[1]王义闹.工具变量的一个性质[J].温州大学学报(自然科学版),2020,(02):001-10.
 Wang Yinao.A Property of Instrumental Variable[J].Journal of Wenzhou University,2020,(02):001-10.
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工具变量的一个性质
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《温州大学学报》(自然科学版)[ISSN:1674-3563/CN:33-1344/N]

卷:
期数:
2020年02期
页码:
001-10
栏目:
数学
出版日期:
2020-05-25

文章信息/Info

Title:
A Property of Instrumental Variable
作者:
王义闹
温州大学数理学院,浙江温州 325035
Author(s):
Wang Yinao
College of Mathematics and Physics, Wenzhou University, Wenzhou, China 325035
关键词:
随机解释变量最小二乘估计量工具变量理想工具变量均方误差
Keywords:
Random Explanatory Variable Ordinary Least Squares Estimator Instrumental Variable Ideal Instrument Variable Mean Square Error
分类号:
O213;F064.1
文献标志码:
A
摘要:
当线性回归模型中的解释变量是随机变量且与随机干扰项同期线性相关时,本文证明了,随机解释变量与工具变量的线性相关系数的平方必然小于或等于1减去随机解释变量与随机干扰项的线性相关系数的平方.这就提醒我们,当随机解释变量与随机干扰项高度相关时,随机解释变量与工具变量的相关系数必然接近0,如果样本容量再不够大,工具变量法估计值将不稳定.本文所作的数值模拟结果也验证了这一推断.
Abstract:
This paper proves that, when the explanatory variable in a linear regression model is a random variable and is linearly correlated with the random interference term contemporaneously, the square of the linear correlation coefficient of the random explanatory variable and the instrumental variable must be less than or equal to 1 minus the square of the linear correlation coefficient of the random explanatory variable and the random interference term. This imply that, when the random explanatory variable is highly correlated with the random interference term, the correlation efficient of the random explanatory and the instrumental variable must be near to 0, in conditions with the sample size not large enough, the instrumental variable estimated value will be unstable, the simulation results in this paper also verifies this inference.

参考文献/References:

[1] 李子奈,潘文卿.计量经济学[M].3版.北京:高等教育出版社,2010:144-153.
[2] 王义闹,吴利丰.控制单个随机解释变量的条件下被解释变量的平均改变量[J].统计与决策,2017(15):27-31.
[3] Stock J H, Watson M W. 计量经济学[M].沈根祥,孙燕,译.3版.上海:格致出版社,2012:341.

相似文献/References:

[1]王义闹.随机解释变量问题的预测与控制方法[J].温州大学学报(自然科学版),2018,(04):001.
 WANG Yinao.On the Method of Prediction and Control for the Problem of Stochastic Explanatory Variables[J].Journal of Wenzhou University,2018,(02):001.

备注/Memo

备注/Memo:
收稿日期:2019-10-10
作者简介:王义闹(1963- ),男,河北安平人,教授,硕士,研究方向:灰色预测与决策,计量经济学
更新日期/Last Update: 2020-05-25