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Causal Inference without Ignorability: Identification with Nonrandom Assignment and Missing Treatment Data

Published online by Cambridge University Press:  04 January 2017

Walter R. Mebane Jr.*
Affiliation:
Department of Political Science and Department of Statistics, University of Michigan, 5700 Haven Hall, Ann Arbor, MI 48109
Paul Poast
Affiliation:
Department of Political Science, Rutgers University, Hickman Hall, New Brunswick, NJ 08901 e-mail: paul.poast@rutgers.edu
*
e-mail: wmebane@umich.edu (corresponding author)

Abstract

How a treatment causes a particular outcome is a focus of inquiry in political science. When treatment data are either nonrandomly assigned or missing, the analyst will often invoke ignorability assumptions: that is, both the treatment and missingness are assumed to be as if randomly assigned, perhaps conditional on a set of observed covariates. But what if these assumptions are wrong? What if the analyst does not know why—or even if—a particular subject received a treatment? Building on Manski, Molinari offers an approach for calculating nonparametric identification bounds for the average treatment effect of a binary treatment under general missingness or nonrandom assignment. To make these bounds substantively more informative, Molinari's technique permits adding monotonicity assumptions (e.g., assuming that treatment effects are weakly positive). Given the potential importance of these assumptions, we develop a new Bayesian method for performing sensitivity analysis regarding them. This sensitivity analysis allows analysts to interpret the assumptions' consequences quantitatively and visually. We apply this method to two problems in political science, highlighting the method's utility for applied research.

Type
Research Article
Copyright
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' note: Thanks to Peter Aronow for many important contributions. Comments from Don Green, Arthur Spirling, Allison Sovey, Rory Truex, and the participants of the 2011 MPSA Annual National Conference and the 2011 Annual Meeting of the Society for Political Methodology are greatly appreciated. Supplementary materials for this article are available on the Political Analysis Web site. Replication materials are in study hdl:1902.1/19368 at IQSS Dataverse Network.

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