The numerical simulation of improving parameter estimation by instrumental variable method

In this paper the stochastic explanatory variables problem is studied using Monte-Carlo method. Taking a linear regression model with intercept of 3, slope of 4 as an example, whose random error in standard normal distribution, it is verified that parameter estimators are biased, especially the average relative error of estimator of slope is significantly large, as more than 10%, when random explanatory variables are in different contemporaneously correlated with random error item. When the instrumental variables, independent with random error item and in varying degrees related to random explanatory variable, is used, the estimation accuracy of the slope are significantly improved and the relative error dropped to less than 4%, but the estimation accuracy of the intercept term no significant improvement using the instrumental variable method.