Recent Advances in the Measurement Error Literature

This article reviews recent significant progress made in developing estimation and inference methods for nonlinear models in the presence of mismeasured data that may or may not conform to the classical assumption of independent zero-mean errors. The aim is to cover a broad range of methods having differing levels of complexity and strength of the required assumptions. Simple approaches that form the elementary building blocks of more advanced approaches are discussed first. Then, special attention is devoted to methods that rely on readily available auxiliary variables (e.g., repeated measurements, indicators, or instrumental variables). Results relaxing most of the commonly invoked simplifying assumptions are presented (linear measurement structure, independent errors, zero-mean errors, availability of auxiliary information). This article also provides an overview of important connections with related fields, such as latent variable models, nonlinear panel data, factor models, and set identification, and applications of the methods to other fields traditionally unrelated to measurement error models.