Estimating Networks: Lasso for Spatial Weights.

In applied work, often the spatial neighbouring matrix is assumed known and available to the researcher. This paper provides a method for estimating it within longitudinal data. The salient feature is the ultra-high dimensionality of the problem, which is addressed with an adaptation of the Least Absolute Shrinkage and Selection Operator (Lasso). The main result is that, under identification and sparsity conditions, the estimator is consistent for the true neighbouring matrix, both under L1 and prediction norms. The proposed model nests a graphical model and suggests several economic applications. Most notably, it provides a framework for estimating networks based on observable cohorts, as opposed to assuming prior knowledge. Finally, Monte Carlo evidence is presented, along with an application for contagion of government bond yields in the wake of the recent European crisis.