Estimating Problems In The Instrumental Variable Regression

When the explanatory variables are endogenous relative to the response ,we always use IV regression.The 2SLS estimator is an estimator has good properties with large sample and finite sample when the the instruments are chosen legitimate ,but if the instruments are not chosen legitimate ,especially weekly correlated with the endogenous explanatory variables ,the 2SLS estimator will be biasd badly. So it is necessary to learn through the properties of the 2SLS estimator and suitable method in different cases.This paper introduces the backgroud of 2SLS estimator first,then expands the consistency and bias of 2STS estimator,discusses the exact distribution and compares two different approximate method.Also I introduce REQML estimator which has good properties in the model have many week instruments,and two moment estimator:MM and MMK estimator.After give the example in Angrist and Krueger(1991) , I analyze each estimation and approximation method .At last I discuss the quality of instruments.