Two-Step Lasso Estimation of the Spatial Weights Matrix

The vast majority of spatial econometric research relies on the assumption that the spatial network structure is known a priori. This study considers a two-step estimation strategy for estimating the n(n−1) interaction effects in a spatial autoregressive panel model. The identifying assumption is approximate sparsity of the spatial weights matrix. The proposed estimation methodology exploits the Lasso estimator and mimics two-stage least squares (2SLS) to account for endogeneity of the spatial lag. The developed two-step estimator is of more general interest. It may be used in applications where the number of endogenous regressors and the number of instrumental variables is larger than the number of observations. We derive convergence rates for the two-step Lasso estimator. We also present Monte Carlo simulation results which show that the two-step estimator is consistent and successfully recovers the spatial network structure for reasonable large sample size, T.