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黄路迦 · 2022年12月04日

如下

NO.PZ2015120204000018

问题如下:

If an omitted variable is correlated with variables already included in the model, coefficient estimates will be biased and inconsistent and standard errors will also be inconsistent. Is this Statement correct?

选项:

A.

Yes.

B.

No, because the model’s coefficient estimates will be unbiased.

C.

No, because the model’s coefficient estimates will be consistent.

解释:

A is correct.

Chang is correct because a correlated omitted variable will result in biased and inconsistent parameter estimates and inconsistent standard errors.  

为什么会导致系数的inconsistent?老师不是说consistent的意思是变量个数n的增加,不会影响它的准确性吗。就算遗漏了某个变量x,但它能体现在残差项中,这个理解有问题吗?

2 个答案

星星_品职助教 · 2023年09月05日

@咩咩

本题为遗漏变量偏差,不是自相关。前者是残差和此时方程里已有的自变量相关,后者是残差和残差之间相关。

星星_品职助教 · 2022年12月04日

同学你好,

1)consistency指的是随着sample size n增加,估计值会逐渐向总体参数靠拢;

2)正是因为遗漏的变量体现在残差中,所以才使得残差和此时方程里已有的自变量相关。这违背了回归的前提假设。后果就是使得系数估计不准确,即使增加n的数量也达不到越来越准确的效果。后者就是inconsistent。

咩咩 · 2023年09月05日

我理解这个就是存在自相关,自相关应该是不影响一致性的?为什么这里会inconsistent呢?

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