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Glucagon-like peptide-1 receptor agonists (GLP-1s) represent a major improvement in the treatment of diabetes, obesity, and cardiovascular risk reduction, but they are also among the most expensive drugs in widespread use and the subject of significant policy debate. A key question is whether their high upfront price overstates their net cost if the health improvements they produce lead to reduced downstream health care use and medical spending, that is, cost offsets. We estimate such offsets using insurance claims data, examining the effects of GLP-1 initiation on subsequent GLP-1 use and spending, as well as on other non-GLP-1 spending. We use a stacked difference-in-differences design, comparing patients initiating GLP-1 medication to not-yet-treated controls who initiate GLP-1s several months or years later, allowing us to control for underlying time trends and baseline characteristics. This approach helps address concerns that GLP-1 initiators may differ systematically from other patients in ways related to spending trends. We examine how spending changes following GLP-1 initiation, both for GLP-1s themselves and for other categories of medical and prescription drug spending. Overall, we do not find a reduction in downstream medical spending. Although GLP-1 initiation reduces spending on other diabetes medications, total non-GLP-1 spending increases, driven by higher outpatient health care use; GLP-1 drug spending rises mechanically. For health care payers, the relevant cost of GLP-1 initiation therefore extends beyond the drug’s sticker price. We find similar results across subgroups of GLP-1 initiators, including those with prior cardiovascular disease and those without diabetes, consistent with the obesity indication. Our main results examine spending responses over the first year after initiation. We also estimate longer-run effects in a smaller sample and find no cost offsets even five years after GLP-1 initiation. Taken together, these results suggest that payers facing the costs of GLP-1 coverage are unlikely to see large savings from reduced spending on other care. If GLP-1 therapies ultimately yield cost savings, they are likely to occur only over longer horizons or through non-medical channels.