Statistical Inference under Performativity
Xiang Li, Yunai Li, Huiying Zhong, Lihua Lei, Zhun Deng
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.