Combining least-squares and quantile regressions

► Efficiency can be gained by combining least-squares and quantile regression moment conditions. ► The difficulty is that the estimating equations associated with the quantiles are non-smooth. ► We develop a kernel-based smoothing technique for non-smooth estimating equations. ► We derive the asymptotic properties of the empirical likelihood and generalized method of moments estimators. ► We examine the small sample properties by simulations and apply the method to real data.