计量经济学实践报告

1、影响中国食品价格指数的多因素分析摘 要食品价格指数受多种因素的影响，包括粮食价格指数、肉禽及其制品价格指数、水产品价格指数、蔬菜价格指数等等。我们研究影响食品价格指数的因素，要进行多因素分析，进行模型预测，再通过各种方法进行分析、修正，以得到正确结果。关键词：食品价格指数 多因素分析 模型预测 引 言“CPI的走势是由猪决定”。由此说法，我们可以看出猪肉影响食品价格指数。猪肉的价格会首先影响粮食价格指数，粮食价格指数通过影响食品价格指数，进而影响CPI.一、 CPI的基本概念及特点食品价格指数是反映不同时期食品价格水平的变化方向、趋势和程度的经济指标。是经济指数的一种，通常以报告期和基期相对比

2、的相对数来表示。食品价格指数是研究食品价格动态变化的一种工具，它为制定、调整和检查各项经济政策，特别是价格政策提供依据。 食品价格指数是价格指数的一个细分类，价格指数按其所包括范围的不同分为：个体指数，反映某一种商品价格水平升降程度的指数；分类指数，即分类商品价格指数，反映某一类商品价格水平升降程度的指数；总指数，反映全部商品价格总水平升降程度的指数。本文用到的是第二种，分类数据。二、 数据的收集 本文获取了2009年5月份到2011年10月的数据如下表。时间/指标食品价格指数 (本期数)Y粮食价格指数 (本期数)X1肉禽及其制品价格指数 (本期数)X2水产品价格指数 (本期数)X3鲜菜价格指

3、数 (本期数)X42009年5月99.35104.9984.53100.86122.242009年6月98.91105.0584.6299.23117.562009年7月98.8105.186.898.2110.12009年8月100.5105.290.598.6121.82009年9月101.5105.593.398.8125.82009年10月101.6106.296.1101.4114.82009年11月103.210798.3103.6123.92009年12月105.3108.698.3105.7136.22010年1月103.7109.896.5103.9117.12010年2月1

4、06.2109.698.4108.8125.52010年3月105.2109.297.8106.3118.52010年4月105.9110.798.2105.5124.92010年5月106.1111.5100.8105.6121.32010年6月105.7111.73101.81106.47114.552010年7月106.83111.75104.09107.6122.292010年8月107.5111.95105.43108.52119.242010年9月108.05112.07105.42110.9118.012010年10月110.06112.34106.8111.15130.9520

5、10年11月111.7114.74109.91111.85121.252010年12月109.55115.57110.23110.8994.282011年1月110.34115.08110.88111.07102.012011年2月111114.83113.27109.09106.052011年3月111.71114.99117.27110.19104.282011年4月111.47113.9121.44111.6492.642011年5月111.74112.85124.27112.4592.882011年6月114.44112.41132.26113.9107.322011年7月114.76

6、112.37133.58115.01107.62011年8月113.39112.23129.27114.71100.062011年9月113.42111.93128.39114.1102.112011年10月111.93111.59126.11112.3893.18三、画散点图；观察图形走向，用已有知识估计模型的函数形式（1）食品价格与粮食价格两者关系的散点图如下有散点图得，食品价格与粮食价格在总趋势上呈正相关形态，二者具有相关性2）食品价格与肉禽价格两者关系的散点图如下。由散点图得，食品价格与肉禽价格在一定程度上具有相关性（3）食品价格与水产品价格两者关系的散点图由散点图得，食品价格和水产品

7、价格具有某种程度上的线性相关（4）食品价格与蔬菜价格两者关系的散点图如下由散点图得食品价格和蔬菜价格的相关性较弱四做一个简单的Granger因果检验Pairwise Granger Causality TestsDate: 06/07/12 Time: 16:55Sample: 1 30Lags: 1 Null Hypothesis:ObsF-StatisticProb.  Y does not Granger Cause X1 29 0.002110.9637 X1 does not Granger Cause Y 1.2

8、36190.2764Granger检验结果显示：粮食价格是自变量，食品价格是因变量Pairwise Granger Causality TestsDate: 06/07/12 Time: 16:56Sample: 1 30Lags: 1 Null Hypothesis:ObsF-StatisticProb.  Y does not Granger Cause X2 29 0.004620.9463 X2 does not Granger Cause Y 0.862200.3617Granger 检验结果显示：肉禽价格是自变量

9、，粮食价格是因变量Pairwise Granger Causality TestsDate: 06/07/12 Time: 16:56Sample: 1 30Lags: 1 Null Hypothesis:ObsF-StatisticProb.  Y does not Granger Cause X3 29 3.701220.0654 X3 does not Granger Cause Y 0.140600.7107Granger检验结果显示，水产品价格为因变量，食品价格是自变量，不具有现实经济意义。Pairwise Gra

10、nger Causality TestsDate: 06/07/12 Time: 16:57Sample: 1 30Lags: 1 Null Hypothesis:ObsF-StatisticProb.  Y does not Granger Cause X4 29 9.119850.0056 X4 does not Granger Cause Y 3.586440.0694Granger检验结果显示，应剔除XX六、选择模型形式，做回归；描绘模型；Dependent Variable: YMethod: Least Squa

11、resDate: 06/07/12 Time: 17:00Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C22.741766.0312983.7706250.0008X10.5415970.0640788.4521270.0000X20.2306320.01500915.365880.0000R-squared0.974958    Mean dependent var107.3283Adjusted R-squa

12、red0.973103    S.D. dependent var4.836987S.E. of regression0.793275    Akaike info criterion2.469346Sum squared resid16.99071    Schwarz criterion2.609466Log likelihood-34.04020    Hannan-Quinn criter.2.514172F-statistic

13、525.6009    Durbin-Watson stat1.630012Prob(F-statistic)0.000000=22.74176+0.541597X+0.23.632XR2=0.974958 Se=0.793275 DW=1.630012 F=525.6009 n=30七，做随机误差项的正态性检验（JB检验）由jb检验，probability=0.368741>0.05，所以随即误差项是正态分布的八、Ramsey reset testRamsey RESET Test:F-statistic1.309491  &

14、#160; Prob. F(1,26)0.2629Log likelihood ratio1.474133    Prob. Chi-Square(1)0.2247Test Equation:Dependent Variable: YMethod: Least SquaresDate: 06/07/12 Time: 17:11Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-45.9902660.3617

15、5-0.7619110.4530X11.7952841.0974151.6359210.1139X20.8063660.5033401.6020290.1212FITTED2-0.0113970.009960-1.1443300.2629R-squared0.976159    Mean dependent var107.3283Adjusted R-squared0.973408    S.D. dependent var4.836987S.E. of regression0.788767  

16、  Akaike info criterion2.486875Sum squared resid16.17600    Schwarz criterion2.673702Log likelihood-33.30313    Hannan-Quinn criter.2.546643F-statistic354.8536    Durbin-Watson stat1.669505Prob(F-statistic)0.000000由输出结果知，Prob. F=0

17、.2629>5%，接受该模型，没有被误设九、做T、F检验Dependent Variable: YMethod: Least SquaresDate: 06/07/12 Time: 17:14Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C22.741766.0312983.7706250.0008X10.5415970.0640788.4521270.0000X20.2306320.01500915.365880.0000R-squared0.9

18、74958    Mean dependent var107.3283Adjusted R-squared0.973103    S.D. dependent var4.836987S.E. of regression0.793275    Akaike info criterion2.469346Sum squared resid16.99071    Schwarz criterion2.609466Log likelihood-3

19、4.04020    Hannan-Quinn criter.2.514172F-statistic525.6009    Durbin-Watson stat1.630012Prob(F-statistic)0.000000由输出结果知，t-statistic的绝对值均大于2，p小于5%，说明通过t检验。Prob(F-statistic)的可能性为0，表示通过f检验。R-squared为0.974958说明拟合度较好十、Wald TestWald Test:Equation: UntitledTest Stati

20、sticValue  df    ProbabilityF-statistic17.68396(1, 27)  0.0003Chi-square17.683961  0.0000Null Hypothesis Summary:Normalized Restriction (= 0)Value  Std. Err.-1 + C(2) + C(3)-0.2277710.054164Restrictions are linear in coefficients.结论：由输出结果可知

21、，回归系数间的关系是C(2)+(3)=1，Prob(F-statistic)=0.1981其p值远大于5%，所以接受约束条件。十二、邹氏突变检验数据平稳，无突变点十三、模型的比较法之一：观察AIC和SC值的变化Dependent Variable: YMethod: Least SquaresDate: 06/07/12 Time: 17:32Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C19.917048.9840952.2169220.0356X1

22、0.5051500.1068964.7256370.0001X20.3520050.2828441.2445220.2244X22-0.0005260.001224-0.4297440.6709R-squared0.975135    Mean dependent var107.3283Adjusted R-squared0.972266    S.D. dependent var4.836987S.E. of regression0.805531    Akaike inf

23、o criterion2.528935Sum squared resid16.87087    Schwarz criterion2.715761Log likelihood-33.93403    Hannan-Quinn criter.2.588702F-statistic339.8811    Durbin-Watson stat1.625123Prob(F-statistic)0.000000十四异方差检验通过散点图可以发现没有异方差十五WHITE检验Heterosk

24、edasticity Test: WhiteF-statistic0.862220    Prob. F(5,24)0.5205Obs*R-squared4.568278    Prob. Chi-Square(5)0.4708Scaled explained SS3.515435    Prob. Chi-Square(5)0.6211Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/

25、07/12 Time: 17:40Sample: 1 30Included observations: 30BPGVariableCoefficientStd. Errort-StatisticProb.  C-114.6269324.8008-0.3529150.7272X12.0180707.2519020.2782810.7832X12-0.0093500.040669-0.2299060.8201X1*X20.0011970.0188810.0633830.9500X20.0062781.7149760.0036610.9971X22-0.0007220.00229

26、6-0.3146460.7557R-squared0.152276    Mean dependent var0.566357Adjusted R-squared-0.024333    S.D. dependent var0.794031S.E. of regression0.803634    Akaike info criterion2.577511Sum squared resid15.49986    Schwarz crit

27、erion2.857750Log likelihood-32.66266    Hannan-Quinn criter.2.667162F-statistic0.862220    Durbin-Watson stat1.627086Prob(F-statistic)0.520502 结论：Obs*R-squared=4.5682785.991所以不存在异方差十六BPG检验Heteroskedasticity Test: Breusch-Pagan-GodfreyF-statistic1.999224 &

28、#160;  Prob. F(2,27)0.1550Obs*R-squared3.869659    Prob. Chi-Square(2)0.1444Scaled explained SS2.977826    Prob. Chi-Square(2)0.2256Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/07/12 Time: 17:48Sample: 1 30Included observatio

29、ns: 30VariableCoefficientStd. Errort-StatisticProb.  C-10.277005.839203-1.7600000.0897X10.1216870.0620371.9615160.0602X2-0.0245880.014531-1.6920820.1021R-squared0.128989    Mean dependent var0.566357Adjusted R-squared0.064469    S.D. dependent var0.7

30、94031S.E. of regression0.768010    Akaike info criterion2.404611Sum squared resid15.92565    Schwarz criterion2.544730Log likelihood-33.06916    Hannan-Quinn criter.2.449436F-statistic1.999224    Durbin-Watson stat1.6349

31、06Prob(F-statistic)0.154996十七、自相关的检验DW检验Dependent Variable: YMethod: Least SquaresDate: 06/07/12 Time: 17:50Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C22.741766.0312983.7706250.0008X10.5415970.0640788.4521270.0000X20.2306320.01500915.365880.0000R-s

32、quared0.974958    Mean dependent var107.3283Adjusted R-squared0.973103    S.D. dependent var4.836987S.E. of regression0.793275    Akaike info criterion2.469346Sum squared resid16.99071    Schwarz criterion2.609466Log lik

33、elihood-34.04020    Hannan-Quinn criter.2.514172F-statistic525.6009    Durbin-Watson stat1.630012Prob(F-statistic)0.000000结论：由DW=1.630012,给定显著性水平=0.05，查Durbin-Watson表，n=30,k(解释变量个数)=2,得下限临界值du =1.57, 4-du=2.43,因为DW统计量为1.630012。du1.6300124-du根据判断区域可知，这时随机误差项不存在

34、自相关LM检验Breusch-Godfrey Serial Correlation LM Test:F-statistic0.869381    Prob. F(2,25)0.4315Obs*R-squared1.950833    Prob. Chi-Square(2)0.3770Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 06/07/12 Time: 18:11Sample: 1 30Included observation

35、s: 30Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.  C-0.5499006.538078-0.0841070.9336X10.0066560.0701770.0948420.9252X2-0.0017780.016218-0.1096290.9136RESID(-1)0.2124670.2008551.0578160.3003RESID(-2)-0.1918060.212061-0.9044830.3744R-squa

36、red0.065028    Mean dependent var-1.10E-14Adjusted R-squared-0.084568    S.D. dependent var0.765432S.E. of regression0.797141    Akaike info criterion2.535441Sum squared resid15.88584    Schwarz criterion2.768974Log like

37、lihood-33.03162    Hannan-Quinn criter.2.610150F-statistic0.434690    Durbin-Watson stat2.005480Prob(F-statistic)0.782249结论：LM=1.9508335.991所以不存在自相关十八，多重共线性的检验YX1X2Y 1.000000 0.869467 0.953258X1 0.869467 1.000000 0.726567X2 0.953258 0.726567 1.000000剔除X1，结果如下：Dependent Variable: YMethod: Least SquaresDate: 06/07/12 Time: 18:45Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C72.846572.08330834.966780.0000X20.3