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Multivariate quantile regression

Author

Listed:
  • Montes Rojas Gabriel
  • Galvao Antonio

Abstract

This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches—such as directional quantiles, vector quantile regression, or copula-based methods—MQR defines quantiles through the conditional probability structure of the joint conditional distribution function. The method constructs multivariate quantile curves using sequential univariate quantile regressions derived from conditioning mechanisms, allowing for an intuitive interpretation and flexible estimation of marginal effects. The paper develops theoretical foundations of MQR, including asymptotic properties of the estimators. Through simulation exercises, the estimator demonstrates robust performance across different dependence structures. As an empirical application, the MQR framework is applied to the analysis of exchange rate pass-through in Argentina from 2004 to 2024.

Suggested Citation

  • Montes Rojas Gabriel & Galvao Antonio, 2025. "Multivariate quantile regression," Asociación Argentina de Economía Política: Working Papers 4821, Asociación Argentina de Economía Política.
    • Handle: RePEc:aep:anales:4821
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    References listed on IDEAS

    as
    1. Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
    2. Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods

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