Approximate Balancing for Observational Studies, Dr. Chen Qiu, December 1|2, 2022

Empirical studies in social sciences often involve observational data with many controls or technical terms. As a way to seek robustness, a common practice is to compute an estimate using different subsets of controls. However, many conventional estimators ignore the additional mean squared error (MSE) incurred due to the presence of many controls or technical terms, which can cause the empirical results to be misinterpreted. Given a set of controls, how can we come up with a more robust estimator? In this talk, we will first review the balancing method as an effective way to estimate some causal effect under unconfoundedness. Then, we will introduce a simple, new balancing estimator that minimizes the worst-case finite-sample MSE among a class of balancing estimators. Therefore, this new estimator is approximately minimax optimal in a finite sample. We characterize our estimator as a solution to a simple minimum-distance problem. We also establish favorable asymptotic properties of our estimator under weak conditions that hold independently of its finite-sample minimax property. Compared to other recent approaches, this new balancing estimator behaves more robustly for the dataset of Ferraz and Finan (2011) and outperforms in a variety of simulation studies in terms of MSE. Slides | Paper1| Paper2