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Modal regression for fixed effects panel data

Author

Listed:
  • Aman Ullah

    (University of California)

  • Tao Wang

    (University of California)

  • Weixin Yao

    (University of California)

Abstract

Most research on panel data focuses on mean or quantile regression, while there is not much research about regression methods based on the mode. In this paper, we propose a new model named fixed effects modal regression for panel data in which we model how the conditional mode of the response variable depends on the covariates and employ a kernel-based objective function to simplify the computation. The proposed modal regression can complement the mean and quantile regressions and provide better central tendency measure and prediction performance when the data are skewed. We present a linear dummy modal regression method and a pseudo-demodeing two-step method to estimate the proposed modal regression. The computations can be easily implemented using a modified modal–expectation–maximization algorithm. We investigate the asymptotic properties of the modal estimators under some mild regularity conditions when the number of individuals, N, and the number of time periods, T, go to infinity. The optimal bandwidths with order $$(NT)^{-1/7}$$ ( N T ) - 1 / 7 are obtained by minimizing the asymptotic weighted mean squared errors. Monte Carlo simulations and two real data analyses of a public capital productivity study and a carbon dioxide emissions study are presented to demonstrate the finite sample performance of the newly proposed modal regression.

Suggested Citation

  • Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    • Handle: RePEc:spr:empeco:v:60:y:2021:i:1:d:10.1007_s00181-020-01999-w
    DOI: 10.1007/s00181-020-01999-w
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    Citations

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    Cited by:

    1. Xin Jing & Jin Seo Cho, 2023. "Forecasting the Confirmed COVID-19 Cases Using Modal Regression," Working papers 2023rwp-217, Yonsei University, Yonsei Economics Research Institute.
    2. Qi Li & Vasilis Sarafidis & Joakim Westerlund, 2021. "Essays in honor of Professor Badi H Baltagi," Empirical Economics, Springer, vol. 60(1), pages 1-11, January.
    3. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    4. Li, Qi & Sarafidis, Vasilis & Westerlund, Joakim, 2020. "Essays in Honor of Professor Badi H Baltagi: Editorial," MPRA Paper 104751, University Library of Munich, Germany.
    5. Smith, Lisa C. & Frankenberger, Timothy R., 2022. "Recovering from severe drought in the drylands of Ethiopia: Impact of Comprehensive Resilience Programming," World Development, Elsevier, vol. 156(C).
    6. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    7. Zhe Sun & Yundong Tu, 2024. "Factors in Fashion: Factor Analysis towards the Mode," Papers 2409.19287, arXiv.org.

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    More about this item

    Keywords

    Asymptotic property; Fixed effects; MEM algorithm; Modal regression; Panel data; Pseudo-demodeing;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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