1、计量经济学作业增加版一计量学习题练习(一)小组成员:产慧贤 高媛 张文晶 陈晓申模型一一参数估计对于该题数据,现将数据进行一下处理,建立模型:地区税收(Y)税收ln(Y)GDPln(GDP)地区税收Y税收ln(Y)GDPln(GDP)北京1435.77.26940789353.39.143485湖北4346.0730459230.79.13029天津438.46.08313175050.48.527223湖南410.76.01786392009.126959河北618.36.426973813709.59.525844广东2415.57.78966231084.410.34446山西430.5
2、6.06494735733.48.654064广西282.75.6443865955.78.692104内蒙古347.95.85191516091.18.714584海南884.4773371223.37.109307辽宁815.76.704046611023.59.307785重庆294.55.6852794122.58.324215吉林237.45.46974655284.78.572571四川6296.44413110505.39.259635黑龙江3355.814130570658.862908贵州211.95.3561142741.97.916406上海1975.57.5885768
3、12188.99.408281云南378.65.936484741.38.464067江苏1894.87.546868625741.210.15585西藏11.72.459589342.25.835395浙江1535.47.336546218780.49.840569陕西355.55.8735255465.88.606266安徽401.95.99620337364.28.904386甘肃142.14.9565312702.47.901896福建5946.38687939249.19.132282青海43.33.768153783.66.663899江西281.95.64155245500.38
4、.612558宁夏58.84.074142889.26.790322山东1308.47.176560325965.910.16454新疆220.65.3963513523.28.167125河南6256.437751615012.59.6166381. 建立一元回归模型Eviews得到以下结果:表1Dependent Variable: LNYMethod: Least SquaresDate: 05/01/13 Time: 14:42Sample: 1 31Included observations: 31LNY=C(1)+C(2)*LNXCoefficientStd. Errort-Sta
5、tisticProb. C(1)-3.3806030.518360-6.5217340.0000C(2)1.0707690.05922618.079240.0000R-squared0.918507 Mean dependent var5.927349Adjusted R-squared0.915697 S.D. dependent var1.156051S.E. of regression0.335659 Akaike info criterion0.716900Sum squared resid3.267345 Schwarz criterion0.809415Log likelihood
6、-9.111948 F-statistic326.8590Durbin-Watson stat1.652914 Prob(F-statistic)0.000000于是得到: (-6.52) (18.079) 2.模型检验,说明在线性模型中,税收值的总离差,由gdp的离差解释部分为91.857%,模型拟合得比之前拟合的较好。 截距项的t值为-6.52,大于显著性水平下自由度为n-2=29的临界值为,斜率项t值为1.107。表明中国2007年各地区,国内生产总值gdp每增加1亿元,税收增加0.0714047亿元。3.预测2008年某地区国内生产总值为8500亿元,代入上述方程可得2008年某地区税
7、收预测的点的估计值为: 二模型的异方差检验1. 图示法(1) 生成残差列e2(2) 画出lnx与e2的散点图由下图可以看出,残差平方项e2对解释变量lnx的散点图主要分布在分布图型中的下三角部分,可以看出平方项随lnx的变动呈现增大趋势。因而,模型很可能存在异方差,下面进行检验。2.G-D检验(1)对变量x取值排列(2)构造子样本空间,建立回归模型在本例中,样本容量n=31,删除中间n/4的观测数值,即大约7个观测值,余下部分平分得两个样本子区间:1-12和20-31,样本个数均是12个。(3) 对1-12个lnx与lny的ls拟合得到:表2Dependent Variable: LNYMet
8、hod: Least SquaresDate: 05/01/13 Time: 15:00Sample: 1 12Included observations: 12LNY=C(1)+C(2)*LNXCoefficientStd. Errort-StatisticProb. C(1)-3.9687760.602761-6.5843270.0001C(2)1.1537810.07738114.910440.0000R-squared0.956956 Mean dependent var4.961365Adjusted R-squared0.952652 S.D. dependent var1.081
9、787S.E. of regression0.235393 Akaike info criterion0.095892Sum squared resid0.554099 Schwarz criterion0.176710Log likelihood1.424648 F-statistic222.3213Durbin-Watson stat2.076750 Prob(F-statistic)0.000000(4) 对20-31个lnx与lny的ls拟合得到:表3Dependent Variable: LNYMethod: Least SquaresDate: 05/01/13 Time: 15:
10、02Sample: 20 31Included observations: 12LNY=C(1)+C(2)*LNXCoefficientStd. Errort-StatisticProb. C(1)-1.4252963.005094-0.4742930.6455C(2)0.8718100.3131922.7836280.0193R-squared0.436575 Mean dependent var6.931704Adjusted R-squared0.380232 S.D. dependent var0.580464S.E. of regression0.456972 Akaike info
11、 criterion1.422623Sum squared resid2.088236 Schwarz criterion1.503441Log likelihood-6.535740 F-statistic7.748583Durbin-Watson stat2.323928 Prob(F-statistic)0.019330(5) F量统计值基于上面表2和表3中残差平方和RSS的数据,即:RSS1=0.554099,RSS2=2.088236,根据G-D检验,F统计量的值为: (6) 判断在自由度为5%和10%的显著性水平下,查表可得:自由度为(9,9)的F分布的临界值分别为和因为F=3.7
12、687 同时F=3.7687,因而在5%和10%的显著性水平下拒绝两组子样本方差相同的假设,即存在异方差。3.White检验由上面表1的结果,在此基础上得到以下结论:White Heteroskedasticity Test:F-statistic0.317344 Probability0.730664Obs*R-squared0.687116 Probability0.709242Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/01/13 Time: 15:24Sample: 1 31Included
13、 observations: 31VariableCoefficientStd. Errort-StatisticProb. C0.1760981.6096480.1094020.9137LNX-0.0474480.392488-0.1208910.9046LNX20.0044620.0237180.1881060.8522R-squared0.022165 Mean dependent var0.105398Adjusted R-squared-0.047680 S.D. dependent var0.186731S.E. of regression0.191131 Akaike info
14、criterion-0.379953Sum squared resid1.022866 Schwarz criterion-0.241180Log likelihood8.889275 F-statistic0.317344Durbin-Watson stat2.243240 Prob(F-statistic)0.730664去掉交叉项的辅助回归结果为: (0.1094)(-0.1208) (0.188106)怀特统计量,在5%的显著性水平下,不能拒绝同方差的假设。三异方差的修正:加权最小二乘(WLS)1. 生成权数2.加权最小二乘Dependent Variable: LNYMethod:
15、Least SquaresDate: 05/01/13 Time: 19:17Sample: 1 31Included observations: 31Weighting series: WVariableCoefficientStd. Errort-StatisticProb. C-3.3022630.007968-414.44550.0000LNX1.0610580.0009481119.1490.0000Weighted StatisticsR-squared0.999999 Mean dependent var5.427339Adjusted R-squared0.999999 S.D
16、. dependent var18.47340S.E. of regression0.020366 Akaike info criterion-4.887589Sum squared resid0.012028 Schwarz criterion-4.795074Log likelihood77.75763 F-statistic24684019Durbin-Watson stat1.887028 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.918403 Mean dependent var5.927349Adjusted
17、R-squared0.915589 S.D. dependent var1.156051S.E. of regression0.335874 Sum squared resid3.271521Durbin-Watson stat2.000877加权后的结果为: (-414,44)(1119.29)D.W=1.887 F=24684019 RSS=0.012可以看出运用加权最小二乘消除异方差后,lnx参数的t的检验有了显著性的改进。这表明,即使在1%的显著性水平下,都不能拒绝参数影响。3.检验加权回归模型的异方差性进行加权回归,得到:Dependent Variable: W*LNYMethod
18、: Least SquaresDate: 05/01/13 Time: 19:20Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. W-3.3022630.007968-414.44550.0000W*LNX1.0610580.0009481119.1490.0000R-squared0.999999 Mean dependent var2914.437Adjusted R-squared0.999999 S.D. dependent var9920.066S.E. of reg
19、ression10.93621 Akaike info criterion7.684377Sum squared resid3468.422 Schwarz criterion7.776892Log likelihood-117.1078 F-statistic24684019Durbin-Watson stat1.887028 Prob(F-statistic)0.000000加权模型为: 对该模型进行怀特检验如下:White Heteroskedasticity Test:F-statistic695.6980 Probability0.000000Obs*R-squared30.7787
20、9 Probability0.000010Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/01/13 Time: 19:21Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C-14.908325.280516-2.8232700.0092W0.0344251.2521830.0274920.9783W20.0071890.0052411.3717830.1823W*(W*LNX)-0.0
21、019230.001393-1.3805200.1796W*LNX0.1724420.1355541.2721300.2150(W*LNX)20.0001228.97E-051.3607470.1857R-squared0.992864 Mean dependent var111.8846Adjusted R-squared0.991437 S.D. dependent var256.7210S.E. of regression23.75590 Akaike info criterion9.345524Sum squared resid14108.57 Schwarz criterion9.6
22、23070Log likelihood-138.8556 F-statistic695.6980Durbin-Watson stat2.036856 Prob(F-statistic)0.000000,怀特统计量为:大于相应的检验值,因而不能拒绝同方差。四序列相关性检验在表1 中得到:DW=1.6529,在5%的显著性水平下,样本容量为31的DW的上限和下限临界值分别为:dl=1.36,du=1.50,因而可以判断序列无相关。模型二下表是中国内地2007年各地区税收Y和国内生产总值GDP的统计资料单位:亿元地区税收YGDP地区税收YGDP北京1435.79353.3湖北4349230.7天津4
23、38.45050.4湖南410.79200河北618.313709.5广东2415.531084.4山西430.55733.4广西282.75955.7内蒙古347.96091.1海南881223.3辽宁815.711023.5重庆294.54122.5吉林237.45284.7四川62910505.3黑龙江3357065贵州211.92741.9上海1975.512188.9云南378.64741.3江苏1894.825741.2西藏11.7342.2浙江1535.418780.4陕西355.55465.8安徽401.97364.2甘肃142.12702.4福建5949249.1青海43.3
24、783.6江西281.95500.3宁夏58.8889.2山东1308.425965.9新疆220.63523.2河南62515012.5根据题意,作出以下分析:一参数估计1建立模型根据题给的数据,建立税收随国内生产总值gdp变化的一元线性回归方程。此处令:gdp为x,我们假设拟建立如下的一元回归模型: 利用eviews得到以下结果:表1.1Dependent Variable: YMethod: Least SquaresDate: 05/01/13 Time: 15:48Sample: 1 31Included observations: 31Y=C(1)+C(2)*XCoefficien
25、tStd. Errort-StatisticProb. C(1)889.7773163.26255.4499800.0000C(2)-0.0302240.014051-2.1510170.0399R-squared0.137594 Mean dependent var621.0548Adjusted R-squared0.107856 S.D. dependent var619.5803S.E. of regression585.2143 Akaike info criterion15.64417Sum squared resid9931799. Schwarz criterion15.736
26、69Log likelihood-240.4847 F-statistic4.626873Durbin-Watson stat1.711522 Prob(F-statistic)0.039941即:回归结果为:(86.06) (0.0047) 2模型检验,说明在线性模型中,税收值的总离差,由gdp的离差解释部分为76.03%,模型拟合得较好。 截距项的t值为86.06,大于显著性水平下自由度为n-2=29的临界值为,斜率项t值为0.0047。表明中国2007年各地区,国内生产总值gdp每增加1亿元,税收增加0.0714047亿元。3.预测2008年某地区国内生产总值为8500亿元,代入上述方程
27、可得2008年某地区税收预测的点的估计值为: 593.26987 预测区间:E(X)=8891.1258 var(x)=5.782E7所以在95%的置信度下税收收入的预测区间为置信上限: =593.26987+115.0716=593.3+115.1置信下限: =593.3+115.1所以95%的置信度下税收收入的预测区间为:(477.6,708.3)二异方差检验1.图示法由上图可以看出,残差平方项e22对解释变量x的散点图主要分布在分布图型中的下三角部分,可以看出平方项随x的变动呈现增大趋势。因而,模型很可能存在异方差,下面进行检验。2.G-D检验(1)对变量x取值排列(2)构造子样本空间,建立回归模型在本例中,样本容量n=31,删除中间n/4的观测数值,即大约7个观测值,余下部分平分得两个样本子区间:1-12和20-31,样本个数均是12个。(3)对1-12个x与y的ls拟合得到:表2.1Dependent Variabl
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