Moran's I Lasso for models with spatially correlated data

TL;DR

This paper introduces Moran's I Lasso, a fast, theoretically grounded method for selecting eigenvectors in spatial models, improving accuracy and efficiency in handling spatially correlated data.

Contribution

The paper develops a novel Moran's I Lasso estimator for eigenvector selection in spatial filtering, with proven performance bounds and faster computation than existing methods.

Findings

Mi-Lasso performs well in finite samples.

It has smaller bias and MSE compared to existing methods.

Demonstrated effectiveness on house price data.

Abstract

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.