Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models

By Susanne M. Schennach. 2004

117 citations recorded by the source corpus.

In linear specifications, the bias due to the presence of measurement error in a regressor can be entirely avoided when either repeated measurements or instruments are available for the mismeasured regressor. The situation is more complex in nonlinear settings. While identification and root n consistent estimation of general nonlinear specifications have recently been proven in the presence of repeated measurements, similar results relying on instruments have so far only been available for polynomial specifications and absolutely integrable regression functions. This paper addresses two unresolved issues. First, it is shown that instruments indeed allow for the fully nonparametric identification of general nonlinear regression models in the presence of measurement error. Second, when the regression function is parametrically specified, a root n consistent and asymptotically normal estimator is provided. The starting point of the proposed approach is a system of two functional equations that relate conditional expectations of observed variables to the regression function of interest, as first proposed by Hausman, Ichimura, Newey and Powell (1991) for polynomial specifications. It is shown that these two equations have a unique solution, thus establishing identification. The proposed estimation procedure relies on the same functional equations, and the proof of asymptotic normality and root n consistency is based on standard results regarding the asymptotics of semiparametric estimators

Subfields: Applied Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ca98d10a663868b6916586f50c34694123cf2fd6

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Citations in the corpus

Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution (2008, unknown): “Estimation of a general nonlinear model with measurement error in the covariates is a notoriously difficult problem that has received considerable attention in the recent econometrics literature (relevant studies using repeated measurements or instrumental variables include Hausman et al., 1991; Wan”
Controlling for endogeneity with instrumental variables in strategic management research (2008, background): “…1958).3, 4 In that case, instrumental variables estimations are the most common way to overcome measurement error problems for linear models (Schennach, 2007).5 In addition, if instrumental variables are measured with error, analysts can still use them as long as their measurement error is…”
ON THE COMPLETENESS CONDITION IN NONPARAMETRIC INSTRUMENTAL PROBLEMS (2010, methodology): “Zero-freeness of the characteristic function is a usual assumption in deconvolution problems (see, e.g., Devroye, 1989; Fan and Truong, 1993; Li and Vuong, 1998; Schennach, 2004, 2007) and is satisfied by, among others, Gaussian, Student, Laplace, and α-stable distributions.”
Local indirect least squares and average marginal effects in nonseparable structural systems (2012, methodology): “More general proxies contaminated by nonclassical or Berkson-type 2 measurement errors can be treated by adapting methods of Hu and Schennach (2008) or Schennach (2007).”