Penalized Estimation of a Quantile Count Model for Panel Data

This paper investigates the estimation of a panel quantile model for count data with individual heterogeneity. The method is needed as a result of the increased availability of digital data, which allows us to track event counts at the individual level for a large number of activities from webclicks and retweets to store visits and purchases. We propose a penalized quantile regression estimator and we show that the slope parameter estimator is consistent and asymptotically Gaussian under similar conditions to the ones used in the literature. The penalty serves to shrink individual effects toward zero, improving the performance of fixed effects quantile regression estimators when the time series dimension is small relative to the number of subjects in the panel. We investigate solutions to the computational challenges resulting from the need to estimate tens of thousands of parameters in high-dimensional settings and several simulation studies are carried out to study the small sample performance of the proposed approach. We present a novel empirical application to individual trip counts to the store based on a large panel of food purchase transactions.