Econometrica: Jan 2007, Volume 75, Issue 1
Instrumental Variable Estimation of Nonlinear Errors‐in‐Variables Models
Susanne M Schennach
This paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of Fourier transforms of conditional expectations of observable variables. For parametrically specified regression functions, we propose a root consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged‐in nonparametric kernel density estimate. Both the identification and the estimation methodologies rely on Fourier analysis and on the theory of generalized functions. The finite‐sample properties of the estimator are investigated through Monte Carlo simulations.
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Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models, Supplementary Material: Review, Proofs, Extensions and Example of ApplicationThis Supplementary Material contains some of the more technical details omitted from the paper ?Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models?. First, a brief review of the Theory of Generalized Functions is presented. Second, proofs regarding some basic properties of Fourier transforms as well as the asymptotics of the proposed GMMestimator are given. Third, the proposed estimator is compared with the one suggested in Hausman, Newey, Ichimura, Powell (1991). Fourth, an alternative derivation of the moment conditions necessitating weaker regularity conditions is provided. Fifth, the details of the Monte Carlo simulations are described. Sixth, an application of the proposed methodology to the estimation of the black-white income gap is presented. Finally, some computational aspects of the implementation of the estimator are described.