Statistical Decisions and Partial Identification: With Application to Boundary Discontinuity Design

TL;DR

This paper explores how statistical decision theory can be applied to situations with partial identification, illustrating its use through a hypothetical policy experiment and discussing open challenges in the field.

Contribution

It introduces a complete solution for decision making under partial identification and applies it to a policy scenario involving educational subsidies.

Findings

Insights into decision-making under partial identification

Application of theory to a hypothetical policy experiment

Discussion of open challenges in the field

Abstract

We are delighted to respond to the excellent surveys by Cattaneo et al. (2026) and Hirano (2026). Our discussion will attempt two things: first, we show how statistical decision theory can be applied to situations with partial identification; second, we connect the surveys' themes by applying these insights to an imagined policy experiment in one of Cattaneo et al.'s (2025) applications. To do so, we lay out a stylized scenario of statistical decision making under partial identification and, drawing on our own and others' earlier work, provide a complete solution for that scenario. We then apply these results to a hypothetical reduction (modelled on actual policies) in eligibility for educational subsidies. We will see that something of interest can be said, but also that bringing the theory to the application involves some leaps of faith and leaves some questions open. This leads to the final section, where we discuss what we see as the main open challenges in statistical decision theory under partial identification.