# Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation

## TL;DR

This paper introduces a new spatial lag model implementation in the R-INLA package, enabling fast Bayesian inference for spatial econometrics models within R, demonstrated on datasets with Gaussian and binary outcomes.

## Contribution

The paper extends R-INLA by implementing a spatial lag model, allowing broader application of INLA to spatial econometrics.

## Key findings

- Efficient Bayesian inference for spatial lag models in R-INLA.
- Application to datasets with Gaussian and binary outcomes.
- Enhanced model fitting and selection capabilities in spatial econometrics.

## Abstract

Integrated Nested Laplace Approximation provides a fast and effective method for marginal inference on Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R statistical software. Although INLA is implemented as a general methodology, its use in practice is limited to the models implemented in the R-INLA package. Spatial autoregressive models are widely used in spatial econometrics but have until now been missing from the R-INLA package. In this paper, we describe the implementation and application of a new class of latent models in INLA made available through R-INLA. This new latent class implements a standard spatial lag model, which is widely used and that can be used to build more complex models in spatial econometrics. The implementation of this latent model in R-INLA also means that all the other features of INLA can be used for model fitting, model selection and inference in spatial econometrics, as will be shown in this paper. Finally, we will illustrate the use of this new latent model and its applications with two datasets based on Gaussian and binary outcomes.