A simple estimator for nonlinear error in variable models

• Published in: Journal of econometrics Vol. 117; no. 1; pp. 1 - 19
• Main Authors: Hong, Han, Tamer, Elie
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2003; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Applied sciences; Data analysis; Distribution; Distributional assumptions; Econometrics; Error; Estimating techniques; Exact sciences and technology; Inference from stochastic processes; time series analysis; Laplace (double exponential) distribution; Mathematical analysis; Mathematics; Measurement; Model testing; Nonlinear models with measurement error; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Parametric inference; Probability and statistics; Revised moment conditions; Sciences and techniques of general use; Simulation; Statistics; Studies; C31; Nonlinear models with measurement error; Revised moment conditions; C13; Laplace (double exponential) distribution; Distributional assumptions; Monte Carlo method; Error estimation; Exponential distribution; Error in variable; Statistical simulation; Economic data; Revised moment condition; Parametric method; Laplace distribution; Non linear model; Marginal distribution; Econometrics; Measurement error
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/S0304-4076(03)00116-7

We propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data, such as validation data or double measurements, are available. We assume that the marginal distributions of the measurement errors are Laplace (double exponential) with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other. Under these assumptions, we derive simple revised moment conditions in terms of the observed variables. They are used to make inference about the model parameters and the variance of the measurement error. The results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest. Our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute. Our estimation method is particularly useful in situations where no additional data are available, which is the case in many economic data sets. Simulation study demonstrates good finite sample properties of our proposed estimator. We also examine the performance of the estimator in the case where the error distribution is misspecified.