计量经济学案例报告

计量经济学案例报告 国民经济核算是反映国民经济运行状况的有效工具；国民经济核算是宏观经济管理的重要依据；国民经济核算是制定和检验国民经济计划的科学方法；国民经济核算是微观决策的重要依据。国民经济统计工作是国家整个统计工作的一个重要核心部分，而GNP又是国民经济生产统计中的一个重要目标，GNP是按国民原则计算的国民经济核算中的重要的综合指标，等于国内生产总值与国外净要素之和。虽然GDP是国民经济的最核心指标，但GNP又有其重要意义，比如，联合国根据连续六年的国民生产总值和人均国民生产总值来决定一个国家的会费；世界银行根据人均国民生产总值来决定一个国家所能享受的硬贷款、软贷款等优惠待遇；国际货币基金组织根据国民生产总值、黄金与外汇储备、进出口额、出口额占国民生产总值的比例等因素来决定一个国家在基金的份额，进而决定在基金的投票权、分配特别提款权的份额及向基金借款的份额等等，在这些方面直接影响到我国的经济利益和政治利益。所以，我们从中国统计年鉴(1999)上查找到1987-1998年的GNP，并找出一些变量建立多元线形回归模型对GNP进行研究。 我们选择选择人均主要产品产量作为影响GNP变化的变量，人均主要产品产量有粮食，棉花，油料，糖料，茶叶，水果，猪牛羊肉，水产品，布，机制纸及纸板，纱，原煤，原油，发电量，钢，水泥等，经过初步考虑，我们决定选用原煤，粮食和棉花作为建立模型所用的三个变量设为X2，X3，X4，设GNP为Y，数据如下： GNP与人均主要产品产量 年Y(GNP)/亿元X2(原煤)/吨X3(粮食)/千克X4(棉花)/千克1987119550.86371.743.921988149220.89357.723.771989169180.94364.323.391990185980.95393.103.971991216630.94378.264.931992266520.96379.973.871993345610.98387.373.171994466701.04373.463.641995574951.13387.283.961996668511.15414.393.451997731431.12401.743.741998780181.01412.423.62（1） 确定样本回归方程：对于中国1987年至1998年国民生产总值及有关影响因素初步建立多元线形回归模型。 Y=1+2*X2+3*X3+4*X4 假设模型中随机误差项ui满足古典假设，运用OLS方法估计模型的参数，利用Eviews计算得出如下输入结果： Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 17:40Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-306717.489148.80-3.4405110.0088X2142124.451901.062.7383720.0255X3570.9199271.56822.1023080.0687X4-4222.6768323.401-0.5073260.6256R-squared0.831636 Mean dependent var38953.65Adjusted R-squared0.768499 S.D. dependent var24406.49S.E. of regression11743.08 Akaike info criterion21.84112Sum squared resid1.10E+09 Schwarz criterion22.00275Log likelihood-127.0467 F-statistic13.17199Durbin-Watson stat1.425642 Prob(F-statistic)0.001839Estimation Command:=LS Y C X2 X3 X4Estimation Equation:=Y = C(1) + C(2)*X2 + C(3)*X3 + C(4)*X4Substituted Coefficients:=Y = -306717.449 + 142124.3822*X2 + 570.9199106*X3 - 4222.676239*X4 Correlation Matrix X2 X3 X4X2 1.000000 0.684966 -0.226024X3 0.684966 1.000000 -0.167105X4 -0.226024 -0.167105 1.000000Y=-306717+142124X2+570.9X3-4223X4 (2.738) （2.102）(-0.5073) R2=0.8316 F=13.17 S=11743 DW=1.426 查表得F(r,n-k)=F0.05(4,8)=3.84,t/2(n-k)=t0.025(8)=2.306,由于F F0.05(4,8)=3.84,所以拒绝假设H0:=0,模型在总体上显著。但是通过t值可以看出X3和X4无法通过显著性检验,说明这个模型建立的不是十分理想。我们进而考虑分别建立一个解释变量和两个解释变量的模型，利用Eviews可以得到如下估计结果：1）对X2Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 17:43Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-180859.942190.69-4.2867250.0016X2220364.442122.475.2315180.0004R-squared0.732397 Mean dependent var38953.65Adjusted R-squared0.705637 S.D. dependent var24406.49S.E. of regression13241.81 Akaike info criterion21.97116Sum squared resid1.75E+09 Schwarz criterion22.05198Log likelihood-129.8269 F-statistic27.36878Durbin-Watson stat0.716502 Prob(F-statistic)0.000383Estimation Command:=LS Y C X2Estimation Equation:=Y = C(1) + C(2)*X2Substituted Coefficients:=Y = -180859.8861 + 220364.4473*X2Y=-180860+220364X2 （a） （5.232）R2=0.7324 F=27.37S=13242 DW=0.71652）对X3Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:17Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-386132.497641.28-3.9546020.0027X31103.697253.26604.3578550.0014R-squared0.655064 Mean dependent var38953.65Adjusted R-squared0.620571 S.D. dependent var24406.49S.E. of regression15033.87 Akaike info criterion22.22501Sum squared resid2.26E+09 Schwarz criterion22.30583Log likelihood-131.3501 F-statistic18.99090Durbin-Watson stat1.466938 Prob(F-statistic)0.001426Estimation Command:=LS Y C X3Estimation Equation:=Y = C(1) + C(2)*X3Substituted Coefficients:=Y = -386132.4019 + 1103.69677*X3Y=-386132+1104X3 （b） (4.538)R2=0.6551 F=18.99S=15034 DW=0.71653）对X4Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:18Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C96133.6064802.431.4834880.1688X4-15103.6617013.62-0.8877400.3955R-squared0.073051 Mean dependent var38953.65Adjusted R-squared-0.019644 S.D. dependent var24406.49S.E. of regression24645.04 Akaike info criterion23.21355Sum squared resid6.07E+09 Schwarz criterion23.29437Log likelihood-137.2813 F-statistic0.788082Durbin-Watson stat0.214148 Prob(F-statistic)0.395531Estimation Command:=LS Y C X4Estimation Equation:=Y = C(1) + C(2)*X4Substituted Coefficients:=Y = 96133.60497 - 15103.66409*X4Y=96134-15104X4 (-0.8877)R2=0.07305 F=0.7881S=24645 DW=0.21414）对X2，X3Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:27Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-327701.575644.37-4.3321340.0019X2146213.849110.472.9772420.0155X3573.3049260.08402.2043070.0550R-squared0.826219 Mean dependent var38953.65Adjusted R-squared0.787601 S.D. dependent var24406.49S.E. of regression11248.17 Akaike info criterion21.70612Sum squared resid1.14E+09 Schwarz criterion21.82734Log likelihood-127.2367 F-statistic21.39463Durbin-Watson stat1.247999 Prob(F-statistic)0.000380Estimation Command:=LS Y C X2 X3Estimation Equation:=Y = C(1) + C(2)*X2 + C(3)*X3Substituted Coefficients:=Y = -327701.5357 + 146213.7762*X2 + 573.304887*X3Y=-327701+146214X2+573.3X3 （c）(2.977) (2.204) R2=0.8262 F=21.39S=11248 DW=1.2485）对X2，X4Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:31Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-159025.264471.72-2.4665880.0358X2215651.145047.384.7872060.0010X4-4525.5889776.199-0.4629190.6544R-squared0.738620 Mean dependent var38953.65Adjusted R-squared0.680536 S.D. dependent var24406.49S.E. of regression13794.82 Akaike info criterion22.11429Sum squared resid1.71E+09 Schwarz criterion22.23552Log likelihood-129.6858 F-statistic12.71635Durbin-Watson stat0.751053 Prob(F-statistic)0.002386Estimation Command:=LS Y C X2 X4Estimation Equation:=Y = C(1) + C(2)*X2 + C(3)*X4Substituted Coefficients:=Y = -159025.2067 + 215651.1045*X2 - 4525.587513*X4Y=-159025+215651X2-4526X4 (4.787) (-0.4629) R2=0.7386 F=12.72 S=13795 DW=0.75116）对X3，X4Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:43Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-344553.1115574.5-2.9812210.0154X31072.042263.30804.0714390.0028X4-7762.56110790.09-0.7194160.4901R-squared0.673822 Mean dependent var38953.65Adjusted R-squared0.601338 S.D. dependent var24406.49S.E. of regression15410.19 Akaike info criterion22.33576Sum squared resid2.14E+09 Schwarz criterion22.45699Log likelihood-131.0146 F-statistic9.296132Durbin-Watson stat1.758444 Prob(F-statistic)0.006465Estimation Command:=LS Y C X3 X4Estimation Equation:=Y = C(1) + C(2)*X3 + C(3)*X4Substituted Coefficients:=Y = -344553.0724 + 1072.042485*X3 - 7762.560522*X4Y=-34553+1072X3-7763X4(4.71) (-0.7194) R2=0.6378 F=9.296 S=15410 DW=1.758 查表得F（2，10）=4.10,F0.05(3,9)=3.86,t0.025(10)=2.228, t0.025（9）=2.262。由以上各样本回归方程可以看出X4（人均棉花产量）对Y（GNP）没有显著影响，应该略去。 再比较不含X4的几个方程（a），（b），（c），可以看出，式（a）稍微优于式（b），在式（c）中，虽然X3没有通过显著性检验，但是相应的t统计量为2.204，很接近临界值t0.025（9）=2.262，且式（c）的可决系数R2明显高于式（a）中的R2，误差项的标准差估计值S明显小于式（a）中的S。因此，最后确定的总体回归模型为 Y=1+2X2+3X3+u根据刚才的输出结果，样本回归方程为Y=-327701+146214X2+573.3X3 (2.977) (2.204) R2=0.8262 F=21.39S=11248 DW=1.248A多重共线性的检验：由刚才确定总体回归模型在的分析过程可知:R2很大,F=21.39显著大于F0.05(3,9)=3.86,而变量X2对应的偏回归系数t值显著,X3的t值接近显著,所以,这个模型是不存在多重共线性的。B异方差性的检验：对X2，X3ARCH Test:F-statistic0.431993 Probability0.739434Obs*R-squared1.852580 Probability0.603560Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/13/03 Time: 17:55Sample(adjusted): 1990 1998Included observations: 9 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1.97E+081.13E+081.7480490.1409RESID2(-1)-0.4816870.671468-0.7173640.5053RESID2(-2)-0.1386260.701171-0.1977060.8511RESID2(-3)-0.6109790.667046-0.9159480.4017R-squared0.205842 Mean dependent var1.20E+08Adjusted R-squared-0.270653 S.D. dependent var1.64E+08S.E. of regression1.85E+08 Akaike info criterion41.21034Sum squared resid1.71E+17 Schwarz criterion41.29800Log likelihood-181.4465 F-statistic0.431993Durbin-Watson stat1.241293 Prob(F-statistic)0.739434从输出的辅助回归函数中得到R2，计算（n-P）R2=（9-3）*0.7282=4.3692,查2分布表,给定=0.05,自由度为P=3,得临界值20.05(3)=7.815, （n-P）R2=4.369220.05(3)=7.815,所以接受H0,表明模型中随机误差项不存在异方差性。从下面的White也可得出相同结果，模型中不存在异方差。White Heteroskedasticity Test:F-statistic4.688229 Probability0.037155Obs*R-squared8.738234 Probability0.067986Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/13/03 Time: 17:56Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C1.51E+101.41E+101.0686970.3207X21.34E+108.16E+091.6362860.1458X22-7.01E+093.99E+09-1.7557790.1226X3-1.18E+0877269611-1.5239850.1713X32161943.799399.141.6292260.1473R-squared0.728186 Mean dependent var94890959Adjusted R-squared0.572864 S.D. dependent var1.48E+08S.E. of regression96545494 Akaike info criterion39.90326Sum squared resid6.52E+16 Schwarz criterion40.10531Log likelihood-234.4196 F-statistic4.688229Durbin-Watson stat2.218332 Prob(F-statistic)0.037155 C自相关性的检验：从图中可以看出残差et没有呈线形自回归，表明随机误差项不存在自相关性（2） 预测：因为GNP具有非常重要的国民经济统计意义，对它的预测也具有现实意义。首先，可以通过相关部门指定的在预测期内的变量计划生产值来对这一期的GNP数值作出定量的估计；其次还可以在实际统计中，根据已统计出的变量实际生产值来估计当期的GNP将在一个范围内达到多少。这样，根据预测值制定经济发展政策或判断相关经济政策的可行性以及了解已实施的经济政策取得的成果都具有重要意义。 结束语 至此，我们完成了对国民经济生产总值满足古典假定的多元线性回归模型的建立及分析。进一步强化了所学知识及处理实际应用问题的能力，由于能力有限，如果这份报告中存在缺陷和不足，请老师谅解。