工具變量法（instrumental variable method）

傳統ols中的hypothesis要求$x_i$與$u_i$無關。但是在實際中很難滿足這個假設，有時候因變量（在單方程模型中就是內生變量）也會反過來影響自變量。ols估計將是有偏和不一致的，（有偏指的是參數估計值於期望值不相等，一致性是大樣本依概率收斂於期望值，可以參考另外一個博文）。這個時候比較有效的方法是採取工具變量法進行估計參數值。
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 一個工具變量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很多估計方法可以利用， 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（識別）
• 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（不能識別）