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

  • Walter R. Mebane (a1) and Paul Poast (a2)

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.

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Corresponding author

e-mail: wmebane@umich.edu (corresponding author)

Footnotes

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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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References

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Arnborg, Stefan. 2006. Robust Bayesianism: Relation to evidence theory. Journal of Advances in Information Fusion 1: 7590.
Aronow, Peter, and Samii, Cyrus. 2012. Estimating average causal effects under general interference. Paper presented at the 2012 Summer Meeting of the Society for Political Methodology, University of North Carolina, Chapel Hill, July 19–21.
Beresteanu, Arie, and Molinari, Francesca. 2008. Asymptotic properties for a class of partially identified models. Econometrica 76: 763814.
Bernhard, Judith K., Goldring, Luin, Young, Julie, Berinstein, Carolina, and Wilson, Beth. 2007. Living with precarious legal status in Canada: Implications for the well-being of children and families. Refuge: Canada's Periodical on Refugees 24: 101–14.
Blattman, C. 2009. From violence to voting: War and political participation in Uganda. American Political Science Review 103: 231–47.
Bowers, Jake, Fredrickson, Mark, and Panagopoulos, Costas. 2012. Interference is interesting: Statistical inference for interference in social network experiments. Paper presented at the 2012 Summer Meeting of the Society for Political Methodology, University of North Carolina, Chapel Hill, July 19–21.
Cederman, Lars-Erik, Weidmann, Nils B., and Gleditsch, Kristian Skrede. 2011. Horizontal inequalities and ethnonationalist civil war: A global comparison. American Political Science Review 105: 478–95.
Cingranelli, David, and Richards, David. 2010. The Cingranelli-Richards (CIRI) human rights dataset. http://www.humanrightsdata.org.
Cochran, William G., and Rubin, Donald B. 1973. Controlling bias in observational studies: A review. Sankya: The Indian Journal of Statistics 35: 417–66.
Davenport, Christian. 2007a. State repression and political order. Annual Review of Political Science 10: 123.
Davenport, Christian. 2007b. State repression and the tyrannical peace. Journal of Peace Research 4: 485504.
Efron, Bradley. 2011. Bayesian inference and the parametric bootstrap. Working paper.
Gleditsch, Nils Petter, Wallensteen, Peter, Eriksson, Mikael, Sollenberg, Margareta, and Strand, Håvard. 2002. Armed conflict 1946–2001: A new dataset. Journal of Peace Research 39: 615–37.
Glynn, Adam N., and Quinn, Kevin M. 2010. An introduction to the augmented inverse propensity weighted estimator. Political Analysis 18: 3656.
Hainmueller, Jens, and Hiscox, Michael J. 2007. Educated preferences: Explaining attitudes toward immigration in Europe. International Organization 61: 399442.
Hainmueller, Jens, and Hiscox, Michael J. 2010. Attitudes toward highly skilled and low-skilled immigration: Evidence from a survey experiment. American Political Science Review 104: 6184.
Hastie, Trevor J. 1992. Generalized additive models. In Statistical models in S, eds. Chambers, John M. and Hastie, Trevor J. New York: Wadsworth & Brooks/Cole.
Holland, Paul W. 1986. Statistics and causal inference. Journal of the American Statistical Association 81: 945–60.
Imai, Kosuke, Keele, Luke, Tingley, Dustin, and Yamamoto, Teppei. 2011. Unpacking the black box of causality: Learning about causal mechanisms from experimental and observational studies. American Political Science Review 105: 765–89.
Imai, Kosuke, Keele, Luke, and Yamamoto, Teppei. 2010. Identification, inference, and sensitivity analysis for causal mediation effects. Statistical Science 25: 5171.
Karlsson, Alexander. 2010. Evaluating credal set theory as a belief framework in high-level information fusion for automated decision-making. Technical Report. Örebro Studies in Technology 38.
Karlsson, Alexander, Johansson, Ronnie, and Andler, Sten F. 2011. Characterization and empirical evaluation of Bayesian and credal combination operators. Journal of Advances in Information Fusion 6: 150–66.
Levi, Isaac. 1983. The enterprise of knowledge. Cambridge, MA: MIT Press.
Lichbach, Mark Irving. 1987. Deterrence or escalation? The puzzle of aggregate studies of repression and dissent. Journal of Conflict Resolution 31: 266–97.
Manski, Charles. 1990. Nonparametric bounds on treatment effects. American Economic Review Papers and Proceedings 80: 319–23.
Manski, Charles. 1995. Identification problems in the social sciences. Cambridge, MA: Harvard University Press.
Manski, Charles. 1997. Monotone treatment response. Econometrica 65: 1311–34.
Manski, Charles. 2011. Identification of treatment response with social interactions. Working paper.
Manski, Charles, and Pepper, John V. 2000. Monotone instrumental variables: With an application to the returns to schooling. Econometrica 68: 9971010.
Molinari, Francesca. 2005. Missing treatments. CAE Working paper #05-11.
Molinari, Francesca. 2007. Missing treatments. Working paper.
Molinari, Francesca. 2010. Missing treatments. Journal of Business and Economic Statistics 28:8295.
Morgan, Stephen L., and Winship, Christopher. 2007. Counterfactuals and causal inference: Methods and principles for social research (Analytical Methods for Social Research). New York: Cambridge University Press.
Newton, Michael A., and Raftery, Adrian E. 1994. Approximate Bayesian inference with the weighted likelihood bootstrap. Journal of the Royal Statistical Society, Series B 56: 348.
Petersen, Roger D. 2002. Understanding ethnic violence: Fear, hatred, and resentment in twentieth-century Eastern Europe. Cambridge, UK: Cambridge University Press.
Poast, Paul. 2012. Does issue linkage work? Evidence from European alliance negotiations, 1860 to 1945. International Organization 66: 277310.
Quinn, Kevin M. 2009. What Can Be Learned from a Simple Table? Bayesian inference and sensitivity analysis for causal effects from 2x2 and 2x2xK tables in the presence of unmeasured confounding. Working paper.
Rosenbaum, Paul. 2002. Covariance adjustment in randomized experiments and observational studies (with discussion). Statistical Science 17: 286327.
Rubin, Donald B. 1978. Bayesian inference for causal effects: The role of randomization. Annals of Statistics 6: 3458.
Rubin, Donald B. 1981. The Bayesian bootstrap. Annals of Statistics 9: 130–4.
Rubin, Donald B. 1991. Practical implications of modes of statistical inference for causal effects and the critical role of the assignment mechanism. Biometrics 47: 1213–34.
Rubin, Donald B. 2006. Matched sampling for causal effects. New York: Cambridge University Press.
Sambanis, Nicholas, and Zinn, Annalisa. 2006. From protest to violence: An analysis of conflict escalation with an application to self-determination movements. Working paper.
Scott, Alastair, and Smith, T. M. F. 1973. Survey design, symmetry and posterior distributions. Journal of the Royal Statistical Society, Series B 35: 5760.
Sharp, Elaine B., and Joslyn, Mark. 2001. Individual and contextual effects on attributions about pornography. Journal of Politics 63: 501–19.
Sugden, R. A., and Smith, T. M. F. 1984. Ignorable and informative designs in survey sampling inference. Biometrika 71: 495506.
Tarrow, Sidney. 1989. Democracy and disorder: Social conflict, political protest and democracy in Italy. New York: Oxford University Press.
Taylor, James W. 2000. A quantile regression neural network approach to estimating the conditional density of multiperiod returns. Journal of Forecasting 19: 299311.
Wahba, Grace. 1983. Bayesian “confidence intervals” for the cross-validated smoothing spline. Journal of the Royal Statistical Society, Series B 45: 133–50.
Wahba, Grace. 1990. Spline models for observational data. Philadelphia: Society for Industrial and Applied Mathematics.
Wang, Yuedong, and Wahba, Grace. 1994. Bootstrap confidence intervals for smoothing splines and their comparison to Bayesian “confidence intervals.” Journal of Statistical Computation and Simulation 51: 263–79.
World Values Survey Association. 2009. WORLD VALUES SURVEY 2005 OFFICIAL DATA FILE v.20090901. Aggregate File Producer: ASEP/JDS, Madrid.
Yamamoto, Teppei. 2012. Understanding the past: Statistical analysis of causal attribution. American Journal of Political Science 56: 237–56.
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Causal Inference without Ignorability: Identification with Nonrandom Assignment and Missing Treatment Data

  • Walter R. Mebane (a1) and Paul Poast (a2)

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