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1、. -中国粮食生产函数模型一、引言根据理论和经历分析,影响粮食生产Y的主要因素有:农业化肥施用量*1、粮食播种面积*2、成灾面积*3、农业机械总动力*4、农业劳动力*5,其中,成灾面积的符号为负,其余均应是正。二、数据来源下表列出了中国粮食生产的相关数据,拟建立中国粮食生产函数。表1 中国粮食生产与相关投入资料年份粮食产量农业化肥施用量粮食播种面积成灾面积农业机械总动力农业劳动力万吨万公斤千公顷公顷万千瓦万人198338728 1660 114047 16209 18022 31151 198440731 1740 112884 15264 19497 30868 198537911 1776
2、 108845 22705 20913 31130 198639151 1931 110933 23656 22950 31254 198740208 1999 111268 20393 24836 31663 198839408 2142 110123 23945 26575 32249 198940755 2357 112205 24449 28067 33225 199044624 2590 113466 17819 28708 38914 199143529 2805 112314 27814 29389 39098 199244266 2930 110560 25893 30308
3、38699 199345649 3152 110509 23134 31817 37680 199444510 3318 109544 31382 33803 36628 199546662 3594 110060 22268 36118 35530 199650454 3828 112548 21234 38547 34820 199749417 3981 112912 30307 42021 34840 199851230 4084 113787 25181 45208 35177 199950839 4124 113161 26734 48996 35768 200046218 4146
4、 108463 34374 52574 36043 200145264 4254 106080 31793 55172 36399 200245706 4339 103891 27160 57930 36640 200343070 4412 99410 32516 60387 36204 200446947 4637 101606 16297 64028 34830 200548402 4766 104278 19966 68398 33442 200649804 4928 104958 24632 72522 31941 200750160 5108 105638 25064 76590 3
5、0731 202152871 5239 106793 22283 82190 29923 202153082 5404 108986 21234 87496 28890 202154648 5562 109876 18538 92780 27931 202157121 5704 110573 12441 97735 26594 202158958 5839 111205 11470 102559 25773 资料来源:中国统计年鉴1995,2021。三、模型设定设粮食生产函数为=四、模型结果与检验1、用普通最小二乘法估计模型运用Eviews软件进展普通最小二乘回归的结果如下:Dependent
6、 Variable: LOG(Y)Method: Least SquaresDate: 03/04/14 Time: 16:55Sample: 1983 2021Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-3.3990261.775984-1.9138830.0676LOG(*1)0.3915560.0499067.8459540.0000LOG(*2)1.1532910.1154179.9923510.0000LOG(*3)-0.0721930.013678-5.2779510.0000LOG
7、(*4)-0.0631700.042789-1.4763030.1529LOG(*5)-0.0992370.055146-1.7995200.0845R-squared0.987725Mean dependent var10.74426Adjusted R-squared0.985168S.D. dependent var0.118062S.E. of regression0.014378Akaike info criterion-5.469319Sum squared resid0.004962Schwarz criterion-5.189079Log likelihood88.03978H
8、annan-Quinn criter.-5.379668F-statistic386.2468Durbin-Watson stat1.842639Prob(F-statistic)0.000000因此,估计的方程为)+1.153log(*2)-0.072log(*3)-0.063log(*4)-0.099log(*5)(-1.91) (7.85) (9.99) (-5.28) (-1.48) (-1.79)R2 =0.9877 =0.9852 F=386.25 D.W.=1.84由于R2 较大且接近于1,而且F=386.25变量间总体线性关系显著。但由于其中*4,*5前参数估计值未能通过t检验
9、,而且符号的经济意义也不合理,故认为解释变量间存在多重共线性。2、 检验简单相关系数log(*1),log(*2),log(*3),log(*4),log(*5)的相关系数如下表所示。表2 相关系数表LOG(*1)LOG(*2)LOG(*3)LOG(*4)LOG(*5)LOG(*1)1.000000-0.456032-0.0052880.966390-0.199163LOG(*2)-0.4560321.000000-0.228430-0.497507-0.052864LOG(*3)-0.005288-0.2284301.000000-0.1330510.657544LOG(*4)0.96639
10、0-0.497507-0.1330511.000000-0.393070LOG(*5)-0.199163-0.0528640.657544-0.3930701.000000由表中数据发现log*1与log*2间存在高度相关性。3、 找出最简单的回归形式分别作log(Y)与log(*1),log*2,log*3,log*4间的回归:1用Eviews作log(Y)与log(*1)间的回归结果如下:Dependent Variable: LOG(Y)Method: Least SquaresDate: 03/04/14 Time: 17:51Sample: 1983 2021Included obs
11、ervations: 30VariableCoefficientStd. Errort-StatisticProb.C8.5405970.20077042.539110.0000LOG(*1)0.2700810.02457910.988390.0000R-squared0.811758Mean dependent var10.74426Adjusted R-squared0.805035S.D. dependent var0.118062S.E. of regression0.052130Akaike info criterion-3.005801Sum squared resid0.0760
12、92Schwarz criterion-2.912388Log likelihood47.08701Hannan-Quinn criter.-2.975917F-statistic120.7447Durbin-Watson stat0.641647Prob(F-statistic)0.000000log=8.541+0.270log*1(42.54) (10.99) R2 =0.8118 D.W.=0.6416(2) 用Eviews作log(Y)与log(*2)间的回归结果如下:Dependent Variable: LOG(Y)Method: Least SquaresDate: 03/04/14 Time: 17:59Sample: 198