Counterfactual reconciliation: Incorporating aggregation constraints for more accurate causal effect estimates

Abstract

We extend the scope of the forecast reconciliation literature and use its tools in the context of causal inference. Researchers are interested in both the average treatment effect on the treated and treatment effect heterogeneity. We show that ex post correction of the counterfactual estimates using the aggregation constraints that stem from the hierarchical or grouped structure of the data is likely to yield more accurate estimates. Building on the geometric interpretation of forecast reconciliation, we provide additional insights into the exact factors determining the size of the accuracy improvement due to the reconciliation. We experiment with U.S. GDP and employment data. We find that the reconciled treatment effect estimates tend to be closer to the truth than the original (base) counterfactual estimates even in cases where the aggregation constraints are non-linear. Consistent with our theoretical expectations, improvement is greater when machine learning methods are used.