Bias in Slope Estimates for the Linear Errors in Variables Model by the Variance Ratio Method

Abstract

Slope estimates for linear measurement error (errors in variables) models based on assumed knowledge of the ratio of measurement error variances are biased if the underlying linear relationship is anything other than a completely deterministic, law-like relationship. This paper describes an eight-parameter linear measurement error model of general applicability that includes an optional "errors in equations" term (Malinvaud, E., 1980, Statistical Methods of Econometrics) that allows the explicit characterization of the asymptotic bias of such slope estimates when the assumption of a law-like relationship does not hold. This bias may be large, underscoring the importance of recognizing the potential influence of errors in equations in measurement error models.