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1、影响GDP增长的经济因素分析 近年来，我国GDP逐年增长，经济发展速度令人瞩目。为更好的了解我国经济增长的原因，我组对影响我国GDP增长的经济因素进行了分析。下表（表1.1）提供了我国19782002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）ObsX1X2X3X4X5X6Y1978571444015218413971558.63553624.1197958588410241971697.61800454.64038.2
2、198060275423612361922.621405704517.8198159447437252492180.622350735.34862.4198262067452952662483.262570771.35294.71983660404643628927502849.4860.15934.5198470904481973273214.133376.412017171198576682498734373619.4943052066.78964.4198680850512824474013.0149502850.410202.2198786632527835084675.7582030
3、84.211962.5198892997543346355865.277440382214928.3198996934553297626534.738101.44155.916909.2199098703567408037662.098300.15560.118547.91991103783583608968157.039415.67229.321617.819921091705943210709084.710993.79119.626638.1199311599360220133110995.512462.11127134634.4199412273761470174615750.51626
4、4.720381.946759.4199513117662388223620340.92062023499.958478.1199613894868850264122353.724774.124133.867884.6199713817369600283423788.427298.926967.274462.6199813221470637297224541.929152.526849.778345.2199913011971394313824519.131134.729896.282067.5200013029772085339732917.9334152.639273.289468.120
5、0113491473025360937213.4937595.242183.697314.8200214822273740379143499.9140910.551378.2104790.6一：现估计模型为Y=A0+A1*X1+A2*X2+A3*X3+A4*X4+A5*X5+A6*X6+U 运用OLS估计方法对上式中得参数进行估计，利用Eviews软件得回归分析结果如下：（表1.2）Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 20:44Sample: 1978 2002Included observations:
6、 25VariableCoefficientStd. Errort-StatisticProb. C5421.2153244.8561.6707100.1121X10.0509330.0302151.6857080.1091X2-0.2244280.113375-1.9795160.0633X321.183872.08494110.160420.0000X4-0.2165350.203877-1.0620840.3022X50.4884900.3118031.5666650.1346X60.3366200.1392082.4181020.0264R-squared0.999725 Mean d
7、ependent var35976.74Adjusted R-squared0.999634 S.D. dependent var34444.88S.E. of regression658.9930 Akaike info criterion16.05080Sum squared resid7816893. Schwarz criterion16.39208Log likelihood-193.6350 F-statistic10925.17Durbin-Watson stat1.748019 Prob(F-statistic)0.000000分析回归结果：从经济意义上讲，就业人口X2的系数为
8、负，可初步认为国民经济在向技术密集型、资本密集型发展。农业总产值的系数为负，不符合实际经济意义。其余解释变量的系数为正，符合实际经济现象。从模型检验上讲，拟合较好。可决系数R（2）=0.999725,F统计量为10925.172.66=F0.05(6,18)表明模型在整体上拟合非常好；系数显著性检验：对于A0,t统计量为1.670710，给定0.05 查t分布表，在自由度为n-k=18下，得临界值T0.025(18)=2.101因为tT0.025(18),所以接受H0:A0=0的原假设。对于A1、A2、A3、A4、A5、A6,除去A3、A6的t统计量大于T0.025(18)之外，其余系数的t统
9、计量均小于T0.025(18) ，因此可初步认为模型存在严重的多重共线性。现重新估计模型为Y=A1X1+A2X2+A3X3+A4X4+A5X5+A6X6得回归结果如下（表1.3）：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 20:57Sample: 1978 2002Included observations: 25VariableCoefficientStd. Errort-StatisticProb. X10.0106560.0190530.5592690.5825X2-0.0412480.030184-1.
10、3665640.1877X322.689741.96667011.537140.0000X4-0.1400060.207819-0.6736920.5086X50.1460230.2457790.5941240.5594X60.3871080.1421502.7232410.0135R-squared0.999683 Mean dependent var35976.74Adjusted R-squared0.999599 S.D. dependent var34444.88S.E. of regression689.3576 Akaike info criterion16.11496Sum s
11、quared resid9029064. Schwarz criterion16.40749Log likelihood-195.4370 Durbin-Watson stat1.704338从模型检验上看，R(2)=0.999683小于第一次模型的可决系数;T检验也并不优于第一次模型的t检验，故仍采用第一次模型。二、多重共线性检验 1、检验：利用Eviews计算线性回归模型中，六个解释变量的如下简单相关系数矩阵(表2.1.1)：X1X2X3X4X5X6X110.9784543274310.920854078840.8881671741190.9111188771040.88347271546
12、2X20.97845432743110.9488157613280.9171258679460.9460360865940.909232951166X30.920854078840.94881576132810.9827864539390.9970082872950.982361794167X40.8881671741190.9171258679460.98278645393910.9907093117320.997396156937X50.9111188771040.9460360865940.9970082872950.99070931173210.98844222336X60.88347
13、27154620.9092329511660.9823617941670.9973961569370.988442223361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X1 X2 X4 X5 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，分别如下：Y=-67070.34+1.029232X1 （式2.1.1） (9781.140) (0.093575)t=(-6.856618) (10.99902) R(2)=0.840254 Se=14063.12 F=1
14、20.9784Y=-133299.7+2.962005X2 （式2.1.2） (12588.50) (0.212476)t=(-10.58901) (13.68286)R(2)=0.890591 Se=11638.38 F=187.2206Y=-2268.943+27.31756X3 （式2.1.3） (348.7497) (0.186822)t=(-6.505936) (146.2225)R(2)=0.998925 Se=1153.406 F=21381.06Y=617.7713+2.752282X4 （式2.1.4） (1669.79)(0.094620)t=(0.369969) (29.
15、08787)R(2)=0.973536 Se=5723.931 F=846.1039Y=-1873.193+2.700977X5 （式2.1.5） (712.2024) (0.037971) t=(-2.630142) (71.13173)R(2)=0.995475 Se=2366.912 F=5059.723Y=5875.266+2.222034X6 （式2.1.6） (1531.230) (0.075790)t=（3.836958）（29.31845）R(2)=0.973940 Se=5680.092 F=859.5713综合分析可见，在七个一元回归模型中，GDP(Y)对居民消费水平(X3
16、)线性关系强，拟合程度好。（2）将其余解释变量逐一带入对X3的一元线性回归方程中，得以下几个模型：Y=-387.7386-0.027368X1+27.93105X3 （式2.2.1） (1367.242) (0.019261) (0.468871)t=(-0.283592) (-1.420886) (59.57089)R(2)=0.998926 Se=1128.676 F=11165.14Y=6262.980+0.029858X1-0.232206X2+28.56686X3 （式2.2.2） (3643.674) (0.034485) (0.119009) (0.548771)t=(1.718
17、864) (0.865831) (-1.951160) (52.05602)R(2)=0.999048 Se=1062.902 F=8394.415Y=4027.197+0.032089X1-0.181952X2+24.94421X3+0.327880X4 （式2.2.3） (2612.367) (0.024319) (0.084582) (0.860040) (0.069519)t=(1.541590) (1.319521) (-2.151190) (29.00354) (4.716419)R(2)=0.999606 Se=749.4065 F=12670.52Y=7124.543+0.06
18、1735X1-0.295985X2+22.25771X3+0.173648X4+0.442008X5 （式2.2.4）(3548.587)(0.033478) (0.122613) (2.282200) (0.13910) (0.348654)t=(2.007713)(1.844017) (-2.413968) (9.753743) (1.243811) (1.267755)R(2)=0.999541 Se=738.2831 F=10444.48Y=5421.215+0.050933X1-0.224428X2+21.18387X3-0.216535X4+0.488490X5+0.336620X
19、6 (式2.2.5) （3244.856）（0.030215）（0.113375）（2.084941）（0.203877）（0.311803）（0.139208）t=（1.670710）（1.685708）（-1.979516）（10.16042）（-1.062084）（1.566665）（2.418102）R(2)=0.999634 Se=658.9930 F=10925.17从式（2.2.1）可以看出，解释变量X1与X2之间存在共线性。又因为X2对Y的经济意义影响低于X1，故舍去X2。从式（2.2.4）（2.2.5）看出，解释变量X4 X5对Y的影响并不显著，故将X4 X5撤去得如下模型（
20、表2.2.1）：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 22:06Sample: 1978 2002Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C-903.4074829.1531-1.0895540.2883X1-0.0052610.012145-0.4332060.6693X323.633610.74070231.907060.0000X60.3188140.0507836.2779440.0000R-squ
21、ared0.999658 Mean dependent var35976.74Adjusted R-squared0.999609 S.D. dependent var34444.88S.E. of regression681.1097 Akaike info criterion16.03097Sum squared resid9742120. Schwarz criterion16.22599Log likelihood-196.3871 F-statistic20452.98Durbin-Watson stat1.631881 Prob(F-statistic)0.000000表2.2.1
22、中能源消费总量x1的系数为负,不符合实际经济意义,现舍去1978至1982年的数据,重新回归如下:(表2.2.2)Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 22:10Sample: 1983 2002Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C-1797.3341438.251-1.2496660.2294X10.0047770.0183430.2604470.7978X323.500090.84188027.9
23、13820.0000X60.3173670.0564105.6260570.0000R-squared0.999589 Mean dependent var43854.06Adjusted R-squared0.999512 S.D. dependent var34234.35S.E. of regression756.2503 Akaike info criterion16.27148Sum squared resid9150632. Schwarz criterion16.47062Log likelihood-158.7148 F-statistic12973.20Durbin-Wats
24、on stat1.689291 Prob(F-statistic)0.000000经过上述逐步回归分析，表明y对x1 x3 x6的回归模型最优。三、异方差性检验1、检验（1）、GoldfeldQuandt检验用OLS方法求得下列结果：Y=-12754.36+0.236669X1+10.96853X3-0.395909X6 （19831989） (6250.887) (0.1134474) (3.689418) (0.767691)R(2)=0.994022 e1(2)=287719.1Y=-5129.215+0.035047X1+23.39430X3+0.304576X6 (19942002)
25、 （7786.425）（0.065303）（1.268709）(0.079944)R(2)=0.996966 e2(2)=5139285求F统计量： F=e2(2)/e1(2)=17.86216139给定显著性水平=0.05，得临界值F0.05(4,4)=4.28,比较F=17.86216139 F0.05(4,4)=6.39可初步认为不存在异方差。（2）、Arch检验利用eviews软件输出结果为（表3.1.1）Dependent Variable: E2Method: Least SquaresDate: 06/03/05 Time: 23:01Sample(adjusted): 1986
26、 2002Included observations: 17 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C602213.2337049.71.7867190.0973E2(-1)-0.2996770.304742-0.9833800.3434E2(-2)0.0872030.2895280.3011880.7680E2(-3)-0.0050350.542470-0.0092820.9927R-squared0.115727 Mean dependent var495758.6Adjusted R-
27、squared-0.088335 S.D. dependent var699258.1S.E. of regression729489.3 Akaike info criterion30.04040Sum squared resid6.92E+12 Schwarz criterion30.23645Log likelihood-251.3434 F-statistic0.567116Durbin-Watson stat1.948353 Prob(F-statistic)0.646348丛输出的辅助回归函数重的R(2)计算（n-p）*R(2)=17*0.115727=1.967359,查(2)分
28、布表给定=0.05得临界值(2)0.05（3）=7.81因为（n-p）*R(2)=17*0.115727=1.967359(2)0.05（3）=7.81所以拒绝H0,表明不存在异方差。四、自相关检验1、检验（1）、图示法由表2.2.2的OLS估计可直接得到残差resid,生成序列E,输出结果如下图：由此图可以看出，残差et不成线性自回归，可初步认为随机误差ut不存在自相关。（2）DW检验根据表2.2.2估计的结果，DW=1.689291.给定显著性水平=0.05，查DW表n=20,k=3得下限临界值dl=0.998上限临界值du=1.676因为duDW统计量=1.6892914-du,表明不存
29、在自相关。五、运用阿尔蒙法进行滞后性修正1，对Y ,X1估计如下有限分布滞后模型Y=A0+B0X1+B1X1（-1）+B2X1(-2)+B3X1(-3)应用EVIEWS软件得回归分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 06/04/05 Time: 23:27Sample: 1983 2002Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C-78223.1710398.98-7.5221950.0000PDL01-0.9142960
30、.400006-2.2857050.0362PDL02-0.8282240.410601-2.0170990.0608PDL031.0872860.3888242.7963490.0129R-squared0.935158Mean dependent var43854.06Adjusted R-squared0.923001S.D. dependent var34234.35S.E. of regression9499.609Akaike info criterion21.33275Sum squared resid1.44E+09Schwarz criterion21.53189Log li
31、kelihood-209.3275F-statistic76.91841Durbin-Watson stat0.481394Prob(F-statistic)0.000000 Lag Distribution of X1iCoefficientStd. ErrorT-Statistic . * |0 1.00121 0.44552 2.24728 * . |1-0.91430 0.40001-2.28570 * . |2-0.65523 0.39089-1.67625 . *|3 1.77840 0.45803 3.88274Sum of Lags 1.21009 0.08629 14.023
32、8即是Y-78223.17+1.00121X10.91430X1(-1) -0.65523X1(-2)+ 1.77840X1(-3)2对Y ,X3有限分布滞后模型Y=A0+B0X3+B1X3(-1)+B2X3(-2)+B3X3(-3)用EVIEWS软件显示回归分如下：Dependent Variable: YMethod: Least SquaresDate: 06/04/05 Time: 23:31Sample: 1983 2002Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C-2497.770
33、516.2504-4.8382920.0002PDL012.1069172.1767250.9679300.3475PDL02-15.958292.156581-7.3998110.0000PDL038.5508662.1502223.9767370.0011R-squared0.998874Mean dependent var43854.06Adjusted R-squared0.998663S.D. dependent var34234.35S.E. of regression1251.806Akaike info criterion17.27942Sum squared resid250
34、72277Schwarz criterion17.47856Log likelihood-168.7942F-statistic4731.442Durbin-Watson stat1.165284Prob(F-statistic)0.000000 Lag Distribution of X3iCoefficientStd. ErrorT-Statistic . *|0 26.6161 2.22221 11.9773 .* |1 2.10692 2.17672 0.96793 * . |2-5.30051 2.11824-2.50232 . * |3 4.39380 2.45928 1.7866
35、2Sum of Lags 27.8163 0.33326 83.4682即是Y-2497.770+26.6161 X3+2.10692 X3 (-1) -5.30051 X3 (-2)+ 4.39380 X3 (-3)3对Y , x6有限分布滞后模型Y=A0+B0 x6+B1 x6 (-1)+B2 x6 (-2)+B3 x6 (-3)用EVIEWS软件显示回归分如下：Dependent Variable: YMethod: Least SquaresDate: 06/04/05 Time: 23:37Sample: 1983 2002Included observations: 20Varia
36、bleCoefficientStd. Errort-StatisticProb. C8207.6061631.5105.0306800.0001PDL010.7740280.3432472.2550150.0385PDL02-0.0758520.363485-0.2086800.8373PDL03-0.0649750.330846-0.1963910.8468R-squared0.983441Mean dependent var43854.06Adjusted R-squared0.980336S.D. dependent var34234.35S.E. of regression4800.5
37、86Akaike info criterion19.96772Sum squared resid3.69E+08Schwarz criterion20.16687Log likelihood-195.6772F-statistic316.7499Durbin-Watson stat0.342226Prob(F-statistic)0.000000 Lag Distribution of X6iCoefficientStd. ErrorT-Statistic . *|0 0.78491 0.39271 1.99867 . *|1 0.77403 0.34325 2.25501 . * |2 0.
38、63320 0.34422 1.83951 . * |3 0.36242 0.46095 0.78625Sum of Lags 2.55456 0.14135 18.0730即是Y=8207.606+0.78491 x6+0.77403 x6 (-1)+ 0.63320 x6 (-2)+ 0.36242 x6 (-3)通过以上一系列统计检验可以说明：我国GDP的增长与能源消费总量X1,居民消费水平X3，进出口贸易总额X6有很高的相关性。其中，又以居民消费水平X3的影响程度最为显著。由此可以看出影响我国GDP的主要因素是居民消费水平，进出口贸易总额，能源消费总量。附本（相关表格）（表2.1.2）
39、Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 21:08Sample: 1978 2002Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C-67070.349781.840-6.8566180.0000X11.0292320.09357510.999020.0000R-squared0.840254 Mean dependent var35976.74Adjusted R-squared0.833308 S.D. dep
40、endent var34444.88S.E. of regression14063.12 Akaike info criterion22.01712Sum squared resid4.55E+09 Schwarz criterion22.11463Log likelihood-273.2140 F-statistic120.9784Durbin-Watson stat0.094594 Prob(F-statistic)0.000000(表2.1.3)Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 21:12Sample: 1978 2002Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C-13329
