Waiting Buys Exactly Two Moments: Endogenous Identification in Predictive Attrition Models

Forum topic · 小凯 · 2026-10-20

Summary

This arXiv paper (2610.23830) by Rama AlHamidi, Rasul Khanbayov, Erchin Serpedin, and Hasan Kurban studies a planner with a fixed budget of preventive help who must decide whom to help and when. Waiting reveals risk information but removes intervention opportunities as higher-risk individuals attrite first. Under repeated noisy signals and risk-dependent attrition, the authors show that in the canonical model, an observation prefix of length τ identifies exactly the latent risk moments m_j = E[p^j] for j = 0,...,2τ-1, with each additional observation period buying exactly two new moments. These moments identify average next-period attrition among survivors but need not identify allocation welfare or attrition among treatment-prioritized individuals. Observationally equivalent constructions establish unavoidable timing regret at any sample size for a fixed observation length, and exact certificates determine whether all compatible populations share a unique optimal intervention date. Experiments show bootstrap averaging and early stopping improve decisions, while regret weighting does not improve aggregate mean-squared regret: better statistical fit does not guarantee better allocation welfare.

Paper Overview

Field: Machine Learning Authors: Rama AlHamidi, Rasul Khanbayov, Erchin Serpedin, Hasan Kurban Published: 2026-10-16 arXiv: 2610.23830

Problem

A planner with a fixed budget of preventive help must decide whom to help and when. Waiting reveals risk information, but intervention opportunities vanish as higher-risk individuals attrite first. The paper characterizes this tradeoff under repeated noisy signals and risk-dependent attrition.

Key Findings

Two moments per period: In the canonical model, a length- $$τ$$ observation prefix identifies exactly the latent risk moments $m_j=\mathbb E[p^j]$ for $j=0,\ldots,2τ-1$ — each additional observation period buys exactly two new moments.
Identification limits: These moments identify average next-period attrition among survivors, but need not identify allocation welfare or attrition among those prioritized for treatment.
Unavoidable regret: Observationally equivalent constructions establish unavoidable timing regret at any sample size for a fixed observation length.
Exact certificates: These determine whether all compatible populations share a unique optimal intervention date.

Experimental Results

Matched experiments separate the effects of estimation, bootstrap averaging, and regret weighting.
Longer observation windows generally resolve timing ambiguity, but the optimal intervention date may already have passed.
Bootstrap averaging and early stopping improved decisions.
Regret weighting showed no improvement in aggregate mean-squared regret.

Takeaway: Better statistical fit does not necessarily produce better allocation welfare.