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Estimation of Nonlinear Models with Measurement Error Using Marginal Information

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  • Geert Ridder
  • Yingyao Hu

Abstract

We consider the problem of consistent estimation of nonlinear models with mismeasured explanatory variables, when marginal information on the true values of these variables is available. The marginal distribution of the true variables is used to identify the distribution of the measurement error, and the distribution of the true variables conditional on the mismeasured and the other explanatory variables. The estimator is shown to be root-n consistent and normally distributed. The simulation results are in line with the asymptotic results. The semi-parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of welfare benefits is obtained from an administrative source

Suggested Citation

  • Geert Ridder & Yingyao Hu, 2004. "Estimation of Nonlinear Models with Measurement Error Using Marginal Information," Econometric Society 2004 North American Summer Meetings 21, Econometric Society.
    • Handle: RePEc:ecm:nasm04:21
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    Cited by:

    1. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    2. Aprajit Mahajan, 2009. "Estimating Price Elasticities with Nonlinear Errors in Variables," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 793-805, November.
    3. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    4. Yingyao Hu & Arthur Lewbel & Susanne M. Schennach, 2007. "Nonparametric identification of the classical errors-in-variables model without side information," CeMMAP working papers CWP14/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    6. 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 for Research in Economics, Yale University.
    7. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information," CeMMAP working papers CWP18/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Shiu, Ji-Liang, 2016. "Identification and estimation of endogenous selection models in the presence of misclassification errors," Economic Modelling, Elsevier, vol. 52(PB), pages 507-518.
    9. Natalia, Khorunzhina & Wayne Roy, Gayle, 2011. "Heterogenous intertemporal elasticity of substitution and relative risk aversion: estimation of optimal consumption choice with habit formation and measurement errors," MPRA Paper 34329, University Library of Munich, Germany.

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    More about this item

    Keywords

    measurement error model; marginal information; deconvolution;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

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