Variable Selection In Instrumental Variable Regression Model

In the linear modle,generally,the interesting problem is the extent that the explanatory variables affect the response wariables.When the data is given,we construct a linear nodel:Y = Xβ+ε, whereβneed to be estimated.In general,when we analyze the model,we often place the variables that affect the response variables a little or the variables that have nothing to do with the response variables into the model.So the accuracy of estimation and prediction will be reduced.Now that how to find the primany factors?We apply the method of variable selection to the regerssion model,the model is:Y = Xβ+ε(1)X = ZΠ+ν(2),where Z is the Instrumental Variable.The main content of this paper is to apply the method of lasso that is propored by Tibshirani(1996)to shrinkage the coefficients of the Instrumental Variable Model and set some coefficients to zero,and use BIC to cut the coefficients that equal to zero,so we can determine the order of the model.