Local spatial difference-in-differences models: treatment correlations, response interactions, and expanded local models

We propose spatial difference-in-differences (DID) models that are able to incorporate treatment effect spillovers through modeling spatial interactions in the response and spatial correlations in treatment status among individuals. We first explore the ways in which combinations of spatial interaction and spatial correlation bias the conventional DID estimator, and then we develop spatial DID models, estimators, and specification tests that allow for a flexible order of local spatial structures. We consider both simultaneous and dynamic treatment. The local spatial DID models with a flexible order of spatial structure allow for different types of heterogeneity in the treatment effects. Monte Carlo simulations support our discussions of the bias in the conventional DID model under spatial interaction and correlation, and demonstrate the finite sample performance of our proposed models, estimators, and tests.