Measurement error in nonlinear models – a review

This overview of the recent econometrics literature on measurement error in nonlinear models centres on the question of the identification and estimation of general nonlinear models with measurement error. Simple approaches that rely on distributional knowledge regarding the measurement error (such as deconvolution or validation data techniques) are briefly presented. Then follows a description of methods that secure identification via more readily available auxiliary variables (such as repeated measurements, measurement systems with a ‘factor model’ structure, instrumental variables and panel data). Methods exploiting higher-order moments or bounding techniques to avoid the need for auxiliary information are 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 covered and applications of measurement error techniques to other fields are outlined.