关于农民人均纯收入的计量经济模型
一、选题目的: 找出1985年到2000年以来影响农民人均纯收入的主要因素.
二、模型中引入的各变量如下：
Y――农民人均纯收入；
Ni――人均农林牧渔纯收入；
Wag――农民人均务工收入；
Gdp――人均国内生产总值；
Pi――农产品收购价格指数；
Lab――农村劳动力；
Pla――农民人均耕地面积；
各变量数据如下：
时间 Y Ni Wag Gdp Pi Lab Pla
1985 397.6 289.6764 72.15 855 108.6 37065.1 2.07
1986 423.8 325.3912 81.58 956 106.4 37989.8 2.07
1987 462.6 379.0199 95.47 1103 112 39000.4 2.07
1988 544.9 466.4907 117.77 1355 123 40066.7 2.06
1989 601.5 508.1007 136.46 1512 115 40938.8 2.11
1990 686.3 610.5754 138.8 1634 97.4 42009.5 2.1
1991 708.6 619.9262 151.92 1879 98 43092.5 2.18
1992 784 701.8716 184.38 2287 103.4 43801.6 2.06
1993 921.6 873.9869 194.51 2939 113.4 44255.7 2.17
1994 1221 1268.619 262.98 3923 139.9 44654.1 2.18
1995 1577.7 1593.989 353.7 4854 119.9 45041.8 2.17
1996 1926.1 1705.466 45.84 5576 104.2 45288 2.3
1997 2090.1 1871.485 536.56 6054 95.5 45962.1 2.07
1998 2162 2011.705 573.56 6307 92 46432.3 2.06
1999 2210.3 2060.407 630.25 6547 87.8 46896.5 2.07
2000 2253.4 2272.278 702.3 7084 96.4 47962.1 1.98
回归分析结果如下：
Dependent Variable: Y
Method: Least Squares
Date: 04/18/04 Time: 16:55
Sample: 1985 2000
Included observations: 16
Variable Coefficient Std. Error t-Statistic Prob.
C 925.5528 686.3476 1.348519 0.2104
WAG -0.108373 0.249359 -0.434604 0.6741
PLA 164.1530 387.2593 0.423884 0.6816
GDP 0.245746 0.111313 2.207704 0.0546
NI 0.305067 0.368009 0.828967 0.4286
PI -3.885557 1.111844 -3.494695 0.0068
LAB -0.018963 0.010761 -1.762136 0.1119
R-squared 0.997286 Mean dependent var 1185.719
Adjusted R-squared 0.995476 S.D. dependent var 723.3491
S.E. of regression 48.65323 Akaike info criterion 10.90695
Sum squared resid 21304.23 Schwarz criterion 11.24496
Log likelihood -80.25560 F-statistic 551.1021
Durbin-Watson stat 1.163461 Prob(F-statistic) 0.000000
相关系数分析如下：
相关系数 WAG PLA GDP NI PI LAB
WAG 1 -0.452545899284 0.84602751546 0.857242572276 -0.441421882671 0.773253805063
PLA -0.452545899284 1 0.00797333588973 -0.00989140238445 0.326623638063 0.105722361638
GDP 0.84602751546 0.00797333588973 1 0.998441234987 -0.358163806801 0.910191214451
NI 0.857242572276 -0.00989140238445 0.998441234987 1 -0.354287009507 0.908093201605
PI -0.441421882671 0.326623638063 -0.358163806801 -0.354287009507 1 -0.304523758706
LAB 0.773253805063 0.105722361638 0.910191214451 0.908093201605 -0.304523758706 1
从上面看出，GDP, NI,和LAB可能存在多重共线性。
剔除GDP，再进行回归分析，结果如下：
Dependent Variable: Y
Method: Least Squares
Date: 04/18/04 Time: 21:35
Sample: 1985 2000
Included observations: 16
Variable Coefficient Std. Error t-Statistic Prob.
C 812.3277 806.1734 1.007634 0.3374
NI 1.105257 0.075034 14.73015 0.0000
PI -4.406978 1.279728 -3.443683 0.0063
WAG -0.211368 0.288528 -0.732571 0.4806
PLA 175.5622 456.1034 0.384918 0.7084
LAB -0.015787 0.012562 -1.256734 0.2374
R-squared 0.995816 Mean dependent var 1185.719
Adjusted R-squared 0.993723 S.D. dependent var 723.3491
S.E. of regression 57.30756 Akaike info criterion 11.21474
Sum squared resid 32841.56 Schwarz criterion 11.50446
Log likelihood -83.71791 F-statistic 475.9620
Durbin-Watson stat 1.557592 Prob(F-statistic) 0.000000
剔除Ni，再进行回归分析，结果如下：
Dependent Variable: Y
Method: Least Squares
Date: 04/18/04 Time: 23:01
Sample: 1985 2000
Included observations: 16
Variable Coefficient Std. Error t-Statistic Prob.
C 890.4914 674.2435 1.320727 0.2160
GDP 0.336627 0.018965 17.75038 0.0000
WAG -0.045217 0.233692 -0.193488 0.8505
PLA 191.1567 379.8033 0.503305 0.6257
PI -3.713520 1.075084 -3.454167 0.0062
LAB -0.019751 0.010550 -1.872068 0.0907
R-squared 0.997078 Mean dependent var 1185.719
Adjusted R-squared 0.995617 S.D. dependent var 723.3491
S.E. of regression 47.88622 Akaike info criterion 10.85553
Sum squared resid 22930.90 Schwarz criterion 11.14525
Log likelihood -80.84423 F-statistic 682.5357
Durbin-Watson stat 1.109253 Prob(F-statistic) 0.000000
剔除GDP和Lab,进行回归分析得到如下结果：
Dependent Variable: Y
Method: Least Squares
Date: 04/18/04 Time: 23:08
Sample: 1985 2000
Included observations: 16
Variable Coefficient Std. Error t-Statistic Prob.
C 797.8466 827.0474 0.964693 0.3554
WAG -0.371500 0.265598 -1.398728 0.1895
PLA -114.1878 403.7706 -0.282804 0.7826
PI -4.286930 1.309335 -3.274128 0.0074
NI 1.081430 0.074486 14.51854 0.0000
R-squared 0.995155 Mean dependent var 1185.719
Adjusted R-squared 0.993393 S.D. dependent var 723.3491
S.E. of regression 58.79741 Akaike info criterion 11.23638
Sum squared resid 38028.49 Schwarz criterion 11.47781
Log likelihood -84.89103 F-statistic 564.8087
Durbin-Watson stat 1.443275 Prob(F-statistic) 0.000000
再剔除PLA, 回归如下：
Dependent Variable: Y
Method: Least Squares
Date: 04/18/04 Time: 23:15
Sample: 1985 2000
Included observations: 16
Variable Coefficient Std. Error t-Statistic Prob.
C 567.7552 142.6820 3.979166 0.0018
WAG -0.307833 0.135416 -2.273241 0.0422
PI -4.366194 1.228978 -3.552704 0.0040
NI 1.064028 0.040333 26.38103 0.0000
R-squared 0.995119 Mean dependent var 1185.719
Adjusted R-squared 0.993899 S.D. dependent var 723.3491
S.E. of regression 56.49851 Akaike info criterion 11.11862
Sum squared resid 38304.98 Schwarz criterion 11.31177
Log likelihood -84.94899 F-statistic 815.5810
Durbin-Watson stat 1.367848 Prob(F-statistic) 0.000000
Dw=1.367848,ɑ=0.01,,dl=0.663<dw<du=1.464,不能判断。
ARCH检验如下所示：
ARCH Test:
F-statistic 0.647842 Probability 0.603769
Obs*R-squared 2.308748 Probability 0.510847
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 04/18/04 Time: 23:16
Sample(adjusted): 1988 2000
Included observations: 13 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 3015.183 1820.098 1.656605 0.1320
RESID^2(-1) -0.321792 0.345083 -0.932508 0.3754
RESID^2(-2) -0.052940 0.346868 -0.152623 0.8821
RESID^2(-3) 0.345297 0.338025 1.021514 0.3337
R-squared 0.177596 Mean dependent var 2913.964
Adjusted R-squared -0.096539 S.D. dependent var 3827.557
S.E. of regression 4008.054 Akaike info criterion 19.67766
Sum squared resid 1.45E+08 Schwarz criterion 19.85149
Log likelihood -123.9048 F-statistic 0.647842
Durbin-Watson stat 1.856843 Prob(F-statistic) 0.603769
Obs*R-squared的p值为0.510847，不显著，不接受存在异方差假设。
利用对数线性回归修正自相关：ly=log(y)
lni=log(ni) ; lwag=log(wag) ; lpi=log(pi);
同时考虑cochrane-orcutt迭代，结果如下
Dependent Variable: LY
Method: Least Squares
Date: 04/18/04 Time: 23:32
Sample(adjusted): 1986 2000
Included observations: 15 after adjusting endpoints
Convergence achieved after 20 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 2.091589 0.565236 3.700381 0.0041
LNI 0.924454 0.035264 26.21497 0.0000
LWAG -0.027155 0.013377 -2.029953 0.0698
LPI -0.286921 0.096489 -2.973602 0.0140
AR(1) 0.523638 0.242689 2.157655 0.0563
R-squared 0.997972 Mean dependent var 6.950034
Adjusted R-squared 0.997161 S.D. dependent var 0.618887
S.E. of regression 0.032978 Akaike info criterion -3.724773
Sum squared resid 0.010875 Schwarz criterion -3.488757
Log likelihood 32.93580 F-statistic 1230.183
Durbin-Watson stat 1.838909 Prob(F-statistic) 0.000000
Inverted AR Roots .52
Dw=1.838909>du=1.446,不接受存在自相关假设。