Variable Selection with Spatially Autoregressive Errors: A Generalized Moments LASSO Estimator

We propose generalized moments LASSO estimator, combining LASSO with GMM, for penalized variable selection and estimation under the spatial error model with spatially autoregressive errors. We establish parameter consistency and selection sign consistency of the proposed estimator in the low dimensional setting when the parameter dimension p < sample size n, as well as the high dimensional setting with p greater than and growing with n. Finite sample performance of the method is examined by simulation, compared against the LASSO for IID data. The methods are applied to estimation of a spatial Durbin model for the Aveiro housing market (Portugal).