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Specification testing for errors-in-variables models

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  • Taisuke Otsu
  • Luke Taylor

Abstract

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the method proposed by Hall and Ma (2007), our test allows general nonlinear regression models. Since our test employs the smoothing approach, it complements the nonsmoothing one by Hall and Main terms of local power properties. The other existing method, by Song (2008), is shown to possess trivial power under certain alternatives. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities and develop a bootstrap method to approximate the critical value. We apply the test to the specification of Engel curves in the US. Finally, some simulation results endorse our theoretical findings: our test has advantages in detecting high frequency alternatives and dominates the existing tests under certain specifications.

Suggested Citation

  • Taisuke Otsu & Luke Taylor, 2016. "Specification testing for errors-in-variables models," STICERD - Econometrics Paper Series /2015/586, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:/2015/586
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    References listed on IDEAS

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    Cited by:

    1. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2022. "Estimation of varying coefficient models with measurement error," Journal of Econometrics, Elsevier, vol. 230(2), pages 388-415.
    2. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2021. "Average Derivative Estimation Under Measurement Error," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1004-1033, October.
    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. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On the uniform convergence of deconvolution estimators from repeated measurements," LSE Research Online Documents on Economics 107533, London School of Economics and Political Science, LSE Library.
    5. Daisuke Kurisu & Taisuke Otsu, 2019. "On the uniform convergence of deconvolution estimators from repeated measurements," STICERD - Econometrics Paper Series 604, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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    More about this item

    Keywords

    specification test; measurement errors; deconvolution;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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