Statistical Inference under Performativity
Journal:
arXiv
Published Date:
May 24, 2025
Abstract
Performativity of predictions refers to the phenomena that
prediction-informed decisions may influence the target they aim to predict,
which is widely observed in policy-making in social sciences and economics. In
this paper, we initiate the study of statistical inference under
performativity. Our contribution is two-fold. First, we build a central limit
theorem for estimation and inference under performativity, which enables
inferential purposes in policy-making such as constructing confidence intervals
or testing hypotheses. Second, we further leverage the derived central limit
theorem to investigate prediction-powered inference (PPI) under performativity,
which is based on a small labeled dataset and a much larger dataset of
machine-learning predictions. This enables us to obtain more precise estimation
and improved confidence regions for the model parameter (i.e., policy) of
interest in performative prediction. We demonstrate the power of our framework
by numerical experiments. To the best of our knowledge, this paper is the first
one to establish statistical inference under performativity, which brings up
new challenges and inference settings that we believe will add significant
values to policy-making, statistics, and machine learning.
