4第四章习题参考答案

第四章习题参考答案P 135

7. 1）用OLS法建立居民人均消费支出与可支配收入的线性模型。create u 20； data consump income；

ls consump c income

Dependent Variable: CONSUMP

Method: Least Squares

Sample: 1 20

Included observations: 20

Variable Coeffic

ient

Std.

Error

t-Stati

stic

Prob.

C

INCOME

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)

线性模型如下：

CONSUMP = 5389 + *INCOME

2）检验模型是否存在异方差性

图：是否有明显的散点扩大/缩小/复杂型趋势

i) X Y

scat income consump

ii)解释变量—残差图：是否形成一条斜率为0的直线

scat income resid^2 或者

genr ei2=resid^2； scat income ei2

由两个图形，均可判定存在递增型异方差。

还可以用帕克检验，戈里瑟检验，戈德菲尔德-匡特检验，怀特检验等方法。

iii) 戈德菲尔德-匡特检验：共有20个样本，去掉中间1/4个样本（4个），剩余大样本、小样本各8个。

Sort income ； smpl 1 8； ls consump C income Smpl 13 20； ls consump C income

2

1

0.050.05615472.0126528.3

4.86

(,)(81,81) 4.28

11

811811

1111RSS RSS F F F n k n k n k n k =

==--=>=

--------------，存在异方差。

iV)怀特检验：因为只有一个变量，故是否含有交叉项是一样的。

2220112231425122

2

01234522011212

2

012:0,(),:0,(),i

i i i i i i i i

i i i

e a a X a X a X a X a X X v H a a a a a nR

q q e

a a X a X v H a a nR

q q χχ=++++++======+++==变量个数

变量个数

View ＼residual test ＼white heteroskedastcity

(cross terms / no cross terms )

White Heteroskedasticity Test: F-statisti c

Probability

Obs*R-squa red

Probability

Dependent Variable: RESID^2 Method: Least Squares Sample: 1 20

Included observations: 20

Variable Coeffic

ient

Std.

Error

t-Stati

stic

Prob.

C

INCOME

INCOME^2

R-squared Mean dependent

var

Adjusted

R-squared

. dependent var . of regression Akaike info

criterion

Sum squared resid +10 Schwarz criterion

Log likelihood F-statistic Durbin-Watson

stat Prob(F-statistic)

2

2220.05(),212.65213(2) 5.99n R q q n R χχ===>，存在异

方差。还可以通过概率()220.0017890.05P n R χ>=<判定存在异方差。

3）若存在异方差，用适当的方法估计模型对数(加权最小二乘法)

ls consump C income ； genr eijdz=abs(resid) ls(w=1/eijdz) consump C income

Dependent Variable: CONSUMP Method: Least Squares Sample: 1 20

Included observations: 20 Weighting series: 1/EIJDZ

Variable

Coeffic ient

Std. Error

t-Stati stic

Prob.

C INCOME

Weighted Statistics R-squared

Mean dependent

var

Adjusted R-squared

. dependent var

. of regression

Akaike info

criterion