Abduction and the Demand Curve

Abstract

Policy counterfactuals such as merger simulation require the demand curve at a specific market's realized conditions, not an average across markets. We characterize when the experimental average coincides with the market-specific curve and what structural estimation adds. The experimental average slope equals every market's demand slope if and only if demand is additively separable in price and the latent state. Linear demand satisfies this condition; standard discrete-choice models violate it. When separability fails, structural estimation identifies the market-specific demand curve if and only if the observed data identify the market's latent demand index; Berry inversion recovers this index from observed shares and prices—the abduction step in Pearl's causal hierarchy. We prove invertibility is necessary, not merely sufficient: without it, even price-only counterfactuals are set-identified. In a merger simulation, market-specific price predictions differ by a factor of two, driven entirely by unobserved demand conditions that experiments cannot distinguish.