A Critical Examination of Orthogonal Regression

Abstract

The method of orthogonal regression has a long and distinguished history in statistics and economics. It has been viewed as superior to ordinary least squares in certain situations. However, our theoretical and empirical study shows that this method is flawed in that it implicitly assumes equations without the error term. A direct result is that it over-optimistically estimates the slope coefficient. It also cannot be applied to testing if there is an equal proportionate relationship between two variables, a case where orthogonal regression has been frequently used in previous research. We offer an alternative adjusted orthogonal estimator and show that it performs better than all the previous orthogonal regression models and, in most cases, better than ordinary least squares.

Keywords: Orthogonal Regression, Errors-in-Variables, OLS

JEL Classification: C20, C52