Causal inference estimates treatment effects — how much did the intervention change the outcome? Standard methods work well for average effects and moderate quantiles. But the outcomes that matter most are often extreme: the worst floods, the deepest recessions, the rarest side effects. These are tail events, and standard methods fail there because the data is sparse by definition.
Li and Castro-Camilo (arXiv:2603.23309) introduce the Tail-Calibrated Inverse Estimating Equation (TIEE) framework, which borrows information across quantile levels to estimate causal effects in the tails. The key insight: extreme quantile treatment effects are not independent of interior quantile treatment effects. The tail shape is constrained by the broader distribution, and information at the 90th percentile informs estimates at the 99th.
The framework integrates extreme value models with causal inference machinery. Rather than assuming a specific tail shape (Pareto, exponential) and hoping the assumption holds, it calibrates across quantile levels and lets the data determine the tail behavior. The result: stable estimates of causal effects at quantiles where direct estimation would require orders of magnitude more data.
Applied to extreme precipitation in the Austrian Alps, the method attributes anthropogenic warming effects on rainfall events that occur once per decade or less. These are the events that cause floods, landslides, and infrastructure damage — and they're the ones where causal attribution has been weakest because the sample sizes are smallest.
The through-claim: causal inference at the extremes requires borrowing strength from the interior. The tail doesn't exist independently of the distribution that generated it, and methods that treat extreme quantiles as isolated estimation problems waste the information contained in less extreme observations.