13-1
计量经济学课件
-----by Dr,F,F,Gong
permanent email address,ffgong(at)hotmail.com
http://blog.sina.com.cn/ffgong
?教材：
? Damodar N.Gujarati,Essentials of Econometrics,3rd
edition,McGraw-Hill Company,2006
?中译本：经济计量学精要
?（本课件已改正了其中的错误）
13-2
?第13章
?异方差：如果误差方差不是常数的结果
?要点：初步掌握异方差时的回归模型处理方法。不满足经典的约束条件。
?
13-3
? 13.1 异方差的性质
? 13.2 异方差的后果
? 13.3 异方差的诊断：如何知道存在异方差问题
? 13.4 观察到异方差该怎么办：补救措施
? 13.5 怀特异方差校正后的标准误和t统计量
? 13.6 若干异方差实例
? 13.7 总结
13-4
? 13.1 异方差的性质
?见教材p285-6
?例子
13-5
异方差
Fig 13-1 (a) Homoscedasticity; (b) heteroscedasticity.
13-6
例13-1 NYSE佣金率趋势
Table 13-1 Commission rate trends,New York Stock Exchange,
April 1975-December 1978.
13-7
例13-1 NYSE佣金率趋势图
Fig 13-2 Commission per share,in cents,NYSE,April 1975 to
December 1978 (based on data of Table 13-1).
13-8
例13-2 研发费用数据
Table 13-2 Innovation in America,Research and development (R&D)
expenditure in the United States ($,in millions),1988.
13-9
例13-2研发费用-销售图
Fig 13-3 Research and development (R&D) expenditure and
sales,U.S,industries,1988.
i
D&R
i
Sales
2
r
= 266.1917 + 0.0309
se = (1002.961) (0.00834)
t = (0.2654) (3.6996)
= 0.4610
原回归结果和图错误
13-10
例13-2研发费用的残差-销售图
Fig 13-4 Residuals from the R&D regression (13.3).
原图错误
13-11
? 13.2 异方差的后果
?见教材p290，（6点）
13-12
Figure 13-5经典的一元线性回归模型的残差图
13-13
? 13.3 异方差的诊断：如何知道存在异方差问题
?见教材p292-297
? 13.3.1 问题的性质p292
? 13.3.2 残差的图形检验p292-294
? 13.3.3 帕克检验p294
? 13.3.4 格莱泽检验p295
? 13.3.5 怀特的一般异方差检验p295
? 13.3.6 异方差的其他检验方法p297
13-14
13.3.2残差的图形检验
Fig 13-6 Hypothetical patterns of e
2
.
13-15
13.3.2 例13-2研发费用的残差平方和-销售图
Fig 13-7 e
i
2
against sales R&D regression (13.3).
原图错误
13-16
? 13.3.3 帕克检验p294
?帕克检验的模型和步骤p294
?例13-3 帕克检验回归结果(原p294计算结果和结论错误)
? Conclusions,The estimated slope coefficient is barely significant at
the 5% level,if we choose a 5% level of significance.
2
i
e
i
Sales
2
r
ln
=3.4118 + 0.9377 ln
se = (4.9725) (0.4520)
t= (0.6861) (2.0745)
= 0.2120
13-17
? 13.3.4 格莱泽检验p295
?格莱泽检验的模型和步骤p295
?例13-4格莱泽检验的回归结果(原p295计算结果和结论错误)
? On the basis of the Glejser test,we see that models (13.10) and (13.11) lead to the
rejection of the null hypothesis of no heteroscedasticity,whereas (13.12) does not,
i
e
i
Sales
2
r
|
| = 573.4053 + 0.0124
t = (0.8511) (2.2127) (13.10)
= 0.2343
|
| = -522.8336 + 8.1747
t = (-0.5209) (2.4483) (13.11)
= 0.2725
|
| = 2315.6584 – 19862635.21
t = (3.7871) (–1.5946) (13.12)
= 0.1371
|
i
e
i
e
2
r
2
r
i
Sales
i
Sales
1
13-18
? 13.3.5 怀特的一般异方差检验p295
?怀特检验的模型和步骤p295
?例13-5 习题13.18中表13-5的怀特检验的回归结果
? (原p295计算结果和结论错误)
i
Y
i
X
2
i
X
3
2
R
2
R
= 196.9790 – 0.0033
– 1.4013
se = (21.7282) (0.0010) (0.2466)
t = (9.0656) (–3.2249) (–5.6815)
p = (0.000)* (0.005) (0.000)*
= 0.8024 = 0.7792
(13-16)
13-19
? 13.4 观察到异方差该怎么办：补救措施
? 13.4.1 当已知时，加权最小二乘法
? 13.4.2 当未知时
? 13.4.3 重新设定模型
?异方差补救的思路：找出异方差的数学表达式，代入模型方程，变换为满足经典约束条件的模型即可。
?见教材p297-301
2
t
σ
2
t
σ
13-20
13.4.2 当未知时
Fig 13-8 Error variance proportional to X.
2
t
σ
13-21
13.4.2当未知时
Fig 13-9 Error variance proportional to X
2
.
2
t
σ
13-22
? 13.4.3 重新设定模型
?见教材p301
?例13-7
? (原p301计算结果错误)
i
D&R
i
Sales
2
r
ln
= –7.2822 + 1.3144 ln
se = (1.8615) (0.1692)
t = (–3.9120) (7.7674)
= 0.7904
13-23
? 13.5 怀特异方差校正后的标准误差和t统计量
?见教材p301-302
13-24
? 13.6 若干异方差实例
?见教材p302-303
?
13-25
例13-9异方差实例
Table 13-3 Per capita income growth and highway
capacity.
13-26
? 13.7 总结
?要点：初步掌握异方差时的回归模型处理方法。不满足经典的约束条件。
13-27
习题13.11
Fig 13-10 Real interest rates,investment,productivity,and
growth in 33 developing countries from 1974 to 1985.
13-28
习题13.14
Table 13-4 Average compensation in relation to productivity by
employment size,U.S,manufacturing industries.
11,754
13-29
习题13.18
Table 13-5 Infant mortality rate in 20 countries.
13-30
习题13.21
Table 13-6 Life expectancy in relation to income and access to
medical care.
13-31
The end of Chapter 13
13-32
计量经济学课件
-----by Dr,F,F,Gong
permanent email address,ffgong(at)hotmail.com
http://blog.sina.com.cn/ffgong
?教材：
? Damodar N.Gujarati,Essentials of Econometrics,3rd
edition,McGraw-Hill Company,2006
?中译本：经济计量学精要
?（本课件已改正了其中的错误）
13-2
?第13章
?异方差：如果误差方差不是常数的结果
?要点：初步掌握异方差时的回归模型处理方法。不满足经典的约束条件。
?
13-3
? 13.1 异方差的性质
? 13.2 异方差的后果
? 13.3 异方差的诊断：如何知道存在异方差问题
? 13.4 观察到异方差该怎么办：补救措施
? 13.5 怀特异方差校正后的标准误和t统计量
? 13.6 若干异方差实例
? 13.7 总结
13-4
? 13.1 异方差的性质
?见教材p285-6
?例子
13-5
异方差
Fig 13-1 (a) Homoscedasticity; (b) heteroscedasticity.
13-6
例13-1 NYSE佣金率趋势
Table 13-1 Commission rate trends,New York Stock Exchange,
April 1975-December 1978.
13-7
例13-1 NYSE佣金率趋势图
Fig 13-2 Commission per share,in cents,NYSE,April 1975 to
December 1978 (based on data of Table 13-1).
13-8
例13-2 研发费用数据
Table 13-2 Innovation in America,Research and development (R&D)
expenditure in the United States ($,in millions),1988.
13-9
例13-2研发费用-销售图
Fig 13-3 Research and development (R&D) expenditure and
sales,U.S,industries,1988.
i
D&R
i
Sales
2
r
= 266.1917 + 0.0309
se = (1002.961) (0.00834)
t = (0.2654) (3.6996)
= 0.4610
原回归结果和图错误
13-10
例13-2研发费用的残差-销售图
Fig 13-4 Residuals from the R&D regression (13.3).
原图错误
13-11
? 13.2 异方差的后果
?见教材p290，（6点）
13-12
Figure 13-5经典的一元线性回归模型的残差图
13-13
? 13.3 异方差的诊断：如何知道存在异方差问题
?见教材p292-297
? 13.3.1 问题的性质p292
? 13.3.2 残差的图形检验p292-294
? 13.3.3 帕克检验p294
? 13.3.4 格莱泽检验p295
? 13.3.5 怀特的一般异方差检验p295
? 13.3.6 异方差的其他检验方法p297
13-14
13.3.2残差的图形检验
Fig 13-6 Hypothetical patterns of e
2
.
13-15
13.3.2 例13-2研发费用的残差平方和-销售图
Fig 13-7 e
i
2
against sales R&D regression (13.3).
原图错误
13-16
? 13.3.3 帕克检验p294
?帕克检验的模型和步骤p294
?例13-3 帕克检验回归结果(原p294计算结果和结论错误)
? Conclusions,The estimated slope coefficient is barely significant at
the 5% level,if we choose a 5% level of significance.
2
i
e
i
Sales
2
r
ln
=3.4118 + 0.9377 ln
se = (4.9725) (0.4520)
t= (0.6861) (2.0745)
= 0.2120
13-17
? 13.3.4 格莱泽检验p295
?格莱泽检验的模型和步骤p295
?例13-4格莱泽检验的回归结果(原p295计算结果和结论错误)
? On the basis of the Glejser test,we see that models (13.10) and (13.11) lead to the
rejection of the null hypothesis of no heteroscedasticity,whereas (13.12) does not,
i
e
i
Sales
2
r
|
| = 573.4053 + 0.0124
t = (0.8511) (2.2127) (13.10)
= 0.2343
|
| = -522.8336 + 8.1747
t = (-0.5209) (2.4483) (13.11)
= 0.2725
|
| = 2315.6584 – 19862635.21
t = (3.7871) (–1.5946) (13.12)
= 0.1371
|
i
e
i
e
2
r
2
r
i
Sales
i
Sales
1
13-18
? 13.3.5 怀特的一般异方差检验p295
?怀特检验的模型和步骤p295
?例13-5 习题13.18中表13-5的怀特检验的回归结果
? (原p295计算结果和结论错误)
i
Y
i
X
2
i
X
3
2
R
2
R
= 196.9790 – 0.0033
– 1.4013
se = (21.7282) (0.0010) (0.2466)
t = (9.0656) (–3.2249) (–5.6815)
p = (0.000)* (0.005) (0.000)*
= 0.8024 = 0.7792
(13-16)
13-19
? 13.4 观察到异方差该怎么办：补救措施
? 13.4.1 当已知时，加权最小二乘法
? 13.4.2 当未知时
? 13.4.3 重新设定模型
?异方差补救的思路：找出异方差的数学表达式，代入模型方程，变换为满足经典约束条件的模型即可。
?见教材p297-301
2
t
σ
2
t
σ
13-20
13.4.2 当未知时
Fig 13-8 Error variance proportional to X.
2
t
σ
13-21
13.4.2当未知时
Fig 13-9 Error variance proportional to X
2
.
2
t
σ
13-22
? 13.4.3 重新设定模型
?见教材p301
?例13-7
? (原p301计算结果错误)
i
D&R
i
Sales
2
r
ln
= –7.2822 + 1.3144 ln
se = (1.8615) (0.1692)
t = (–3.9120) (7.7674)
= 0.7904
13-23
? 13.5 怀特异方差校正后的标准误差和t统计量
?见教材p301-302
13-24
? 13.6 若干异方差实例
?见教材p302-303
?
13-25
例13-9异方差实例
Table 13-3 Per capita income growth and highway
capacity.
13-26
? 13.7 总结
?要点：初步掌握异方差时的回归模型处理方法。不满足经典的约束条件。
13-27
习题13.11
Fig 13-10 Real interest rates,investment,productivity,and
growth in 33 developing countries from 1974 to 1985.
13-28
习题13.14
Table 13-4 Average compensation in relation to productivity by
employment size,U.S,manufacturing industries.
11,754
13-29
习题13.18
Table 13-5 Infant mortality rate in 20 countries.
13-30
习题13.21
Table 13-6 Life expectancy in relation to income and access to
medical care.
13-31
The end of Chapter 13
13-32
