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Attributable Effects and Full Matching for Binary Outcomes in Field Experiments and Observational Studies
| | Unformatted Document Text:
Attributing Effects to a Get-Out-The-Vote Campaign Using Full
Matching and Randomization Inference
∗
Jake Bowers and Ben Hansen
Political Science and Statistics
## email not listed ## and ## email not listed ##
University of Michigan
April 4, 2005
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 theanalysis is to infer Z’s effects on Y , this requirement introduces an element of circularity: inorder to decide how Z affects Y , the analyst first determines, speculatively, the manner of Y ’sdependence on Z and other variables. This paper takes a statistical perspective that avoids suchcircles, permitting analysis of Z’s effects on Y even as the statistician remains entirely agnosticabout the conditional distribution of Y given X and Z, or perhaps even denies that such adistribution exists. Our assumptions instead pertain to the conditional distribution Z|X, andthe role of speculation in settling them is reduced by the use of such techniques as propensityscores, poststratification, testing for overt bias before accepting a poststratification, and optimalfull 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 politicalscience 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 asboth a get-out-the-vote campaign and a field experiment in political participation, the campaignas it turned out was in some ways more similar to an observational study than to a randomizedexperiment. Our analysis uses the strengths of the design of their study while adjusting forirregularities ignored by the original analysis. We estimate the number of voters who wouldnot have voted had the campaign not prompted them to — that is, the total number of votesattributable to the interventions of the campaigners. Both our statistical inferences about theseattributable effects and the stratification and matching that precede them rely on quite recentdevelopments from statistics; our matching, in particular, has novel features of potentially wideapplicability. Our broad findings resemble those of the original analysis by Gerber and Green(2000), although in the small, the method offers additional information as to the campaign’seffects upon interestingly different subgroups, such as older voters or those who have not votedin a previous election.
∗
We are grateful to participants in workshops at the annual meetings of the Royal Statistical Society, September
2004 and at the Department of Political Science at the University of Illinois, July 2004 for helpful comments on muchearlier versions of this work.
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| | Authors: Bowers, Jake. and Hansen, Ben. |
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Attributing Effects to a Get-Out-The-Vote Campaign Using Full
Matching and Randomization Inference
∗
Jake Bowers and Ben Hansen
Political Science and Statistics
## email not listed ## and ## email not listed ##
University of Michigan
April 4, 2005
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|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 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 campaign
as it turned out was in some ways more similar to an observational study than to a randomized
experiment. Our analysis uses the strengths of the design of their study while adjusting for
irregularities ignored by the original analysis. 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. 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 Gerber and Green
(2000), although in the small, the method offers additional information as to the campaign’s
effects upon interestingly different subgroups, such as older voters or those who have not voted
in a previous election.
∗
We are grateful to participants in workshops at the annual meetings of the Royal Statistical Society, September
2004 and at the Department of Political Science at the University of Illinois, July 2004 for helpful comments on much
earlier versions of this work.
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