Attributing Effects to a Get-Out-The-Vote Campaign Using Full Matching and Randomization Inference.” Working Paper

Statistical analysis requires a probability model: commonly, a model for the dependence of outcomes Y on confounders X and a potentially causal variable Z. When the goal of the analysis is to infer Z’s effects on Y, this requirement introduces an element of circularity: in order to decide how Z affects Y, the analyst first determines, speculatively, the manner of Y ’s dependence on Z and other variables. This paper takes a statistical perspective that avoids such circles, permitting analysis of Z’s effects on Y even as the statistician remains entirely agnostic about the conditional distribution of Y given X and Z, or perhaps even denies that such a distribution exists. Our assumptions instead pertain to the conditional distribution Z|X, and the role of speculation in settling them is reduced by the use of such techniques as propensity scores, poststratification, testing for overt bias before accepting a poststratification, and optimal full matching. Such beginnings pave the way for “randomization inference”, an approach which, despite a long history in the analysis of designed experiments, is relatively new to political science and to other fields in which experimental data are rarely available. The approach applies to both experiments and observational studies. We illustrate this b