Endogenous Selection and Spillovers: Bayesian Inference for Policy-Relevant Causal Effects

Abstract

This paper develops a new econometric framework to identify and estimate policy-relevant causal effects in contexts with endogenous selection into treatment and spillovers within single large networks or spatial settings. Conventional causal inference methods relying on either unconfoundedness or no-interference assumptions are generally inadequate in these scenarios. We introduce a Spillover Roy model that jointly models endogenous treatment selection and potential outcomes while allowing spillovers through a low-dimensional exposure mapping of neighbors' treatments. The model captures heterogeneous treatment responses across levels of latent resistance to treatment and neighborhood exposure. Within this framework, we define policy-relevant direct, spillover, and total effects under feasible policy changes and show that the total effect decomposes into a direct component from policy-induced participation and a spillover component from policy-induced changes in neighborhood treatment exposure. For estimation and inference, we develop a Bayesian data-augmentation algorithm with parameter expansion that enables efficient posterior computation and coherent uncertainty quantification for heterogeneous causal effects and policy counterfactuals. An application to the U.S. Opportunity Zones program finds positive direct effects on housing development but limited spillover benefits, while counterfactual policy analysis reveals diminishing returns from program expansion.