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  2. ASSA Annual Meeting
  3. 2027
  4. Preliminary Program
  5. Empirical Bayes, Machine Learning, and Policy Learning
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Empirical Bayes, Machine Learning, and Policy Learning

Paper Session

Sunday, Jan. 3, 2027 8:00 AM - 10:00 AM (EST)

Marriott Marquis Washington DC
Hosted By: Econometric Society
  • Chair: Matthew Masten, Duke University

ReLU-Based and DNN-Based Generalized Maximum Score Estimators

Xiaohong Chen
,
Yale University
Wayne Gao
,
University of Pennsylvania
Likang Wen
,
University of Pennsylvania

Abstract

We propose a new formulation of the maximum score estimator that uses compositions of rectified linear unit (ReLU) functions, instead of indicator functions as in Manski (1975, 1985) to encode the sign alignment restrictions. Since the ReLU function is Lipschitz, our new ReLU-based maximum score criterion function is substantially easier to optimize using standard gradient-based optimization pacakges. We also show that our ReLU-based maximum score (RMS) estimator can be generalized to an umbrella framework defined by multi-index single-crossing (MISC) conditions, while the original maximum score estimator cannot be applied. We establish the $n^{-s/(2s+1)}$ convergence rate and asymptotic normality for the RMS estimator under order-$s$ Holder smoothness. In addition, we propose an alternative estimator using a further reformulation of RMS as a special layer in a deep neural network (DNN) architecture, which allows the estimation procedure to be implemented via state-of-the-art software and hardware for DNN.

Policy Learning with Compliance Guarantee

Thomas Chan
,
University of British Columbia
Vadim Marmer
,
University of British Columbia
Kyungchul Song
,
University of British Columbia

Abstract

We study optimal policy learning where a policymaker (PM) uses data from a source population to design treatment assignments for a target population under a budget constraint. Because of the budget constraint, the PM needs to consider both treatment effects and individuals’ incentives for treatment participation to minimize wasted resources. The main challenge is that treatment participation incentives may differ between the two populations. We develop a maximin approach that maximizes the minimum of the PM’s expected objective across all possible incentive configurations. We show that this optimal policy learning problem can be reformulated using stochastic dominance constraints, where the optimal assignment prioritizes individuals most likely to comply with the treatment.

Automatic Inference for Value-Added Regressions

Tian Xie
,
University College London

Abstract

A large empirical literature regresses outcomes on empirical Bayes shrinkage estimates of value-added, yet little is known about whether this approach leads to unbiased estimates and valid inference for the downstream regression coefficients. We study a general class of empirical Bayes estimators and the properties of the resulting regression coefficients. We show that estimators can be asymptotically biased and inference can be invalid if the shrinkage estimator does not account for heteroskedasticity in the noise when estimating value added. By contrast, shrinkage estimators properly constructed to model this heteroskedasticity perform an automatic bias correction: the associated regression estimator is asymptotically unbiased, asymptotically normal, and efficient in the sense that it is asymptotically equivalent to regressing on the true (latent) value-added. Further, OLS standard errors from regressing on shrinkage estimates are consistent in this case. As such, efficient inference is easy for practitioners to implement: simply regress outcomes on shrinkage estimates of value-added that account for noise heteroskedasticity.

Compound Selection Decisions: An Almost SURE Approach

Jiafeng Chen
,
Stanford University
Lihua Lei
,
Stanford University
Timothy Sudijono
,
Stanford University
Liyang Sun
,
University College London and CEMFI
Tian Xie
,
University College London

Abstract

This paper proposes methods for compound selection decisions in a Gaussian sequence model  where welfare, defined as the expected utility of a data-dependent decision rule, is the objective. Inspired by Stein’s unbiased risk estimate (SURE), we introduce ASSURE, a family of estimators for welfare. ASSURE enables selection of rules from a pre-specified class by optimizing estimated welfare, thereby borrowing strength across noisy payoff estimates. A leading variant ASSURE* is nearly unbiased and achieves near-parametric rates, yielding rules with favorable regret properties conditional on unknown parameters. When the pre-specified class is derived from random-effects models for decision payoffs, these regret guarantees provide robustness to potential prior misspecification, improving the empirical Bayes approach. We apply ASSURE to the selection of Census tracts for economic opportunity, the identification of discriminating firms, and the analysis of p-value decision procedures in A/B testing.
JEL Classifications
  • C1 - Econometric and Statistical Methods and Methodology: General