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.

翻译：我们研究了在市场层面数据中，当产品特征可能具有内生性时，差异化产品需求的识别问题。以往的研究表明，非参数识别可能无法实现：即除了标准的价格工具变量外，本质上还需要基于外生特征的工具变量，才能在标准的指数限制下识别足够灵活的需求模型。然而，我们证明，在较弱的指数限制和一个我们称之为“忠实性”的新条件下，通过使用重中心化的工具变量——该变量结合了外生的价格工具变量与可能具有内生性的产品特征——价格反事实可以实现非参数识别。我们认为，忠实性与非参数工具变量识别中通常的完备性条件类似，最好将其视为对识别变异强度的技术要求，而非实质性的经济或统计限制。我们证明这两个条件密切相关，但通常有所区别。最后，我们讨论了参数化估计需求反事实的几个实际意义。