我国粮食生产与相关投入计量经济学模型分析

1、我国粮食生产与相关投入计量经济学模型分析一， 引言著名经济学家李子奈教授在曾对我国19831995年粮食生产数据进行过研究分析,他选取的影响因素数据是:农用化肥施用量,粮食播种面积,成灾面积,农业机械动力和农业劳力,并拟合出了关于我国粮食生产的线性回归模型.在本文中,我们将运用计量经济学的方法对上述模型问题进行研究.对于粮食产量的影响,除了选取上述影响因素外,还把农村用电量、国家财政用于农业的支出和灌溉面积的影响因素数据也加到了模型中去.二，变量的确定与C-D生产函数模型i. 被解释变量与解释变量的确定最终确定的模型的被解释变量为:粮食总产量;解释变量为:播种面积、成灾面积、化肥施用量、农业机

2、械动力、国家财政用于农业的支出、灌溉面积和农业劳动力.由初步的分析知,粮食产量与成灾面积是负相关的,而与其它变量则是正相关的.ii. C-D生产函数模型我们选择在经济领域应用最广泛的一种生产函数模型C-D生产函数模型来进行研究.即Y=f(A,K,L,)其中Y为产出量,A,K,L分别为技术、资本、劳动的投入要素.生产要素对生产函数的作用与影响,主要是由一定的技术条件决定的,从本质上讲,生产函数反映了生产过程中投入要素与产出量之间的技术关系.2数据收集根据上面的所确定的模型的变量,我们收集到了1980年2004年主要粮食生产数据(表一)。iii. 模型的估计 设定:粮食总产量为Y播种面积为X1成灾

3、面积为X2,化肥施用量为X3,灌溉面积为X4,国家财政用于农业资金为X5,农机动力为X6,农村劳动力为X7.由C-D生产函数模型,得模型形式如下:Yt=AXitbit(i=1,2,7)(1)两边取对数并进行变换,得:log Yt =b0+bilogXit+t(i=1,2,7)(2)其中b0=logA,t=logt.运用Eviews软件对模型(2)进行OLS估计,我们得到估计结果Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/10/09 Time: 03:55Sample: 1980 2004Included observation

4、s: 25VariableCoefficientStd. Errort-StatisticProb. C3.3758955.5021110.6135640.5476LOG(X1)0.9587450.2795123.4300650.0032LOG(X2)-0.1037040.040353-2.5699500.0199LOG(X3)0.4948670.1044504.7378190.0002LOG(X4)-0.5649730.462026-1.2228180.2381LOG(X5)-0.0143810.074375-0.1933540.8490LOG(X6)0.0183880.1192590.15

5、41820.8793LOG(X7)-0.0694990.137533-0.5053240.6198R-squared0.963763 Mean dependent var10.66170Adjusted R-squared0.948842 S.D. dependent var0.127561S.E. of regression0.028852 Akaike info criterion-3.998937Sum squared resid0.014151 Schwarz criterion-3.608897Log likelihood57.98671 F-statistic64.59068Dur

6、bin-Watson stat1.245744 Prob(F-statistic)0.000000从表2可以看出,回归估计的判决系数R2很高,方程很显著,但是8个参数的t检验值中，却只有两个略微显著.显然,出现了严重的多重共线性。iv. 模型的检验1）多重共线性的检验与消除1相关系数法.从各解释变量之间的相关系数(表3)也能初步看出各变量之间存在着多重共线性:检验简单相关系数：2修正的Frish方法.下面我们用修正的Frish方法来消除该模型的多重共线性。首先,做出被解释变量logY关于解释变量logXi的每一个回归方程,得各判决系数R2i依次为:R12=0.098512;R22=0.1546

7、83;R32=0.825167;R42=0.586538;R52=0.629207;R62=0.687181;R72= 0.581854.从上面我们知道判决系数R2最大的为R32,从而可选取X3作为模型的出发点进行估计,Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/10/09 Time: 04:51Sample: 1980 2004Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C8.4718850.21045940.254320.00

8、00LOG(X3)0.2767310.02656010.418940.0000R-squared0.825167 Mean dependent var10.66170Adjusted R-squared0.817566 S.D. dependent var0.127561S.E. of regression0.054484 Akaike info criterion-2.905185Sum squared resid0.068277 Schwarz criterion-2.807675Log likelihood38.31482 F-statistic108.5543Durbin-Watson

9、 stat0.733968 Prob(F-statistic)0.000000在Y, X3中加入解释变量X1进行估计,常数项不显著,在去掉常数项后再一次估计VariableCoefficientStd. Errort-StatisticProb. LOG(X1)0.7044220.01355751.961760.0000LOG(X3)0.3135990.01986815.784330.0000R-squared0.894484 Mean dependent var10.66170Adjusted R-squared0.889897 S.D. dependent var0.127561S.E.

10、of regression0.042327 Akaike info criterion-3.410155Sum squared resid0.041207 Schwarz criterion-3.312645Log likelihood44.62693 Durbin-Watson stat0.783868从结果可以看出在加入解释变量X1之后,其判决系数R2的值有了明显的变化,并且对X3的系数值和t检验值没有多大影响,因此可以加入变量X1.同理,在Y,X1,X3中加入解释变量X2进行估计得常数项不显著,在去掉常数项后,得下表logY对logXt(t=1,2,3)的回归VariableCoeffi

11、cientStd. Errort-StatisticProb. LOG(X1)0.7913390.02214635.732830.0000LOG(X2)-0.1491430.033820-4.4099140.0002LOG(X3)0.3763580.02053218.330150.0000R-squared0.943993 Mean dependent var10.66170Adjusted R-squared0.938901 S.D. dependent var0.127561S.E. of regression0.031531 Akaike info criterion-3.963536S

12、um squared resid0.021872 Schwarz criterion-3.817271Log likelihood52.54420 Durbin-Watson stat0.855241从结果可以看出:在加入变量X2之后,其判决系数R2的值有了明显变化,并且对X1, X3的系数值和t检验值没有多大影响,并且X2的估计系数是负值,符合经济意义,加入变量X2.在Y, X1, X2, X3中加入变量X4进行估计得常数项不显著,去掉常数项后,再一次估计得下表.从结果可以看出加入解释变量X4之后,其判决系数R2的值虽然有变化,但对X2的系数值和t检验值有较大影响,且X4的估计系数是负值,不

13、符合经济意义.它的t检验值也不太显著,因此暂时不考虑加入变量X4VariableCoefficientStd. Errort-StatisticProb. LOG(X1)1.1221880.1135989.8785990.0000LOG(X2)-0.1035570.032933-3.1445050.0049LOG(X3)0.4612170.03372013.677790.0000LOG(X4)-0.4611060.156080-2.9543010.0076R-squared0.960436 Mean dependent var10.66170Adjusted R-squared0.954784

14、 S.D. dependent var0.127561S.E. of regression0.027125 Akaike info criterion-4.231099Sum squared resid0.015451 Schwarz criterion-4.036079Log likelihood56.88874 Durbin-Watson stat0.947940运用同样的方法逐个加入变量X5, X6进行估计知,加入的变量对表7的判决系数R2没有多大影响,但对t检验值有较大影响,因此暂时不考虑加入上述变量.在Y, X1, X2, X3中加入解释变量X7进行估计得下表：VariableCoe

15、fficientStd. Errort-StatisticProb. C-2.2993632.950548-0.7793000.4449LOG(X1)0.9742660.2277764.2772970.0004LOG(X2)-0.1378920.037783-3.6496210.0016LOG(X3)0.3824680.03317811.527730.0000LOG(X7)0.0012580.1259820.0099840.9921R-squared0.945786 Mean dependent var10.66170Adjusted R-squared0.934943 S.D. depend

16、ent var0.127561S.E. of regression0.032536 Akaike info criterion-3.836071Sum squared resid0.021172 Schwarz criterion-3.592296Log likelihood52.95089 F-statistic87.22663Durbin-Watson stat0.770568 Prob(F-statistic)0.000000从结果可以看出,在加入解释变量X7之后,其判决系数R2的值有较大变化,况且它对其余解释变量的t检验值和系数没有多大影响,因此可以加入该变量.最终,我们确定模型的形式

17、为:log Yt =b0+b1logX1t+ b2logX2t+ b3logX3t + b4logX7t +t从而我们有如下的回归模型:log(Y) =0.974266log(X1) -0.137892log（X2) +0.382468log(X3) +0.001258log(X7)- 2.299363 (0.227776)(0.037783) (0.033178) (0.125982) (2.950548) (4.277297)(-3.649621) (13.67779) （0.009984） (-0.779300)R2=0.945786SE=0.032536DW=0.770568F=87.

18、22663从报告可以看出, X1, X7和常数项的t检验值并不太显著,模型拟合得并不是太好,且常数项为负值,这也不符合经济含义.从DW表中可以看到,对于n=25,k=4,在5%的显著水平下,有dL=0.953和dU=1.886,而表中的DW值仅为d=0.770568,明显比dL值要小,这说明模型存在严重的序列自相关性,这有可能是导致上述t检验值并不显著的重要原因.因此,为了使模型更具有价值,我们首先必须消除模型的自相关.自相关的消除下面试着用迭代法来消除自相关.经过多次反复拟合,得较理想的回归结果 VariableCoefficientStd. Errort-StatisticProb. LO

19、G(X1)0.8038200.02386433.683510.0000LOG(X2)-0.1085590.033016-3.2880490.0041LOG(X3)0.2821770.0356007.9263580.0000Y(-1)5.78E-062.66E-062.1725680.0434Y(-2)-1.16E-063.00E-06-0.3879450.7026R-squared0.954228 Mean dependent var10.68601Adjusted R-squared0.944057 S.D. dependent var0.100122S.E. of regression0.

20、023681 Akaike info criterion-4.458614Sum squared resid0.010094 Schwarz criterion-4.211767Log likelihood56.27406 Durbin-Watson stat1.415754从表可以看出,添入Y(-1)和Y(-2)项后,DW值由0.770568提高到了1.415754,自相关得到了消除,且各统计量均能显著通过.下面再来看表9的异方差检验.异方差的检验采用怀特检验法，辅助回归模型的估计结果如下：White Heteroskedasticity Test:F-statistic6.446908 P

21、robability0.001765Obs*R-squared19.39070 Probability0.035572Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/11/09 Time: 00:44Sample: 1982 2004Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C0.69446510.704310.0648770.9493LOG(X1)0.0163161.8525080.0088080.99

22、31(LOG(X1)2-0.0004920.079981-0.0061570.9952LOG(X2)-0.1222230.043327-2.8209250.0154(LOG(X2)20.0061120.0021352.8630900.0143LOG(X3)-0.0542750.032070-1.6923930.1164(LOG(X3)20.0034750.0020301.7117620.1126Y(-1)-9.25E-075.87E-07-1.5768410.1408Y(-1)28.46E-126.79E-121.2456550.2367Y(-2)1.27E-065.34E-072.38531

23、80.0344Y(-2)2-1.38E-115.88E-12-2.3370470.0376R-squared0.843074 Mean dependent var0.000439Adjusted R-squared0.712302 S.D. dependent var0.000718S.E. of regression0.000385 Akaike info criterion-12.58009Sum squared resid1.78E-06 Schwarz criterion-12.03703Log likelihood155.6710 F-statistic6.446908Durbin-

24、Watson stat2.441613 Prob(F-statistic)0.001765在同方差的条件下：n，h=3,为解释变量的个数从上图可知n19.390702，在显著水平0.05的情况下，7.82，由于n>7.82,故存在异方差性。克服异方差，采用加权最小二乘法（WLS）,以为权数进行WLS估计，得估计结果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/11/09 Time: 01:30Sample(adjusted): 1982 2004Included observations: 23 after adju

25、sting endpointsWeighting series: 1/ABS(RESID)White Heteroskedasticity-Consistent Standard Errors & CovarianceVariableCoefficientStd. Errort-StatisticProb. LOG(X1)0.8102180.004790169.16200.0000LOG(X2)-0.1092530.005836-18.720180.0000LOG(X3)0.2684210.01691515.868420.0000Y(-1)1.020 9920.200 1010.961

26、870.0000Y(-2)-0.498 950.216 003-0.3980640.6953Weighted StatisticsR-squared1.000000 Mean dependent var10.72762Adjusted R-squared1.000000 S.D. dependent var31.92350S.E. of regression0.001570 Akaike info criterion-9.885525Sum squared resid4.44E-05 Schwarz criterion-9.638679Log likelihood118.6835 Durbin

27、-Watson stat1.776039Unweighted StatisticsR-squared0.953685 Mean dependent var10.68601Adjusted R-squared0.943392 S.D. dependent var0.100122S.E. of regression0.023821 Sum squared resid0.010214Durbin-Watson stat1.409905最终拟合的回归方程为log(Y)= 0.810218log(X1)- 0.109253log(X2)+ 0.268421log(X3)(0.004790)(0.0058

28、36) (0.016915) (169.1620)(-18.72018) (15.86842)+1.020 992log Yt-1-0.498 95log Yt-2(10.96187)(-0.398064)(0.200 10) (0.216 003)R2=1.000000SE=0.001570DW=1.776039和初始方程比较，无论是拟合优度还是个参数的t值都有显著的改善。拟合结果可以由下图形象的看出：三，经济意义检验对于方程,经济含义上logX1的系数为0.810218,logX2的系数为-0.109253,logX3的系数为0.268421.三者之和为0.969386,约等于1,这说明该模型是规模报酬不变的,符合预测值四，模型预测检验根据方程,我们可以推出序列Yt的预测公式为:log(Y)= 0.810218log(X1)- 0.109253log(X2)+ 0.268421log(X3)(0.004790)(0.005836) (0.016915) (169.1620)(-18.72018) (15.86842)+1.020 992log Yt-1