Description:
This chapter overviews the recent progress towards the identification and the estimation of models in which some of the variables are either imperfectly measured or even entirely unobserved, with a special focus on models with nonlinear, nonparametric, nonclassical or nonseparable features. Starting from the basic treatment of nonlinear models with measurement error assuming a known measurement error distribution or validation data availability, we then turn to the methods relying on more readily available auxiliary variables (such as repeated measurements, instrumental variables or general indicators). These models are then extended to fully nonlinear nonparametric and nonseparable factor models and to general latent (i.e. unobserved) variables models, in which the features of the latent variables are indirectly inferred from their effects on observables. We also identify important connections with related fields, such as nonlinear panel data, limited dependent variables, game theoretic models, dynamic models and set-identification.