Identifying Causal Effects in the Presence of Missing Outcome Values
Alessandra Mattei1, Fabrizia Mealli1, Barbara Pacini2
1Department of Statistics, University of Florence; 2Department of Statistics and Applied Mathematics, University of Pisa

We tackle the problem of identifying causal effects in the presence of missing outcome values, primarily due to nonresponse. Because nonresponse occurs after treatment assignment, respondents are not comparable by treatment status: the observed and unobserved characteristics of respondents in each treatment group are likely to differ and may be associated with the values of the missing outcome, making the missing mechanism nonignorable (Little and Rubin, 2002).

The potential outcomes approach to causal inference (Rubin, 1974, 1978) has contributed to a substantial convergence of methods from statistics and econometrics. In this perspective, a causal inference problem is viewed as a problem of missing data, where the assignment mechanism is explicitly modeled as a process for revealing the observed data. The assumptions on the assignment mechanism are crucial for identifying and deriving methods to estimate causal effects. A commonly invoked identifying assumption is unconfoundedness (Rosenbaum and Rubin, 1983), which usually holds by design in randomized experiments. However, inference on causal effects may be invalidated due to the presence of post-treatment complications, such as noncompliance, censoring “due to death”, and missing outcome values.

Outcome missingness is a pervasive problem in empirical studies, characterizing most of the longitudinal surveys and social experiments with follow-ups. Standard procedures to handle missing data generally lead to valid inferences only under strong ignorability assumptions of the missing mechanism.

In this paper, we apply principal stratification (Frangakis and Rubin, 2002) to develop a novel approach to deal with nonignorable missing outcomes without imposing any restriction on treatment effect heterogeneity. We rely on the presence of a binary instrument for nonresponse and provide new sufficient conditions for partial and point identification of causal effects for subsets of units (unions of principal strata) defined by their nonresponse behavior in all possible combinations of treatment and instrument values. The framework allows us to clarify and discuss substantive behavioral assumptions, which may differ from those required by other approaches.

Examples are provided as possible scenarios where our assumptions may be plausible, and they are used to discuss the key role of the instrument for nonresponse in identifying average causal effects in presence of nonignorable missing outcomes.


Frangakis, C. E. and Rubin, D. B. (2002). Principal stratification in causal inference. Biometrics 58, 21-29.

Little, R.J.A. and D.B. Rubin, Statistical Analysis with Missing Data, 2nd Edition, New York: John Wiley (2002).

Rosenbaum, P., and D.B. Rubin D.B., “The Central Role of the Propensity Score in Observational Studies for Causal Effects”, Biometrika 70 (1983), 41-55.

Rubin, D.B. “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies”, Journal of Educational Psycology 66 (1974), 688-701.

Rubin, D.B., “Bayesian Inference for Causal Effects”, Annals of Statistics 6 (1978), 34-58.

Keywords: Bounds; missing outcomes; principal stratification; instrumental variables

Biography: Alessandra Mattei is research assistant in Statistics at the University of Florence.

Her research interests include causal inference in experiments and observational studies, missing

data models, application of Bayesian techniques, and program evaluation methods.