2025/12/29 by Borusyak, Kirill, Chen, Jiafeng, Hull, Peter +1
#Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2512.23211
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.