计量经济学实验报告(财政支出的计量经济学分析)

计量经济学实验报告

小组成员：

财政支出的计量经济学分析

一、综述：

人口口增长将给财政支出带来的压力，表现在人口总量的增加必然要求政府增加各种最基本的社会公共需求，否则将降低国民享有的公共服务及社会福利水平。从长期趋势考查，各国的物价水平呈上升趋势，政府财政支出因此而逐年增长是不争的事实，并且在政府规模日趋扩大的情况下，物价上升将引起公共支出更快地增长。物价影响财政支出增长还表现在物价总水平的起伏，尤其是剧烈动荡的时期。当物价总水平下降时，通常反映经济不景气、失业增加，政府财政的转移支出将扩大，或是增加对社会的失业和基本生活补贴，或是对一些重要的国民经济部门给以补贴。

以下数据来自2013统计年鉴 财政支出(Y) GDP（X1） 人口数（X2） 物价指数（X3）

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

9233.56 10798.18 13187.67 15886.50 18902.58 22053.15 24649.95 28486.89 33930.28 40422.73 49781.35 62592.66 76299.93 89874.16 109247.79 125,952.97

78973.0 84402.3 89677.1 99214.6 109655.2 120332.7 135822.8 159878.3 183084.8 216314.4 265810.3 314045.4 340902.8 401512.8 473104.1 519470.10

123626 124761 125786 126743 127627 128453 129227 129988 130756 131448 132129 132802 133450 134091 134735 135404

102.8 99.2 98.6 100.4 100.7 99.2 101.2 103.9 101.8 101.5 104.8 105.9 99.3 103.3 105.4 102.6

本文获取了我国从1997年到2012年的统计数据，Y为我国1997年至今2012年的财政支出，X1为GDP数，X2为人口数，X3为物价指数。 二、模型的设定与检验

首先对被解释变量Y与解释变量X1，X2，X3做回归分析，方程形式设定为： Y = α + β1X1 + β2X2 + β3X3 + ui Eviews的最小二乘计算结果如下：

Dependent Variable: Y Method: Least Squares Date: 06/14/14 Time: 19:31 Sample: 1997 2012 Included observations: 16

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C X1 X2 X3

R-squared

182697.3 0.279195 -0.768558 -978.4087

56831.24 0.010489 0.415591 302.7010

3.214733 26.61681 -1.849313 -3.232262

0.0074 0.0000 0.0892 0.0072

45706.27 36828.86 18.49965 18.69279 18.50954 0.621628

0.996978 Mean dependent var 0.996222 S.D. dependent var 2263.632 Akaike info criterion 61488351 Schwarz criterion -143.9972 Hannan-Quinn criter. 1319.534 Durbin-Watson stat 0.000000

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

1、T检验,变量的显著性检验

在95%的显著性水平下，X1的T指为26.6168>Ta/2=2.179（查表可知，其中自由度为16-3-1=12）,所以X1的T检验显著，即GDP对财政支出的影响是显著的。

但是对X2、X3来看，其T值均为负值，不具有实际意义，且T值检验不显著（检验方法同上）

2、F检验，方程的显著性检验

ESS/k=1319.543>F(16,12)=2.68(查表可知),所以防尘

RSS/nk1的F检验显著，即整个方程是显著的。

构造统计量F=

3、异方差检验

Heteroskedasticity Test: White F-statistic

2.000938 Prob. F(9,6)

0.2056 0.2132 0.9946

t-Statistic 1.284474

Prob. 0.2463

Obs*R-squared Scaled explained SS

Test Equation:

12.00141 Prob. Chi-Square(9) 1.774295 Prob. Chi-Square(9)

Coefficient 1.21E+10

Std. Error 9.46E+09

Dependent Variable: RESID^2 Method: Least Squares Date: 06/15/14 Time: 12:15 Sample: 1997 2012 Included observations: 16

Variable C

X1 X1^2 X1*X2 X1*X3 X2 X2^2 X2*X3 X3 X3^2

R-squared

34502.73 0.002366 -0.236914 -35.88180 -134673.0 0.194710 951.2476 -90538147 -131716.1

14356.96 0.000990 0.105068 9.350046 130756.3 0.491775 284.3059 49258191 236756.8

2.403205 2.388982 -2.254860 -3.837607 -1.029954 0.395932 3.345860 -1.838032 -0.556335

0.0531 0.0541 0.0650 0.0086 0.3427 0.7059 0.0155 0.1157 0.5981

3843022. 2877649. 32.38166 32.86453 32.40639 1.997217

0.750088 Mean dependent var 0.375220 S.D. dependent var 2274581. Akaike info criterion 3.10E+13 Schwarz criterion -249.0533 Hannan-Quinn criter. 2.000938 Durbin-Watson stat 0.205621

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) nR

2

=12.00141,由White检验知，在α=0.05下，查χ2分布表，得临界值χ20.05

（10）=18.3070。因为nR2=12.00141＜χ20.05（10）=18.3070。 所以拒绝备择假设，不拒绝原假设，表明模型不存在异方差。

4、自相关检验

3,0002,0001,0000-1,000-2,000-3,000-4,000-4,000-3,000-2,000-1,000RESID01,0002,0003,000RESID(-1)

由上图可知，e和e（-1）散点图大部分点落在第Ⅰ、Ⅲ象限，表明随机扰动项u可能存在正自相关。

Dependent Variable: E Method: Least Squares Date: 06/15/14 Time: 12:51 Sample (adjusted): 1998 2012

Included observations: 15 after adjustments

Variable C E(-1)

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 122.8542 0.720031

Std. Error 416.6378 0.218888

t-Statistic 0.294870 3.289497

Prob. 0.7727 0.0059 -5.434830 2095.595 17.72513 17.81953 17.72412 0.898360

0.454258 Mean dependent var 0.412278 S.D. dependent var 1606.547 Akaike info criterion 33552895 Schwarz criterion -130.9385 Hannan-Quinn criter. 10.82079 Durbin-Watson stat 0.005865

由上表可得DW=0.898360；给定显著性水平α=0.05，n=16，K=3时，查Durbin

—Watson表得下限临界值dL=0.98，上限临界值dU=1.54，可知DW＜dl＜dU，由此可判断模型存在正自相关。

5、1多重共线的检验

Dependent Variable: Y Method: Least Squares Date: 06/14/14 Time: 19:31 Sample: 1997 2012 Included observations: 16

Variable C X1 X2 X3

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

Coefficient 182697.3 0.279195 -0.768558 -978.4087

Std. Error 56831.24 0.010489 0.415591 302.7010

t-Statistic 3.214733 26.61681 -1.849313 -3.232262

Prob. 0.0074 0.0000 0.0892 0.0072 45706.27 36828.86 18.49965 18.69279

0.996978 Mean dependent var 0.996222 S.D. dependent var 2263.632 Akaike info criterion 61488351 Schwarz criterion

Log likelihood F-statistic Prob(F-statistic)

-143.9972 Hannan-Quinn criter. 1319.534 Durbin-Watson stat 0.000000

18.50954 0.621628

从t检验及其伴随概率来看，只有变量X1较为显著，其他解释变量均不显著；并且方程拟和优度R2为0.996978、同时方程整体的F检验很显著。因此可以怀疑在变量X2和X3之间存在多重共线性。

计算其简单的相关系数如下

X1 X2 X3

X1 1

0.9217917927403665 0.5431430650859964

X2

0.9217917927403665

1

0.5399890207159324

X3

0.5431430650859964 0.5399890207159324

1

由上图可得出。X1和X2的相关系数很高为0.92，因此解释变量之间的相关程度较高，即存在多重共线。 5、2多重共线的消除

采用逐步回归法进行消除多重共线

Dependent Variable: Y Method: Least Squares Date: 06/15/14 Time: 14:00 Sample: 1997 2012 Included observations: 16

Variable C X1

R-squared

Coefficient -11067.38 0.252875

Std. Error 1495.959 0.005648

t-Statistic -7.398183 44.77246

Prob. 0.0000 0.0000

45706.27 36828.86 19.08032 19.17690 19.08527 0.707680

0.993064 Mean dependent var 0.992569 S.D. dependent var 3174.765 Akaike info criterion 1.41E+08 Schwarz criterion -150.6426 Hannan-Quinn criter. 2004.573 Durbin-Watson stat 0.000000

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

单独对X1回归时，可见其R-squared=0.9931，拟合优度较高。

Dependent Variable: Y Method: Least Squares Date: 06/15/14 Time: 14:00 Sample: 1997 2012 Included observations: 16

Variable C X2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient -1140191. 9.117786

Std. Error 149306.4 1.147520

t-Statistic -7.636583 7.945646

Prob. 0.0000 0.0000 45706.27 36828.86 22.34493 22.44151 22.34988 0.191808

0.818496 Mean dependent var 0.805531 S.D. dependent var 16241.01 Akaike info criterion 3.69E+09 Schwarz criterion -176.7595 Hannan-Quinn criter. 63.13329 Durbin-Watson stat 0.000001

单独对X2回归时，其R-squared=0.8184Dependent Variable: Y

Method: Least Squares Date: 06/15/14 Time: 14:00 Sample: 1997 2012 Included observations: 16

Variable C X3

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient -756084.9 7867.447

Std. Error 376369.7 3692.172

t-Statistic -2.008889 2.130845

Prob. 0.0642 0.0513 45706.27 36828.86 23.77051 23.86709 23.77546 0.570520

0.244896 Mean dependent var 0.190960 S.D. dependent var 33126.32 Akaike info criterion 1.54E+10 Schwarz criterion -188.1641 Hannan-Quinn criter. 4.540500 Durbin-Watson stat 0.051313

但是X3的拟合优度较低，仅为0.24489.，所以保留X1再与X2、X3进行回归检验。下面是对X1和X2进行的回归检验。

Dependent Variable: Y Method: Least Squares Date: 06/15/14 Time: 14:06 Sample: 1997 2012 Included observations: 16

Variable C X1 X2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 105150.5 0.274480 -0.930836

Std. Error 67698.51 0.013650 0.542108

t-Statistic 1.553217 20.10886 -1.717066

Prob. 0.1444 0.0000 0.1097 45706.27 36828.86 19.00092 19.14578 19.00834 0.915298

0.994347 Mean dependent var 0.993477 S.D. dependent var 2974.529 Akaike info criterion 1.15E+08 Schwarz criterion -149.0074 Hannan-Quinn criter. 1143.244 Durbin-Watson stat 0.000000

对X1和X3进行回归检验

Dependent Variable: Y Method: Least Squares Date: 06/15/14 Time: 14:13 Sample: 1997 2012 Included observations: 16

Variable C X1 X3

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

Coefficient 93500.61 0.261944 -1046.034

Std. Error 32735.41 0.005224 327.2588

t-Statistic 2.856253 50.14664 -3.196352

Prob. 0.0135 0.0000 0.0070 45706.27 36828.86 18.62540 18.77026 18.63282 0.637251

0.996116 Mean dependent var 0.995519 S.D. dependent var 2465.334 Akaike info criterion 79012312 Schwarz criterion -146.0032 Hannan-Quinn criter. 1667.234 Durbin-Watson stat

在X1和X2以及X1和X3进行回归时，虽然其拟合优度较高，但是没有通过T检验和DW检验，所以剔除X2和X3.方程Y=-11067.38+0.2528X1