Nonparametric Identification of Demand without Exogenous Product Characteristics

We study identification of differentiated product demand from market-level data when product characteristics can be endogenous. Past work suggests nonparametric identification may be impossible: that is, in addition to standard price instruments, exogenous characteristic-based instruments are essentially necessary to identify sufficiently flexible demand models with standard index restrictions. We show, however, that price counterfactuals are nonparametrically identified using recentered instruments – which combine exogenous price instruments with possibly 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 instrumental variable identification, is best viewed as a technical requirement on the strength of identifying variation rather than a substantive economic or statistical restriction. We show the two conditions are closely related, though generally distinct. We conclude with several practical implications for the parametric estimation of demand counterfactuals.

💡 Research Summary

This paper revisits the problem of identifying differentiated‑product demand using market‑level data when product characteristics are potentially endogenous. Earlier work, most notably Berry and Haile (2014), argued that without exogenous characteristic‑based instruments, price instruments alone cannot non‑parametrically identify the demand function or price counterfactuals. Their argument relied on a linear index restriction (δ = X + ξ) and a completeness condition that required instruments to vary both shares and prices jointly.

The authors introduce a novel identification strategy based on “recentered instruments.” A recentered instrument is formed by taking an exogenous price shock Z and subtracting its conditional mean given the possibly endogenous characteristics X, i.e., Z − E