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Threshold regression with nonparametric sample splitting

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  • Lee, Yoonseok
  • Wang, Yulong

Abstract

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator. We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. We illustrate empirical relevance of this new model by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery.

Suggested Citation

  • Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:816-842
    DOI: 10.1016/j.jeconom.2022.07.005
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    Cited by:

    1. Yoonseok Lee & Yulong Wang, 2020. "Inference in Threshold Models," Center for Policy Research Working Papers 223, Center for Policy Research, Maxwell School, Syracuse University.

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    More about this item

    Keywords

    Threshold regression; Sample splitting; Nonparametric; Random field; Tipping point; Metropolitan area boundary;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics

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