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High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing

Author

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  • Belloni, Alexandre

    (Fuqua Business School, Duke University)

  • Chen, Mingli

    (Department of Economics, University of Warwick)

  • Madrid Padilla, Oscar Hernan

    (Department of Statistics, University of California, Los Angeles)

  • Wang, Zixuan (Kevin)

    (Harvard University)

Abstract

We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: sparse means while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represented by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional sparse estimators, such as the `1-penalised Quantile Regression, and for traditional latent factor estimator, such as PCA. We propose a new estimation procedure, based on the ADMM algorithm, that consists of combining the quantile loss function with `1 and nuclear norm regularization. We show, under general conditions, that our estimator can consistently estimate both the nonzero coefficients of the covariates and the latent low-rank matrix. Our proposed model has a “Characteristics + Latent Factors” Asset Pricing Model interpretation: we apply our model and estimator with a large-dimensional panel of financial data and find that (i) characteristics have sparser predictive power once latent factors were controlled (ii) the factors and coefficients at upper and lower quantiles are different from the median.

Suggested Citation

  • Belloni, Alexandre & Chen, Mingli & Madrid Padilla, Oscar Hernan & Wang, Zixuan (Kevin), 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," The Warwick Economics Research Paper Series (TWERPS) 1230, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:1230
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    3. Babii, Andrii & Ball, Ryan T. & Ghysels, Eric & Striaukas, Jonas, 2023. "Machine learning panel data regressions with heavy-tailed dependent data: Theory and application," Journal of Econometrics, Elsevier, vol. 237(2).
    4. Ma, Shujie & Su, Liangjun & Zhang, Yichong, 2020. "Detecting Latent Communities in Network Formation Models," Economics and Statistics Working Papers 12-2020, Singapore Management University, School of Economics.
    5. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2218, Faculty of Economics, University of Cambridge.
    6. Yiren Wang & Liangjun Su & Yichong Zhang, 2022. "Low-rank Panel Quantile Regression: Estimation and Inference," Papers 2210.11062, arXiv.org.
    7. Michael Vogt & Christopher Walsh & Oliver Linton, 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org.
    8. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    9. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

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