Strategic instrumental variable regression: recovering causal relationships from strategic responses

In social domains, machine learning algorithms often prompt individuals to strategically modify their observable attributes to receive more favorable predictions. As a result, the distribution the predictive model is trained on may differ from the one it operates on in deployment. While such distribution shifts, in general, hinder accurate predictions, we identify a unique opportunity associated with shifts due to strategic responses. In particular, we show that we can use strategic responses effectively to recover causal relationships between observable features and the outcomes we wish to predict. More specifically, we study a game-theoretic model in which a decision-maker deploys a sequence of models to predict an outcome of interest (e.g., college GPA) for a sequence of strategic agents (e.g., college applicants).