483755831.130555467622603-2.075302604790402-4.706987305005896-9.010129107335353-2.727309400155605-3.452771889540848-2.6047627777539557.6832853513845847.087521751466175.786371769840066-0.18173536095704897.4683729606522042.206659904875522-2.243012885258935-6.286316222062766-10.063598007776852.4780210291062593.474021064943272 然后以et作为解释变量，做回归检验：Dependent Variable: UMethod: Least SquaresDate: 04/25/11 Time: 08:49Sample (adjusted): 2 30Included observations: 29 after adjustmentsU=C(1)*U(-1)CoefficientStd. Errort-StatisticProb.C(1)0.5041170.1642263.0696440.0047R-squared0.251578Mean dependent var0.082342Adjusted R-squared0.251578S.D. dependent var4.966333S.E. of regression4.296443Akaike info criterion5.787326Sum squared resid516.8637Schwarz criterion5.834474Log likelihood-82.91623Hannan-Quinn criter.5.802092Durbin-Watson stat1.727824Dependent Variable: UMethod: Least SquaresDate: 04/25/11 Time: 08:51Sample (adjusted): 3 30Included observations: 28 after adjustmentsU=C(1)*U(-1)+C(2)*U(-2)CoefficientStd. Errort-StatisticProb.C(1)0.6287380.1887293.3314250.0026C(2)-0.2686160.188790-1.4228230.1667R-squared0.299136Mean dependent var0.214791Adjusted R-squared0.272180S.D. dependent var5.005036S.E. of regression4.269915Akaike info criterion5.809814Sum squared resid474.0366Schwarz criterion5.904972Log likelihood-79.33740Hannan-Quinn criter.5.838905Durbin-Watson stat2.047637由上可知，存在着一阶滞后相关性。然后，用广义差分法重新估计模型：Dependent Variable: YT-0.628738*YT(-1)Method: Least SquaresDate: 04/25/11 Time: 09:21Sample (adjusted): 6 30Included observations: 25 after adjustmentsYT-0.628738*YT(-1)=C(1)*(1-0.628738)+C(2)*(X1-0.628738*X1(-1)+C(3)*(X2-0.628738*X2(-1)-0.628738*X2(-2)+C(4)*(X3-0.628738*X3(-1)-0.628738*X3(-2)-0.628738*X3(-3)+C(5)*(X4-0.628738*X4(-1)-0.628738*X4(-2)-0.628738*X4(-3)-0.628738*X4(-4)+C(6)*(X5-0.628738*X5(-1)-0.628738*X5(-2)-0.628738*X5(-3)-0.628738*X5(-4)-0.628738*X5(-5)CoefficientStd. Errort-StatisticProb.C(1)54.1061831.183051.7351150.0989C(2)0.0452430.0070896.3817870.0000C(3)-0.3619470.226487-1.5980960.1265C(4)0.0346220.0101523.4102930.0029C(5)0.0018520.0028740.6445770.5269C(6)0.1923520.1710951.1242390.2749R-squared0.846850Mean dependent var20.24555Adjusted R-squared0.806548S.D. dependent var11.56849S.E. of regression5.088193Akaike info criterion6.297286Sum squared resid491.9045Schwarz criterion6.589816Log likelihood-72.71607Hannan-Quinn criter.6.378421F-statistic21.01230Durbin-Watson stat1.861499Prob(F-statistic)0.000000 经过回归检验得出，原模型存在一阶自相关性，然后利用广义差分法，消除自相关性，作OLS检验，经过杜宾估计，得到DW=1.86 近似于2，而之前总体回归得到 DW=0.98372所以，消除了自相关性。第五次作业步骤： （一）：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 08:11Sample: 1 16Included observations: 16Y=C(1)+C(2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5CoefficientStd. Errort-StatisticProb.C(1)2933.9068172.2570.3590080.7271C(2)50.5377669.700810.7250670.4850C(3)-103.504251.14744-2.0236440.0705C(4)6.1157953.7136791.6468290.1306C(5)-105.9787151.9428-0.6974910.5014C(6)0.1237970.1226721.0091740.3367R-squared0.754505Mean dependent var10005.13Adjusted R-squared0.631757S.D. dependent var1163.645S.E. of regression706.1345Akaike info criterion16.23749Sum squared resid4986260.Schwarz criterion16.52721Log likelihood-123.8999Hannan-Quinn criter.16.25232F-statistic6.146800Durbin-Watson stat1.593265Prob(F-statistic)0.007426（二)：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 08:15Sample: 1 16Included observations: 16Y=C(1)+C(2)*X1CoefficientStd. Errort-StatisticProb.C(1)10311.801271.7028.1086580.0000C(2)-1.8905777.617774-0.2481800.8076R-squared0.004380Mean dependent var10005.13Adjusted R-squared-0.066735S.D. dependent var1163.645S.E. of regression1201.846Akaike info criterion17.13757Sum squared resid20222065Schwarz criterion17.23415Log likelihood-135.1006Hannan-Quinn criter.17.14252F-statistic0.061593Durbin-Watson stat0.859574Prob(F-statistic)0.807599（三）：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 08:16Sample: 1 16Included observations: 16Y=C(1)+C(2)*X2CoefficientStd. Errort-StatisticProb.C(1)10363.67967.506810.711730.0000C(2)-1.6360734.197959-0.3897310.7026R-squared0.010733Mean dependent var10005.13Adjusted R-squared-0.059929S.D. dependent var1163.645S.E. of regression1198.005Akaike info criterion17.13117Sum squared resid20093037Schwarz criterion17.22775Log likelihood-135.0494Hannan-Quinn criter.17.13612F-statistic0.151890Durbin-Watson stat0.859635Prob(F-statistic)0.702600（四）：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 08:17Sample: 1 16Included observations: 16Y=C(1)+C(2)*X3CoefficientStd. Errort-StatisticProb.C(1)9991.850790.917512.633240.0000C(2)0.0076050.4189830.0181520.9858R-squared0.000024Mean dependent var10005.13Adjusted R-squared-0.071403S.D. dependent var1163.645S.E. of regression1204.472Akaike info criterion17.14194Sum squared resid20310554Schwarz criterion17.23851Log likelihood-135.1355Hannan-Quinn criter.17.14688F-statistic0.000329Durbin-Watson stat0.858220Prob(F-statistic)0.985774（五）：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 08:19Sample: 1 16Included observations: 16Y=C(1)+C(2)*X4CoefficientStd. Errort-StatisticProb.C(1)11933.09835.748914.278320.0000C(2)-239.219998.83971-2.4202810.0297R-squared0.294986Mean dependent var10005.13Adjusted R-squared0.244628S.D. dependent var1163.645S.E. of regression1011.349Akaike info criterion16.79243Sum squared resid14319561Schwarz criterion16.88900Log likelihood-132.3394Hannan-Quinn criter.16.79737F-statistic5.857762Durbin-Watson stat1.142905Prob(F-statistic)0.029692（六）：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 08:20Sample: 1 16Included observations: 16Y=C(1)+C(2)*X5CoefficientStd. Errort-StatisticProb.C(1)9484.9613195.9852.9677740.0102C(2)0.0054870.0335660.1634810.8725R-squared0.001905Mean dependent var10005.13Adjusted R-squared-0.069387S.D. dependent var1163.645S.E. of regression1203.339Akaike info criterion17.14006Sum squared resid20272332Schwarz criterion17.23663Log likelihood-135.1204Hannan-Quinn criter.17.14500F-statistic0.026726Durbin-Watson stat0.852765Prob(F-statistic)0.872476（七）：X1X2X3X4X5YX110.99686458431953140.99135367483618340.52582967962665850.9721445541852306-0.06618337684642819X20.996864584319531410.99127363298876510.54331289997658480.9652392295537309-0.1035993957454895X30.99135367483618340.991273632988765110.46143627803746880.97261537151444790.004851189897237788X40.52582967962665850.54331289997658480.461436278037468810.5361847937136976-0.5431261590668503X50.97214455418523060.96523922955373090.97261537151444790.536184793713697610.04365057323348519Y-0.06618337684642819-0.10359939574548950.004851189897237788-0.54312615906685030.043650573233485191（八）：Dependent Variable: YMethod: Least SquaresDate: 05/09/11 Time: 09:14Sample: 1 16Included observations: 16Y=C(1)+C(2)*X4+C(3)*X3CoefficientStd. Errort-StatisticProb.C(1)11576.53858.547513.483850.0000C(2)-305.1874108.6036-2.8101030.0147C(3)0.5088480.3865571.3163580.2108R-squared0.377906Mean dependent var10005.13Adjusted R-squared0.282200S.D. dependent var1163.645S.E. of regression985.8759Akaike info criterion16.79230Sum squared resid12635366Schwarz criterion16.93716Log likelihood-131.3384Hannan-Quinn criter.16.79972F-statistic3.948586Durbin-Watson stat1.332619Prob