Instrumental variable estimator of the slope parameter when the explanatory variable is subject to measurement error

Abstract

This paper proposes a new instrumental variable to estimate the parameters of a simple linear regression model where the explanatory variable is subject to measurement error. The new instrumental variable is defined using reflection of the observed values of the explanatory variable. Like other instrumental variable estimators it is unbiased and consistent, but over performs estimators proposed by Wald (1940),Bartlett (1949), and Durbin (1954) if the ratio of the error variances is equal or less than one. The method is straightforward, easy to implement, and performs much better than the existing instrumental variable based estimators. The theoretical superiority of the proposed estimator over the existing instrumental variable based estimators is established by analytical results of simulation. Two illustrative examples for numerical comparisons of the results are also included.