Abduction and the Demand Curve

Brian C. Albrecht and James Traina

(Working Paper) April 2026

Abstract

We prove that Berry inversion (recovering a market's latent demand index from observed shares) is necessary, not just sufficient, for identifying every market's demand curve. The experimental average equals the market-specific demand curve if and only if demand is additively separable in price and the latent state, a condition standard discrete-choice models violate. When separability fails, Berry inversion is the abduction step (recovering the market's latent state from data) in Pearl's causal hierarchy: without it, even price-only counterfactuals are set-identified, and counterfactuals that also change product characteristics require a stronger recoverability condition. In a merger simulation, market-specific price predictions differ by a factor of two, driven entirely by unobserved demand conditions that experiments cannot distinguish.

Key Insight

Experimental average demand slopes only equal market-specific slopes under additive separability; otherwise, structural estimation requires Berry inversion to recover the latent demand index.

Keywords

  • demand estimation
  • abduction
  • causal hierarchy
  • counterfactual identification
  • additive separability
  • merger simulation

Citation

Brian C. Albrecht and James Traina (2026). "Abduction and the Demand Curve."

BibTeX

@article{abduction_demand_curve,
  title = {Abduction and the Demand Curve},
  author = {Brian C. Albrecht and James Traina},
  year = {2026},
  url = {https://briancalbrecht.com/Albrecht-Traina-Demand-Curve.pdf}
}