Inference for Directional Population Sensitivity: Fragility Curves and Breakdown in Linear Projections
Published in Working paper, 2026
Abstract: Precise regression estimates may still strongly depend on the composition of the population itself. We develop √N inference for a directional fragility curve that traces the worst-case change in a target contrast as an increasing share of the population is removed. The directional curve holds the full-sample contrast direction fixed and adjusts for the remaining leverage among retained observations, rather than refitting for each subset. We derive pointwise confidence intervals and simultaneous confidence bands for the curve, accounting for first-stage estimation of both the regression residuals and the design matrix. Inverting the curve yields inference for a breakdown fraction—the smallest removed population share needed to overturn a threshold of interest. We characterize when this directional curve coincides with unrestricted subset refitting and show that it provides a valid lower bound whenever deletion does not rotate the design direction.
Status: Working paper (October 2026)
Co-author: Nikolas Kuschnig