Measurement Error Models

Many economic data sets are contaminated by the mismeasured variables. The problem of measurement errors is one of the most fundamental problems in empirical economics. The presence of measurement errors causes biased and inconsistent parameter estimates and leads to erroneous conclusions to various degrees in economic analysis. Techniques for addressing measurement error problems can be classified along two dimensions. Different techniques are employed in linear errors-in-variables (EIV) models and in nonlinear EIV models. (In this article, a “linear” EIV model means it is linear in both the mismeasured variables and the parameters of interest; a “nonlinear” EIV model means it is nonlinear in the mismeasured variables.) Different methods are used to treat classical measurement errors and nonclassical measurement errors. (A measurement error is “classical” if it is independent of the latent true variable; otherwise it is “nonclassical”.) Since various methods for linear EIV models with classical measurement errors are already known and are widely applied in empirical economics, in this survey we shall focus more on recent theoretical advances on methods for identification and estimation of nonlinear EIV models with classical or nonclassical measurement errors. While measurement error problems can be as severe with time series data as with cross sectional data, in this survey we shall focus on cross Department of Economics, New York University and Department of Economics, Stanford University and