Sensitivity and Partial Identification
Sensitivity and Partial Identification
Robustness is not a list of specifications
Adding controls, deleting outliers and changing standard errors asks whether results are numerically stable. Sensitivity analysis asks a sharper question:
How large must a specified violation of the identifying assumption be to change the conclusion?
The answer is conditional on the sensitivity model. It does not certify that the violation is smaller.
Match the sensitivity analysis to the design
| Design threat | Sensitivity parameter or bound | Useful output |
|---|---|---|
| unmeasured confounding | strength of omitted treatment/outcome association | adjusted effect or robustness value |
| DID trend violation | permitted post-period deviation from pre-trend | interval over deviation sizes |
| IV exclusion/ignorability | instrument side effect or instrument confounding | adjusted IV estimate/interval |
| attrition | missing potential-outcome range or monotonicity | identified effect interval |
| hidden bias after matching | odds-of-treatment departure | conclusion across |
Use the design’s weak point. An IV exclusion analysis does not address weak instruments; a DID trend analysis does not address anticipation.
Benchmark omitted confounding
Suppose adjustment gives an eight-point completion effect. Rather than “results survive many controls,” compare a hypothetical omitted variable with observed adviser support:
- how strongly would it need to explain scholarship receipt, conditional on controls?
- how strongly would it need to explain completion residuals?
- would that joint strength reduce the estimate to zero or only below a policy threshold?
Cinelli and Hazlett (2020) express omitted-variable sensitivity using partial measures and observed-variable benchmarks. For IV, Cinelli and Hazlett (2025) separately quantify possible side effects of the instrument and confounding of the instrument. Zhang and Zhao (2026) bound average, rather than only worst-case, confounding strength in a newer marginal-sensitivity model.
Always label new methods by publication status and implementation maturity in the reading map.
Bounds expose what missing outcomes permit
Completion is binary. Response is 80% in the offer arm with observed mean 0.60, and 90% in control with mean 0.50. Without assumptions about missing outcomes:
Therefore the effect lies in
The data alone permit harm or substantial benefit. A credible monotonicity, response or administrative-linkage assumption can narrow the set—but must be stated.
Sensitivity curves beat a single threshold
Show the effect estimate and interval over a substantively interpretable range. Mark:
- zero;
- a policy-relevant minimum effect;
- benchmarks from observed covariates or pre-trends;
- the range experts regard as plausible;
- where support becomes too weak to calculate reliably.
For staggered DID, Rambachan and Roth (2023) make conclusions conditional on restrictions relating post-treatment trend violations to pre-treatment deviations.
Quick check
The effect remains statistically non-zero until an omitted confounder is twice as strong as any observed covariate. Is the study now proven causal?