Minimax causal inference under tail heterogeneity

Standard causal estimators deteriorate when treatment modifies the tail index of outcomes. I generalize the maximum domain of attraction to nonstationary triangular arrays, establishing uniform convergence of block maxima to time-varying generalized extreme value distributions. Under such shifts, the supports of the limiting distributions separate, likelihood ratios are unbounded, and inverse probability weighting loses root-n consistency and asymptotic normality once the heavier tail index exceeds one half. I derive minimax lower bounds for the causal estimation rate; a tail-adaptive doubly robust estimator attains them up to logarithms. In simulations, tail adaptation cuts integrated mean absolute error by 20 to 41 percent at crisis-scale samples and stabilizes performance under strong tail heterogeneity. An application to bank stock returns around the 2020 Federal Reserve emergency facilities