A Two-Step Procedure for Estimating Spatial Error Quantile Regression Models

Conditional quantile regression models are complementary to the conditional median model in that they provide a complete representation of the conditional distribution of the response variable given the predictors and not only of their conditional mean. This is crucial in situations where the relationship between predictors and responses is not uniform across all levels, for example, in fields like housing market analysis where the impact of factors such as location, size, and amenities can vary significantly between low-priced and high-priced homes. They have also been considered in the spatial econometric literature as a robust alternative to the standard linear regression when data are characterized by non-normality. So far, the spatial econometric literature concentrated on conditional quantile spatial lag specifications which incorporate spatial correlation in the form of a spatially lagged variable included in the list of predictors. This paper aims at exploring the other side of the moon by specifying conditional spatial quantile models in the form of a spatial error correlation (termed Spatial Error Quantile Model) and by suggesting feasible estimators of the parameters involved. In particular, we propose an estimation procedure analogous to the feasible GLS suggested by Keleijian and Prucha (J Real Estate Finance Econ 17:99–121, 1998) for the standard linear regression models, we prove its asymptotic properties, and we examine its small sample behaviour through a set of Monte Carlo experiments. We also illustrate the improved efficiency of the proposed estimator by re-examining a set of real data already employed by Chasco and Le Gallo (Spat Economic Anal 10(3):317–343, 2015) to estimate a hedonic house price model.