Sharp Hybrid Confidence Bands for Partially Identified Treatment Effects under Tail Uncertainty with an Application to Workforce Gender Diversity and Firm Performance

Grace Lordan and Kaveh Salehzadeh Nobari

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Abstract: Manski's nonparametric bounds partially identify the average treatment effects (ATEs) under minimal assumptions, yielding an interval-valued estimand with endpoints that depend on the outcome support - typically treated as known or fixed. In many empirical settings, however, credible bounds on the outcome support are often unavailable and outcomes may be heavy-tailed, so common empirical implementations that rely on ad-hoc truncation or observed extrema can compromise finite-sample coverage. We develop concATE, a hybrid confidence band for interval-identified ATEs that explicitly accounts for tail uncertainty without imposing parametric assumptions. The inference method combines a distribution-free concentration bound for the outcome distribution based on the Dvoretzky-Kiefer-Wolfowitz inequality with the asymptotic delta-method inference for smooth mean components, and allocates size across bound endpoints using Bonferroni's inequality to guarantee joint coverage. We further extend concATE to a group-sequential procedure that controls the family-wise error rate using Pocock correction. Applying the method to panel data on 901 listed firms (2015Q2--2022Q1), we find that senior-level gender diversity has a statistically significant positive effect on firm value (Tobin's Q) only after crossing substantial representation thresholds: in Growth & Innovation sectors, significance emerges at approximately 55% female leadership, while in Defensive sectors it appears only beyond about 60%.

Date: 2025-09, Revised 2026-04
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