Instrumental Variable Quantile Estimation of Spatial Autoregressive Models∗

We propose a spatial quantile autoregression (SQAR) model, which allows cross-sectional dependence among the responses, unknown heteroscedasticity in the disturbances, and heterogeneous impacts of covariates on different points (quantiles) of a response distribution. The instrumental variable quantile regression (IVQR) method of Chernozhukov and Hansen (2006) is generalized to allow the data to be non-identically distributed and dependent, an IVQR estimator for the SQAR model is then defined, and its asymptotic properties are derived. Simulation results show that this estimator performs well in finite samples at various quantile points. In the special case of spatial median regression, it outperforms the conventional QML estimator without taking into account of heteroscedasticity in the errors; it also outperforms the GMM estimators with or without heteroscedasticity. An empirical illustration is provided. JEL classifications: C13, C21, C26, C51