Bounding Treatment Effects Under Interference in Geographic Natural Experiments: An Application to All-Mail Voting in Colorado∗

Political scientists often seek to understand whether modes of voting influence turnout rates. Two states and many localities have either adopted or experimented with all-mail elections, where voters no longer travel in-person to central locations to vote. Instead voters are mailed ballots and voting often starts as much as two weeks before election day. We analyze a natural experiment from the 2010 Colorado primary on all-mail voting. In that election, counties in Colorado had the option of an all-mail election or could retain traditional in-person voting on election day. We found that the town of Basalt, in the southwestern part of the state, was split in half by two counties that chose different modes of voting. We exploit this natural experiment to understand whether turnout levels were altered by all-mail elections. We adopt three different designs in our analysis: a geographic regression discontinuity design, differences-in-differences, and adjustment via a penalized match on geographic distance. However, social interactions often give rise to spillover effects in which the exposure of one individual to the treatment may affect outcomes of untreated units. In our application, treated and control voters lived in very close proximity and spillovers are probable. We develop a method of bounds to investigate whether our inference is a function of treatment spillovers. Using a model of treatment spillovers based on geographic proximity, we adjust unit level outcomes under different possible patterns of treatment spillovers. We then re-estimate the vote by mail treatment effect using these adjusted outcomes to create bounds on the estimate. These bounds allow us to observe whether an inference based on the assumption of no interference is plausible. ∗Authors are in alphabetical order. We thank participants at the Causality in Political Networks Conference (University of Chicago, 2013) for valuable comments and discussion. †Associate Professor, Department of Political Science, 211 Pond Lab, Penn State University, University Park, PA 16802 Phone: 814-863-1592, Email: [email protected] ‡Assistant Professor, Department of Political Science, University of Michigan, 5700 Haven Hall, 505 South State St., Ann Arbor, MI 48109 Phone: 734-615-9114, Email: [email protected]