Quantile regression (QR) is a powerful tool in exploring the heterogeneous impact of covariates on different quantiles of an outcome distribution. However, many economic outcomes are results of individual interactions (e.g., social, spatial, industrial), making standard QR inference invalid and therefore is inappropriate for exploring the impact of those interactions on quantiles of economic outcomes. This article introduces the QR method for cross-section data that features the local cross-section dependence stemming from interactions between individual specific observations and investigates asymptotic properties of the estimator in this environment. We show that, in general the QR estimator is inconsistent. Necessary conditions are given to establish the consistency and the asymptotic normality of the estimator. The quasi-maximum likelihood estimator (QMLE) is suggested as an alternative approach to relax those assumptions.
The potential of the model is highlighted with an empirical application to the wage data from the United States.