Autoregressive models for panel data causal inference with application to state-level opioid policies

Motivated by the study of state opioid policies, we propose a novel approach using autoregressive models for causal effect estimation in panel data settings. We estimate the impact of key opioid-related policies, specifically must-access prescription drug monitoring programs (PDMPs), naloxone access laws (NALs), and medical marijuana laws, on opioid prescribing. Existing methods, such as difference-in-differences and synthetic controls, are difficult to apply in dynamic policy environments with multiple overlapping policies and small sample sizes. While autoregressive models have been used in similar contexts, they have lacked formal justification until now. We outline assumptions that link these models to causal effects and study the bias of resulting estimates when key assumptions are violated. Through simulation studies mirroring our application, we show that our proposed estimators often outperform existing methods. We thus provide a formal justification for using autoregressive models to evaluate the effectiveness of state policies in addressing the opioid crisis.