# Statistical Inference under Performativity

arXiv: https://arxiv.org/abs/2505.18493 · HTML: https://mlsanity.com/paper/2505.18493/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 24 May 2025.

## Builds on (most cited first, 24 of 24)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Data Feedback Loops: Model-driven Amplification of Dataset Biases](https://mlsanity.com/paper/2209.03942/) (2022)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Stratified Prediction-Powered Inference for Hybrid Language Model Evaluation](https://mlsanity.com/paper/2406.04291/) (2024)
- [Treatment Effects in Market Equilibrium](https://mlsanity.com/paper/2109.11647/) (2021)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)
- [Incentivizing honest performative predictions with proper scoring rules](https://mlsanity.com/paper/2305.17601/) (2023)
- [Bayesian Prediction-Powered Inference](https://mlsanity.com/paper/2405.06034/) (2024)
- [FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference](https://mlsanity.com/paper/2502.02363/) (2025)
- [Policy design in experiments with unknown interference](https://mlsanity.com/paper/2011.08174/) (2020)
- [Optimized Regression Discontinuity Designs](https://mlsanity.com/paper/1705.01677/) (2017)
- [Tight Lower Bounds and Improved Convergence in Performative Prediction](https://mlsanity.com/paper/2412.03671/) (2024)
- [Bias-Aware Inference in Fuzzy Regression Discontinuity Designs](https://mlsanity.com/paper/1906.04631/) (2019)
- [Microfoundation Inference for Strategic Prediction](https://mlsanity.com/paper/2411.08998/) (2024)
- [Bias-Aware Inference in Regularized Regression Models](https://mlsanity.com/paper/2012.14823/) (2020)

## Built on by (most cited first, 4 of 4)

- [Revisiting Active Sequential Prediction-Powered Mean Estimation](https://mlsanity.com/paper/2604.18569/) (2026)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Performative Learning Theory](https://mlsanity.com/paper/2602.04402/) (2026)

## Abstract (arXiv)

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.