Maximum score and non-smooth M-estimators with multiway dependence

Harold D. Chiang and Ahnaf Rafi

Papers from arXiv.org

Abstract: Under i.i.d. sampling, the maximum score estimator of Manski (1975) converges at the cube-root rate to a non-Gaussian limit. We show that, under multiway dependence and low-level conditions, it is asymptotically normal at a parametric rate in the smallest number of clusters and, when the cluster-level variance is non-degenerate, as fast as regular estimators such as probit. The result rests on a general theory for non-smooth M-estimators, under which a modified bootstrap is first-order valid given a consistent Hessian estimate. With two-way clustering, a cube-root term can remain; under high-level conditions, symmetric bootstrap intervals for suitable scalar parameters still control size uniformly.

Date: 2026-04, Revised 2026-10
New Economics Papers: this item is included in nep-dcm and nep-ecm
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