Measurement errors in economic data are pervasive and nontrivial in size. The presence of measurement errors causes biased and inconsistent parameter estimates and leads to erroneous conclusions to various degrees in economic analysis. While linear errors-in-variables models are usually handled with well-known instrumental variable methods, this article provides an overview of recent research papers that derive estimation methods that provide consistent estimates for nonlinear models with measurement errors. We review models with both classical and nonclassical measurement errors, and with misclassification of discrete variables. For each of the methods surveyed, we describe the key ideas for identification and estimation, and discuss its application whenever it is currently available.

A variety of identification strategies have a common cell structure, in which the observed heterogeneity of the regression defines a partition of the sample into cells. Typically in the presence of exogenous covariates that define the cell structure, identification assumptions are imposed conditional on each value of the covariate, or cell by cell. Treatment effects across cells are typically heterogeneous. Researchers might be interested in unconditional parameters which are the averaged treatment effects across the cells. Alternatively, treatment effects can be estimated more efficiently if researchers are willing to impose additional parametric and semiparametric structures on the heterogeneous treatment effects across cells.