We study the identification and estimation of preferences in hedonic discrete choice models of demand for differentiated products. In the hedonic discrete choice model, products are represented as a finite dimensional bundle of characteristics, and consumers maximize utility subject to a budget constraint. Our hedonic model also incorporates product characteristics that are observed by consumers but not by the economist. We demonstrate that, unlike the case where all product characteristics are observed, it is not in general possible to uniquely recover consumer preferences from data on a consumer's choices. However, we provide several sets of assumptions under which preferences can be recovered uniquely, that we think may be satisfied in many applications. Our identification and estimation strategy is a two stage approach in the spirit of Rosen (1974). In the first stage, we show under some weak conditions that price data can be used to nonparametrically recover the unobserved product characteristics and the hedonic pricing function. In the second stage, we show under some weak conditions that if the product space is continuous and the functional form of utility is known, then there exists an inversion between a consumer's choices and her preference parameters. If the product space is discrete, we propose a Gibbs sampling algorithm to simulate the population distribution of consumers' taste coefficients.
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