Attrition (Field Experiments, Ch. 7)
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Causal Question / Estimand
The average treatment effect in a randomized experiment when outcome data are missing for some subjects — and when, despite randomization, the observed- sample estimator is still unbiased.
Identification Strategy
Randomization makes the difference in group means unbiased only if outcomes are observed for all assigned units. The chapter classifies Attrition by its relationship to potential outcomes and derives the conditions under which it does or does not bias estimates. Unconditional unbiasedness survives when outcomes are missing independently of potential outcomes (MIPO). When attrition is ignorable only given covariates (MIPO conditional on — an Ignorability-type assumption on the missingness), unbiased estimates are recovered by inverse-probability reweighting of observed units. When no such assumption is credible, the effect is only partially identified: worst-case extreme-value bounds (and trimming bounds) bracket it. A design remedy, double sampling, intensively re-contacts a random subset of missing subjects to restore identification.
Key Assumptions
Randomization (assignment); for point identification under attrition, MIPO or MIPO given (Ignorability of missingness, Attrition); SUTVA. Bounds require only that outcomes lie in a known range.
Threats to Validity
Attrition correlated with potential outcomes (differential, treatment-related dropout) is the central threat — it breaks the comparability that randomization established. Naively analysing only observed cases (“complete-case” analysis) is biased; reweighting fails if the missingness model is wrong.
Setting / Data
n/a — methodological textbook chapter; motivated by examples such as the RAND Health Insurance Experiment.
Key Claims
- Randomization does not by itself protect against attrition; bias depends on whether missingness is related to potential outcomes.
- Reweighting recovers unbiasedness only under (conditional) MIPO; otherwise report bounds rather than a point estimate.
- Double sampling is a powerful design-stage tool: collect outcomes from a random sample of the missing to bound or identify the effect.
Connections
- A core RCT internal-validity topic alongside design/power: AtheyImbens2017-EconometricsOfRandomizedExperiments, BruhnMcKenzie2009-InPursuitOfBalance.
- The conditional-ignorability remedy mirrors selection-on-observables reweighting in PSM (Imbens2004-NonparametricATEReview, Propensity-Score).
- Develops the Attrition concept. See also RCT, Foundations.
Citation
Gerber, A. S., & Green, D. P. (2012). Field Experiments: Design, Analysis, and Interpretation (Chapter 7: Attrition). New York: W. W. Norton.