Conditional vs unconditional quantile regression models: A guide to practicioners

Gabriel Montes-Rojas ^[1] ; Javier Alejo ^[2] ; Federico Favata ^[4] ; Martín Trombetta ^[3]
1. [1] Universidad de Buenos Aires
  
  Universidad de Buenos Aires
  
  Argentina
2. [2] Universidad de la República
  
  Universidad de la República
  
  Uruguay
3. [3] Universidad Nacional de General Sarmiento
  
  Universidad Nacional de General Sarmiento
  
  Argentina
4. [4] Universidad de Nacional de San Martín
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Localización: Economía, ISSN 0254-4415, Vol. 44, Nº. 88 (SPECIAL: Preferential Trade Agreements, Trade and Multilateral Liberalization), 2021, págs. 76-93
Idioma: inglés
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Resumen
- 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.