A Consistent Estimator of the Slope in a Regression Model with Errors in the Variables

Abstract

Consistent estimators for the slope coefficient in a regression model, where both variables are subject to errors, do not exist without some restrictions on the model. When the serial correlation of (lag 1) of the regression is known to be nonzero, one can obtain extra information from the first differences and get a consistent estimator for the slope. It turns out that this estimator is (asymptotically) equivalent to an estimator which uses as instrumental variable the average of the values of the regression, advanced and lagged by a single period. Using lagged values only is less efficient.