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1、我国改革开放以来固定资产投资与GDP关系分析【摘要】本文旨在对我国改革开放以来固定资产投资与GDP关系进行计量分析。首先我们对已有的部分关于固定资产投资的观点和评论进行了评述;然后再收集的数据的基础上利用EViews软件进行了计量分析，从数据本身出发验证了两者的因果关系，并寻求设定合理的经济关系模型;接着运用软件对设定的模型进行了参数估计，检验及修正；最后我们利用所得的结果进行了经济预测以评估所得结果的价值并对结果本身提出了政策意见。一 问题的提出我国自改革开放以来已保持了国民经济20多年的快速增长，GDP年均增长率在10%以上，如此高的增长速度不经要引起人们对其增长动力或原因的兴趣。今年来关
2、于投资，消费和出口“三驾马车”拉动经济增长的理论较为突出。尤其是进入90年代后直到90年代末到新世纪最近几年，不论是学术界还是公众媒体都对固定资产投资的高增长表现出不同程度的担忧，因而才引出关于经济软着陆和怎样减少固定资产投资的讨论。那么，究竟固定资产投资同GDP之间的关系如何？新世纪的前后几年是不是存在固定资产投资过热拉动经济过热的情况？本文试图运用计量经济学的方法寻求答案。二 数据收集为进行计量分析，我们寻求改革开放至今的GDP和固定资产的可比数据，数据来源为中国统计年鉴及中国国家统计局网站（）的数据资料，两项数据样本数都为27，满足一元回归的要求。1978-2004年GDP及固定资产投资
3、年度数据obsGDPFAI19783624.100780.200019794038.200846.200019804517.800910.900019814862.400961.000019825294.7001230.40019837171.0001430.10019847171.0001832.90019858964.4002543.200198610202.203120.600198711962.503791.700198814928.304753.800198916909.204410.400199018547.904517.000199121617.805594.5001992266
4、38.108080.100199334634.4013072.30199446759.4017042.94199558478.1020019.26199667884.6022974.03199774462.6024941.10199878345.2028406.17199982067.5029854.71200089468.1032917.73200197314.8037213.492002104790.643499.912003117251.955566.612004136515.070072.71三 数据分析由于相关数据为时间序列，很可能为非平稳序列，直接回归可能造成伪回归。因此对两时间序
5、列进行平稳性检验，方法为ADF检验。EViews5默认情况下检验结果如下：GDP的ADF检验Null Hypothesis: GDP has a unit rootExogenous: ConstantLag Length: 2 (Automatic based on SIC, MAXLAG=6)t-StatisticProb.*Augmented Dickey-Fuller test statistic2.5889251.0000Test critical values:1% level-3.7378535% level-2.99187810% level-2.635542*MacKinno
6、n (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(GDP)Method: Least SquaresDate: 05/28/05 Time: 16:45Sample (adjusted): 1981 2004Included observations: 24 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.GDP(-1)0.0457720.0176802.5889250.0175D(GDP(-1)
7、1.3275620.2171506.1135740.0000D(GDP(-2)-0.7328310.231507-3.1654850.0049C399.8333664.79320.6014400.5543R-squared0.851066Mean dependent var5499.883Adjusted R-squared0.828726S.D. dependent var4860.139S.E. of regression2011.383Akaike info criterion18.20204Sum squared resid80913219Schwarz criterion18.398
8、39Log likelihood-214.4245F-statistic38.09586Durbin-Watson stat2.019994Prob(F-statistic)0.000000FAI的ADF检验Null Hypothesis: FAI has a unit rootExogenous: ConstantLag Length: 6 (Automatic based on SIC, MAXLAG=6)t-StatisticProb.*Augmented Dickey-Fuller test statistic4.2612021.0000Test critical values:1%
9、level-3.8085465% level-3.02068610% level-2.650413*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(FAI)Method: Least SquaresDate: 05/28/05 Time: 16:48Sample (adjusted): 1985 2004Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-St
10、atisticProb.FAI(-1)0.2595730.0609154.2612020.0011D(FAI(-1)0.7625700.2319303.2879250.0065D(FAI(-2)-0.2729570.300382-0.9086990.3814D(FAI(-3)-0.7451330.292414-2.5482100.0255D(FAI(-4)-0.6089930.290971-2.0929660.0583D(FAI(-5)0.7392930.3387122.1826550.0497D(FAI(-6)-1.2579950.331724-3.7922980.0026C189.1530
11、376.01380.5030480.6240R-squared0.956233Mean dependent var3411.991Adjusted R-squared0.930703S.D. dependent var3814.703S.E. of regression1004.198Akaike info criterion16.95094Sum squared resid12100974Schwarz criterion17.34923Log likelihood-161.5094F-statistic37.45431Durbin-Watson stat2.303034Prob(F-sta
12、tistic)0.000000由上述结果可以看到两序列的ADF统计量均大于5%水平下的临界值，因而不能拒绝原假设，序列为非平稳序列。由于两序列均为非平稳序列，因而需要进行两序列协整的检验，否则其回归将是没有意义的。协整检验第一步，对两序列运用OLS法进行简单一元回归，得到回归参数估计和残差序列。回归结果：Dependent Variable: GDPMethod: Least SquaresDate: 05/30/05 Time: 02:57Sample: 1978 2004Included observations: 27VariableCoefficientStd. Errort-Stat
13、isticProb.C7569.4842054.4443.6844450.0011FAI2.1573120.08369625.775560.0000R-squared0.963736Mean dependent var42756.36Adjusted R-squared0.962285S.D. dependent var41079.01S.E. of regression7977.694Akaike info criterion20.87787Sum squared resid1.59E+09Schwarz criterion20.97386Log likelihood-279.8513F-s
14、tatistic664.3797Durbin-Watson stat0.288516Prob(F-statistic)0.000000残差序列Last updated: 05/30/05 - 02:571978-5628.5191979-5356.8011980-5016.7801981-4780.2611982-4929.1411983-3483.6561984-4352.6211985-4091.5601986-4099.3931987-3786.8651988-2896.6151989-174.893919901233.83719911979.23319921637.3171993-11
15、36.11719942422.97219957720.820199610752.96199713087.3719989494.736199910092.08200010884.7920019464.19620023378.2252003-10192.122004-22223.20协整检验第二步，运用ADF法检验残差序列平稳性从而检验两序列是否存在协整。残差序列ADF检验Null Hypothesis: ET has a unit rootExogenous: ConstantLag Length: 5 (Automatic based on SIC, MAXLAG=6)t-StatisticP
16、rob.*Augmented Dickey-Fuller test statistic-3.7308540.0113Test critical values:1% level-3.7880305% level-3.01236310% level-2.646119*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(ET)Method: Least SquaresDate: 05/30/05 Time: 03:25Sample (adjusted): 1984
17、 2004Included observations: 21 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.ET(-1)-0.3704680.099298-3.7308540.0022D(ET(-1)0.9620630.1628165.9088960.0000D(ET(-2)0.4618810.2884971.6009930.1317D(ET(-3)0.2454610.2770220.8860710.3905D(ET(-4)0.3073360.2722551.1288530.2779D(ET(-5)1.2036760
18、.2856654.2135920.0009C-1293.088582.6998-2.2191320.0435R-squared0.846063Mean dependent var-892.3584Adjusted R-squared0.780090S.D. dependent var4690.288S.E. of regression2199.491Akaike info criterion18.49104Sum squared resid67728663Schwarz criterion18.83922Log likelihood-187.1559F-statistic12.82436Dur
19、bin-Watson stat1.764056Prob(F-statistic)0.000055由结果显示残差序列的ADF统计量小于5%水平下的临界值，因而不能拒绝原假设残差序列是平稳的，因而就有两序列间存在协整。也证实了两序列间存在长期稳定关系。由于两序列被证实存在长期稳定关系，进一步检验GDP同固定资产投资间因果关系及程度。采用检验方法为Granger检验。调整滞后长度为2-5，得到如下结果。Pairwise Granger Causality TestsDate: 05/30/05 Time: 03:33Sample: 1978 2004Lags: 2Null Hypothesis:Ob
20、sF-StatisticProbabilityGDP does not Granger Cause FAI251.510060.24503FAI does not Granger Cause GDP12.80150.00026Pairwise Granger Causality TestsDate: 05/30/05 Time: 03:34Sample: 1978 2004Lags: 3Null Hypothesis:ObsF-StatisticProbabilityGDP does not Granger Cause FAI240.609660.61786FAI does not Grang
21、er Cause GDP6.405750.00422Pairwise Granger Causality TestsDate: 05/30/05 Time: 03:34Sample: 1978 2004Lags: 4Null Hypothesis:ObsF-StatisticProbabilityGDP does not Granger Cause FAI230.439050.77841FAI does not Granger Cause GDP4.745510.01249Pairwise Granger Causality TestsDate: 05/30/05 Time: 03:34Sam
22、ple: 1978 2004Lags: 5Null Hypothesis:ObsF-StatisticProbabilityGDP does not Granger Cause FAI223.056270.05695FAI does not Granger Cause GDP3.697200.03297对上述结果总结如下：滞后长度m=nGranger因果性F值P值结论2GDP-FAI1.510060.24503拒绝FAI-GDP12.80150.00026不拒绝3GDP-FAI0.609660.61786拒绝FAI-GDP6.405750.00422不拒绝4GDP-FAI0.439050.77
23、841拒绝FAI-GDP4.745510.01249不拒绝5GDP-FAI3.056270.05695不拒绝FAI-GDP3.69720.03297不拒绝可见GDP与固定资产投资存在明显的因果关系，受制于序列的不平稳才使得结论看上去仍受滞后长度的影响。四 模型设定，参数估计与检验由数据分析可知，GDP与固定资产投资不但存在长期稳定关系更存在因果关系。因此可设定初步模型为：GDP=C+1* FAI+u应用OLS法进行参数估计。得到如下结果：Dependent Variable: GDPMethod: Least SquaresDate: 05/31/05 Time: 14:13Sample: 1
24、978 2004Included observations: 27VariableCoefficientStd. Errort-StatisticProb.C7569.4842054.4443.6844450.0011FAI2.1573120.08369625.775560.0000R-squared0.963736Mean dependent var42756.36Adjusted R-squared0.962285S.D. dependent var41079.01S.E. of regression7977.694Akaike info criterion20.87787Sum squa
25、red resid1.59E+09Schwarz criterion20.97386Log likelihood-279.8513F-statistic664.3797Durbin-Watson stat0.288516Prob(F-statistic)0.000000a经济意义检验：由经济理论以及此前的因果检验可知固定资产投资与GDP存在长期稳定的正线性关系，模型估计与此相符。b统计推断检验：可决系数为0.963736，模型拟合情况较理想。T统计量为25.77556而显著水平0.05下临界值为2.060因此T统计量显著。说明参数估计是显著的，固定资产投资对GDP有显著影响。F统计量为664.
26、3797，0.05显著水平下临界值为3.33，因此F统计量也是显著的。说明模型设定也是显著的。c计量经济检验 1 多重共线性检验。由于是一元回归不存在多重共线性问题，无须检验。 2 异方差检验。 ARCH检验，设定滞后期为3得到如下结果ARCH Test:F-statistic10.08751Probability0.000294Obs*R-squared14.45014Probability0.002352Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/31/05 Time: 14:53Sample
27、(adjusted): 1981 2004Included observations: 24 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C9059274.203799130.4445200.6614RESID2(-1)1.8209830.4217534.3176530.0003RESID2(-2)-2.1438680.567807-3.7756970.0012RESID2(-3)1.4886240.4913053.0299390.0066R-squared0.602089Mean dependent var627
28、31107Adjusted R-squared0.542403S.D. dependent var1.04E+08S.E. of regression70486751Akaike info criterion39.13076Sum squared resid9.94E+16Schwarz criterion39.32710Log likelihood-465.5691F-statistic10.08751Durbin-Watson stat1.787900Prob(F-statistic)0.000294比较obj*R2=14.45014显著程度0.05，自由度P=3时的临界值7.81473。
29、因此决绝原假设，判断模型误差项存在异方差。 3 自相关检验。由此前回归结果可知D-W统计量为0.288516。给定显著水平0.05，查D-W表n=27,k=1得下限临界值为1.316，上限临界值为1.469。而0.288516下限1.316因此模型误差项存在一阶自相关。五 模型修正（一）异方差修正 WLS估计法。生成权数w=1/fai的估计结果为Dependent Variable: GDPMethod: Least SquaresDate: 05/31/05 Time: 15:16Sample: 1978 2004Included observations: 27Weighting seri
30、es: 1/FAIVariableCoefficientStd. Errort-StatisticProb.C1984.233211.10949.3990780.0000FAI2.7579950.10987425.101510.0000Weighted StatisticsR-squared0.779430Mean dependent var10214.52Adjusted R-squared0.770607S.D. dependent var2721.756S.E. of regression1303.584Akaike info criterion17.25481Sum squared r
31、esid42483299Schwarz criterion17.35080Log likelihood-230.9399F-statistic630.0859Durbin-Watson stat0.677084Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.878099Mean dependent var42756.36Adjusted R-squared0.873223S.D. dependent var41079.01S.E. of regression14626.47Sum squared resid5.35E+09Dur
32、bin-Watson stat0.201485换用对数变换法将gdp和fai替换成Lgdp和Lfai。的如下结论Dependent Variable: LGDPMethod: Least SquaresDate: 05/31/05 Time: 15:22Sample: 1978 2004Included observations: 27VariableCoefficientStd. Errort-StatisticProb.C2.7136610.11595723.402220.0000LFAI0.8290080.01290464.242410.0000R-squared0.993979Mean
33、 dependent var10.06867Adjusted R-squared0.993738S.D. dependent var1.208213S.E. of regression0.095609Akaike info criterion-1.785921Sum squared resid0.228525Schwarz criterion-1.689933Log likelihood26.10993F-statistic4127.088Durbin-Watson stat0.876328Prob(F-statistic)0.000000比较两种方法可知gdp与固定资产投资在对数线性回归下拟
34、合最好！此时的ARCH检验结果为ARCH Test:F-statistic0.685945Probability0.571103Obs*R-squared2.239024Probability0.524303Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/31/05 Time: 15:24Sample (adjusted): 1981 2004Included observations: 24 after adjustmentsVariableCoefficientStd. Errort-Statist
35、icProb.C0.0060410.0030461.9833330.0612RESID2(-1)0.1732730.2268380.7638640.4539RESID2(-2)-0.0153200.226278-0.0677050.9467RESID2(-3)0.2320250.2256401.0282980.3161R-squared0.093293Mean dependent var0.009341Adjusted R-squared-0.042713S.D. dependent var0.007696S.E. of regression0.007859Akaike info criter
36、ion-6.703393Sum squared resid0.001235Schwarz criterion-6.507051Log likelihood84.44072F-statistic0.685945Durbin-Watson stat1.892617Prob(F-statistic)0.571103其obj*R2=2.239024临界值7.81473。异方差修正！此时模型修正为：LGDP=C+1* LFAI+u二 自相关修正广义差分。此前结论有DW=0.876328，因此计算出估计量为0.561836，从而分别得到GDP和FAI的差分序列，再进行OLS参数估计得到：Dependent Variable: DLGDPMethod: Least SquaresDate: 06/07/05 Time: 02:13Sample (adjusted): 1979 2004Included observations: 26 after adjustmentsVariableCoefficientStd. Errort-StatisticProb
