影响GDP增长的经济因素分析

影响GDP增长的经济因素分析 国际经济与贸易 钟颀 1978年十一届三中全会以后，在邓小平总设计师的指引下，中国开始了改革开放。改革开放的三十年中，我国GDP逐年增长，经济发展速度令世界瞩目。为更好的了解我国经济增长的原因，现对影响我国GDP增长的经济因素进行了分析。下表提供了我国19782005年的GDP及其主要影响因素的数据。其中Y=GDP(亿元)；X1能源消费总量（万吨标准煤）；X2就业人员（万人）；X3=居民消费水平（元）；X4农业总产值（亿元）；X5社会消费品零售总额（亿元）；X6进出口贸易总额（亿元）ObsX1X2X3X4X5X6Y1978571444015218413971558.63553645.2175197958588410242081697.61800454.64062.5792198060275423612381922.621405704545.624198159447437252642180.622350735.34889.4611198262067452952882483.262570771.35330.4511983660404643631627502849.4860.15985.5516198470904481973613214.133376.412017243.7517198576682498734463619.4943052066.79040.7366198680850512824974013.0149502850.410274.379198786632527835654675.758203084.212050.615198892997543347145865.277440382215036.823198996934553297886534.738101.4415617000.919199098703647498337662.098300.15560.118718.3221991654919328157.039415.67225.821826.19919926615211169084.710993.79119.626937.276199366808139310995.514270.41127135260.025199467455183315750.518622.920381.948108.456199568065235520340.923613.823499.959810.529199668950278922353.728360.224133.870142.492199769820300223788.431252.926967.277653.135199870637315924541.933378.126849.783024.281999.9771394334624519.135647.929896.288188.9552000.5872085363232917.9339105.739273.298000.4542001.2173025386937213.4943055.442183.6.222002.2573740410643499.9148135.951378.2.692003.374432441129691.852516.370483.52004.775200492536238.995950195539.1.7200575825543939450.8967现估计模型为Y=c+A1*X1+A2*X2+A3*X3+A4*X4+A5*X5+A6*X6+U 一、平衡性检验和协整检验将被解释变量Y与解释变量X1、X2、X3、X4、X5、X6进行多元回归，可以得出残差序列e,通过残差序列的线性图形（表1.1）: 由图可知，残差序列是有截距无明显趋势的时间序列。因此选择模型2进行单位根检验，结果如下（表1.2）：Null Hypothesis: E has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=6)t-StatisticProb.*Augmented Dickey-Fuller test statistic-3.0.0347Test critical values:1% level-3.5% level-2.10% level-2.*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(E)Method: Least SquaresDate: 12/17/07 Time: 22:15Sample (adjusted): 1979 2005Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.E(-1)-0.0.-3.0.0042C-29.52296117.8645-0.0.8043R-squared0.Mean dependent var-18.20297Adjusted R-squared0.S.D. dependent var709.4155S.E. of regression612.1570Akaike info criterion15.74304Sum squared resid.Schwarz criterion15.83903Log likelihood-210.5311F-statistic9.Durbin-Watson stat1.Prob(F-statistic)0.由上面的结果可以看出，残差序列e在显著性水平为0.05的条件下，没有通过显著性检验，即e平稳，因此可以得出原模型协整，可以进行下面的回归。二、多重共线性检验 1、检验：利用OLS对以上参数进行估计，结果如下（表2.1.1）:Dependent Variable: YMethod: Least SquaresDate: 12/11/07 Time: 20:56Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C526.04171206.6350.0.6673X1-0.0.-2.0.0231X.2844X312.9138000X4-0.0.-0.0.4611X.0001X06380.0000R-squared0.Mean dependent var51166.32Adjusted R-squared0.S.D. dependent var52735.89S.E. of regression635.9707Akaike info criterion15.96050Sum squared resid.Schwarz criterion16.29355Log likelihood-216.4470F-statistic30938.68Durbin-Watson stat1.Prob(F-statistic)0.结果分析：可决系数为0.，F统计量为30938.68，通过F检验，表明模型拟合优度较好。对于A1、A2、A3、A4、A5、A6，X2和X4的T统计量均小于临界值T0.025(21)=0., 而X1和X4的系数为负，与经济意义和实际情况不符。因此，可初步认为此模型存在严重的多重共线性。六个解释变量的如下简单相关系数矩阵(表2.1.2)：X1X2X3X4X5X6X110.65750.60320.19750.68050.9166X20.657510.53270.04630.54850.4794X30.60320.532710.08140.47970.3225X40.19750.04630.081410.04310.1564X50.68050.54850.47970.043110.5825X60.91660.47940.32250.15640.58251从上表可以看出，各解释变量之间存在高度线性相关。同时由表1.2又可看出，尽管整体上线性回归拟合较好，但X2， X4变量的参数T值并不显著，表明模型中解释变量确实存在严重的多重共线性。2、修正：运用OLS方法逐一求出Y对各个解释变量的回归，结果如下（表2.2.1）：变量x1x2x3x4x5x6参数估计值23693.2.1.t统计量18.445357.39.2513816.8133696.4994619.28887R(2).0.0.R(2).0.0.综合分析可见，在六个一元回归模型中，加入X5 的方程R(2)最大，以X5为基础，顺次加入其他变量逐步回归，结果如表（表2.2.2）：x1x2x3x4x5x6R(2)x5 x10.2.0.(+1.)(+25.59707)x5 x2-0.2.0.(-2.)(+58.19202)x5 x3-12.232623.0.(-4.)(+15.27659)x5 x4-0.3.0.(-4.)(+38.18075)x5 x62.0.0.(+65.79107)(-12.67189)经比较，新加入X6的方程R(2)= 0. ，改进最大，而且各参数t值显著，选择保留X6，再加入其它新变量逐步回归，结果如下（表2.2.3）：x1x2x3x4x5x6R(2)x5 x6 x.(+0.)(+49.09533)(+11.97611)x5 x6 x20.2.228580.0.(+0.)(+42.81782)10.85269x5 x6 x.9998(+5.)(+6.)(+13.87153)x5 x6 x4-.(-0.51554)(+23.14678)(+8.)在X5、X6基础上加入X3后的方程R(2)明显增大，而且各参数t值显著。加入X1、X2后，虽然R(2)有所上升，但参数检验不显著；加入X4后，不仅t检验不显著，X4的符号不合理。所以选择保留X3，继续逐步回归，结果如下(表2.2.4)：x1x2x3x4x5x6R(2)x5 x6 x3 x1-0.15.438510.0.0.(-3.)(+6.)(+5.)(+15.43851)x5 x6 x3 x2-0.11.346641.0.0.(-2.)6.(+5.)(+15.1407)x5 x6 x3 x49.-.(+4.)(-0.)(+5.)(+11.29637)加入X1、X2、X4后，不仅参数t值不再全部显著，参数符号也不合理。因此，X1、X2、X4引起严重多重共线性，应予以剔除。剩下的变量为X3、X5、X6，修定模型为：Y=C+A3*X3+A5*X5+A6*X6+U，最后修正严重多重共线性影响的回归结果为(表2.2.5)：Dependent Variable: YMethod: Least SquaresDate: 12/17/07 Time: 19:38Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C-1264.654249.9107-5.0.0000X.0000X.0000X71530.0000R-squared0.Mean dependent var51166.32Adjusted R-squared0.S.D. dependent var52735.89S.E. of regression746.4204Akaike info criterion16.20002Sum squared residSchwarz criterion16.39033Log likelihood-222.8003F-statistic44917.00Durbin-Watson stat0.Prob(F-statistic)0.根据回归结果,得回归模型:Y=-1264.654+9.X3+1.X5+0.X6t =（-5.）（5.）（6.）（13.87153）R(2)=0. R(2)=0.F=44917.00 DW=0.三、异方差性检验 1、White 检验：表(3.1)White Heteroskedasticity Test:F-statistic0.Prob. F(9,18)0.Obs*R-squared9.Prob. Chi-Square(9)0.Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/17/07 Time: 19:57Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C.11.0.2085X3-21662.4113609.43-1.0.1289X3211.3772716.261900.0.4931X3*X5-1.2.-0.0.5919X3*X.9495X52129.3051179.7041.0.0878X5.7186X5*X6-0.0.-0.0.9190X6-80.84421234.4271-0.0.7342X6.6778R-squared0.Mean dependent var.5Adjusted R-squared-0.S.D. dependent var.6S.E. of regression.4Akaike info criterion29.35689Sum squared resid4.51E+12Schwarz criterion29.83268Log likelihood-400.9965F-statistic0.Durbin-Watson stat2.Prob(F-statistic)0.由表知：nR(2)= 9.，由White检验知，在=0.05下，查(2)分布表，得临界值(2)0.05(9)=16.919.比较计算的(2)统计量与临界值，因为nR(2)= 9.(2)0.05(9)=16.919，所以接受原假设，表明模型不存在异方差。2、Arch检验：表(3.2):ARCH Test:F-statistic0.Prob. F(1,25)0.Obs*R-squared0.Prob. Chi-Square(1)0.Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/17/07 Time: 20:14Sample (adjusted): 1979 2005Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C.068RESID2(-1).5201R-squared0.Mean dependent var.1Adjusted R-squared-0.S.D. dependent var.6S.E. of regression.7Akaike info criterion29.14082Sum squared resid6.17E+12Schwarz criterion29.23680Log likelihood-391.4010F-statistic0.Durbin-Watson stat2.Prob(F-statistic)0.从表知，(n-p)R(2)= 0.，由Arch检验知，在=0.05下，查(2)分布表，得临界值(2)0.05(1)=3.841, 比较计算的(2)统计量与临界值，因为(n-p)R(2)= 0.(2)0.05(1)=3.841,所以接受原假设，表明模型不存在异方差。通过White检验和Arch检验，表明模型是不存在异方差的。四、自相关检验 根据表2.2.5，DW值为0.，查DW统计表可知，在=0.05的水平下，dL=1.328，模型中DW dL，显然存在正自相关。这一点从残差图中也可以看出，如图4.1:在图4.1中，残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关，模型中t统计量和F统计量的结论不可信，需采取补救措施。为解决自相关问题，选用科克伦-奥克特迭代法。利用Eviews软件，可得回归方程：e(t)= 0.e(t-1).由上式可知=0.,对原模型进行广义差分，结果如下（表4.2）：Dependent Variable: Y-0.*Y(-1)Method: Least SquaresDate: 12/17/07 Time: