中国食品价格指数的影响因素分析

1、关键词：食品价格指数 多因素分析 预测模型 模型检测与修正二、模型设定在本文中，我们选取粮食价格指数、肉禽及制品价格指数、水产品价格指数、蔬菜价格指数作为解释变量，选取食品价格指数作为被解释变量，构建多元线性回归模型：y=0+1x1 +2x2 +3x3 +4x4 +i其中：y 食品价格指数 x1 粮食价格指数 x2 肉禽价格指数 x3 水产品价格指数 x4 蔬菜价格指数三、模型的估计与调整通过使用eviews计量经济学分析软件，得到了一下回归分析结果dependent variable: ymethod: least squaresdate: 05/03/14 time: 19:50sampl

2、e: 2014:01 2014:04included observations: 27variablecoefficientstd. errort-statisticprob. c7.2991204.8192871.5145640.1441x10.4531110.0604837.4915000.0000x20.2255630.02100210.740120.0000x30.1764920.0642352.7475760.0118x40.0593710.0123924.7909120.0001r-squared0.990031 mean dependent var108.2515adjusted

3、 r-squared0.988219 s.d. dependent var4.152074s.e. of regression0.450673 akaike info criterion1.409427sum squared resid4.468336 schwarz criterion1.649396log likelihood-14.02726 f-statistic546.2222durbin-watson stat0.901780 prob(f-statistic)0.0000001.多重共线性检验。（1） 直观的来看，x1、x3的相关系数达到了0.80，x2、x3的相关系数达到了0.

4、88。所以可以认为存在较严重的多重共线性。（2） 修正多重共线性现剔除x3进行回归，结果如下：dependent variable: ymethod: least squaresdate: 05/03/14 time: 21:40sample: 2014:01 2014:04included observations: 27variablecoefficientstd. errort-statisticprob. c5.2102285.3941020.9659120.3441x10.5787620.04486712.899600.0000x20.2749320.01232422.308120.

5、0000x40.0758200.0122986.1650940.0000r-squared0.986610 mean dependent var108.2515adjusted r-squared0.984864 s.d. dependent var4.152074s.e. of regression0.510823 akaike info criterion1.630366sum squared resid6.001621 schwarz criterion1.822342log likelihood-18.00994 f-statistic564.9205durbin-watson sta

6、t0.921999 prob(f-statistic)0.000000由上图可看出，剔除x3后，拟合优度非常好，且显著性明显。再剔除x1进行回归，结果入下：dependent variable: ymethod: least squaresdate: 05/03/14 time: 21:43sample: 2014:01 2014:04included observations: 27variablecoefficientstd. errort-statisticprob. c32.394936.3853025.0733580.0000x20.1426790.0329004.3367320.0

7、002x30.5403430.0774786.9741530.0000x40.0144350.0199850.7222650.4774r-squared0.964601 mean dependent var108.2515adjusted r-squared0.959983 s.d. dependent var4.152074s.e. of regression0.830589 akaike info criterion2.602589sum squared resid15.86718 schwarz criterion2.794565log likelihood-31.13496 f-sta

8、tistic208.9094durbin-watson stat1.044482 prob(f-statistic)0.000000由上图可以看出，剔除x1后，导致x4通不过t检验。剔除x2进行回归，结果如下：dependent variable: ymethod: least squaresdate: 05/03/14 time: 21:41sample: 2014:01 2014:04included observations: 27variablecoefficientstd. errort-statisticprob. c16.3409511.595881.4092020.1722x1

9、0.1109050.1256320.8827720.3865x30.7667330.0812689.4346090.0000x4-0.0321650.021984-1.4630590.1570r-squared0.937763 mean dependent var108.2515adjusted r-squared0.929645 s.d. dependent var4.152074s.e. of regression1.101317 akaike info criterion3.166844sum squared resid27.89668 schwarz criterion3.358820

10、log likelihood-38.75239 f-statistic115.5183durbin-watson stat1.495176 prob(f-statistic)0.000000由上图可知，剔除x2后，导致x1，x4都通不过t检验，且可决系数大幅降低。剔除x4进行回归，结果入下：dependent variable: ymethod: least squaresdate: 05/03/14 time: 21:44sample: 2014:01 2014:04included observations: 27variablecoefficientstd. errort-statist

11、icprob. c21.060075.4100843.8927440.0007x10.3128540.0739924.2282150.0003x20.1563630.0213157.3358800.0000x30.3251700.0786274.1355880.0004r-squared0.979631 mean dependent var108.2515adjusted r-squared0.976974 s.d. dependent var4.152074s.e. of regression0.630052 akaike info criterion2.049924sum squared

12、resid9.130200 schwarz criterion2.241900log likelihood-23.67397 f-statistic368.7162durbin-watson stat2.010366 prob(f-statistic)0.000000 由上图可看出，x4的存在不影响本文的分析结果，没必要剔除。所以综上所述，剔除x3，得到一下回归分析结果：dependent variable: ymethod: least squaresdate: 05/31/12 time: 21:40sample: 2014:01 2014:04included observations:

13、 27variablecoefficientstd. errort-statisticprob. c5.2102285.3941020.9659120.3441x10.5787620.04486712.899600.0000x20.2749320.01232422.308120.0000x40.0758200.0122986.1650940.0000r-squared0.986610 mean dependent var108.2515adjusted r-squared0.984864 s.d. dependent var4.152074s.e. of regression0.510823

14、akaike info criterion1.630366sum squared resid6.001621 schwarz criterion1.822342log likelihood-18.00994 f-statistic564.9205durbin-watson stat0.921999 prob(f-statistic)0.000000得到的回归方程为=5.210228+0.578762x1 +0.274932x2 +0.07582x4 (0.965912) (12.8996) (22.3081) (6.165094) r2=0.9866 adjusted r-squared =0

15、.9849 f=564.9205从回归的结果可以得到r2=0.9866，修正的可决系数为0.9849，这说明模型对样本的拟合度非常好。 2.相关性检验从估计的结果可以看出，模型拟合较好，可决系数r²=0.9866，修正的可决系数为0.9849，表明模型在整体上拟合比较好。3.显著性检验（1）对于ß1，t统计量为12.8996。给定=0.05，查t分布表，在自由度为n-4=23下，得临界值t0.025(23)=2.069，因为t>t0.025(23)，所以拒绝原假设h0: ß1=0，表明粮食价格指数对食品价格指数有显著性影响；（2）对于ß2，t统计量

16、为22.3081。给定=0.05，查t分布表，在自由度为n-4=23下，得临界值t0.025(23)= 2.069，因为t>t0.025(23)，所以拒绝原假设h0: ß2=0，表明肉禽价格指数对食品价格指数有显著性影响。（3）对于ß4，t统计量为6.165094。给定=0.05，查t分布表，在自由度为n-4=23下，得临界值t0.025(23)= 2.069，因为t>t0.025(23)，所以拒绝原假设h0: ß4=0，表明蔬菜价格指数对食品价格指数有显著性影响。 （4）对于f=564.9205>f(3,23)=3.03(显著性水平为0.05)

17、，表明模型从整体上看食品价格指数与各解释变量之间线性关系显著。 4序列相关检验（1） 由图可知，存在一阶自相关。（2） 修正：用科克伦-奥克特迭代方程法对模型进行修正，得到如下结果：dependent variable: ymethod: least squaresdate: 05/03/14 time: 13:10sample(adjusted): 2014:01 2014:04included observations: 26 after adjusting endpointsconvergence achieved after 10 iterationsvariablecoefficie

18、ntstd. errort-statisticprob. c5.1691879.8464600.5249790.6051x10.5631620.0877866.4151880.0000x20.2821290.01771215.928550.0000x40.0845860.0103308.1882700.0000ar(1)0.5840820.1869773.1238250.0051r-squared0.989380 mean dependent var108.5496adjusted r-squared0.987357 s.d. dependent var3.928543s.e. of regr

19、ession0.441736 akaike info criterion1.374831sum squared resid4.097737 schwarz criterion1.616772log likelihood-12.87280 f-statistic489.0816durbin-watson stat1.380596 prob(f-statistic)0.000000inverted ar roots .58得到一阶自相关系数估计为0.584082再次检验是否存在自相关：由上图可知，修正后不再存在自相关。综上，本研究模型估计的最终结果为得到的回归方程为=5.1691+0.5631x1

20、 +0.2821x2 +0.0846x4 (0.5250) (6.4152) (15.9286) (8.1883) r2=0.9894 adjusted r-squared =0.9874 f=489.0816经济意义检验：从经济意义上来看,该模型说明了在假定其他变量不变的情况下，粮食价格指数每上升1%，食品价格指数上涨0.5631%；肉禽及制品价格指数每上升1%，食品价格指数上涨0.2821%；蔬菜价格指数每上升1%，食品价格指数上涨0.0846%。由于各变量都通过了检验，所以说明各变量对被解释变量都起到了很好的作用。5因果关系检验对x1，y进行因果关系检验，结果如下：pairwise gr

21、anger causality testsdate: 05/03/14 time: 21:54sample: 2014:01 2014:04lags: 2 null hypothesis:obsf-statisticprobability y does not granger cause x125 1.09403 0.35409 x1 does not granger cause y 2.86637 0.08043由上图可知，选定显著性水平（如10%），0.35>0.1，则在该显著性水平下，接受原假设，表示食品价格指数对粮食价格指数没有影响；0.08<0.1，拒绝原假设，表示粮食价格指数对食品价格指数有显著性的影响。对x2，y进行因果关系检验，结果如下：pairwise granger causality testsdate: 05/03/14 time: 20:32sample: 2014:01 2014:04lags: 1 null hypothesis:obsf-statisticprobability y does not granger cause x226 0.00457 0