8 - Measurement Error in Nonlinear Models – A Review

Summary

Introduction

Measurement error is widespread in statistical and/or economic data and can have substantial impact on point estimates and statistical inference in general. Accordingly, there exists a vast literature focused on addressing this problem. The present overview emphasizes the recent econometric literature on the topic and mostly centers on the author's interest in the question of identification (and consistent estimation) of general nonlinear models with measurement error without simply assuming that the distribution of the measurement error is known.

This chapter is organized as follows. First, we explain the origins of measurement-error bias before describing simple approaches that rely on distributional knowledge regarding the measurement error (e.g., decon-volution or validation-data techniques). We then describe methods that secure identification via more readily available auxiliary variables (e.g., repeated measurements, measurement systems with a “factor model” structure, instrumental variables, and panel data). An overview of methods exploiting higher-order moments or bounding techniques to avoid the need for auxiliary information is presented next. Special attention is devoted to a recently introduced general method to handle a broad class of latent variable models, called Entropic Latent Variable Integration via Simulation (ELVIS). Finally, the complex but active topic of nonclassical measurement error is discussed and applications of measurement-error techniques to other fields are outlined.