Mid-quantile regression for discrete panel data

Abstract

We propose novel quantile regression methods when the response is discrete and the data come from a longitudinal design. The approach is based on conditional mid-quantiles, which have good theoretical properties even in the presence of ties. Optimization of a ridge-type penalized objective function accommodates for the data dependence. We investigate the performance and pertinence of our methods in a simulation study and an original application to macroprudential policies use in more than one hundred countries over a period of seventeen years.

Keywords:

• Cluster design
• fixed effects
• mid-quantile regression
• panel data
• random effects

Supplementary Materials

The results of the simulation study are fully described in a Web Appendix. An R implementation of our approach, the macroprudential policy data and the code to reproduce the analyses in Section 5 are publicly available at https://github.com/aruxxo/Mid-quantilePanelRegression.

Acknowledgments

The authors are grateful to an associate editor and a referee for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first and second authors have been partially funded by the European Union–NextGenerationEU, within the framework GRINS – Growing Resilient, INclusive and Sustainable project (GRINS PE00000018 – CUP E83C22004690001). The views and opinions expressed are solely those of the authors and do not necessarily reflect those of the European Union, nor can the European Union be held responsible for them. The second author has been partially funded by the PRIN funding scheme of the Italian Ministry of University and Research (Grant No. 2022LANNKC CUP E53D23005810006). The third author has been partially funded by the Sapienza University of Rome funding scheme (Grant No. RM122181611FD6AB).