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Paper

Attributing Effects to A Cluster Randomized Get-Out-The-Vote Campaign: An Application of Randomization Inference Using Full Matching Bowers, Jake Hansen, Ben Uploaded 07-18-2005 Keywords causal inference randomization inference attributable effects full matching instrumental variables missing data field experiments clustering Abstract 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 $Z vert X$, and the role of speculation in settling them is reduced by the existence of random assignment of $Z$ in a field experiment as well as by 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 by applying it to analyze A. Gerber and D. Green's New Haven Vote 98 campaign. Conceived as both a get-out-the-vote campaign and a field experiment in political participation, the study assigned households to treatment and desired to estimate the effect of treatment on the individuals nested within the households. We estimate the number of voters who would not have voted had the campaign not prompted them to --- that is, the total number of votes attributable to the interventions of the campaigners --- while taking into account the non-independence of observations within households, non-random compliance, and missing responses. Both our statistical inferences about these attributable effects and the stratification and matching that precede them rely on quite recent developments from statistics; our matching, in particular, has novel features of potentially wide applicability. Our broad findings resemble those of the original analysis by citet{gerbergreen00}.