Mid-quantile regression for discrete panel data

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.