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Nonparametric regression with multiple thresholds: Estimation and inference

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  • Chiou, Yan-Yu
  • Chen, Mei-Yuan
  • Chen, Jau-er

Abstract

This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties of the local constant estimator for a nonparametric regression with multiple thresholds. However, the number of thresholds and corresponding threshold values are typically unknown in practice. We then use our testing procedure to determine the unknown number of thresholds and derive the limiting distribution of the proposed test. The Monte Carlo simulation results indicate the adequacy of the modified test and accuracy of the sequential estimation of the threshold values. We apply our testing procedure to an empirical study of the 401(k) retirement savings plan with income thresholds.

Suggested Citation

  • Chiou, Yan-Yu & Chen, Mei-Yuan & Chen, Jau-er, 2018. "Nonparametric regression with multiple thresholds: Estimation and inference," Journal of Econometrics, Elsevier, vol. 206(2), pages 472-514.
    • Handle: RePEc:eee:econom:v:206:y:2018:i:2:p:472-514
    DOI: 10.1016/j.jeconom.2018.06.011
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    Citations

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    Cited by:

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    2. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    3. Jau-er Chen & Chen-Wei Hsiang, 2019. "Causal Random Forests Model Using Instrumental Variable Quantile Regression," Econometrics, MDPI, vol. 7(4), pages 1-22, December.
    4. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    5. Christis Katsouris, 2023. "Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors," Papers 2305.00860, arXiv.org, revised May 2023.
    6. Takayuki Toda & Ayako Wakano & Takahiro Hoshino, 2019. "Regression Discontinuity Design with Multiple Groups for Heterogeneous Causal Effect Estimation," Papers 1905.04443, arXiv.org.

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    More about this item

    Keywords

    Nonparametric regression; Threshold variable; Threshold value; Significance test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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