The numerical simulation of improving parameter estimation by instrumental variable method

This paper aims to study the improved effect of the instrumental variable method to estimate parameters of linear regression model with the stochastic explanatory variables problem.

By 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, to test whether parameter estimators are biased and how about the average relative error of estimator of slope when random explanatory variables are in different contemporaneously correlated with random error item. By the instrumental variables which are independent with random error item and in varying degrees related to random explanatory variable, the study tests the estimation accuracy of the slope using the instrumental variable method.

This paper tests that the ordinary least square parameter estimators are biased, and especially that the average relative error of estimator of slope is significantly large, more than 10 percent, when random explanatory variables are different and contemporaneously correlated with the random error item. For the instrumental variables that are independent from random error item and in varying degrees related to the random explanatory variable, the estimation accuracy of the slope is significantly improved and the relative error dropped to less than 4 percent, but the estimation accuracy of the intercept term showed no significant improvement by the instrumental variable method.

The method exposed in the paper shows how to improve estimation by an instrumental variable method.

The paper succeeds in showing how to improve estimation by the instrumental variable method of numerical simulation.