Inference on Dynamic Spatial Autoregressive Models with Change Point Detection

TL;DR

This paper develops a flexible dynamic spatial autoregressive model with multiple spatial weight matrices, incorporating change point detection, and provides theoretical and empirical validation for its effectiveness.

Contribution

It introduces a novel model combining multiple spatial weight matrices with change point detection, along with penalized estimation methods and theoretical guarantees.

Findings

Establishes oracle properties of estimators.

Demonstrates consistent change point detection.

Validates methods through simulations and real data.

Abstract

We analyze a varying-coefficient dynamic spatial autoregressive model with spatial fixed effects. One salient feature of the model is the incorporation of multiple spatial weight matrices through their linear combinations with varying coefficients, which help solve the problem of choosing the most ``correct'' one for applied econometricians who often face the availability of multiple expert spatial weight matrices. We estimate and make inferences on the model coefficients and coefficients in basis expansions of the varying coefficients through penalized estimations, establishing the oracle properties of the estimators and the consistency of the overall estimated spatial weight matrix, which can be time-dependent. We further consider two applications of our model in change point detections in dynamic spatial autoregressive models, providing theoretical justifications in consistent change point locations estimation and practical implementations. Simulation experiments demonstrate the performance of our proposed methodology, and real data analyses are also carried out.