关于农民人均纯收入的计量经济模型(1)

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 1985 1986 1987 1988 19 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Y 397.6 423.8 462.6 4.9 601.5 686.3 708.6 784 921.6 1221 1577.7 1926.1 2090.1 2162 2210.3 2253.4 Ni 2.67 325.3912 379.0199 466.4907 508.1007 610.57 619.9262 701.8716 873.9869 1268.619 1593.9 1705.466 1871.485 2011.705 2060.407 2272.278 Wag 72.15 81.58 95.47 117.77 136.46 138.8 151.92 184.38 194.51 262.98 353.7 45.84 536.56 573.56 630.25 702.3 Gdp 855 956 1103 1355 1512 1634 1879 2287 2939 3923 48 5576 60 6307 67 7084 Pi 108.6 106.4 112 123 115 97.4 98 103.4 113.4 139.9 119.9 104.2 95.5 92 87.8 96.4 Lab 37065.1 379.8 39000.4 40066.7 40938.8 42009.5 43092.5 43801.6 44255.7 446.1 45041.8 45288 45962.1 432.3 466.5 47962.1 Pla 2.07 2.07 2.07 2.06 2.11 2.1 2.18 2.06 2.17 2.18 2.17 2.3 2.07 2.06 2.07 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 C WAG PLA GDP NI

Coefficient 925.5528 -0.108373 1.1530 0.245746 0.305067

Std. Error t-Statistic Prob. 0.2104 0.6741 0.6816 0.06 0.4286

686.3476 1.348519 0.249359 -0.434604 387.2593 0.423884 0.111313 2.207704 0.368009 0.8267

PI

相关系数 WAG PLA GDP NI PI WAG PLA -3.885557

GDP 1.111844 -3.494695

NI PI 0.0068

LAB 1 -0.45259284 0.846027516 0.857242572276 -0.441421882671 -0.45259284 1 0.007973335873 -0.009140238445 0.326623638063 0.105722361638 0.846027516 0.007973335873 1 0.998441234987 -0.358163806801 0.910191214451 -0.0163 0.857242572276 -0.009140238445 0.998441234987 1 -0.3287009507 0.908093201605 -0.441421882671 0.326623638063 -0.358163806801 -0.3287009507 1 -0.304523758706 0.773253805063 0.105722361638 0.910191214451 0.908093201605 -0.304523758706 1 LAB 0.773253805063 LAB R-squared

0.010761 -1.762136 0.1119 1185.719 723.3491 10.90695 11.24496 551.1021 0.000000 Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Durbin-Watson stat 0.997286 Mean dependent

var

0.9976 S.D. dependent var 48.65323 Akaike info criterion 21304.23 Schwarz criterion -80.25560 F-statistic

1.163461 Prob(F-statistic) 相关系数分析如下：

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 C NI PI WAG PLA LAB R-squared

Coefficient 812.3277 1.105257 -4.406978 -0.211368 175.5622 -0.015787 Std. Error t-Statistic Prob. 0.3374 0.0000 0.0063 0.4806 0.7084 0.2374 1185.719

806.1734 1.007634 0.075034 14.73015 1.279728 -3.443683 0.288528 -0.732571 456.1034 0.384918 0.012562 -1.256734 0.995816 Mean dependent

var

Adjusted R-squared 0.993723 S.D. dependent var S.E. of regression 57.30756 Akaike info criterion Sum squared resid 32841.56 Schwarz criterion Log likelihood -83.71791 F-statistic Durbin-Watson stat 1.557592 Prob(F-statistic) 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 C GDP WAG PLA PI LAB R-squared

Coefficient 0.4914 0.336627 -0.045217 191.1567 -3.713520 -0.019751 Std. Error t-Statistic Prob. 0.2160 0.0000 0.8505 0.6257 0.0062 0.0907 1185.719 723.3491 10.85553 11.14525 682.5357 0.000000 723.3491 11.21474 11.50446 475.9620 0.000000 674.2435 1.320727 0.0165 17.75038 0.233692 -0.193488 379.8033 0.503305 1.075084 -3.4167 0.010550 -1.872068 0.997078 Mean dependent

var

Adjusted R-squared 0.995617 S.D. dependent var S.E. of regression 47.88622 Akaike info criterion Sum squared resid 22930.90 Schwarz criterion Log likelihood -80.84423 F-statistic Durbin-Watson stat 1.109253 Prob(F-statistic)

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 C WAG PLA PI NI R-squared

Coefficient 797.8466 -0.371500 -114.1878 -4.286930 1.081430 Std. Error t-Statistic Prob. 0.35 0.15 0.7826 0.0074 0.0000 1185.719

827.0474 0.9693 0.265598 -1.398728 403.7706 -0.282804 1.309335 -3.274128 0.074486 14.518 0.995155 Mean dependent

var

Adjusted R-squared 0.993393 S.D. dependent var S.E. of regression 58.79741 Akaike info criterion Sum squared resid 38028.49 Schwarz criterion Log likelihood -84.103 F-statistic Durbin-Watson stat 1.443275 Prob(F-statistic)

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 C WAG PI NI R-squared

Coefficient 567.7552 -0.307833 -4.366194 1.0028 Std. Error t-Statistic 723.3491 11.23638 11.47781 5.8087 0.000000 Prob. 0.0018 0.0422 0.0040 0.0000 1185.719 723.3491 11.11862 11.31177 815.5810 0.000000 142.6820 3.979166 0.1316 -2.273241 1.2278 -3.552704 0.040333 26.38103 0.995119 Mean dependent

var

Adjusted R-squared 0.9939 S.D. dependent var S.E. of regression 56.49851 Akaike info criterion Sum squared resid 38304.98 Schwarz criterion Log likelihood -84.949 F-statistic Durbin-Watson stat 1.367848 Prob(F-statistic) Dw=1.367848,ɑ=0.01,,dl=0.663Obs*R-squared 0.7842 Probability 2.308748 Probability 0.603769 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 C

RESID^2(-1) RESID^2(-2)

Coefficient 3015.183 -0.321792 -0.052940

Std. Error t-Statistic Prob. 0.1320 0.37 0.8821

1820.098 1.656605 0.345083 -0.932508 0.346868 -0.152623

RESID^2(-3) R-squared

0.345297 0.338025 1.021514 0.3337 2913.9 3827.557 19.67766 19.85149 0.7842 0.603769 0.177596 Mean dependent

var

Adjusted R-squared -0.096539 S.D. dependent var S.E. of regression 4008.0 Akaike info criterion Sum squared resid 1.45E+08 Schwarz criterion Log likelihood -123.9048 F-statistic Durbin-Watson stat 1.856843 Prob(F-statistic) 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 C LNI LWAG LPI AR(1) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Durbin-Watson stat Inverted AR Roots Coefficient 2.0915 0.9244 -0.027155 -0.286921 0.523638 Std. Error t-Statistic Prob. 0.0041 0.0000 0.0698 0.0140 0.0563 0.565236 3.700381 0.0352 26.21497 0.013377 -2.029953 0.09 -2.973602 0.2426 2.157655 0.997972 Mean dependent 6.950034

var

0.997161 S.D. dependent var 0.618887 0.032978 Akaike info criterion -3.72477

3

0.010875 Schwarz criterion -3.48875

7

32.93580 F-statistic 1230.183 1.8309 Prob(F-statistic) 0.000000 .52 Dw=1.8309>du=1.446,不接受存在自相关假设。