Conditional vs Unconditional Quantile Regression Models: A Guide to Practitioners

  • Javier Alejo Universidad de la República Uruguay

    IECON - Universidad de la República Uruguay.

  • Federico Favata Universidad de Nacional de San Martín

    Centro de Investigaciones Macroeconómicas para el Desarrollo - Universidad de Nacional de San Martín.

  • Gabriel Montes-Rojas Universidad de Buenos Aires
    Instituto Interdisciplinario de Economía Política, Universidad de Buenos Aires, CONICET and Universidad de San Andrés.
  • Martín Trombetta niversidad Nacional de General Sarmiento

    CONICET and Universidad Nacional de General Sarmiento.

Keywords: Quantile regression, Unconditional quantile regression, Influence functions


This paper analyzes two econometric tools that are used to evaluate distributional effects, conditional quantile regression (CQR) and unconditional quantile regression (UQR). Our main objective is to shed light on the similarities and differences between these methodologies. An interesting theoretical derivation to connect CQR and UQR is that, for the effect of a continuous covariate, the UQR is a weighted average of the CQR. This imposes clear bounds on the values that UQR coefficients can take and provides a way to detect misspecification. The key here is a match between CQR whose predicted values are the closest to the unconditional quantile. For a binary covariate, however, we derive a new analytical relationship. We illustrate these models using age returns and gender gap in Argentina for 2019 and 2020.


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How to Cite
Alejo, J., Favata, F., Montes-Rojas, G., & Trombetta, M. (2021). Conditional vs Unconditional Quantile Regression Models: A Guide to Practitioners. Economia, 44(88), 76-93.