Many economic decisions target units at the extremes, such as the most effective teachers, the worst-performing schools, or the most productive firms. These decisions often rely on fixed-effect estimates, but in short panels extreme estimates may reflect unusually large estimation error rather than extreme latent effects. We develop a semiparametric framework for identification and inference on the tails of latent group effects in short panels, where estimation error need not vanish. We show that within-group differences remove the group effect and provide observable information about the tail of the estimation error in group averages. This yields a conservative one-sided test of whether latent effects have a heavier tail than estimation error. Under regular variation and this tail dominance condition, tail estimators based on noisy group averages are asymptotically equivalent to infeasible estimators based on the latent effects. We use this oracle-equivalence result to derive frequentist inference for the Pareto exponent, extreme quantiles, and tail conditional expectations, and to establish consistent rankings of a fixed number of extreme units. We apply the method to administrative data on Italian middle schools to quantify the gains from replacing schools in the lower tail with average-quality schools.