  This paper proposes a Lasso-based estimator which uses information embedded
in the Moran statistic to develop a selection procedure called Moran's I Lasso
(Mi-Lasso) to solve the Eigenvector Spatial Filtering (ESF) eigenvector
selection problem. ESF uses a subset of eigenvectors from a spatial weights
matrix to efficiently account for any omitted cross-sectional correlation terms
in a classical linear regression framework, thus does not require the
researcher to explicitly specify the spatial part of the underlying structural
model. We derive performance bounds and show the necessary conditions for
consistent eigenvector selection. The key advantages of the proposed estimator
are that it is intuitive, theoretically grounded, and substantially faster than
Lasso based on cross-validation or any proposed forward stepwise procedure. Our
main simulation results show the proposed selection procedure performs well in
finite samples. Compared to existing selection procedures, we find Mi-Lasso has
one of the smallest biases and mean squared errors across a range of sample
sizes and levels of spatial correlation. An application on house prices further
demonstrates Mi-Lasso performs well compared to existing procedures.
