影响GDP增长的经济因素分析

1、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）ObsX1X2X3X4X5X6Y19785714440152184

2、13971558.63553645.2175197958588410242081697.61800454.64062.5792198060275423612381922.621405704545.624198159447437252642180.622350735.34889.4611198262067452952882483.262570771.35330.4511983660404643631627502849.4860.15985.5516198470904481973613214.133376.412017243.7517198576682498734463619.4943052066

3、.79040.7366198680850512824974013.0149502850.410274.379198786632527835654675.758203084.212050.615198892997543347145865.277440382215036.823198996934553297886534.738101.4415617000.919199098703647498337662.098300.15560.118718.3221991103783654919328157.039415.67225.821826.19919921091706615211169084.71099

4、3.79119.626937.276199311599366808139310995.514270.41127135260.025199412273767455183315750.518622.920381.948108.456199513117668065235520340.923613.823499.959810.529199613894868950278922353.728360.224133.870142.492199713779869820300223788.431252.926967.277653.135199813221470637315924541.933378.126849.

5、783024.281999133830.9771394334624519.135647.929896.288188.9552000138552.5872085363232917.9339105.739273.298000.4542001143199.2173025386937213.4943055.442183.6108068.222002151797.2573740410643499.9148135.951378.2119095.692003174990.374432441129691.852516.370483.51351742004203226.775200492536238.99595

6、0195539.1159586.7200522331975825543939450.8967176.6116921.8183956.1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）: 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 L

7、ength: 0 (Automatic based on SIC, MAXLAG=6)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-3.149281 0.0347Test critical values:1% level-3.6998715% level-2.97626310% level-2.627420*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(

8、E)Method: Least SquaresDate: 12/17/07 Time: 22:15Sample (adjusted): 1979 2005Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  E(-1)-0.5340390.169575-3.1492810.0042C-29.52296117.8645-0.2504820.8043R-squared0.284036    Mean depende

9、nt var-18.20297Adjusted R-squared0.255398    S.D. dependent var709.4155S.E. of regression612.1570    Akaike info criterion15.74304Sum squared resid9368406.    Schwarz criterion15.83903Log likelihood-210.5311    F-statist

10、ic9.917968Durbin-Watson stat1.880914    Prob(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）:Dependent Variable: YMethod: Least SquaresDate: 12/11/07 Time: 20:56Sample: 1978 2005Included observati

11、ons: 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-squared

12、0.999887    Mean dependent var51166.32Adjusted R-squared0.999855    S.D. dependent var52735.89S.E. of regression635.9707    Akaike info criterion15.96050Sum squared resid8493633.    Schwarz criterion16.29355Log likelihoo

13、d-216.4470    F-statistic30938.68Durbin-Watson stat1.728146    Prob(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(

14、表)：X1X2X3X4X5X6X110.9084887587265750.959220601016032X20.90848875872657510.8753031501153270.8708801885104630.8494794271754850.729465723394794X30.9592206010160320.87530315011532710.9766776942108140.9960884743647970.926876994823225X40.8708801885104630.97667769421081410.9676296414504310.867243928971564X

15、50.8494794271754850.9960884743647970.96762964145043110.953292642725825X60.7294657233947940.9268769948232250.8672439289715640.9532926427258251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：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）：变量x1x2x3x4x5x6参数估计值1.1580853.612

16、64931.223693.6942342.6484951.704013t统计量18.445357.75800839.2513816.8133696.4994619.28887R(2)0.9290070.6983290.9834040.9157730.9972160.934683R(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）：x1x2x3x4x5x6R(2)x5 x10.0578862.5256310.997182(+1

17、.294999)(+25.59707)x5 x2-0.1962132.7507510.997612(-2.546525)(+58.19202)x5 x3-12.232623.6748640.998266(-4.283421)(+15.27659)x5 x4-0.5649643.0240760.998466(-4.900573)(+38.18075)x5 x62.2376380.2864180.999595(+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）：x1x

18、2x3x4x5x6R(2)x5 x6 x10.0046512.2299840.2848720.999579(+0.260774)(+49.09533)(+11.97611)x5 x6 x20.0087422.228580.2895560.999579(+0.233341)(+42.81782)10.85269x5 x6 x39.4952861.2513410.4185940.9998(+5.152867)(+6.487128)(+13.87153)x5 x6 x4-0.0449462.2853250.2740040.999583(-0.51554)(+23.14678)(+8.238447)在

19、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)：x1x2x3x4x5x6R(2)x5 x6 x3 x1-0.04033815.438510.9849220.4766010.999858(-3.302717)(+6.944039)(+5.434718)(+15.43851)x5 x6 x3 x2-0.06005411.346641.1212610.4228050.999829(-2.269412)6.013285(+5.9

20、92658)(+15.1407)x5 x6 x3 x49.458897-0.0108461.2666280.4150920.999791(+4.997874)(-0.174824)(+5.878828)(+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)：Dependent Variable: YMethod: Least SquaresDate: 12/17/07 Ti

21、me: 19:38Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  C-1264.654249.9107-5.0604230.0000X39.4952861.8427195.1528670.0000X51.2513410.1928966.4871280.0000X60.4185940.03017613.871530.0000R-squared0.999822    Mean dependent var5116

22、6.32Adjusted R-squared0.999800    S.D. dependent var52735.89S.E. of regression746.4204    Akaike info criterion16.20002Sum squared resid13371443    Schwarz criterion16.39033Log likelihood-222.8003    F-statistic44917.00D

23、urbin-Watson stat0.979249    Prob(F-statistic)0.000000根据回归结果,得回归模型:Y=-1264.654+9.495286X3+1.251341X5+0.418594X6t =（-5.060423）（5.152867）（6.487128）（13.87153）R(2)=0.999822 R(2)=0.999800F=44917.00 DW=0.979249三、异方差性检验 1、White 检验：表(3.1)White Heteroskedasticity Test:F-statistic0.980384&

24、#160;   Prob. F(9,18)0.487547Obs*R-squared9.210473    Prob. Chi-Square(9)0.418077Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/17/07 Time: 19:57Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb. 

25、0;C1037033.794984.11.3044700.2085X3-21662.4113609.43-1.5917210.1289X3211.3772716.261900.6996270.4931X3*X5-1.6362882.998311-0.5457370.5919X3*X60.0319320.4969710.0642530.9495X52129.3051179.7041.8049490.0878X520.0528100.1442880.3660050.7186X5*X6-0.0050260.048723-0.1031590.9190X6-80.84421234.4271-0.3448

26、590.7342X620.0018730.0044350.4223580.6778R-squared0.328945    Mean dependent var477551.5Adjusted R-squared-0.006582    S.D. dependent var498819.6S.E. of regression500458.4    Akaike info criterion29.35689Sum squared resid4.51E+12  

27、;  Schwarz criterion29.83268Log likelihood-400.9965    F-statistic0.980384Durbin-Watson stat2.169849    Prob(F-statistic)0.487547由表知：nR(2)= 9.210473，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)= 9.210473<(2)0.05(9)=16.91

28、9，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-statistic0.425586    Prob. F(1,25)0.520117Obs*R-squared0.451939    Prob. Chi-Square(1)0.501415Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/17/07 Time: 20:14Sample (adjusted): 1979 2005In

29、cluded observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  C392816.1133202.62.9490110.0068RESID2(-1)0.1252500.1919920.6523700.5201R-squared0.016738    Mean dependent var453325.1Adjusted R-squared-0.022592    S.D. dependen

30、t var491248.6S.E. of regression496766.7    Akaike info criterion29.14082Sum squared resid6.17E+12    Schwarz criterion29.23680Log likelihood-391.4010    F-statistic0.425586Durbin-Watson stat2.049189    Prob(F-statistic)0

31、.520117从表知，(n-p)R(2)= 0.451939，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)= 0.451939<(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，DW值为0.979249，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)= 0.467257e(t-1).由上式可知=0.467257,对原模型进行广义差分，结果如下（表4.2）：Dependent Variable: Y-0.467257*Y(-1)Method: Least SquaresDate: 12/17/07 Time: 21:21Sample