CATE Estimation or Empirical Welfare Maximization? A Statistical Analysis of Causal Decision Making under a Hard Budget

Causal decision making under limited resources requires choosing whom to treat while respecting operational constraints. Two widely studied approaches to treatment allocation are (i) first estimating the conditional average treatment effect (CATE) and then using the estimated effects to determine a feasible allocation, and (ii) directly selecting an allocation by empirical welfare maximization (EWM). Their relative statistical performance, however, remains unclear when treatment costs are heterogeneous, and every deployment batch must satisfy a hard budget. To bridge this gap, we study the statistical comparison between CATE estimation and EWM for finite-batch treatment allocation under a hard budget. We develop a common framework that relates treatment effect estimation to allocation regret and characterizes the local regret of the two approaches under correct specification and model misspecification. Our analysis shows that CATE estimation can achieve lower regret by pooling information under correct specification, while misspecification can reverse the comparison in favor of EWM, with an explicit threshold separating the two cases. We extend these results to observational data using cross-fitted doubly robust scores. Finite-sample experiments confirm the predicted variance advantage and the reversal under misspecification. Source code is available at https://anonymous.4open.science/r/STEM-B0E3.