Heterogeneous Treatment Effects in Panel Data: Insights into the Healthy Incentives Program

Problem definition: We study how adding new vendors to the Massachusetts Healthy Incentives Program (HIP), a food subsidy program, affects program utilization. This is an instance of a core problem in causal inference: estimating heterogeneous treatment effects (HTEs) using panel data. Existing methods either do not utilize the underlying structure in the panel data or do not accommodate the general vendor addition patterns in the HIP data. Methodology/results: We propose the panel clustering estimator (PaCE), a novel method that first partitions observations into disjoint clusters with similar treatment effects using a regression tree and then, leverages the (assumed) low-rank structure of the panel data to estimate the average treatment effect (ATE) for each cluster. Our theoretical results establish the convergence of the resulting estimates to the true treatment effects. Computational experiments with semisynthetic data show that PaCE achieves superior accuracy for ATE and HTE estimation compared with existing approaches. This performance was achieved using a regression tree with no more than 40 leaves, making PaCE both more accurate and interpretable. Managerial implications: Applying PaCE to HIP data, we discern the heterogeneous impacts of vendor additions on program utilization across different regions of Massachusetts. These findings provide valuable insights for future budget planning and for identifying which Massachusetts zip codes to target with vendor additions.

History: This paper was selected as part of the 1RR initiative between the M&SOM Journal and the MSOM Society. This paper was part of the 2025 MSOM Sustainable Operations SIG Conference.

Funding: This work was supported by the National Science Foundation [Grant 2141064].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2025.0522.