1、1752.372742.7784193692.856113.1124041451.291973.8227204732.909228.2522255149.305917.01327212180.232866.658062291.161758.77120222539.762545.639671345.17939.1058233046.954787.908656.77694.9431242192.633255.291639370.18363.4816255364.838129.68244101590.362511.9966264834.685260.2014511616.71973.737549.5
2、87518.7913812617.94516.0128867.91984.5246134429.193785.91294611.3918626.94218145749.028688.0325430170.30610.91151781.372798.9083325.531523.19451243.071808.4433 假设有人不同意原幂函数模型是正确设定的模型,而下面的线性形式是正确设定的模型,将如何检验哪一个模型设定更正确? 1.建立工作工作文件并录入数据,得到图1.1图1.12.采用RESET检验来检验模型的设定偏误2.1对于原幂函数形式的模型,变换成双对数模型采用OLS进行估计,估计结果
3、如图1.2。图1.2 首先,尽管K与L的参数估计值的t统计量在5%的显著性水平下都是显著的,但拟合优度比原幂函数的模型低。由F统计量的伴随概率知,在5%的显著性水平下,拒绝原模型没有设定偏误的假设。可见,相比较而言,线性模型确有设定偏误,而原幂函数模型没有设定偏误问题。二、通过Box-Cox变换检验中国居民总量消费函数的建立中,原线性模型与双对数线性模型哪一个最优?表2.6.3 中国居民总量消费支出与收入资料单位:亿元年份GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.56678.83806.719794092.62011.547.0753
4、7.828694.27551.64273.219804592.92331.250.62571.709073.77944.24605.519815008.82627.951.90629.899651.88438.05063.919825590.02902.952.95700.0210557.39235.25482.419836216.23231.154.00775.5911510.810074.65983.219847362.73742.055.47947.3513272.811565.06745.719859076.74687.460.652040.7914966.811601.77729.2
5、198610508.55302.164.572090.3716273.713036.58210.9198712277.46126.169.302140.3617716.314627.78840.0198815388.67868.182.302390.4718698.715794.09560.5198917311.38812.697.002727.4017847.415035.59085.5199019347.89450.9100.002821.8616525.9199122577.410730.6103.422990.1721830.918939.610375.8199227565.21300
6、0.1110.033296.9125053.022056.511815.3199336938.116412.1126.204255.3029269.125897.313004.7199450217.421844.2156.655126.8832056.228783.413944.2199563216.928369.7183.416038.0434467.531175.415467.9199674163.633955.9198.666909.8237331.933853.717092.5199781658.536921.5204.218234.0439988.535956.218080.6199
7、886531.639229.3202.599262.8042713.138140.919364.1199991125.041920.4199.7210682.5845625.840277.020989.3200098749.045854.6200.5512581.5149238.042964.622863.92001108972.449213.2201.9415301.3853962.546385.424370.12002120350.352571.3200.3217636.4560078.051274.026243.22003136398.856834.4202.7320017.316728
8、2.257408.128035.02004160280.463833.5210.6324165.6876096.364623.130306.22005188692.171217.5214.4228778.5488002.174580.433214.42006221170.580120.5217.6534809.72101616.385623.136811.21.建立工作工作文件并录入数据,得到图2.1图2.12.采用Box-Cox变换检验原线性模型与双对数线性模型的优劣2.1对原线性模型采用OLS进行估计,估计结果如图2.2。图2.2 由图中2.2的数据,可得: (6.242914)(47.0
9、5950)2.2对双数线性模型采用OLS进行估计,估计结果如图2.3。图2.3由图2.3的数据,可得: (4.112865) (61.89235)虽然双对数线性模型的可决系数大于原线性模型,残差平方和小于原线性模型,但不能就此认为双对数线性模型“优于”线性模型。2.3采用Box-Cox变换后再进行比较在主界面菜单选择“QuickGenerate Series”,在出现的“Generate Series by Equation”窗口中输入“LY=LOG(Y)”,点击OK按钮即可生成Y的对数序列LY。然后在主页的命令编辑区域中输入“scalar Y1=exp(sum(LY)/29)”,如图2.4,点回车键生成一个标量Y1。图2.4选择“QuickGenerate Series”,在出现的“Generate Series by Equation”窗口中输入“Y2=Y/Y1”,点击OK按钮即可生成Y的对数序列Y2。作Y2关于X的线性OLS回归得如图2.5所示结果。图2.5由图2.5的回归结果可得:(6.242914)(47.05950)作Y2关于X的双对数线性OLS回归得如图2.6所示结果。图2.6由图2.6的回归结果可得: (-61.72335)(61.89235)于是该值大于在5%显著性水平下自由度为1的分布的临界值3.841,因此可判断双对数模型确实“优于”原线性模型。
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