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A Theory of Statistical Inference for Matching Methods in Causal Research

Published online by Cambridge University Press:  04 October 2018

Stefano M. Iacus ,
Gary King  and
Giuseppe Porro
Stefano M. Iacus*
Affiliation:
Department of Economics, Management and Quantitative Methods, University of Milan, Via Conservatorio 7, I-20124 Milan, Italy. Email: stefano.iacus@unimi.it
Gary King
Affiliation:
Institute for Quantitative Social Science, 1737 Cambridge Street, Harvard University, Cambridge MA 02138, USA. Email: king@harvard.edu, URL: https://gking.harvard.edu/
Giuseppe Porro
Affiliation:
Department of Law, Economics and Culture, University of Insubria, Via S.Abbondio 12, I-22100 Como, Italy. Email: giuseppe.porro@uninsubria.it
*
*Email: stefano.iacus@unimi.it
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Abstract

Researchers who generate data often optimize efficiency and robustness by choosing stratified over simple random sampling designs. Yet, all theories of inference proposed to justify matching methods are based on simple random sampling. This is all the more troubling because, although these theories require exact matching, most matching applications resort to some form of ex post stratification (on a propensity score, distance metric, or the covariates) to find approximate matches, thus nullifying the statistical properties these theories are designed to ensure. Fortunately, the type of sampling used in a theory of inference is an axiom, rather than an assumption vulnerable to being proven wrong, and so we can replace simple with stratified sampling, so long as we can show, as we do here, that the implications of the theory are coherent and remain true. Properties of estimators based on this theory are much easier to understand and can be satisfied without the unattractive properties of existing theories, such as assumptions hidden in data analyses rather than stated up front, asymptotics, unfamiliar estimators, and complex variance calculations. Our theory of inference makes it possible for researchers to treat matching as a simple form of preprocessing to reduce model dependence, after which all the familiar inferential techniques and uncertainty calculations can be applied. This theory also allows binary, multicategory, and continuous treatment variables from the outset and straightforward extensions for imperfect treatment assignment and different versions of treatments.

Keywords

causal inferencematchingobservational studiesmultiple treatmentsstratification
Type
Articles
Information
Political Analysis , Volume 27 , Issue 1 , January 2019 , pp. 46 - 68
Copyright
Copyright © The Author(s) 2018. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

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Footnotes

Authors’ note: Our thanks to Alberto Abadie, Adam Glynn, Kosuke Imai, and Molly Roberts for helpful comments on an earlier draft. The replication code can be found in Iacus (2018).

Contributing Editor: Jonathan N. Katz

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