计量经济学 案例分析 Eviews

一、研究课题：通过对1984——2003年某国GDP和出口的分析，研究GDP和出口量的相关关系并对参数估计值进行检验。二、模型及数据来源：GDP为因变量，出口量为自变量。选择模型是一元线性回归模型y=c0+c1x+u（y代表GDP，x代表出口量，u表示残差项）数据来自《计量经济学软件——eviews的使用》135页表12.1。提取其进口和国内生产总值两列数据：annualexportgdp1984580.571711985808.98964.419861082.110202.21987147011962.519881766.714928.31989195616909.219902985.818547.919913827.121617.819924676.326638.119935284.834634.4199410421.846759.4199512451.858478.1199612576.467884.6199715160.774462.6199815233.678345.2199916159.882067.5200020634.489468.1200122024.497314.8200226947.4105172.3200336287.9117251.9三、作业1、根据表格得到曲线图、散点图、X-Y曲线图：02000040000600008000010000012000084868890929496980002GDPEXPORT曲线图050000100000150000010000200003000040000EXPORTGDP散点图020000400006000080000100000120000100002000030000EXPORTGDPX-Y曲线图2、数据描述统计分析0246810010000200003000040000Series:EXPORTSample19842003Observations20Mean10616.82Median7853.300Maximum36287.90Minimum580.5000Std.Dev.10076.01Skewness0.954931Kurtosis3.161824Jarque-Bera3.061464Probability0.2163770123456020000400006000080000100000120000Series:GDPSample19842003Observations20Mean49439.02Median40696.90Maximum117251.9Minimum7171.000Std.Dev.36735.19Skewness0.374595Kurtosis1.689884Jarque-Bera1.898075Probability0.3871133、简单的回归估计DependentVariable:GDPMethod:LeastSquaresDate:06/14/09Time:16:38Sample:19842003Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C11772.772862.4194.1128730.0007EXPORT3.5477900.19791917.925480.0000R-squared0.946953Meandependentvar49439.02AdjustedR-squared0.944006S.D.dependentvar36735.19S.E.ofregression8692.656Akaikeinfocriterion21.07298Sumsquaredresid1.36E+09Schwarzcriterion21.17256Loglikelihood-208.7298F-statistic321.3229Durbin-Watsonstat0.604971Prob(F-statistic)0.000000根据输出结果，写出OLS估计式，并进行分析说明：yt=-11772.77+3.547790xtR2=0.946953df=18检验回归系数显著性的原假设和备择假设是（给定=0.05）H0：c1=0；H1：c10。因为t=17.92548t0.025(18)=2，所以检验结果是拒绝c1=0，即认为进口额和GDP之间存在回归关系，二者正方向变化。上述模型的经济解释是，对于出口量每增加1亿元，GDP将平均增加3.54779亿元。拟合优度为0.946953说明上式的拟合情况较好。GDP变动的94.7%可以由出口量的变动解释。4、自相关及其解决残差：残差序列图717113832.2580652-6661.25806521|.*|.|8964.414642.5733286-5678.17332857|.*|.|10202.215611.8295893-5409.62958929|.*|.|11962.516988.0173767-5025.51737674|.*|.|14928.318040.6467053-3112.34670528|.*|.|16909.218712.2433749-1803.04337495|.*|.|18547.922365.7576403-3817.85764028|.*|.|21617.825350.513468-3732.71346804|.*|.|26638.128363.2968377-1725.19683774|.*|.|34634.430522.12712564112.27287438|.|*.|46759.448747.1249708-1987.72497084|.*|.|58478.155949.1389142528.96108604|.|*.|67884.656391.193562911493.4064371|.|.*|74462.665559.74756948902.85243061|.|*|78345.265818.381469112526.8185309|.|.*|82067.569104.34467812963.155322|.|.*|89468.184979.28634794488.81365206|.|*.|97314.889910.71461447404.08538558|.|*.|105172.3107376.485374-2204.18537401|.*|.|117251.9140514.618988-23262.7189877|*.|.|由图看出残差具有较明显的自相关趋势，同时由简单回归估计的D-W值0.604971，远小于2，也可推出模型存在自相关可能。AR（1）模型的估计消除自相关的回归分析DependentVariable:GDPMethod:LeastSquaresDate:06/14/09Time:15:46Sample(adjusted):19852003Includedobservations:19afteradjustingendpointsConvergenceachievedafter30iterationsVariableCoefficientStd.Errort-StatisticProb.C-80417.9387670.31-0.9172770.3726EXPORT0.7969100.3427642.3249550.0336AR(1)1.0361310.02818436.763690.0000R-squared0.994780Meandependentvar51663.65AdjustedR-squared0.994127S.D.dependentvar36331.34S.E.ofregression2784.259Akaikeinfocriterion18.84529Sumsquaredresid1.24E+08Schwarzcriterion18.99441Loglikelihood-176.0303F-statistic1524.449Durbin-Watsonstat0.560294Prob(F-statistic)0.000000InvertedARRoots1.04EstimatedARprocessisnonstationary经过GLS处理以后，我们可以看出G-W的值由原来的0.604971改进为0.560294，基本上消除了自相关性。GDP=-80417.93181+0.7969104937*EXPORT+[AR(1)=1.036130591]5、异方差性及其修正先看散点图：010000200003000040000050000100000150000GDPEXPORT由图可以看出，残差随着GDP的增大其分散程度也增大，这是存在异方差性的初步经验证据。怀特检验：WhiteHeteroskedasticityTest:F-statistic14.97532Probability0.000178Obs*R-squared12.75835Probability0.001697TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/14/09Time:23:22Sample:19842003Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C41955477317976011.3194540.2045EXPORT-7517.7835261.145-1.4289250.1711EXPORT^20.5061300.1617753.1286120.0061R-squared0.637918Meandependentvar68006039AdjustedR-squared0.595320S.D.dependentvar1.23E+08S.E.ofregression78013471Akaikeinfocriterion39.32014Sumsquaredresid1.03E+17Schwarzcriterion39.46950Loglikelihood-390.2014F-statistic14.97532Durbin-Watsonstat1.737044Prob(F-statistic)0.000178辅助回归模型中，取显著性水平a=0.05，由于Obs*R-squared=12.75835＜Xa/20.05（10）=18.31，所以函数不存在异方差性。由输出结果的概率值（P值）可以看出，函数不存在异方差性。因为存在异方差性，OLS所估计出来的参数标准有误，我们采用怀特法重新估计参数解决这一问题。DependentVariable:GDPMethod:LeastSquaresDate:06/14/09Time:20:08Sample:19842003Includedobservations:20WhiteHeteroskedasticity-ConsistentStandardErrors&CovarianceVariableCoefficientStd.Errort-StatisticProb.C11772.772757.3044.2696660.0005EXPORT3.5477900.34264110.354260.0000R-squared0.946953Meandependentvar49439.02AdjustedR-squared0.944006S.D.dependentvar36735.19S.E.ofregression8692.656Akaikeinfocriterion21.07298Sumsquaredresid1.36E+09Schwarzcriterion21.17256Loglikelihood-208.7298F-statistic3