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Understanding the effectiveness of policies aimed at curbing the spread of COVID-19 is an urgent task, and studies evaluating specific policies are appearing at a rapid clip. A credible evaluation, we argue, ought to consider interactions with other policies---which may function as complements or substitutes---as well as adjacent geographies, whose policies and conditions could easily spill over. Using mobility and epidemiological data from Mexico, and relying on high-dimensional panel models and Lasso techniques, we show that widely-used methods to estimate the effects of policies are highly sensitive to interactions with other policies within the same locality and across neighboring localities. For robustness, we identify unconditional and first-order interaction effects of social distancing policies.