This talk summarizes work with coauthors (https://arxiv.org/abs/2312.17623, https://arxiv.org/abs/2408.09187, https://joseluismontielolea.com/epsilon_minimax_v2.pdf) that brings statistical decision theory to problems where robustness, e.g. to model uncertainty or limitations of external validity, is a major concern. The language used is that of partial identification; the application discussed is to optimal treatment choice and optimal experimental design in development economics. Part of the contribution is computational: Minimax decision rules can be hard to discover, and we leverage recent progress in computer science toward automated such discovery.

We show that when the propensity score is estimated using a suitable covariate balancing procedure, the commonly used inverse probability weighting (IPW) estimator, augmented inverse probability weighting (AIPW) with linear conditional mean, and inverse probability weighted regression adjustment (IPWRA) with linear conditional mean are all numerically the same for estimating the average treatment effect (ATE) or the average treatment effect on the treated (ATT). Further, suitably chosen covariate balancing weights are automatically normalized, which means that normalized and unnormalized versions of IPW and AIPW are identical. For estimating the ATE, the weights that achieve the algebraic equivalence of IPW, AIPW, and IPWRA are based on propensity scores estimated using the inverse probability tilting (IPT) method of Graham, Pinto and Egel (2012). For the ATT, the weights are obtained using the covariate balancing propensity score (CBPS) method developed in Imai and Ratkovic (2014). These equivalences also make covariate balancing methods attractive when the treatment is confounded and one is interested in the local average treatment effect.

We introduce a novel methodology for estimating heterogeneous net treatment effects under unit-varying treatment and cost effects. Our approach is designed for optimal assignment of a binary treatment that induces a cost-benefit trade-off: First, it enables identification of the target population, for which the treatment effect is larger than or equal to the cost effect. Second, it allows for direct prioritization of the treatment assignment via the effect size. Using a generalized random forest, we minimize a joint loss function based on the local difference between the two effects. We formally show that our approach achieves a lower mean squared error compared to separate effect estimation and subsequent differencing, if the treatment and cost effects are correlated. In a simulation study, we confirm these findings for finite samples. Additionally, we discuss two empirical applications. In the first example, we use semi-synthetic marketing data to evaluate customer conversion by balancing increased sales against discount offers. In the second example, we use data from a large nonprofit organization to analyze the net effect of a fundraising campaign to increase pledge payments while avoiding donor attrition.