A Dual Least-Squares Estimator of the Errors-in-Variables Model Using Only First and Second Moments

Abstract

The paper presents an estimator of the errors-in-variables in multiple regressions using only first and second-order moments. The consistency property of the estimator is explored by Monte Carlo experiments. Based on these results, we conjecture that the estimator is consistent. The proof of consistency, to be dealt in another paper, is based upon the assumptions of Kiefer and Wolfowitz (1956). The novel treatment of the errors-in-variables model relies crucially upon a neutral parameterization of the error terms of the dependent and the explanatory variables. The estimator does not have a closed form solution. It requires the maximization of a dual least-squares objective function that guarantees a global optimum. This estimator, therefore, includes the naïve least-squares method (when only the dependent variable is measured with error) as a special case.

Keywords: errors-in-variables, measurement errors, dual least squares, first moments, second moments, Monte Carlo

JEL Classification: C30