求教控制变量的作用

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我知道控制变量的意思，却不知道什么时候带入控制变量进行分析，比如相关分析中需要把控制变量带入验算吗？回归分析中呢？我看有些作者将控制变量带入回归方程中，请问是啥意思呢？谢谢！

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关键词：控制变量 回归方程 回归分析 相关分析 不知道 回归分析

本来就和解释变量没多大区别，放入研究也很正常

Control variables are those put into regression to control the Omitted Variable Bias (OVB).
Consider Regression Y=Xb+e
In Randomized Control Trials (RCT)  X and e are uncorrelated, therefore OLS estimates are both unbiased and inconsistent.
In social sciences studies. X are normally choices of human being, which is highly possible to be correlated with e, therefore  induce the endogeneity problem.
e.g In wage regression, wage= education*b+e.
here education is endogeneous because it is correlated with 'ability'  which is not observed. In the presence of endogeneity, b can not be consistently estimated.
Therefore, if we could put ability (or its proxy) into the regression, the OVB could then be controled and we call the variable ability-control variable.
However ability cannot be observed, that's why we use other approach- IV regression, Panel data, Difference in Differences etc to control this bias.