Penalized quantile regression with semiparametric correlated effects: an application with heterogeneous preferences

This paper proposes new ℓ₁-penalized quantile regression estimators for panel data, which explicitly allows for individual heterogeneity associated with covariates. Existing fixed-effects estimators can potentially suffer from three limitations which are overcome by the proposed approach: (i) incidental parameters bias in nonlinear models with large N and small T; (ii) lack of efficiency; and (iii) inability to estimate the effects of time-invariant regressors. We conduct Monte Carlo simulations to assess the small-sample performance of the new estimators and provide comparisons of new and existing penalized estimators in terms of quadratic loss. We apply the technique to an empirical example of the estimation of consumer preferences for nutrients from a demand model using a large transaction-level dataset of household food purchases. We show that preferences for nutrients vary across the conditional distribution of expenditure and across genders, and emphasize the importance of fully capturing consumer heterogeneity in demand modeling.