Daily Summary for 2026-10-17

Introduction to the show: ident: Economics. The day in economics: theory, mechanisms and the evidence beneath them.

Ruth: It's the seventeenth of October, twenty twenty-six, and this is the day's research.

Warren: One new paper came out today.

Ruth: I'm Ruth.

Warren: And I'm Warren, here with Iris.

Ruth: We'll take the day in one pass, then pull out the paper we're staying with.

Warren: Start us off with Identification and Inference for Algorithmic Frontiers with Selective Labels.

The day's research: Iris: This work by Identification and Inference for Algorithmic Frontiers with Selective Labels focuses on understanding fairness when data is only available for certain people.

Warren: How does that paper characterize a fairness-accuracy frontier?

Ruth: It tries to characterize a fairness-accuracy frontier using only selected outcomes.

Iris: What methods does it provide to test hypotheses about that frontier?

Warren: It provides methods to test hypotheses about that frontier based on those selected outcomes.

Iris: The core idea is determining the sharp identification region of this frontier when data comes from specific individuals.

Warren: That depends on how the loss functions are measured in particular ways.

Ruth: Furthermore, if observed data shows a certain algorithm cannot be on that frontier, what happens?

Iris: The authors build one alternative algorithm.

Warren: This new algorithm boosts accuracy for both groups without harming fairness across all possible missing label distributions.

Ruth: Observed distribution rules out binary status quo algorithms.

Warren: Then authors construct one alternative algorithm for both groups?

Iris: It boosts accuracy without harming fairness across all admissible distributions of missing labels.

Ruth: That leads to point identification and a debiased machine learning estimator.

Warren: Proposed under selection on observables and strict overlap assumptions, correct?

Iris: This allows us to derive the asymptotic distribution for inference on the fairness-accuracy frontier.

Ruth: Identification and Inference for Algorithmic Frontiers with Selective Labels provides tools to test hypotheses when only some outcomes are known.

Warren: The authors show how to find an alternative algorithm that improves both groups' accuracy without making things unfair, even when some data is missing.

Iris: For certain loss functions, they propose a debiased machine learning estimator to help infer where the fairness-accuracy frontier lies.

Ruth: I see the connection between those concepts.

Warren: Agreed, it moves from ruling out status quo to proposing new solutions.

Iris: Indeed, the focus shifts to inference under missing data scenarios.

Lucky paper: 2606.14977: Ruth: So we are looking at the theoretical framework of Identification and Inference for Algorithmic Frontiers with Selective Labels now.

Warren: The paper builds on work by Liang, Lu, Mu, and Okumura from two thousand twenty-six regarding fairness-accuracy frontiers under broad preferences over group-specific expected losses.

Iris: How does the support function of a convex feasible set E play a crucial role in characterizing this fairness-accuracy frontier?

Ruth: The support function hE (q) is characterized by a formula involving population means and conditional expectations of loss functions.

Warren: That formula is hE (q) equals E*

q T theta0(X): plus sup a E*

a(X) q T delta theta(X): .

Iris: Theorem two point one establishes that the set E is strictly convex, and the fairness-accuracy frontier F is defined by a condition involving the minimum of hC (epsilon*) times q squared plus hE (-q).

Ruth: That’s a bit dense for what it means for us to understand where an algorithm sits in terms of accuracy and fairness when data is incomplete.

Warren: This paper addresses the selective labels problem where outcomes are only observed for selected individuals, denoted as Y equals ZY star, with Z indicating observability.

Iris: The paper provides point identification of the FA-frontier under a missing-at-random assumption where conditional on attributes, outcome observability doesn't convey additional information on Y star.

Ruth: That identification is achieved by deriving a debiased machine learning estimator for the FA-frontier based on inverse probability weighting.

Warren: The inference part involves proposing a debiased machine learning estimator whose asymptotic distribution is derived using Lemma three point one, and they also derive a test statistic to check whether the FA-frontier coincides with the Pareto frontier, PF.

Iris: They propose a test statistic T LDA n to reject the LDA hypothesis when no less discriminatory alternative exists.

Ruth: So, if we only observe some outcomes, we can use inverse propensity score weighting and this debiased machine learning estimator to build a confidence set around the partially identified FA-frontier.

Warren: This method is particularly appropriate in governance contexts where high-dimensional administrative data enable flexible nonparametric modeling of the selection process.

Iris: When the selection process is left completely unrestricted, they provide a tractable characterization of the sharp identification region for the FA-frontier, which collapses to a finite-dimensional criterion involving only corner distributions lambda0 and lambda1.

Ruth: How does this specific collapse help us when we are dealing with real world data that might not fit those assumptions?

Warren: The paper specializes the analysis to binary outcomes and classification loss for accuracy and statistical parity for fairness, which helps narrow down what can be learned about F.

Iris: The debiased machine learning estimator hE (q) is defined as E

zeta i(q; L, eta): where zeta i(q; L, eta) includes a term accounting for the local effect of the first-step function pi on the original estimand.

Ruth: That term accounting for the local effect of the first-step function seems like it's where most of that identification magic happens.

Warren: And they show that this estimator converges to a Gaussian process uniformly in q squared.

Iris: The Bayesian bootstrap procedure is consistent and provides an asymptotically valid confidence set for F by test inversion, which is useful for building those confidence sets around the partially identified FA-frontier.