中国粮食生产函数模型

中国粮食生产函数模型一、引言根据理论和经验分析，影响粮食生产（Y）的主要因素有：农业化肥施用量（X1）、粮食播种面积（X2）、成灾面积（X3）、农业机械总动力（X4）、农业劳动力（X5），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198338728166011404716209180223115119844073117401128841526419497308681985379111776108845227052091331130198639151193111093323656229503125419874020819991112682039324836316631988394082142110123239452657532249198940755235711220524449280673322519904462425901134661781928708389141991435292805112314278142938939098199244266293011056025893303083869919934564931521105092313431817376801994445103318109544313823380336628199546662359411006022268361183553019965045438281125482123438547348201997494173981112912303074201634840199851230408411378725181452083517719995083941241131612673448996357682000462184146108463343745257436043200145264425410608031793551723639920024570643391038912716057930366402003430704412994103251660387362042004469474637101606162976402834830200548402476610427819966683983344220064980449281049582463272522319412007501605108105638250647659030731200852871523910679322283821902992320095308254041089862123487496288902010546485562109876185389278027931201157121570411057312441977352659420125895858391112051147010255925773资料来源：《中国统计年鉴》（1995，2012）。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软件进行普通最小二乘回归的结果如下：DependentVariable:LOG(Y)Method:LeastSquaresDate:03/04/14Time:16:55Sample:19832012Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-3.3990261.775984-1.9138830.0676LOG(X1)0.3915560.0499067.8459540.0000LOG(X2)1.1532910.1154179.9923510.0000LOG(X3)-0.0721930.013678-5.2779510.0000LOG(X4)-0.0631700.042789-1.4763030.1529LOG(X5)-0.0992370.055146-1.7995200.0845R-squared0.987725Meandependentvar10.74426AdjustedR-squared0.985168S.D.dependentvar0.118062S.E.ofregression0.014378Akaikeinfocriterion-5.469319Sumsquaredresid0.004962Schwarzcriterion-5.189079Loglikelihood88.03978Hannan-Quinncriter.-5.379668F-statistic386.2468Durbin-Watsonstat1.842639Prob(F-statistic)0.000000因此，估计的方程为̂=−3.3990.391og⁡()+1.153log(X2)-0.072log(X3)-0.063log(X4)-0.099log(X5)(-1.91)(7.85)(9.99)(-5.28)(-1.48)(-1.79)R2=0.9877𝑅=0.9852F=386.25D.W.=1.84由于R2较大且接近于1，而且F=386.25𝐹.(5,24)=2.62，故认为粮食生产与上述解释变量间总体线性关系显著。但由于其中X4，X5前参数估计值未能通过t检验，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(X1)，log(X2)，log(X3)，log(X4)，log(X5)的相关系数如下表所示。表2相关系数表LOG(X1)LOG(X2)LOG(X3)LOG(X4)LOG(X5)LOG(X1)1.000000-0.456032-0.0052880.966390-0.199163LOG(X2)-0.4560321.000000-0.228430-0.497507-0.052864LOG(X3)-0.005288-0.2284301.000000-0.1330510.657544LOG(X4)0.966390-0.497507-0.1330511.000000-0.393070LOG(X5)-0.199163-0.0528640.657544-0.3930701.000000由表中数据发现log（X1）与log（X2）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(X1)，log（X2），log（X3），log（X4）间的回归：（1）用Eviews作log(Y)与log(X1)间的回归结果如下：DependentVariable:LOG(Y)Method:LeastSquaresDate:03/04/14Time:17:51Sample:19832012Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C8.5405970.20077042.539110.0000LOG(X1)0.2700810.02457910.988390.0000R-squared0.811758Meandependentvar10.74426AdjustedR-squared0.805035S.D.dependentvar0.118062S.E.ofregression0.052130Akaikeinfocriterion-3.005801Sumsquaredresid0.076092Schwarzcriterion-2.912388Loglikelihood47.08701Hannan-Quinncriter.-2.975917F-statistic120.7447Durbin-Watsonstat0.641647Prob(F-statistic)0.000000log（̂）=8.541+0.270log（X1）(42.54)(10.99)R2=0.8118D.W.=0.6416(2)用Eviews作log(Y)与log(X2)间的回归结果如下：DependentVariable:LOG(Y)Method:LeastSquaresDate:03/04/14Time:17:59Sample:19832012Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C13.657437.4087421.8434210.0759LOG(X2)-0.2510950.638580-0.3932090.6971R-squared0.005492Meandependentvar10.74426AdjustedR-squared-0.030027S.D.dependentvar0.118062S.E.ofregression0.119822Akaikeinfocriterion-1.341281Sumsquaredresid0.402004Schwarzcriterion-1.247868Loglikelihood22.11921Hannan-Quinncriter.-1.311397F-statistic0.154613Durbin-Watsonstat0.175494Prob(F-statistic)0.697143log（̂）=13.657-0.251log（X2）(1.84)(-0.39)R2=0.0055D.W.=0.1755(3)用Eviews作log(Y)与log(X3)间的回归结果如下：DependentVariable:LOG(Y)Method:LeastSquaresDate:03/04/14Time:18:03Sample:19832012Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C11.945390.79929214.944960.0000LOG(X3)-0.1198820.079748-1.5032640.1440R-squared0.074680Meandependentvar10.74426AdjustedR-squared0.041633S.D.dependentvar0.118062S.E.ofregression0.115579Akaikeinfocriterion-1.413390Sumsquaredresid0.374036Schwarzcriterion-1.319977Loglikelihood23.20085Hannan-Quinncriter.-1.383506F-statistic2.259803Durbin-Watsonstat0.080387Prob(F-statistic)0.143967log（̂）=11.945-0.120log（X3）(14.945)(-1.50)R2=0.0747D.W.=0.0804(4)用Eviews作log(Y)与log(X4)间的回归结果如下：DependentVariable:LOG(Y)Method:LeastSquaresDate:03/04/14Time:18:07Sample:19832012Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C8.6306530.22379138.565690.0000LOG(X4)0.1977380.0209139.4553950.0000R-squared0.761508Meandependentvar10.74426AdjustedR-squared0.752991S.D.dependentvar0.118062S.E.ofregression0.058677Akaikeinfocriterion-2.769195Sumsquaredresid0.096404Schwarzcrite