This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models, where products are differentiated along more than one dimension and agents are characterized by several dimensions of unobserved heterogeneity. With products differentiated along a quality index and agents characterized by scalar unobserved heterogeneity, single crossing conditions on preferences and technology provide identifying restrictions in Ekeland, Heckman and Nesheim (2004) and Heckman, Matzkin and Nesheim (2010). We develop similar shape restrictions in the multi-attribute case. These shape restrictions, which are based on optimal transport theory and generalized convexity, allow us to identify preferences for goods differentiated along multiple dimensions, from the observation of a single market. We thereby derive nonparametric identification results for nonseparable simultaneous equations and multi-attribute hedonic equilibrium models with (possibly) multiple dimensions of unobserved heterogeneity. One of our results is a proof of absolute continuity of the distribution of endogenously traded qualities, which is of independent interest.

中文翻译：

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特征平衡与不可分联立方程的辨识

本文推导出在享乐均衡模型中以非参数方式识别偏好和技术的条件，其中产品沿不止一个维度进行区分，而代理的特征在于未观察到的异质性的几个维度。Ekeland、Heckman 和 Nesheim（2004 年）以及 Heckman、Matzkin 和 Nesheim（2010 年）根据质量指标区分产品，而代理以标量未观察到的异质性为特征，偏好和技术的单一交叉条件提供了识别限制。我们在多属性情况下开发了类似的形状限制。这些基于最优运输理论和广义凸性的形状限制使我们能够从对单一市场的观察中识别出对多维差异化商品的偏好。因此，我们为不可分离的联立方程和多属性享乐均衡模型推导出非参数识别结果（可能）具有未观察到的异质性的多个维度。我们的结果之一是证明了内生交易质量分布的绝对连续性，这是具有独立意义的。