Estimation of Spatial Weight Matrices via LASSO andAdaptive LASSO in Spatial Econometric Models:Simulation and Empirical Analysis

This study explores data-driven estimation of the spatial weights matrix in the spatial lag model, addressing the arbitrariness inherent in exogenously specified spatial structures. We compare two frameworks for estimating spatial dependence using LASSO and adaptive LASSO: a row-wise approach and a simultaneous approach that estimates the entire matrix jointly. Furthermore, we examine the impact of incorporating the row-sum constraint within the optimisation process, as opposed to applying post-estimation normalisation, resulting in twelve distinct estimation settings. Simulation results demonstrate that the optimisation-based constraint yields superior performance in terms of estimation accuracy, sparsity, and interpretability. Adaptive LASSO consistently outperforms standard LASSO in coefficient recovery and theoretical coherence. In an empirical analysis using international index data, where spatial proximity cannot be explicitly defined, our approach successfully identifies meaningful interdependencies among countries. Accounting for spatial dependence leads to smaller and more interpretable coefficient magnitudes compared with conventional models. Overall, the findings underscore the potential of regularisation-based, data-driven approaches for uncovering spatial and network structures, offering a more realistic and parsimonious representation of interdependent relationships in spatial econometric analysis.