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Instrumental Variable Estimation of Nonlinear Errors‐in‐Variables Models
Author(s) -
Schennach Susanne M
Publication year - 2007
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2007.00736.x
Subject(s) - estimator , mathematics , nonparametric statistics , instrumental variable , monte carlo method , nonparametric regression , conditional expectation , errors in variables models , kernel density estimation , kernel (algebra) , kernel regression , generalized method of moments , observable , statistics , physics , quantum mechanics , combinatorics
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 n 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.