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影响GDP增长的经济因素分析国际经济与贸易钟颀405020491978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1978——2005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）ObsX1X2X3X4X5X6Y1978571444015218413971558.63553645.2175197958588410242081697.61800454.64062.5792198060275423612381922.621405704545.624198159447437252642180.622350735.34889.4611198262067452952882483.262570771.35330.4511983660404643631627502849.4860.15985.5516198470904481973613214.133376.412017243.7517198576682498734463619.4943052066.79040.7366198680850512824974013.0149502850.410274.379198786632527835654675.758203084.212050.615198892997543347145865.277440382215036.823198996934553297886534.738101.4415617000.919199098703647498337662.098300.15560.118718.3221991103783654919328157.039415.67225.821826.19919921091706615211169084.710993.79119.626937.276199311599366808139310995.514270.41127135260.025199412273767455183315750.518622.920381.948108.456199513117668065235520340.923613.823499.959810.529199613894868950278922353.728360.224133.870142.492199713779869820300223788.431252.926967.277653.135199813221470637315924541.933378.126849.783024.281999133830.9771394334624519.135647.929896.288188.9552000138552.5872085363232917.9339105.739273.298000.4542001143199.2173025386937213.4943055.442183.6108068.222002151797.2573740410643499.9148135.951378.2119095.692003174990.374432441129691.852516.370483.51351742004203226.775200492536238.995950195539.1159586.7200522331975825543939450.8967176.6116921.8183956.1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）:-1500-1000-5000500100015007880828486889092949698000204E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）：NullHypothesis:EhasaunitrootExogenous:ConstantLagLength:0(AutomaticbasedonSIC,MAXLAG=6)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-3.1492810.0347Testcriticalvalues:1%level-3.6998715%level-2.97626310%level-2.627420*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(E)Method:LeastSquaresDate:12/17/07Time:22:15Sample(adjusted):19792005Includedobservations:27afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.E(-1)-0.5340390.169575-3.1492810.0042C-29.52296117.8645-0.2504820.8043R-squared0.284036Meandependentvar-18.20297AdjustedR-squared0.255398S.D.dependentvar709.4155S.E.ofregression612.1570Akaikeinfocriterion15.74304Sumsquaredresid9368406.Schwarzcriterion15.83903Loglikelihood-210.5311F-statistic9.917968Durbin-Watsonstat1.880914Prob(F-statistic)0.004207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）:DependentVariable:YMethod:LeastSquaresDate:12/11/07Time:20:56Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.C526.04171206.6350.4359570.6673X1-0.0681080.027789-2.4508890.0231X20.0601750.0547801.0985010.2844X312.913811.8696506.9070750.0000X4-0.0405530.054016-0.7507710.4611X50.9890140.1968575.0240230.0001X60.4992210.04415411.306380.0000R-squared0.999887Meandependentvar51166.32AdjustedR-squared0.999855S.D.dependentvar52735.89S.E.ofregression635.9707Akaikeinfocriterion15.96050Sumsquaredresid8493633.Schwarzcriterion16.29355Loglikelihood-216.4470F-statistic30938.68Durbin-Watsonstat1.728146Prob(F-statistic)0.000000结果分析：可决系数为0.999855，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)=0.435957,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)：X1X2X3X4X5X6X110.9084887587265750.9592206010160320.9121594537919750.9615563612868050.937316682829166X20.90848875872657510.8753031501153270.8708801885104630.8494794271754850.729465723394794X30.9592206010160320.87530315011532710.9766776942108140.9960884743647970.926876994823225X40.9121594537919750.8708801885104630.97667769421081410.9676296414504310.867243928971564X50.9615563612868050.8494794271754850.9960884743647970.96762964145043110.953292642725825X60.9373166828291660.7294657233947940.9268769948232250.8672439289715640.9532926427258251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：⑴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1.1580853.61264931.223693.6942342.6484951.704013t统计量18.445357.75800839.2513816.8133696.4994619.28887R^(2)0.9290070.6983290.9834040.9157730.9972160.934683￣R^(2)0.9262760.6867270.9827660.9125330.9971090.932171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）：x1x2x3x4x5x6￣R^(2)x5x10.0578862.5256310.997182(+1.294999)(+25.59707)x5x2-0.1962132.7507510.997612(-2.546525)(+58.19202)x5x3-12.232623.6748640.998266(-4.283421)(+15.27659)x5x4-0.5649643.0240760.998466(-4.900573)(+38.18075)x5x62.2376380.2864180.999595(+65.79107)(-12.67189)经比较，新加入X6的方程￣R^(2)=0.999595，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）：x1x2x3x4x5x6￣R^(2)x5x6x10.0046512.2299840.2848720.999579(+0.260774)(+49.09533)(+11.97611)x5x6x20.0087422.228580.2895560.999579(+0.233341)(