工具变量法（instrumental variable method）

传统ols中的hypothesis要求$x_i$与$u_i$无关。但是在实际中很难满足这个假设，有时候因变量（在单方程模型中就是内生变量）也会反过来影响自变量。ols估计将是有偏和不一致的，（有偏指的是参数估计值于期望值不相等，一致性是大样本依概率收敛于期望值，可以参考另外一个博文）。这个时候比较有效的方法是采取工具变量法进行估计参数值。
Namely， an apppropriate instrumental variable(s) should be incorporated in the equation, which is used to replace the dependent variable in the right hand side of the equation. And 一个工具变量should meet the following requriements:

• VI should be high correlated with the endongenous variable
• VI is independent with $u_i$
• At the same, VI has relatively lower collinearity with other explanary variables.

s很多估计方法可以利用， 比如2ls， gmm，sgmm。 which can be found in STATA.
about identification definition：

• This process of using extra exogenous variables as instruments for endogenous RHS variables is known as identification（识别）
• If there are no additional exogenous variables outside the original equation that can be used as instruments for the endogenous RHS variables then the equation is said to be unidentified（不能识别）