我国农民收入影响因素的回归分析
本文力图应用适当的多元线性回归模型,对有关农民收入的历史数据和现状进行分析,探讨影响农民收入的主要因素,并在此基础上对如何增加农民收入提出相应的政策建议。?农民收入水平的度量常采用人均纯收入指标。影响农民收入增长的因素是多方面的，既有结构性矛盾因素，又有体制性障碍因素。但可以归纳为以下几个方面：一是农产品收购价格水平。二是农业剩余劳动力转移水平。三是城市化、工业化水平。四是农业产业结构状况。五是农业投入水平。考虑到复杂性和可行性，所以对农业投入与农民收入，本文暂不作讨论。因此，以全国为例，把农民收入与各影响因素关系进行线性回归分析，并建立数学模型。
一、计量经济模型分析 (一)、数据搜集
根据以上分析，我们在影响农民收入因素中引入7个解释变量。即： 2x -财政用于农业的支出的比重，3x -第二、三产业从业人数占全社会从业人数的比重，4x -非农村人口比重，5x -乡村从业人员占农村人口的比重，6x -农业总产值占农林牧总产值的比重，7x -农作物播种面积，8x —农村用电量。
资料来源《中国统计年鉴2006》。
(二)、计量经济学模型建立 我们设定模型为下面所示的形式：
利用Eviews 软件进行最小二乘估计，估计结果如下表所示：
Dependent Variable: Y Method: Least Squares Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C X1 X3 X4 X5 X6 X7 X8
R-squared
Mean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat
Prob(F-statistic)
表1 最小二乘估计结果
回归分析报告为：
()
()()()()()()()()()()()()()()()
2345678
2? -1102.373-6.6354X +18.2294X +2.4300X -16.2374X -2.1552X +0.0100X +0.0634X 375.83 3.7813 2.066618.37034 5.8941 2.77080.002330.02128 -2.933 1.7558.820900.20316 2.7550.778 4.27881 2.97930.99582i Y SE t R ===---=230.99316519 1.99327374.66
R Df DW F ====二、计量经济学检验
(一)、多重共线性的检验及修正
①、检验多重共线性
(a)、直观法
从“表1 最小二乘估计结果”中可以看出，虽然模型的整体拟合的很好，
但是x4 x6的t统计量并不显着，所以可能存在多重共线性。
(b)、相关系数矩阵
X2X3X4X5X6X7X8 X2
X3
X4
X5
X6
X7
X8
表2 相关系数矩阵
从“表2 相关系数矩阵”中可以看出，个个解释变量之间的相关程度较
高，所以应该存在多重共线性。
②、多重共线性的修正——逐步迭代法
A、一元回归
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X2
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表3 y对x2的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表4 y对x3的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X4
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表5 y对x4的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X5
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表6 y对x5的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X6
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表7 y对x6的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X7
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表8 y对x7的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X8
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
表9 y对x8的回归结果
综合比较表3~9的回归结果，发现加入x3的回归结果最好。以x3为基础顺次加入其他解释变量，进行二元回归，具体的回归结果如下表10~15所示：Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X2
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X4
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X5
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X7
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X8
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
综合表10~15所示，加入x7的模型的R最大,以x3、x7为基础顺次加入其他解释变量，进行三元回归，具体回归结果如下表16~20所示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X7
X2
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X7
X4
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X7
X5
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X7
X6
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X7
X8
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
综合上述表16~20的回归结果所示，其中加入x6的回归结果最好，以x3 x6 x7为基础一次加入其他解释变量，作四元回归估计，估计结果如表21~24所
示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X2
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X4
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X5
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X8
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
综合表21~24所示的回归结果，其中加入x8的回归结果最好，以x3 x6 x7 x8为基础顺次加入其他的解释变量，其回归结果如表25~27所示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X8
X2
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X8
X5
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X8
X4
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
据表25~27所示，分别加入x2 x4 x5后R均有所增加，但是参数的T检验均不显着，所以最终的计量模型如下表所示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X6
X7
X8
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
回归分析报告为：
(二)、异方差的检验
A、相关图形分析
图1
图 2
图3
图4
从图1~4可以看出y 并不随着x的增大而变得更离散，表明模型可能不存
在异方差。
B、残差分析图
图5
图6
图7
图 8
从图5~8看出，e2并不随x的增大而变化，表明模型可能不存在异方差。
C、ARCH检验
ARCH Test:
F-statistic Probability
Obs*R-squared Probability
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Sample(adjusted): 1989 2004
Included observations: 16 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C
RESID^2(-1)
RESID^2(-2)
RESID^2(-3)
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid1081774. Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
D、White检验
White Heteroskedasticity Test:
F-statistic Probability
Obs*R-squared Probability
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable Coefficient Std. Error t-Statistic Prob.
C
X3
X3^2
X3*X6
X3*X7
X3*X8
X6
X6^2
X6*X7
X6*X8
X7
X7^2
X7*X8
X8
X8^2
R-squared Mean dependent var
Adjusted R-squared . dependent var
. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)
综合上述4种方法得出的结论，说明模型中不存在异方差。
(三)、自相关检验及修正
①自相关的检验
A、DW检验
已知，查表得DL= ，DU=，所以4-DU= B、图示法： 图 9 从图中可以看出大部分点落在1、3象限，表明存在正自相关。 图 10 从图中可以看出，随着t的变化逐次变化，并不频繁改变符号，而是正的后面跟着几个负的，表明存在正自相关。 综上所述，说明模型存在自相关性。 ②自相关的修正——德宾两步法 Dependent Variable: Y Method: Least Squares Sample(adjusted): 1987 2003 Included observations: 17 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C X3 X6 X7 X8 X3(1) X6(-1) X7(-1) X8(-1) Y(-1) R-squared Mean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Dependent Variable: Y+Y(-1)* Method: Least Squares Sample(adjusted): 1987 2004 Included observations: 18 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C X3+X3(-1)* X6+X6(-1)* X7+X7(-1)* X8+X8(-1)* R-squared Mean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) 此时DW= ，查表得DL=，DU=，DU (四)、模型的最终结果为： 三、经济意义检验 模型估计结果表明： 在假定其他解释变量不变的情况下，当第二、三产业从业人数占全社会从 业人数的比重增长一个百分点，农民人均纯收入就会增加元； 在假定其他解释变量不变的情况下，当农业总产值占农林牧总产值的比重 增长一个百分点，农民人均纯收入就会增加元； 在假定其他解释变量不变的情况下，当农作物播种面积增长一千公顷，农 民人均纯收入就会增加元； 在假定其他解释变量不变的情况下，当农村用电量增长一亿千瓦时，农民 人均纯收入就会增加元； （四）?、统计检验 A 、拟合优度检验 B 、F 检验 C 、t 检验 (五)、回归预测 ①、点预测 使用Eview 软件进行点预测： 首先在Workfile 窗口点击Range ，出现Change Workfile Range 窗口，将End Data 改为2005； 然后在Workfile 中点击Sample ，将窗口中的1986 2004改为1986 2005； 使用命令Data X3 X6 X7 X8，在数据表中将2005年的数据输入； 在Equation 中，点击Forecast ，确定后可得到如下图所示的结果，同时在Workfile 中生成一新的序列Yf 。 在Workfile 中双击Yf 就可以看到其具体的数值。 最终得到的点预测的纸如下表33所示： (附：??f Y f X β点预测公式为：) ②、区间预测 A、平均值区间预测 B、个别值区间预测
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