※ 引述《liton (欧吉桑留学生)》之铭言： : ※ 引述《[email protected] (老怪物)》之铭言： : : In statistics, an instrumental variable (IV, or instrument) : : can be used in regression analysis to produce a consistent : : estimator when the explanatory variables (covariates) are : : correlated with the error terms. : : http://en.wikipedia.org/wiki/Instrumental_variable : 我们讲的是同一件事 No! yhliu is correct and unfortunately you were not saying the same thing. : 自变数彼此间的高度相关会造成 : explanatory variables与 error terms之间的高度相关 Why? : 这整个课题是orthogonality conditions所探讨的 You did not get the point. Take ARMA(1,1) for example. x_{t}=ax_{t-1}+e_{t}+be_{t-1}, where x_{t}'s are observed and e_{t}'s are errors and unobservable. If you regeress x_{t} on x_{t-1}, then, due to the correlation between the explanatory variable, x_{t-1}, and the error, e_{t}+be_{t-1}, the lse of a, \hat{a}, is not consistent. However, according the spirit of IV, we can try to find another explanatory variable that is dependent of x_{t-1} but independent of e_{t}+be_{t-1} to overcome this difficulty. This new variable is what we call IV. In this case, x_{t-k} with k>=2 can serve as an IV. You can regreee x_{t} on x_{t-k}, k>=2, and obtain a consistent estimator of a after suitable correction. Think again! --

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