消费与收入关系的实证研究.doc

消费与收入关系的实证研究学号：081015027 姓名：徐晔摘要：消费总量与收入的关系是个长期争论的话题。本文以中国城镇居民为研究对象，用数据说话，对其消费总量与收入的关系进行了实证研究，得到结论：凯恩斯理论中的基本消费(截距项)不明显，消费基本上与收入成正比；当期消费与前期随机项高度正相关，消费存在明显的惯性。关键词：消费 收入 自相关消费是宏观经济活动中必不可少的一个环节。研究消费总量变动的规律，对预测宏观经济走向，从而制定财政与货币政策，有重要的意义。拉动消费可以促进我国经济增长，且有助于解决经济体中因为长期依赖投资和出口来推动经济增长而累积下的一些矛盾，对于实现我国经济的持续发展和健康稳定有十分重大的意义。作为宏观变量的消费总量，主要受着国民可支配收入的影响，但关于这种影响的持久性与稳定性，不同的经济学家有着不同的看法。本文拟用数据说话，以中国城镇居民为研究对象，研究他们的消费规律。一、理论简述消费理论的著作很多，其中比较经典的有凯恩斯的消费行为函数、杜森伯瑞的相对收入假说、弗里德曼的持久收入假说和莫迪格里安尼等人的生命周期假说。这些理论有着不同的假设，从而推导出了不同的消费关于收入的函数。凯恩斯消费函数为：(1)杜森伯瑞消费函数为：(2)其中Gy表示稳定的收入增长率。适应预期的弗里德曼消费函数为：(3)其中(4)r表示利率，q表示效用贴现率。莫迪格里安尼的消费函数为：(5)各理论虽然对参数之间的关系有着不同的要求，但它们却可以用一个统一的形式概括：(6)实际应用中，对函数究竟取何种形式，应该根据数据反映的具体情况，来进行判断和验证。二、数据选取本文采用的数据为中国城镇居民人均消费性支出和中国城镇居民人均可支配收入的年度数据，从首次有该项年度统计的1990年起，至已公布的最新一期2007年止，共18组数据。数据均来自中国统计年鉴。三、普通最小二乘法回归分析首先假设城镇居民人均消费ct只与当期城镇居民人均收入yt有关，做最小二乘回归，结果如下：表1 OLS输出结果Dependent Variable: CONSMethod: Least SquaresDate: 07/02/09 Time: 20:57Sample: 1990 2007Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C198.737170.001392.8390440.0118YIELD0.5085570.00987251.514670.0000R-squared0.994007Mean dependent var3353.111Adjusted R-squared0.993632S.D. dependent var1803.609S.E. of regression143.9232Akaike info criterion12.88088Sum squared resid331422.0Schwarz criterion12.97981Log likelihood-113.9279F-statistic2653.761Durbin-Watson stat0.301235Prob(F-statistic)0.000000估计所得方程为：ct = 198.7371 - 0.508557 * yt + u(7)( 2.839044 ) ( 51.51467 )四、参数检验对方程各参数做t检验，从表1中可以看到，t指标的p值均小于0.05，拒绝参数零假设，认为各参数均显著。且从表5中可以看到，F指标的p值远小于0.05，拒绝参数全零假设，认为方程显著。检验方程的判定系数R2为0.994007，即收入的变化可以解释消费总量变动的99.4%。再尝试对滞后一期的方程进行回归：(8)表2 滞后一期OLS输出结果Dependent Variable: CONSMethod: Least SquaresDate: 07/03/09 Time: 20:31Sample (adjusted): 1991 2007Included observations: 17 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C237.788356.408804.2154460.0009YIELD0.1715030.0914481.8754120.0817YIELD(-1)0.3739170.1021513.6604480.0026R-squared0.996738Mean dependent var3501.353Adjusted R-squared0.996272S.D. dependent var1742.422S.E. of regression106.3935Akaike info criterion12.33095Sum squared resid158474.2Schwarz criterion12.47799Log likelihood-101.8131F-statistic2138.686Durbin-Watson stat0.539250Prob(F-statistic)0.000000滞后一期收入yt-1的引入使得yt变得不显著(t检验p值大于0.05)，故认为滞后效应不存在。五、残差分析与异常现象检验做出残差序列图：表3 残差列表与残差序列图从图中可以看出，没有残差超过标准差的两倍，认为没有异常值存在。残差序列有较大的连贯性，怀疑有误差序列相关，以下将做进一步的检验。五、误差序列相关检验与克服对无滞后方程做杜宾-瓦森检验，其中(9)如表1所示，DW值为0.301235，查表可知显著性水平为0.05时的临界值为下确界dl=1.16，上确界du=1.39，DWdl。因此，方程存在序列正相关。为了克服误差序列相关问题，考虑引入AR(1)项来改善回归效果，回归结果如下：表4 引入AR(1)后的回归结果Dependent Variable: CONSMethod: Least SquaresDate: 07/02/09 Time: 20:58Sample (adjusted): 1991 2007Included observations: 17 after adjustmentsConvergence achieved after 6 iterationsVariableCoefficientStd. Errort-StatisticProb.C523.2396327.81041.5961650.1328YIELD0.4781030.02378420.101880.0000AR(1)0.8425880.1166397.2239070.0000R-squared0.998350Mean dependent var3501.353Adjusted R-squared0.998115S.D. dependent var1742.422S.E. of regression75.65417Akaike info criterion11.64901Sum squared resid80129.76Schwarz criterion11.79605Log likelihood-96.01656F-statistic4236.565Durbin-Watson stat1.159398Prob(F-statistic)0.000000Inverted AR Roots.84从表4中可以看到，F统计量显著，yt和ut-1项的t统计量显著，但常数项的t统计量不显著。因此考虑使用无常数项和带AR(1)的方程进行回归。结果如下：表5 无常数项和带AR(1)的回归结果Dependent Variable: CONSMethod: Least SquaresDate: 07/02/09 Time: 20:58Sample (adjusted): 1991 2007Included observations: 17 after adjustmentsConvergence achieved after 6 iterationsVariableCoefficientStd. Errort-StatisticProb.YIELD0.5026660.02711218.540500.0000AR(1)0.9691640.1011059.5856970.0000R-squared0.998000Mean dependent var3501.353Adjusted R-squared0.997867S.D. dependent var1742.422S.E. of regression80.47031Akaike info criterion11.72378Sum squared resid97132.05Schwarz criterion11.82181Log likelihood-97.65217Durbin-Watson stat1.118406Inverted AR Roots.97ct = 0.502666 * yt + 0.969164 * ut-1 + ut(10)( 18.54050 ) ( 9.585697 )从表5中可以看到，F统计量显著，yt和ut-1项的t统计量显著。对方程使用拉格朗日乘子法进行检验，结果如下：表6 序列相关拉格朗日乘子法检验输出结果Breusch-Godfrey Serial Correlation LM Test:F-statistic2.404420Probability0.129271Obs*R-squared4.271539Probability0.118154Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 07/03/09 Time: 21:06Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.YIELD0.0019180.0277640.0690800.9460AR(1)-0.0209670.113683-0.1844360.8565RESID(-1)0.5900540.2712452.1753530.0486RESID(-2)-0.2888350.305370-0.9458520.3615R-squared0.251267Mean dependent var11.96443Adjusted R-squared0.078482S.D. dependent var76.93282S.E. of regression73.85220Akaike info criterion11.64433Sum squared resid70903.92Schwarz criterion11.84038Log likelihood-94.97683Durbin-Watson stat1.831378从表6中可知，由F检验和TR2统计量的c2检验得出的p值都大于0.05，接受误差自相关不显著的原假设，认为不存在误差序列相关。因此，(10)式克服了误差序列相关的问题。六、异方差检验异方差问题可使参数检验变得无效。为检验模型是否存在异方差问题，对方程做不含交叉项的怀特检验，方程为e2 = c + b1 *yt + b2 * yt2 + u(11)以下为EViews的输出结果：表7 怀特检验输出结果White Heteroskedasticity Test:F-statistic1.064141Probability0.371347Obs*R-squared2.243313Probability0.325740Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 07/03/09 Time: 21:11Sample: 1991 2007Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-4917.4609286.111-0.5295500.6047YIELD3.8446912.8165631.3650290.1938YIELD2-0.0002690.000186-1.4489170.1694R-squared0.131960Mean dependent var5713.650Adjusted R-squared0.007954S.D. dependent var9389.178S.E. of regression9351.764Akaike info criterion21.28330Sum squared resid1.22E+09Schwarz criterion21.43034Log likelihood-177.9081F-statistic1.064141Durbin-Watson stat1.939718Prob(F-statistic)0.371347从表7中可知，由F检验和TR2统计量的c2检验得出的p值都大于0.05，接受怀特检验方程不显著的原假设，认为不存在异方差。七、条件异方差检验为检验模型是否存在条件异方差问题，对方程进行广义条件异方差(GARCH)检验，方程为ht = c + b1 * ut-12 + b2 * ht-1(12)其中ht为GARCH项。表8 GARCH(1,1)模型输出结果Dependent Variable: CONSMethod: ML - ARCH (Marquardt) - Normal distributionDate: 07/03/09 Time: 21:15Sample (adjusted): 1991 2007Included observations: 17 after adjustmentsFailure to improve Likelihood after 41 iterationsVariance backcast: ONGARCH = C(3) + C(4)*RESID(-1)2 + C(5)*GARCH(-1)CoefficientStd. Errorz-StatisticProb.YIELD0.4429930.1806652.4520100.0142AR(1)1.1218680.07170715.645250.0000Variance EquationC18960.9612699.191.4930840.1354RESID(-1)20.3394620.3022421.1231450.2614GARCH(-1)-0.9353960.134416-6.9589450.0000R-squared0.997175Mean dependent var3501.353Adjusted R-squared0.996233S.D. dependent var1742.422S.E. of regression106.9363Akaike info criterion12.06536Sum squared resid137224.4Schwarz criterion12.31043Log likelihood-97.55560Durbin-Watson stat0.851375Inverted AR Roots1.12Estimated AR process is nonstationary对此方程做ARCH拉格朗日乘子检验，结果如下：表9 ARCH LM检验输出结果ARCH Test:F-statistic0.347736Probability0.564794Obs*R-squared0.387781Probability0.533468Test Equation:Dependent Variable: STD_RESID2Method: Least SquaresDate: 07/03/09 Time: 21:24Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.6132040.3337501.8373160.0875STD_RESID2(-1)0.1552010.2631900.5896910.5648R-squared0.024236Mean dependent var0.724955Adjusted R-squared-0.045461S.D. dependent var1.074756S.E. of regression1.098914Akaike info criterion3.142991Sum squared resid16.90658Schwarz criterion3.239565Log likelihood-23.14393F-statistic0.347736Durbin-Watson stat1.990052Prob(F-statistic)0.564794从表9中可知，由F检验和TR2统计量的c2检验得出的p值都大于0.05，接受条件异方差不显著的原假设，认为不存在条件异方差。八、单整和协整检验为了建立误差修正模型，下面将验证各变量的一阶单整和所有变量的协整(即长期方程中残差的零阶单整)，方法是扩展的迪基-富勒(ADF)检验。表10 yt的I(0)检验Null Hypothesis: YIELD has a unit rootExogenous: ConstantLag Length: 1 (Automatic based on SIC, MAXLAG=3)t-StatisticProb.*Augmented Dickey-Fuller test statistic1.2543870.9969Test critical values:1% level-3.9203505% level-3.06558510% level-2.673459*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20observations and may not be accurate for a sample size of 16Augmented Dickey-Fuller Test EquationDependent Variable: D(YIELD)Method: Least SquaresDate: 07/03/09 Time: 21:31Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.YIELD(-1)0.0388420.0309651.2543870.2318D(YIELD(-1)0.9311000.2926203.1819450.0072C-75.01795148.8930-0.5038380.6228R-squared0.746178Mean dependent var755.3256Adjusted R-squared0.707129S.D. dependent var446.5194S.E. of regression241.6456Akaike info criterion13.98018Sum squared resid759103.5Schwarz criterion14.12504Log likelihood-108.8415F-statistic19.10851Durbin-Watson stat1.174416Prob(F-statistic)0.000135由t检验p值可知，y不平稳。因此再做Dy的ADF检验：表11 yt的I(1)检验Null Hypothesis: D(YIELD) has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=3)t-StatisticProb.*Augmented Dickey-Fuller test statistic0.9926350.9940Test critical values:1% level-3.9203505% level-3.06558510% level-2.673459*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20observations and may not be accurate for a sample size of 16Augmented Dickey-Fuller Test EquationDependent Variable: D(YIELD,2)Method: Least SquaresDate: 07/03/09 Time: 21:37Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(YIELD(-1)0.2009200.2024110.9926350.3377C-13.95735143.5642-0.0972200.9239R-squared0.065753Mean dependent var114.7475Adjusted R-squared-0.000979S.D. dependent var246.4246S.E. of regression246.5452Akaike info criterion13.96944Sum squared resid850983.5Schwarz criterion14.06601Log likelihood-109.7555F-statistic0.985325Durbin-Watson stat1.219167Prob(F-statistic)0.337735由t检验p值可知，Dy仍然不平稳。因此再做D2y的ADF检验：表12 yt的I(2)检验Null Hypothesis: D(YIELD,2) has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=3)t-StatisticProb.*Augmented Dickey-Fuller test statistic-1.3896700.5588Test critical values:1% level-3.9591485% level-3.08100210% level-2.681330*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20observations and may not be accurate for a sample size of 15Augmented Dickey-Fuller Test EquationDependent Variable: D(YIELD,3)Method: Least SquaresDate: 07/03/09 Time: 21:40Sample (adjusted): 1993 2007Included observations: 15 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(YIELD(-1),2)-0.5029600.361928-1.3896700.1880C77.7013468.930181.1272470.2800R-squared0.129339Mean dependent var41.62067Adjusted R-squared0.062365S.D. dependent var255.3955S.E. of regression247.3035Akaike info criterion13.98268Sum squared resid795067.0Schwarz criterion14.07708Log likelihood-102.8701F-statistic1.931182Durbin-Watson stat1.509743Prob(F-statistic)0.187970由t检验p值可知，D2y仍然不平稳。因此再做D3y的ADF检验：表13 yt的I(3)检验Null Hypothesis: D(DY,2) has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=3)t-StatisticProb.*Augmented Dickey-Fuller test statistic-3.4495290.0270Test critical values:1% level-4.0044255% level-3.09889610% level-2.690439*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20observations and may not be accurate for a sample size of 14Augmented Dickey-Fuller Test EquationDependent Variable: D(DY,3)Method: Least SquaresDate: 07/03/09 Time: 21:43Sample (adjusted): 1994 2007Included observations: 14 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(DY(-1),2)-1.1918370.345507-3.4495290.0048C39.0369072.715240.5368460.6012R-squared0.497892Mean dependent var33.97500Adjusted R-squared0.456050S.D. dependent var368.8260S.E. of regression272.0201Akaike info criterion14.18119Sum squared resid887939.3Schwarz criterion14.27249Log likelihood-97.26835F-statistic11.89925Durbin-Watson stat1.728662Prob(F-statistic)0.004809由t检验p值可知，D3y平稳，故认为y三阶单整。表14 ct的I(0)检验Null Hypothesis: CONS has a unit rootExogenous: ConstantLag Length: 2 (Automatic based on SIC, MAXLAG=3)t-StatisticProb.*Augmented Dickey-Fuller test statistic1.6851120.9989Test critical values:1% level-3.9591485% level-3.08100210% level-2.681330*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20observations and may not be accurate for a sample size of 15Augmented Dickey-Fuller Test EquationDependent Variable: D(CONS)Method: Least SquaresDate: 07/03/09 Time: 21:47Sample (adjusted): 1993 2007Included observations: 15 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.CONS(-1)0.0427770.0253851.6851120.1201D(CONS(-1)1.3947340.3097244.5031450.0009D(CONS(-2)-0.6696190.333625-2.0071020.0699C-24.0955290.63932-0.2658400.7953R-squared0.770618Mean dependent var397.6667Adjusted R-squared0.708059S.D. dependent var218.0559S.E. of regression117.8190Akaike info criterion12.59936Sum squared resid152694.6Schwarz criterion12.78817Log likelihood-90.49517F-statistic12.31829Durbin-Watson stat1.637143Prob(F-statistic)0.000770由t检验p值可知，c不平稳。因此再做Dc的ADF检验：表15 ct的I(1)检验Null Hypothesis: D(CONS) has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=3)t-StatisticProb.*Augmented Dickey-Fuller test statistic0.4251530.9773Test critical values:1% level-3.9203505% level-3.06558510% level-2.673459*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20observations and may not be accurate for a sample size of 16Augmented Dickey-Fuller Test EquationDependent Variable: D(CONS,2)Method: Least SquaresDate: 07/03/09 Time: 21:49Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsVaria