Mathematical reflection approach to instrumental variable estimation method for simple regression model

The measurement errors problem is endemic in many econometric studies,and one of the oldest known statistical problems. instrumental variable (iv) method is one of the popular solutions adopted to deal with the mismeasured variables in statistical and econometric analyses. this paper proposes an efficient iv estimator to the parameters of the simple regression model where both variables are subject to measurement errors. the proposed iv is defined using simple mathematical transformation of the manifest independent variable (mismeasured variable). the proposed method is straightforward,and easy to implement. the theoretical superiority of the proposed estimator over the existing iv based estimators due to wald (1940),bartlett (1949) and durbin (1954) is established by analytical comparison and geometric expositions. simulation based numerical comparisons of the proposed estimator with four different existing estimators are also included. © 2016 pakistan journal of statistics.