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Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments

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Author Info
Yingyao Hu
Susanne Schennach () (Institute for Fiscal Studies and University of Chicago)

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Abstract

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, this paper establishes that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. The main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to order the eigenfunctions so that the decomposition is unique. The authors propose a convenient sieve-based estimator, derive its asymptotic properties and investigate its finite-sample behavior through Monte Carlo simulations. An example of application to the relationship between earnings and divorce rates is also provided.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP17/06.

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Length: 64 pp.
Date of creation: Sep 2006
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Handle: RePEc:ifs:cemmap:17/06

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andrew Chesher, 2001. "Parameter approximations for quantile regressions with measurement error," CeMMAP working papers CWP02/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  2. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  3. Susanne M. Schennach, 2004. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometric Society 2004 North American Summer Meetings 602, Econometric Society. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation, Yale University. [Downloadable!]
  2. Yingyao Hu and Geert Ridder, 2009. "Estimation of Nonlinear Models with Mismeasured Regressors Using Marginal Information," Economics Working Paper Archive 554, The Johns Hopkins University,Department of Economics. [Downloadable!]
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  3. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification of Regression Models Containing a Misclassified Dichotomous Regressor Without Instruments," Boston College Working Papers in Economics 675, Boston College Department of Economics. [Downloadable!]
    Other versions:
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