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On Deconvolution as a First Stage Nonparametric Estimator

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  • Yingyao Hu
  • Geert Ridder

Abstract

We reconsider Taupin’s (2001) Integrated Nonlinear Regression (INLR) estimator for a nonlinear regression with a mismeasured covariate. We find that if we restrict the distribution of the measurement error to the class of range-restricted distributions, then weak smoothness assumptions suffice to ensure sqrt(n) consistency of the estimator. The restriction to such distributions is innocuous, because it does not affect the fit to the data. Our results show that deconvolution can be used in a nonparametric first step without imposing restrictive smoothness assumptions on the parametric model.

Suggested Citation

  • Yingyao Hu & Geert Ridder, 2005. "On Deconvolution as a First Stage Nonparametric Estimator," IEPR Working Papers 05.29, Institute of Economic Policy Research (IEPR).
    • Handle: RePEc:scp:wpaper:05-29
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    Cited by:

    1. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    3. Kato, Kengo & Sasaki, Yuya, 2019. "Uniform confidence bands for nonparametric errors-in-variables regression," Journal of Econometrics, Elsevier, vol. 213(2), pages 516-555.
    4. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
    5. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    6. Botosaru, Irene, 2023. "Time-varying unobserved heterogeneity in earnings shocks," Journal of Econometrics, Elsevier, vol. 235(2), pages 1378-1393.
    7. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.
    8. Karen X. Yan & Qi Li, 2018. "Nonparametric Estimation of a Conditional Quantile Function in a Fixed Effects Panel Data Model," JRFM, MDPI, vol. 11(3), pages 1-10, August.
    9. An, Yonghong & Hu, Yingyao, 2012. "Well-posedness of measurement error models for self-reported data," Journal of Econometrics, Elsevier, vol. 168(2), pages 259-269.
    10. Hu, Yingyao & Schennach, Susanne M. & Shiu, Ji-Liang, 2017. "Injectivity of a class of integral operators with compactly supported kernels," Journal of Econometrics, Elsevier, vol. 200(1), pages 48-58.
    11. Kato, Kengo & Sasaki, Yuya, 2018. "Uniform confidence bands in deconvolution with unknown error distribution," Journal of Econometrics, Elsevier, vol. 207(1), pages 129-161.
    12. Irene Botosaru, 2017. "Identifying Distributions in a Panel Model with Heteroskedasticity: An Application to Earnings Volatility," Discussion Papers dp17-11, Department of Economics, Simon Fraser University.

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