Statistical Inference under Performativity

TL;DR

This paper develops a statistical inference framework for performative prediction, establishing a central limit theorem and enabling more accurate policy-related inference in settings where predictions influence outcomes.

Contribution

It introduces the first comprehensive framework for statistical inference under performativity, including a central limit theorem and prediction-powered inference methods.

Findings

Established a central limit theorem for performative inference

Developed prediction-powered inference for tighter confidence regions

Validated the framework through numerical experiments

Abstract

Performativity of predictions refers to the phenomenon where prediction-informed decisions influence the very targets they aim to predict -- a dynamic commonly observed in policy-making, social sciences, and economics. In this paper, we initiate an end-to-end framework of statistical inference under performativity. Our contributions are twofold. First, we establish a central limit theorem for estimation and inference in the performative setting, enabling standard inferential tasks such as constructing confidence intervals and conducting hypothesis tests in policy-making contexts. Second, we leverage this central limit theorem to study prediction-powered inference (PPI) under performativity. This approach yields more precise estimates and tighter confidence regions for the model parameters (i.e., policies) of interest in performative prediction. We validate the effectiveness of our framework through numerical experiments. To the best of our knowledge, this is the first work to establish a complete statistical inference under performativity, introducing new challenges and inference settings that we believe will provide substantial value to policy-making, statistics, and machine learning.