我国粮食生产与相关投入计量经济学模型分析

我国粮食生产与相关投入计量经济学模型分析一 理论分析二 建立模型以19802003年各年粮食产量作为被解释变量，解释变量中，包括农业化肥施用量，粮食播种面积，成灾面积，农业机械总动力，农业劳动力。模型设定为其中 Y：粮食产量（万吨） X1：农业化肥试用量（万吨） X2：粮食播种面积（千公顷） X3：成灾面积（千公顷） X4：农业机械总动力（万千瓦） X5：农业劳动力（万人）显著性水平0.05三 估计参数假定模型中随机项满足基本假定，用OLS法估计参数，估计结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/15/06 Time: 00:16Sample: 1980 2003Included observations: 24VariableCoefficientStd. Errort-StatisticProb. C-5410.50021545.50-0.2511200.8046X18.1646181.6115125.0664330.0001X20.1639010.1519251.0788300.2949X3-0.2307920.103152-2.2373990.0381X4-0.2516210.131538-1.9129190.0718X50.6388690.4294961.4874850.1542R-squared0.922443 Mean dependent var42847.33Adjusted R-squared0.900899 S.D. dependent var5325.186S.E. of regression1676.383 Akaike info criterion17.89898Sum squared resid Schwarz criterion18.19350Log likelihood-208.7878 F-statistic42.81740Durbin-Watson stat0.415364 Prob(F-statistic)0.000000估计方程为t: (-0.25) (5.07) (1.08) (-2.24) (-1.91) (1.49) =0.9224 F=42.8174由于，未通过t检验，而且前的符号经济意义也不合理，因此解释变量键可能存在多重共线性。四 多重共线性分析1. 检验简单相关系数，的相关系数表如下：X1X2X3X4X5X1 1.000000-0.844852 0.375109 0.980034 0.396547X2-0.844852 1.000000-0.400823-0.822917-0.195668X3 0.375109-0.400823 1.000000 0.500381-0.603832X4 0.980034-0.822917 0.500381 1.000000 0.268218X5 0.396547-0.195668-0.603832 0.268218 1.0000002. 用Y分别关于，作一元线性回归得：变量参数估计值4.255-0.3480.4690.2813.235t统计量8.29-1.192.5285.1184.5220.75760.06060.22510.54350.4817 由上表知，解释变量的重要程度依次为，3. 将各解释变量按以上顺序分别引入基本回归模型中，并用OLS法估计。先把引入模型，用Y关于，做回归并用OLS法估计得：Dependent Variable: YMethod: Least SquaresDate: 12/15/06 Time: 18:13Sample: 1980 2003Included observations: 24VariableCoefficientStd. Errort-StatisticProb. C29444.911146.28725.687210.0000X110.230871.3090057.8157650.0000X4-0.4845980.101949-4.7533260.0001R-squared0.883222 Mean dependent var42847.33Adjusted R-squared0.872101 S.D. dependent var5325.186S.E. of regression1904.447 Akaike info criterion18.05824Sum squared resid Schwarz criterion18.20550Log likelihood-213.6989 F-statistic79.41445Durbin-Watson stat0.893524 Prob(F-statistic)0.000000 =0.9224 t (25.69)(7.82) (-4.75)可见，引入后，拟合优度有所提高，但回归参数的符号不对，所以应该把从模型中删除。按照上面的方法依次引入，经过检验均可保留。删去不符合条件的解释变量，得到Y关于，的方程： (-1.95) (8.51) (2.37) (-2.39) (2.34) =0.9067 F=46.1480 DW=0.38Dependent Variable: YMethod: Least SquaresDate: 12/15/06 Time: 12:41Sample: 1980 2003Included observations: 24VariableCoefficientStd. Errort-StatisticProb. C-33196.4016990.08-1.9538700.0656X15.2902390.6217618.5084710.0000X20.3221970.1360352.3684980.0286X3-0.2603400.108892-2.3908070.0273X50.9777980.4177312.3407360.0303R-squared0.906676 Mean dependent var42847.33Adjusted R-squared0.887029 S.D. dependent var5325.186S.E. of regression1789.857 Akaike info criterion18.00071Sum squared resid Schwarz criterion18.24614Log likelihood-211.0085 F-statistic46.14801Durbin-Watson stat0.380375 Prob(F-statistic)0.000000五 序列相关性分析对上一步得到的回归方程做序列相关性分析，采用LM检验法：1. 阶滞后： Breusch-Godfrey Serial Correlation LM Test:F-statistic24.93890 Probability0.000009Obs*R-squared17.89932 Probability0.000130Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/15/06 Time: 13:05Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb. C5709.0289294.2960.6142510.5472X10.0787650.3324010.2369590.8155X2-0.0934320.075415-1.2388990.2322X3-0.1035490.060792-1.7033260.1067X50.2165530.2248040.9632970.3489RESID(-1)1.2239900.1896966.4523910.0000RESID(-2)-0.5186400.195301-2.6555860.0166R-squared0.745805 Mean dependent var1.33E-11Adjusted R-squared0.656089 S.D. dependent var1626.789S.E. of regression954.0127 Akaike info criterion16.79772Sum squared resid Schwarz criterion17.14132Log likelihood-194.5727 F-statistic8.312966Durbin-Watson stat2.552423 Prob(F-statistic)0.000262得估计结果为：t(0.61) (0.24) (-1.24) (-1.70) (0.96) (6.45) (-2.66)=0.7458 N=24 P=2 K=5（包含常数项）LM=(N-P)*=(24-2)*0.7458=16.4076=5.99 由于LM,而且，的回归系数显著不为零，表明此模型存在一阶，二阶自相关2. 阶滞后： Breusch-Godfrey Serial Correlation LM Test:F-statistic17.48614 Probability0.000026Obs*R-squared18.39076 Probability0.000365Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/15/06 Time: 13:27Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb. C2300.2259626.9830.2389350.8142X1-0.0114400.337259-0.0339200.9734X2-0.0905930.074578-1.2147460.2421X3-0.0770940.064106-1.2025960.2466X50.3020660.2336371.2928830.2144RESID(-1)1.0685910.2288684.6690250.0003RESID(-2)-0.2018090.329957-0.6116210.5494RESID(-3)-0.3025460.255535-1.1839710.2537R-squared0.766282 Mean dependent var1.33E-11Adjusted R-squared0.664030 S.D. dependent var1626.789S.E. of regression942.9348 Akaike info criterion16.79707Sum squared resid Schwarz criterion17.18976Log likelihood-193.5649 F-statistic7.494061Durbin-Watson stat2.363537 Prob(F-statistic)0.000442得估计结果为：t (0.24) (-0.03) (-1.21) (-1.20) (1.29) (4.67) (-0.61) (-1.18)=0.7663 N=24 P=3 K=5（包含常数项）LM=(24-3)*0.7663=16.0923=7.81，表明存在自相关；但由于的回归系数不显著，故不存在三阶序列相关性。3. 运用广义差分法进行自相关的处理Dependent Variable: YMethod: Least SquaresDate: 12/15/06 Time: 13:43Sample(adjusted): 1982 2003Included observations: 22 after adjusting endpointsConvergence achieved after 22 iterationsVariableCoefficientStd. Errort-StatisticProb. C-28788.979833.202-2.9277310.0104X14.8123620.5116299.4059550.0000X20.5602300.0907246.1751160.0000X3-0.1841120.034253-5.3750180.0001X50.0302050.3362940.0898170.9296AR(1)0.7999790.2239273.5724940.0028AR(2)-0.1932200.187475-1.0306480.3190R-squared0.985985 Mean dependent var43808.09Adjusted R-squared0.980378 S.D. dependent var4410.156S.E. of regression617.7612 Akaike info criterion15.94345Sum squared resid5724433. Schwarz criterion16.29060Log likelihood-168.3780 F-statistic175.8753Durbin-Watson stat2.504680 Prob(F-statistic)0.000000Inverted AR Roots .40 -.18i .40+.18i结果表明，调整后的模型的DW=2.5047=1.78,广义差分后的模型已不存在序列相关性，得到的回归方程为：六 异方差性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-statistic2.936941 Probability0.054487Obs*R-squared19.69010 Probability0.140219Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/15/06 Time: 14:08Sample: 1980 2003Included observations: 24VariableCoefficientStd. Errort-StatisticProb. C4.25E+081.49E+090.2859720.7814X133760.9382018.780.4116240.6902X120.7255983.1583020.2297430.8234X1*X2-0.6906530.673699-1.0251660.3320X1*X30.1291840.4770890.2707750.7927X1*X51.1287582.8949520.3899060.7057X223241.7824004.530.9682250.3582X22-0.1760490.106109-1.6591300.1315X2*X3-0.0754480.093210-0.8094420.4391X2*X50.6207110.5226401.1876450.2654X38993.28513257.930.6783320.5146X32-0.0545730.058218-0.9373820.3730X3*X50.0543380.2370930.2291850.8238X5-115713.965324.90-1.7713600.1103X520.6278270.9646220.6508530.5314R-squared0.820421 Mean dependent var2536174.Adjusted R-squared0.541075 S.D. dependent var3247638.S.E. of regression2200079. Akaike info criterion32.31506Sum squared resid4.36E+13 Schwarz criterion33.05134Log likelihood-372.7807 F-statistic2.936941Durbin-Watson stat2.136747 Prob(F-statistic)0.054487在同方差的条件下：n，h=4,为解释变量的个数从上图可知n19.6901，在显著性水平0.05的情况下，9.49，由于n9.49,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: YMethod: Least SquaresDate: 12/15/06 Time: 14:22Sample: 1980 2003Included observations: 24Weighting series: 1/ABS(RESID)VariableCoefficientStd. Errort-StatisticProb. C-38848.226162.635-6.3038330.0000X15.6263340.05743597.960400.0000X20.3996690.03619411.042280.0000X3-0.2747060.020876-13.158680.0000X50.8696750.0875909.9289660.0000Weighted StatisticsR-squared1.000000 Mean dependent var41264.31Adjusted R-squared1.000000 S.D. dependent var179318.7S.E. of regression37.90557 Akaike info criterion10.29112Sum squared resid27299.81 Schwarz criterion10.53655Log likelihood-118.4935 F-statistic6319.212Durbin-Watson stat0.924452 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.904028 Mean dependent var42847.33Adjusted R-squared0.883823 S.D. dependent var5325.186S.E. of regression1815.075 Sum squared residDurbin-Watson stat0.387567最终拟合的回归方程为t (-6.30) (97.96) (11.04) (-13.16) (9.93) =1.0000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：七 模型的经济含义经过以上分析，得出模型的回归方程为1.0000表明，粮食总产量的变化可以完全由化肥施用量，粮食播种面积，成灾面积和农业劳动力的数值来解释；的回归参数5.63表示：在其他条件不变的情况下，化肥施用量每增加万吨，粮食产量增加5.63万吨；的回归参数0.40表示：在其他条件不变的情况下，粮食播种面积每增加1000公顷，粮食产量增加4000吨；的回归参数-0.27表示：在其他条件不变的情况下，成灾面积每减少1000公顷，粮食产量增加2700吨；的回归参数0.87表示：在其他条件不变的情况下，农业劳动力每增加万人，粮食产量增加8700吨；八 模型预测以此模型预测2004年的粮食产量，由统计年鉴的数据知，2004年各解释变量的数值如下：=4636.6 =101606=16297 =30596代入模型中得Y=49979.33而2004年实际粮食总产量为50146.03，误差率为0.059%，Eviews模型如下：附：中国粮食生产与相关投入资料年份粮食产量（万吨）Y化肥施用量（万吨）粮食播种面积千公顷）成灾面积千公顷农业机械总动力万千瓦农业劳动力（万人）1980 32056.00 1269.400 117234.0 22317.30 14746.00 29808.401981 32502.00 1334.900 114958.0 18743.30 15680.00 30677.601982 35450.00 1513.400 113463.0 16120.30 16614.00 31152.701983 38728.00 1659.800 114047.0 16209.30 18022.00 31645.101984 40731.00 1739.800 112884.0 15264.00 19497.00 31685.001985 37911.00 1775.800 108845.0 22705.30 20913.00 30351.501986 39151.00 1930.600 110933.0 23656.00 22950.00 30467.001987 40208.00 1999.300 111268.0 20392.70 24836.00 30870.001988 39408.00 2141.500 110123.0 23944.70 26575.00 31455.701989 40755.00 2357.100 112205.0 24448.70 28067.00 32440.501990 44624.00 2590.300 113466.0 17819.30 28708.00 33330.401991 43529.00 2806.100 112314.0 27814.00 29389.00 34186.301992 44264.00 2930.200 110560.0 25894.70 30308.00 34037.001993 45649.00 3151.900 110509.0 23133.00 31817.00 33258.201994 44510.00 3317.900 109544.0 31383.00 33802.00 32690.301995 46662.00 3593.700 110060.0 22267.00 36118.00 32334.501996 50454.00 3827.900 112548.0 21233.00 38547.00 32260.401997 49417.00 3980.700 112912.0 30309.00 42016.00 32434.901998 51230.00 4083.700 113787.0 25181.00 45208.00 32626.401999 50839.00 4124.300 113161.0 26731.00 48996.00 32911.802000 46218.00 4146.400 108463.0 34374.00 52574.00 32797.502001 45264.00 4253.800 106080.0 31793.00 55172.00 32451.002002 45706.00 4339.400 103891.0 27319.00 57930.00 31990.602003 43070.00 4411.600 99410.00 32516.00 60387.00 31259.602004 50146.03 4636.600101606.0016297.0064028.0030596.00资料来源：中国统计年鉴（2005,1985）