关于出口总额的影响因素分析

摘要：中国的对外贸易的高速增长是伴随着改革开放和经济持续增长的一个重要现象。 关键词： 主要因素引入： 出口总额： GDP; 外商直接投资 汇率

全社会固定资产投资 商品零售价格指数 一,建立模型

假设建立如下一元回归模型:

Y01X12X23X34X45X5

Dependent Variable: Y Method: Least Squares Date: 12/10/11 Time: 18:34 Sample: 1980 2009 Included observations: 30

Variable C X1 X2 X3 X4 X5

R-squared Adjusted R-squared

Coefficient -4067.814 0.062050 0.044213 -622.3321 -0.058620 51.95826

Std. Error 2190.731 0.013789 0.021704 124.0865 0.021917 20.41625

t-Statistic -1.856830 4.499821 2.037070 -5.015308 -2.674600 2.544946

Prob. 0.0757 0.0001 0.0528 0.0000 0.0133 0.0178 3019.066 4046.010

0.977685 Mean dependent var 0.973036 S.D. dependent var

S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

664.3856 Akaike info criterion 10593797 Schwarz criterion -234.1869 F-statistic 1.452958 Prob(F-statistic)

216.01246 16.29270 210.3005 0.000000

模型检验:从回归估计的结果看，模型的拟合度较好：可绝系数R=0.977685，表明我国的出口总额的变化的97.7685%可由GDP,外商直接投资，汇率，全社会固定资产投资，商品零售价格指数的平均变化来解释。在5%的显著性水平下，F统计量的临界值为F(0.05) (5,28)=2.95<210.3005，表明模型的线性关系显著成立。关于经济意义的检验，由回归结果可以看出，GDP和外商直接投资与出口是正相关，汇率与出口负相关，全社会固定资产投资与出口是正相关，这些与现实是相符的，而商品零售价格指数与出口是正相关，这与现实是不符的。

多重共线性的检验： 相关系数表：

由表中数据可知X1与X4高度相关。 找出最简单的回归形式

分别作出Y与X1，X2，X3，X4，X5间的回归： （1）Y = -517.9605296 + 0.0357854014*X1 (-2.225227) (22.53238)

R2=0.947733 D.W.=1.047731 (2) Y = -802.1931266 + 0.1154461939*X2

(-1.778224) (11.67278)

R2= 0.829532 D.W.=0.171409

(3) Y = -1360.36896 + 740.2962964*X3

(-0.802645) (2.808488)

R2=0.219786 D.W.=0.098191 (4) Y = 287.1586597 + 0.0702468582*X4 (1.227168) （20.16337）

R2=0.935585 D.W.=1.203818 （5）Y = 16984.94699 - 133.1033332*X5 (1.409259) (-1.157646)

R2=0.045676 D.W.=0.113301

可见，出口总额受GDP的影响最大，因此选（1）为初始的回归模型。 逐步回归

Y=F(X1) T值 Y=F(X1，C -517.9605 -2.225227 -391.2487 X1 0.035785 22.53238 0.041808 X2 X3 X4 X5 R2 0.947733 0.950502 D.W. 1.047731 1.446328 -0.021812 X2) T值 Y=F(X1,X2,-1.548480 1146.525 8.123168 0.027117 -1.229015 0.052476 -430.1403 0.967511 1.066745 X3) T值 Y=F(X1，2.459833 1404.002 4.656496 0.053253 2.701263 0.046105 -3.689361 -579.5828 -0.044892 0.971663 1.116466 X2，X3，X4 T值 Y=F(X1，3.026825 -2968.302 3.613063 0.027713 1.925046 0.052518 -4,269655 -427.9517 -1.913960 38.51853 0.971034 1.151744 X2，X3，X5) T值 -1.235720 4932932 2.190152 -3.811673 1.743733 讨论：第一步，在初始模型中引入X2，模型拟合优度提高，但参数符号不合理，变量X2的显著性水平也不高，D.W.检验无法判断是否存在一阶相关

第二步，引入X3，模型拟合优度提高，参数符号也合理，变量也通过了T检验，但是D.W.表明存在1阶序列相关性。

第三步，引入X4，模型拟合优度提高，参数符号也合理，变量不能通过显著性为5%的T检验，D.W.表明存在一阶序列相关。 第四步；去掉X4,引入X5,拟合优度虽有所提高,但X5的经济意义不能通过,也不能通过T检验.

第三步与第四步表明, X4与X5都是多余的,同样还可以继续验证,且

X1与X4高度相关

普通最小二乘法的估计结果如下:

Y = 1146.525184 + 0.02711663944*X1 + 0.05247603427*X2 - 430.1402805*X3

(2.459833) (4.656496) (2.107263) (-3.689361)

R2=0.967511 D.W.=1.066745 F=258.0865

下面进行异方差检验: 1,图示检验法

2,怀特检验

无交叉项的怀特检验，显示结果如下

White Heteroskedasticity Test: F-statistic Obs*R-squared

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares Date: 12/10/11 Time: 21:24 Sample: 1980 2009 Included observations: 30

Variable C X1 X1^2 X2 X2^2 X3

Coefficient -206258.1 -11.01589 6.84E-05 10.93593 -0.000393 184209.1

Std. Error 260491.5 4.024307 7.32E-06 18.01178 0.000124 121669.4

90.74355 Probability 28.78406 Probability

t-Statistic -0.791803 -2.737338 9.341971 0.607154 -3.170585 1.514013

0.000000 0.000067

Prob. 0.4366 0.0117 0.0000 0.5497 0.0043 0.1436

X3^2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood8. Durbin-Watson stat

-7106.717 14430.61 -0.492475 0.6271 514130.2 1025062. 27.74549 28.07244 90.74355 0.000000

0.959469 Mean dependent var 0.948895 S.D. dependent var 231729.3 Akaike info criterion 1.24E+12 Schwarz criterion -409.1824 F-statistic 1.481354 Prob(F-statistic)

无交叉项的辅助回归结果为：

e2206258.111.01589X16.84X1210.93593X20.000393X22184209.1X37106.717X32

(-0.791803) (-2.737338) (9.341971) (0.607154) (-3.710585) (1.514013) (-0.492475)

R2=0.959469

怀特统计量nR2=28.78406该值大于5%显著性水平下，自由度为6的

2分布的相应临界值X20.05(6)=14.45,因此，拒绝同方差的原假设。

有交叉项的怀特检验;

White Heteroskedasticity Test: F-statistic Obs*R-squared

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares Date: 12/10/11 Time: 21:35 Sample: 1980 2009 Included observations: 30

Variable C X1 X1^2 X1*X2

Coefficient 718721.3 -25.80299 0.000443 -0.003362

Std. Error 395452.2 41.73105 0.000115 0.000931

102.7169 Probability 29.36471 Probability

t-Statistic 1.817467 -0.618316 3.857298 -3.612499

0.000000 0.000562

Prob. 0.0842 0.5433 0.0010 0.0017

X1*X3 X2 X2^2 X2*X3 X3 X3^2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

210.11283 118.6620 0.006521 -41.98128 -470992.2 77163.55

6.202900 80.88355 0.001950 17.75755 226368.9 30457.56

1.630339 1.467072 3.344353 -2.364137 -2.080640 2.533478

0.1187 0.1579 0.0032 0.0283 0.0505 0.0198 514130.2 1025062. 27.29630 27.76336 102.7169 0.000000

0.978824 Mean dependent var 0.969294 S.D. dependent var 179621.8 Akaike info criterion 6.45E+11 Schwarz criterion -399.4444 F-statistic 1.832053 Prob(F-statistic)

记e为对原模型进行普通最小二乘回归得到的残差平方项，将其与X1,X2,X3及其平方项

与交叉项作辅助回归，得

e2718721.325.80299X10.000443X120.003362X1*X210.11283X1*X3118.6620*X20.006521X241.98128X2*X3470992.2*X377163.55X3222

怀特检验nR=29.36471，因此，在5%的显著性水平下，仍是拒绝同方差这一假设。 下面，我们采用加权最小二乘法对原模型进行回归。 得到的结果显示如下

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 14:05 Sample: 1980 2009 Included observations: 30 Weighting series: 1/RESID^2

Variable C X1 X2 X3

R-squared Adjusted R-squared S.E. of regression

Coefficient 813.4365 0.032676 0.026244 -315.6770

Std. Error 196.4144 0.003241 0.015382 66.56028

t-Statistic 4.141430 10.08345 1.706213 -4.742723

Prob. 0.0003 0.0000 0.0999 0.0001 373.3256 1447.286 6.551388

Weighted Statistics

0.999984 Mean dependent var 0.999983 S.D. dependent var 6.019311 Akaike info criterion

Sum squared resid Log likelihood Durbin-Watson stat

R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat

942.0347 Schwarz criterion -94.27083 F-statistic 1.080718 Prob(F-statistic) Unweighted Statistics

6.738215 46688.18 0.000000

3019.066 4046.010 16136625

0.966009 Mean dependent var 0.962087 S.D. dependent var 787.8067 Sum squared resid 1.275827

最后，给出异方差稳健标准误法修正的结果：

Y813.43650.032676X10.026244X2315.6770X3

(4.141430) (10.08345) (1.706213) (-4.742723)

R2=0.999984 D.W.=1.275827 F=46688.18

可以看出，估计的参数与普通最小二乘法的结果相同，只是由于参数的标准差得到了修正，从而使得T检验值与普通最小二乘法的结果不同。 接下来进行序列相关性检验。 一，图示检验

du=1.65 D.W.检验结果表明，在5%的显著性水平下，n=30,k=4(包含常数项)，查表得dL=1.21，

由于D.W.= 1.275827,由于D.W.=1.275827>1.21又D.W.=1.275827,因此无法判断是否存在一阶

序列相关.

由于时间序列容易出现伪回归现象，因为Y与X都是时间按序列，因此有理由怀疑较高的R2是由于Y与X的共同变化的趋势引起的，为了排除时间序列模型中的这种随时间变化而具有的共同变化趋势的影响，在模型中引入时间趋势项：

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 15:00 Sample: 1980 2009 Included observations: 30

Variable C X1 X2 X3 T^2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient 1252.654 0.023660 0.050990 -480.3943 1.846731

Std. Error 515.3447 0.008916 0.025423 153.0122 3.567735

t-Statistic 2.430710 2.653648 2.005638 -3.139581 0.517620

Prob. 0.0226 0.0136 0.0558 0.0043 0.6093 3019.066 4046.010 16.31078 16.54431 188.1817 0.000000

0.967855 Mean dependent var 0.962712 S.D. dependent var 781.2902 Akaike info criterion 15260358 Schwarz criterion -239.6617 F-statistic 1.059869 Prob(F-statistic)

这里，D.W.值较低，没有通过5%显著性水平下得D.W检验，因此判断存在一阶自相关。由于T^2的T检验无法通过，因此删除T这个选项

下面对模型进行序列相关性的拉格朗日乘数检验，含一阶滞后项的残差项的辅助结果如下所示

Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared

Test Equation:

Dependent Variable: RESID Method: Least Squares Date: 12/11/11 Time: 16:27

Presample missing value lagged residuals set to zero.

Variable

Coefficient

Std. Error

t-Statistic

Prob.

6.605609 Probability 6.270035 Probability

0.016510 0.012280

C X1 X2 X3 RESID(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

-55.37198 -0.005649 0.012601 23.85064 0.724268

423.2976 0.005721 0.023112 106.1523 0.281801

-0.130811 -0.987460 0.545185 0.224683 2.570138

0.8970 0.3329 0.5905 0.8241 0.0165 9.09E-13 729.2865 16.08698 16.32052 1.651402 0.192756

0.209001 Mean dependent var 0.082441 S.D. dependent var 698.5783 Akaike info criterion 12200292 Schwarz criterion -236.3048 F-statistic 1.211841 Prob(F-statistic)

2

20.05（1）

于是，LM=6.270035，该值大于显著性水平为5%，自由度为1的分布的临界值=3.84，由此判断原模型存在一阶序列相关性 含2阶滞后残差项的辅助回归结果显示如下：

Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared

Test Equation:

Dependent Variable: RESID Method: Least Squares Date: 12/11/11 Time: 16:28

Presample missing value lagged residuals set to zero.

Variable C X1 X2 X3 RESID(-1) RESID(-2) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -29.57665 -0.006321 0.015530 11.93835 1.242577 -0.710376

Std. Error 400.6083 0.005422 0.021912 100.5887 0.373110 0.357817

t-Statistic -0.073829 -1.165856 0.708736 0.118685 3.330323 -1.985305

Prob. 0.9418 0.2551 0.4853 0.9065 0.0028 0.0587 9.09E-13 729.2865 16.00159 16.28183 2.264849 0.080371

5.662123 Probability 9.617399 Probability

0.009675 0.008158

0.320580 Mean dependent var 0.179034 S.D. dependent var 660.7859 Akaike info criterion 10479311 Schwarz criterion -234.0239 F-statistic 1.739654 Prob(F-statistic)

于是，LM=10.11278，该值大于显著性水平为5%，自由度为2的分布的临界值为22（2）0.05=5.99，仍说明原模型存在序列相关性，但RESID(-2)的参数未通过5%的显著性检验，表明并

不存在2阶序列相关的模型，综上所述，可判断该模型存在一阶序列相关性。 运用广义残差分法进行自相关的处理 显示结果如下

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 16:32 Sample (adjusted): 1981 2009

Included observations: 29 after adjustments Convergence achieved after 12 iterations

Variable C X1 X2 X3 AR(1)

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 16:33 Sample (adjusted): 1982 2009

Included observations: 28 after adjustments Convergence achieved after 13 iterations

Variable C

Coefficient 228.9778

Std. Error 374.6325

t-Statistic 0.611207

Prob. 0.5473

Coefficient 358.2879 0.013165 0.085661 -256.6643 0.804858

Std. Error 1620.043 0.005198 0.018015 233.1552 0.154219

t-Statistic 0.221160 2.532642 4.755110 -1.100830 5.218930

Prob. 0.8268 0.0183 0.0001 0.2819 0.0000 3116.931 4081.331 15.98433 16.22008 259.9729 0.000000

0.977441 Mean dependent var 0.973682 S.D. dependent var 662.1129 Akaike info criterion 10521445 Schwarz criterion -226.7729 F-statistic 1.090295 Prob(F-statistic) .80

X1 X2 X3 AR(1) AR(2)

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots

-0.004910 0.024511 90.05258 2.964793 -2.364213

0.005921 0.011725 63.07601 0.466969 0.587041

-0.829383 2.090561 1.427684 6.349018 -4.027336

0.4158 0.0483 0.1674 0.0000 0.0006 3220.390 4117.316 15.36253 15.64800 397.0441 0.000000

0.989040 Mean dependent var 0.986549 S.D. dependent var 477.5276 Akaike info criterion 5016718. Schwarz criterion -209.0754 F-statistic 2.243597 Prob(F-statistic) 1.48+.41i 1.48-.41i

Estimated AR process is nonstationary

修正后再对其进行拉格朗日乘数检验，结果如下 Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared

Test Equation:

Dependent Variable: RESID Method: Least Squares Date: 12/11/11 Time: 16:33

Presample missing value lagged residuals set to zero.

Variable C X1 X2 X3 AR(1) AR(2) RESID(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Coefficient -0.174396 0.000396 0.000298 -20.19249 0.165501 -0.194780 -0.278165

Std. Error 374.6747 0.005935 0.011730 66.25197 0.495623 0.618735 0.278879

t-Statistic -0.000465 0.066765 0.025416 -0.304783 0.333926 -0.314804 -0.997438

Prob. 0.9996 0.9474 0.9800 0.7635 0.7417 0.7560 0.3299 2.29E-09 431.0503 15.38767 15.72072 0.165814

0.994883 Probability 1.266509 Probability

0.329907 0.260423

0.045232 Mean dependent var -0.227558 S.D. dependent var 477.5832 Akaike info criterion 4789799. Schwarz criterion -208.4274 F-statistic

Durbin-Watson stat

Dependent Variable: Y Method: Least Squares

2.130549 Prob(F-statistic)

0.983171

Std. Error 126.1866 0.004355 71.15595

t-Statistic 2.610575 8.684466 -2.436508

Prob. 0.0146 0.0000 0.0217 1850.591 2353.228 15.40093 15.54105 427.2147 0.000000

Date: 12/11/11 Time: 19:19 Sample: 1980 2009 Included observations: 30 Weighting series: 1/ABS(X3)

Variable C X1 X3

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat

Coefficient 329.4197 0.037824 -173.3720

White Heteroskedasticity-Consistent Standard Errors & Covariance

Weighted Statistics

0.956288 Mean dependent var 0.953050 S.D. dependent var 509.8951 Akaike info criterion 7019811. Schwarz criterion -228.0139 F-statistic 1.542393 Prob(F-statistic) Unweighted Statistics

3019.066 4046.010 18533263

0.960961 Mean dependent var 0.958069 S.D. dependent var 828.5030 Sum squared resid 1.451471