This paper clarifies how and why structural demand models (Berry and Haile, 2014, 2024) predict unit-level counterfactual outcomes. We do so by casting structural assumptions equivalently as restrictions on the joint distribution of potential outcomes. Our reformulation highlights a counterfactual homogeneity assumption underlying structural demand models: The relationship between counterfactual outcomes is assumed to be identical across markets. This assumption is strong, but cannot be relaxed without sacrificing identification of market-level counterfactuals. Absent this assumption, we can interpret model-based predictions as extrapolations from certain causally identified average treatment effects. This reinterpretation provides a conceptual bridge between structural modeling and causal inference.

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