The Attribution Ceiling

01What is already known

Causal inference has become technically sophisticated: instruments, discontinuities, synthetic controls. What is less discussed is that identification depends on variation, and in many systems the variation available for identification is small relative to the system's own noise. This is usually treated as a power problem rather than a structural limit.

02The mechanism

Attribution requires comparing what happened to a counterfactual. The comparison is informative only to the extent that the intervention moves the system outside its natural range. When the intervention is small relative to natural variability, the counterfactual is inside the noise and the estimate is dominated by which noise happened to be present. The ratio of intervention to variability therefore sets an information ceiling, not an effort ceiling.

03Predictions

1. Estimated effect sizes should attenuate as natural variability in the study population rises, holding intervention fixed.
2. Meta-analyses pooling settings with different variability should show heterogeneity tracking that variability.
3. Larger interventions should not merely be more precise but should reveal effects that smaller ones systematically missed.

04Refutation

If effect estimates are stable across populations with very different natural variability, the ceiling is not binding and attribution is limited only by design.