北京市城镇居民消费模型

1、北京市城镇居民消北京市城镇居民消费模型一切经济活动的目的都是为了满足人们不断增长的消费需求，消费活动是经济活动的起点，也是经济活动的终点， 是推动经济增长的真正和持久的拉动力，这里仅从一个侧面来说明我国居民的消费行为。1. 模型变量的选择经济社会中，影响消费的因素有很多，如：收入水平、收入分配情况、家庭财产情况、商品价格等等。在我国，国内生产总值是居民消费的重要影响因素，而且居民消费的多少很大程度上取决于居民收入情况，居民的储蓄也直接影响到消费支出。2. 样本数据的及理论模型以t代表年份，c代表北京市城镇居民年人均消费额，y代表市年人均国内生产总值，I代表市城镇人均可支配收入，s代表市城镇居民

2、年人均储蓄余额。（数据来源：北京统计年鉴）消费模型样本数据元年份t居民消费c国内生产总值y可支配收入I储蓄余额s1978359.861290365.4185.81979408.661391414.95204.711980490.441582501.36255.851981511.431558514.14295.311982534.821704561.05352.761983574.061977590.47450.811984666.752308693.7563.861985923.322704907.72720.8219861067.3829551067.52895.6519871147.63

3、3381181.871180.3819881455.5541251436.971393.0819891520.4144991787.082014.3119901646.0548811787.082793.9119911860.1757812040.433658.5719922134.6668052363.684742.9219932939.682403296.046824.3319944134.12102654731.241028819955019.76130735868.3613638.0419965729.45150446885.4818436.7919976531.81167357813

4、.1121439.47利用以上观测值，由此可得该模型的理论方程：C= 3 0+ 3 1Y+ 3 21+ 3 3S+ 1(1)其中，3 i为待估参数，i=0 , 1, 2, 3; 1为随机变量。3. 计量经济模型的参数估计与和检验:A.首先，对(1)由OLS法估计得:Depe ndent VariablesMethod: Least SquaresDate: 5/3/04 Time: 19:27Sample: 1978 1997In cluded observati ons: 20VariableCoefficie ntStd. Errort-StatisticProb.C0-6.3273993

5、3.77952-0.1873150.8538Y0.0539610.0312841.7248970.1038I0.8579750.0919149.3345240.0000S-0.0510410.015858-3.2185600.0054R-squared0.999433Mean depe ndent var1982.795Adjusted R-squared0.999327S.D.dependent var1893.425S.E. of regressi on49.12271Akaike info criteri on10.80338Sum squared resid38608.65Schwar

6、z criteri on11.00252Log likelihood-104.0338F-statistic9404.109Durbi n- Watson stat2.375901Prob(F-statistic)0.000000查表知t 0.01 ( 16) =2.583 , F0.01 (3, 16) =5.29 ,常数项与变量y的系数不能通过t检验。 去掉变量Y，修正模型如下：C= 3 0+ 3 2I+ 3 3S+i(2)再次用OLS估计得：Depe ndent Variable: CMethod: Least SquaresDate: 5/3/04 Time: 19:31Sample:

7、 1978 1997In cluded observati ons: 20VariableCoefficie ntStd. Errort-StatisticProb.C021.5087031.352010.6860390.5019I0.9998670.04332123.080570.0000S-0.0617250.015424-4.0019460.0009R-squared0.999328Mea n depe ndent var1982.795Adjusted R-squared0.999249S.D.dependent var1893.425S.E. of regressi on51.898

8、14Akaike info criteri on10.87392Sum squared resid45788.10Schwarz criteri on11.02328Log likelihood-105.7392F-statistic12636.42Durb in -Watson stat2.321029Prob(F-statistic)0.000000查表得：1 0.01 ( 17) =2.567 , Fo.oi (2, 17) =6.11，对模型进行统计检验，只有常数项不能 通过t检验，暂时先不做处理，从经济意义上检验，参数3 2在经济理论中表示边际消费倾向，预期值在0, 1之间，3 2的

9、估计值=0.9999是符合理论预期的。3 3的估计值=-0.0617 ,符号为负，表明居民储蓄增加，会使居民消费额下降，这符合实际生活情况。B随机误差项的序列相关性检验：利用DW佥验，样本容量n=20,解释变量个数k=2 ,可查表得 dl=1.2 , du=1.41，从而(du=1.41 ) (DW=2.32) (4-du=2.59 ),说明模型不存 在一阶自相关性。C.异方差性检验：做三期滞后的ARCH佥验：ARCH Test:F-statistic0.149239Probability0.928330Obs*R-squared0.565983Probability0.904174Test

10、Equati on:Dependent Variable: RESIDA2Method: Least SquaresDate: 5/3/04Time: 19:40Sample(adjusted): 19811997Included observations: 17 after adjusting endpointsVariableCoefficie ntStd. Errort-StatisticProb.C2594.9292062.3701.2582270.2304RESIDA2(-1)0.1416980.2772480.5110900.6179RESIDA2(-2)-0.1367310.27

11、6914-0.4937650.6297RESIDA2(-3)0.0124170.2760580.0449800.9648R-squared0.033293Mean depe ndent var2649.652Adjusted R-squared-0.189793S.D.dependent var6421.104S.E. of regressi on7003.989Akaike info criteri on20.74867Sum squared resid6.38E+08Schwarz criteri on20.94472Log likelihood-172.3637F-statistic0.

12、149239Durb in -Watson stat2.000002Prob(F-statistic)0.928330由 X2 0.05 (3) =7.81 , ( n-p) *r 2 =0.565983 ,故不存在异方差性。D.模型的共线性检验：居民的可支配收入I与居民储蓄余额S间存在相关关系的可能性不能被排除。下面采用一阶差分法消除共线性。将模型化为差分模型： Ct= 3 2A It+ 3 3 St(3)进行OLS估计得到Depe nde nt Variable: DCMethod: Least SquaresDate: 5/3/04 Time: 20:36Sample(adjusted)

13、: 1979 1997In eluded observati ons: 19 after adjusti ng en dpo intsVariableCoefficie ntStd. Errort-StatisticProb.DI0.8846330.0968219.1367920.0000DS-0.0274690.031363-0.8758250.3933R-squared0.958312Mean depe ndent var324.8395Adjusted R-squared0.955860S.D.dependent var361.3966S.E. of regressi on75.9278

14、7Akaike info criteri on11.59675Sum squared resid98005.70Schwarz criteri on11.69616Log likelihood-108.1691Durbi n- Watson stat3.042976 St的系数不能通过t检验，所以将模型(2)中的储蓄变量s删除，得到:C= 3 0+3 2I(4)进行OLS估计得到：Depe ndent Variable: YMethod: Least SquaresDate: 5/3/04 Time: 20:38Sample: 1978 1997In cluded observati ons:

15、 20VariableCoefficie ntStd. Errort-StatisticProb.C128.302322.288345.7564730.0000I0.8277570.007054117.34540.0000R-squared0.998695Mean depe ndent var1982.795Adjusted R-squared0.998622S.D.dependent var1893.425S.E. of regressi on70.28700Akaike info criteri on11.43769Sum squared resid88924.72Schwarz crit

16、eri on11.53726Log likelihood-112.3769F-statistic13769.95Durb in -Watson stat1.193999Prob(F-statistic)0.000000=故该这便是西方经济学中绝对收入假说下的消费函数模型。该模型的各项检测指标都显著，模型也可行。4联系实际但若考虑到1989年前后，我国的经济发生了很大的变化，会影响居民消费行为，仍可将模 型进一步改进。1989年以前，我国经济处于低产出、低消费的状态，市场上商品极为短缺，居民消费普遍不足，1989年以后，人们的可支配收入大幅度提高，消费水平也有所提高。所以考虑将19781997年

17、分为两个时期：19781988 , 19891997，分阶段建模：(! ) 19781988 年： C= 3 2I 做 OLS估计得到：Depe ndent Variable: CMethod: Least SquaresDate: 5/3/04 Time: 20:41Sample: 1978 1988In eluded observati ons: 11VariableCoeffieie ntStd. Errort-StatistieProb.I0.9926400.006624149.85440.0000R-squared0.997432Mean depe ndent var739.9882

18、Adjusted R-squared0.997432S.D.dependent var355.3521S.E. of regressi on18.00874Akaike info eriteri on8.706099Sum squared resid3243.146Schwarz eriteri on8.742272Log likelihood-46.88355Durbi n- Watson stat2.183329 (2) 19891997 年：C= 3 o+3 2I做 OLS估计得到:Method: Least SquaresCDate: 5/3/04 Time: 20:48Sample: 1989 1997In eluded observati ons: 9VariableCoeffieie ntStd. Errort-StatistieProb.C186.527750.252463.7118120.0075I0.8158390.01087275.039720.0000R-squared0.998758Mean depe ndent var3501.781Adjusted R-squared0.998581S.D.dependent var1907.132S.E. of regressi on71.83974Akaike in