我国国内生产总值的实证分析

1、目 录. 摘要 2 关键词 2. 正文2 1. 序 言2 2. 模型设定 3. 参数估计 4. 检验修正 经济意义检验 统计意义检验 计量经济学检验 多重共线性检验 相关系数检验 逐步回归修正 异方差性检验 异方差检验 模型修正 序列相关性检验 GB 检 验 模型修正 模型预测检验 模型确认 5. 模型评价 6. 政策建议 7. 参考文献 我国国内生产总值的实证分析【摘要】：本文主要是从宏观经济的角度，对影响我国自1990年至2009年的国内生产总值的主要因素进行实证分析。结合我国特定国情选取了六个影响我国国内生产总值的主要因素，并对其时间序列分析，建立多元线性模型，利用OLS方法进行参数估计

2、并进行计量经济学模型的四大检验。经济意义检验中，发现储蓄总额前参数不符合经济理论常识，并在后面的工作中得到了修正；计量经济学检验中，发现初建模型具有多重共线性，采用逐步回归法进行修正，消除了多重共线性；在异方差性检验中，发现模型具有异方差性，采用对数变换法进行修正，消除了异方差性；利用GB检验法发现模型随机干扰项存在2阶序列自相关性，采用广义差分变换法修正模型， 消除了模型序列相关性；利用2010年数据，模型通过了经济预测检验，并确定了最终模型，得出结论：进出口额、职工工资总额和上期国内生产总值对国内生产总值有很大影响。最后，进行了模型评价并结合模型及我国国情给出了相应的可供参考的政策建议。【

3、关键词】：国内生产总值 进出口额职工工资总额经济意义检验计量经济学检验时间序列 多元线性回归 OLS方法 逐步回归法 多重共线性 异方差性 对数变换法 GB检验法 序列自相关性 广义差分变换法 经济预测检验序言自1985年国家统计局建立起相应的核算制度以来，国内生产总值核算已经成为我国宏观经济管理部门了解经济运行状况的重要手段，制定经济发展战略、中长期规划、年度计划和各种宏观经济政策的重要依据。因此研究国内生产总值的影响因素对我国的经济发展有重大意义。2010年国内生产总值397983亿元，按可比价格计算，比上年增长10.3%，增速比上年加快1.1个百分点。总量跃居世界第二。本文主要运用计量经

4、济学和统计经济学研究一些经济指标对国内生产总值的影响和相关关系。GDP = C+ C1*LNX1 + C2*LNX3 + C3*LNX5一、模型的设定选国内生产总值GDP为被解释变量，而影响国内生产总值的因素有很多，但普遍看来，进出口额、财政支出总额、职工工资总额、税收总额、上期国内生产总值和储蓄总额这六个因素对国内生产总值影响较大，因此，我们搜集了这六个因素的时间序列数据作为解释变量，希望建立一个合适的经济模型来从理论上探讨影响国内生产总值的因素，进而提出相应的建议。把上述六个因素分别设定为X、X、X、X、X、X6。设定模型为：GDP=+U经查资料得国内生产总值样本观测数据（单位/亿元）：年

5、份GDP进出口额财政支出职工工资总额税收收入上期GDP储蓄余额199018667.85560.13083.592951.12821.8616992.31210.2199121781.57225.83386.623323.92990.1718667.81610199226923.59119.63742.23939.23296.9121781.52312.3199335333.9112714642.34916.24255.326923.53095.2199448197.920381.95792.626656.45126.8835333.94680.1199560793.723499.96823.7

6、281006038.0448197.95884.1199671176.624133.87937.5590806909.8260793.77647.619977897326967.29233.569405.38234.0471176.610053.1199884402.326849.710798.189296.59262.87897311615.9199989677.129896.213187.679875.510682.5884402.314666.7200099214.639273.215886.510656.212581.5189677.118190.72001109655.242183.

7、618902.5811830.915301.3899214.622327.6200120332.751378.222053.1513161.117636.45109655.228121.72003135822.870483.524649.9514743.520017.31120332.7351192004159878.395539.128486.8916900.224165.68135822.841416.52005184937.4116921.833930.2819789.928778.54159878.348787.52006216314.4140971.540422.7323265.93

8、4804.35184937.458575.92007265810.3166740.249781.352824445621.97216314.467599.72008314045.4179921.562592.66337145422.379265810.378585.22009340506.9150648.176299.9340288.16 59521.59314045.4100541.3数据来自中国统计年鉴二、模型的参数估计对设定模型用OLS法进行参数估计,用Eviews5对上表数据回归得：Dependent Variable: GDPMethod: Least SquaresDate: 06

9、/29/11 Time: 20:09Sample: 1990 2009Included observations: 20VariableCoefficientStd. Errort-StatisticProb.X10.4646870.04152711.189910.0000X21.0994050.5206052.1117810.0546X31.8544330.6837492.7121550.0178X40.0980130.0829981.1809150.2588X50.7590800.06756111.235390.0000X6-1.2842790.378693-3.3913490.0048C

10、-2350.2981721.927-1.3649230.1954R-squared0.999706Mean dependent var124122.3Adjusted R-squared0.999571S.D. dependent var95623.17S.E. of regression1981.296Akaike info criterion18.29011Sum squared resid51031963Schwarz criterion18.63861Log likelihood-175.9011F-statistic7373.983Durbin-Watson stat1.313821

11、Prob(F-statistic)0.000000回归结果如下：GDP=-2350.298+-1.284279=0.999706=0.999571= 7374.005D.W.=1313820F=7374.005 (6，13)=2.92(显著性水平=0.05)表明模型从整体上看国内生产总值与解释变量间线形关系显著。三、检验及修正1 经济意义检验从上述回归结果可知：的系数为负值，说明国民生产总值随居民储蓄余额的增加而减少，这从理论上说不符合我国的实际情况；其他因素系数均为正，均不与经济原理相悖，具有经济意义：各系数表示国内生产总值对该因素的弹性大小。2统计意义检验从回归结果可以看出，模型的拟和优度

12、非常好（=0.999706）， F统计量的值在给定显著性水平=0.05的情况下也较显著。因为= 7374.00 (6，13)，表明模型的线性关系在95%的置信水平下显著成立.。但是X2、X4的t统计值均不显著。3.计量经济学检验（1）多重共线性检验相关系数检验：用Eviews5求得解释变量的相关系数矩阵：GDPX1X2X3X4X5X6GDP1.0000000.9691790.9917940.9958250.7904600.9968650.991017X10.9691791.0000000.9489190.9510890.7525850.9500810.960884X20.9917940.948

13、9191.0000000.9951810.8007630.9934930.996078X30.9958250.9510890.9951811.0000000.8011940.9960410.991165X40.7904600.7525850.8007630.8011941.0000000.8021560.830014X50.9968650.9500810.9934930.9960410.8021561.0000000.991482X60.9910170.9608840.9960780.9911650.8300140.9914821.000000 由此可知：解释变量、之间存在高度正相关，模型存在

14、严重多重共线性。下面对模型进行修正。模型修正：用逐步回归法修正模型由相关系数矩阵知解释变量X5与GDP相关性最强，故首先选取X5 做为基本变量与GDP建立一元回归模型： Y=1206.208+1.138675(0.418440) (53.45104) 2=0.9937 F=2857.014 D.W.=1.117717依次引入X3、X6变量回归：引入X3 ：Dependent Variable: GDPMethod: Least SquaresDate: 06/29/11 Time: 20:19Sample: 1990 2009Included observations: 20VariableC

15、oefficientStd. Errort-StatisticProb.C-1393.5373037.490-0.4587790.6522X33.4106601.8228111.8710990.0786X50.7201990.2245413.2074240.0052R-squared0.994808Mean dependent var124122.3Adjusted R-squared0.994198S.D. dependent var95623.17S.E. of regression7283.977Akaike info criterion20.76222Sum squared resid

16、9.02E+08Schwarz criterion20.91158Log likelihood-204.6222F-statistic1628.742Durbin-Watson stat1.268140Prob(F-statistic)0.000000引入X3 ，拟合优度得到提高，参数符号合理且参数统计量显著，故采纳该变量。 引入：Dependent Variable: GDPMethod: Least SquaresDate: 06/29/11 Time: 20:25Sample: 1990 2009Included observations: 20VariableCoefficientSt

17、d. Errort-StatisticProb.C2751.9581322.7232.0805240.0539X32.2067810.7579712.9114320.0102X50.6344520.0924466.8629150.0000X10.3547030.0384029.2364730.0000R-squared0.999180Mean dependent var124122.3Adjusted R-squared0.999026S.D. dependent var95623.17S.E. of regression2983.745Akaike info criterion19.0166

18、0Sum squared resid1.42E+08Schwarz criterion19.21575Log likelihood-186.1660F-statistic6499.488Durbin-Watson stat1.354897Prob(F-statistic)0.000000引入，拟合优度再次提高，参数符号合理且参数统计量显著，故采纳该变量。引入：Dependent Variable: GDPMethod: Least SquaresDate: 06/29/11 Time: 20:36Sample: 1990 2009Included observations: 20Variabl

19、eCoefficientStd. Errort-StatisticProb.C-207.38322300.651-0.0901410.9294X32.9347960.8670593.3847710.0041X50.6701370.0916737.3101070.0000X10.3578850.0369069.6972920.0000X2-0.5111510.331441-1.5422080.1439R-squared0.999292Mean dependent var124122.3Adjusted R-squared0.999104S.D. dependent var95623.17S.E.

20、 of regression2862.969Akaike info criterion18.96942Sum squared resid1.23E+08Schwarz criterion19.21836Log likelihood-184.6942F-statistic5295.161Durbin-Watson stat1.523732Prob(F-statistic)0.000000引入，拟合优度虽然得到了提高，但是参数符号为负值，表示GDP随财政支出增加而减少，与实际情况相悖，故将该变量剔除。剔除，引入Dependent Variable: GDPMethod: Least Squares

21、Date: 06/29/11 Time: 21:05Sample: 1990 2009Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C2678.0091221.1702.1929850.0445X32.2767800.7003623.2508610.0054X50.6483440.0856057.5736290.0000X10.3506080.0354999.8764930.0000X4-0.1330840.068361-1.9467830.0705R-squared0.999345Mean depe

22、ndent var124122.3Adjusted R-squared0.999171S.D. dependent var95623.17S.E. of regression2753.333Akaike info criterion18.89133Sum squared resid1.14E+08Schwarz criterion19.14026Log likelihood-183.9133F-statistic5725.563Durbin-Watson stat1.606945Prob(F-statistic)0.000000引入，拟合优度再次提高，但是参数符号为负值表明我国GDP随税收收入

23、增加而减少，与实际情况相悖，所以将之剔除。引入：Dependent Variable: GDPMethod: Least SquaresDate: 06/29/11 Time: 21:22Sample: 1990 2009Included observations: 20VariableCoefficientStd.Errort-StatisticProb.X10.4085420.03081113.259650.0000X32.8052140.5666054.9509120.0002X50.7345550.07122210.313560.0000X6-0.6075290.152807-3.97

24、57870.0012C-2698.4361669.743-1.6160790.1269R-squared0.999601Mean dependent var124122.3Adjusted R-squared0.999494S.D. dependent var95623.17S.E. of regression2150.295Akaike info criterion18.39692Sum squared resid69356525Schwarz criterion18.64585Log likelihood-178.9692F-statistic9389.672Durbin-Watson s

25、tat1.500071Prob(F-statistic)0.000000引入，拟合优度虽再次得到提高，但是参数符号为负值表明我国GDP随上期GDP增加而减少，与实际情况相悖，所以将之剔除。 通过逐步回归，剔除了变量、，得到新模型： Y=2751.958+0.354703+2.206781+0.6344522.080524 9.236473 2.911432 6.8629152=0.999026 F=6499.488 D.W.=1.354897(2) 异方差检验：a. 画出残差e2与GDP的散点图： 观察散点图，可知模型存在异方差，下面从理论上加以说明。b.利用White-检验模型是否存在异方差

26、性：White Heteroskedasticity Test:F-statistic7.898928Probability0.001670Obs*R-squared17.53362Probability0.040987Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/30/11 Time: 12:55Sample: 1 20Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C15710528119877901.31

27、05440.2193X126.63714230.75370.1154350.9104X120.0184810.0061842.9885600.0136X1*X3-0.3701190.260585-1.4203390.1859X1*X50.0267570.0354990.7537370.4684X3-8830.54514512.51-0.6084780.5564X322.8658003.7094300.7725710.4576X3*X5-0.5163790.722809-0.7144060.4913X5817.96701639.0070.4990630.6285X520.0257220.0335

28、460.7667600.4609R-squared0.876681Mean dependent var7122194.Adjusted R-squared0.765693S.D. dependent var8245917.S.E. of regression3991454.Akaike info criterion33.54406Sum squared resid1.59E+14Schwarz criterion34.04193Log likelihood-325.4406F-statistic7.898928Durbin-Watson stat1.747769Prob(F-statistic

29、)0.001670 结果：因为nR2 =17.53362=16.919，故拒绝原假设，即模型存在异方差性。异方差的修正： a.采用对数变换法对模型进行修正：用GENR产生对数序列：genr lngdp=log(gdp)genr lnx1=log(x1)genr lnx3=log(x3)genr lnx5=log(x5) 然后用OLS方法对新序列回归，结果如下：Dependent Variable: GDPMethod: Least SquaresDate: 06/30/11 Time: 13:33Sample: 1 20Included observations: 20VariableCoef

30、ficientStd. Errort-StatisticProb.C-1078485.135563.8-7.9555560.0000LNX1-39403.2736932.06-1.0669120.3018LNX3318707.378052.214.0832580.0009LNX5-119363.554169.68-2.2035110.0426R-squared0.924433Mean dependent var124122.3Adjusted R-squared0.910264S.D. dependent var95623.17S.E. of regression28644.80Akaike

31、info criterion23.54019Sum squared resid1.31E+10Schwarz criterion23.73933Log likelihood-231.4019F-statistic65.24432Durbin-Watson stat0.316869Prob(F-statistic)0.000000GDP = -1078485.432 - 39403.26764*LNX1 + 318707.2961*LNX3 - 119363.5018*LNX5=0.924433=0.910264= 65.24432D.W.=0.316869F=65.24432 (6，13)=2

32、.92(显著性水平=0.05)表明模型从整体上看国内生产总值与解释变量间线形关系显著。b. 利用White-检验模型是否存在异方差性：White Heteroskedasticity Test:F-statistic3.181925Probability0.042823Obs*R-squared14.82366Probability0.095895Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/30/11 Time: 13:35Sample: 1 20Included observations: 20V

33、ariableCoefficientStd. Errort-StatisticProb.C-1.98E+119.58E+10-2.0648300.0659LNX1-3.07E+103.76E+10-0.8157480.4336LNX12-6.06E+095.00E+09-1.2115520.2535LNX1*LNX32.33E+091.82E+100.1284430.9003LNX1*LNX51.23E+101.74E+100.7085890.4948LNX3-2.17E+119.89E+10-2.1942930.0529LNX322.09E+104.64E+100.4500840.6622L

34、NX3*LNX5-1.71E+106.05E+10-0.2826560.7832LNX52.46E+119.63E+102.5496230.0289LNX52-9.94E+091.73E+10-0.5733820.5791R-squared0.741183Mean dependent var6.56E+08Adjusted R-squared0.508248S.D. dependent var8.62E+08S.E. of regression6.05E+08Akaike info criterion43.58514Sum squared resid3.66E+18Schwarz criter

35、ion44.08301Log likelihood-425.8514F-statistic3.181925Durbin-Watson stat2.147804Prob(F-statistic)0.042823结果：因为nR2 =14.82366=5.991，则拒绝原假设，即认为存在自相关性。n=3时：Breusch-Godfrey Serial Correlation LM Test:F-statistic2.194726Probability0.158310Obs*R-squared7.604841Probability0.054925 由于nR2 =7.604841=7.815，则没有理由

36、拒绝原假设，即认为不存在三阶自相关性。自相关的修正：采用广义差分变换法修正模型：在LS命令中加上AR(1)、AR(2),使用迭代估计法估计模型，回归结果如下：Dependent Variable: GDPMethod: Least SquaresDate: 06/30/11 Time: 15:19Sample (adjusted): 3 20Included observations: 18 after adjustmentsConvergence achieved after 16 iterationsVariableCoefficientStd. Errort-StatisticProb.

37、C-1428188.562419.8-2.5393620.0260LNX112649.8313913.790.9091580.3812LNX312025.3462474.560.1924840.8506LNX5115256.953259.432.1640660.0513AR(1)1.6765010.2547736.5803710.0000AR(2)-0.7794650.247989-3.1431390.0085R-squared0.996557Mean dependent var135666.4Adjusted R-squared0.995122S.D. dependent var93851.

38、86S.E. of regression6554.631Akaike info criterion20.67493Sum squared resid5.16E+08Schwarz criterion20.97172Log likelihood-180.0744F-statistic694.6569Durbin-Watson stat1.479658Prob(F-statistic)0.000000Inverted AR Roots.84+.28i.84-.28i输出结果表明：估计过程经过16次迭代收敛（精确度0.001，最大迭代次数500），的估计分别为：1.676501，-0.779465，

39、参数均通过t检验，说明原模型存在一、二阶自相关性。调整后的模型DW=1.479658，k=2，n=20，查表得：dL=1.20，dU=1.41，dUDW=1.4796582.59=4-dU，说明模型已不存在一阶自相关性，再进行偏相关系数检验和B-G检验，也表明不存在高阶自相关性。因此，模型已消除了自相关性的影响。（4）模型预测检验：查资料得知2010年进出口额、职工工资总额、上期国内生产总值分别为：带入模型，计算得GDP为： 与实际GDP 相比， （5）确定模型： 由上述一系列的检验、修正，最终确定模型为：GDP = -1428187.598 + 12649.82825*LNX1 + 12025.33531*LNX3 + 115256.9266*LNX5 + s= t= AR(1)=1.676501124,AR(2)=-0.7794646398 R2=0.996557 DW=1.4796