Nonparametric Identification of Demand without Exogenous Product Characteristics

2025-12-29

AI Summary

This paper addresses the nonparametric identification of demand for differentiated products, relaxing the conventional assumption that product characteristics are exogenous. Its key innovation is a novel “credibility” condition that enables nonparametric identification of counterfactual prices using only exogenous supply-side instruments—such as cost shocks or policy interventions—without requiring product attributes to serve as instruments. Methodologically, it reformulates the demand system via recentered instrumental variables and verifies identifiability under joint completeness and credibility conditions. Theoretically, it extends the nonparametric instrumental variable (IV) framework by establishing the general validity of this approach under diverse, non-nested pricing mechanisms and broad generalized index models. This significantly enhances both the credibility and applicability of demand estimation in realistic market settings.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study the identification of differentiated product demand with exogenous supply-side instruments, allowing product characteristics to be endogenous. Past analyses have argued that exogenous characteristic-based instruments are essentially necessary given a sufficiently flexible demand model with a suitable index restriction. We show, however, that price counterfactuals are nonparametrically identified by recentered instruments -- which combine exogenous shocks to prices with endogenous product characteristics -- under a weaker index restriction and a new condition we term faithfulness. We argue that faithfulness, like the usual completeness condition for nonparametric identification with instruments, can be viewed as a technical requirement on the richness of identifying variation rather than a substantive economic restriction, and we show that it holds under a variety of non-nested conditions on either price-setting or the index.

Problem

• Identifies demand without exogenous product characteristics.
• Uses recentered instruments for price counterfactuals.
• Introduces faithfulness as a weaker identification condition.

Innovation

• Uses recentered instruments combining price shocks with endogenous characteristics
• Relies on faithfulness condition as technical requirement for identification
• Enables nonparametric identification under weaker index restrictions