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Fused LASSO as Non-crossing Quantile Regression

Author

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  • Szendrei, Tibor

    (National Institute of Economic and Social Research (NIESR))

  • Bhattacharjee, Arnab

    (Heriot-Watt University, Edinburgh)

  • Schaffer, Mark E

    (Heriot-Watt University, Edinburgh)

Abstract

Quantile crossing has been a challenge for quantile regression, leading to research in how to obtain monotonically increasing quantile estimates. While important contributions, these papers do not provide insight into how enforcing monotonicity influences the estimated coefficients. This paper fills this gap and shows that non-crossing constraints are a type of fused-shrinkage. The proposed estimator has good fit and (fused) variable selection properties: it can reliably identify quantile varying parameters. We investigate the 'heat-or-eat' dilemma and show that prepayment has a non-linear impact on households' consumption choices. In a growth-at-risk application the estimator has the best forecast performance.

Suggested Citation

  • Szendrei, Tibor & Bhattacharjee, Arnab & Schaffer, Mark E, 2024. "Fused LASSO as Non-crossing Quantile Regression," IZA Discussion Papers 17149, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp17149
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    References listed on IDEAS

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    1. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    2. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    3. Burlinson, Andrew & Davillas, Apostolos & Law, Cherry, 2022. "Pay (for it) as you go: Prepaid energy meters and the heat-or-eat dilemma," Social Science & Medicine, Elsevier, vol. 315(C).
    4. Alberto Abadie & Maximilian Kasy, 2019. "Choosing Among Regularized Estimators in Empirical Economics: The Risk of Machine Learning," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 743-762, December.
    5. Bhattacharya, J. & DeLeire, T. & Haider, S. & Currie, J., 2003. "Heat or Eat? Cold-Weather Shocks and Nutrition in Poor American Families," American Journal of Public Health, American Public Health Association, vol. 93(7), pages 1149-1154.
    6. Timothy K. M. Beatty & Laura Blow & Thomas F. Crossley, 2014. "Is there a ‘heat-or-eat’ trade-off in the UK?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 281-294, January.
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    More about this item

    Keywords

    fused-shrinkage; quantile regression; non-crossing constraints; LASSO;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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