On the surjectivity of the mapping between utilities and choice probabilities
On the surjectivity of the mapping between utilities and choice probabilities
复制标题
关于效用与选择概率之间映射的满射性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Takahashi
中科院分区：
文献类型：
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作者：
Andriy Norets;S. Takahashi
本说明考虑标准多项选择模型。结果表明，如果加性效用冲击的分布具有密度，那么从效用的确定性成分到选择概率的映射就是满射的。换句话说，任何选择概率向量都可以通过选择合适的替代方案来获得。这一结果至少对计量经济学家感兴趣的三个领域有影响：结构动态离散选择模型的 Hotz 和 Miller (1993) 估计器、多项选择模型的非参数识别以及基于协变量相关混合的条件密度估计器的一致性。关键词。多项选择模型、识别、Hotz 和 Miller 估计量、协变量依赖混合物。 JEL分类。 C35、C61。
This note considers a standard multinomial choice model. It is shown that if the distribution of additive utility shocks has a density, then the mapping from de- terministic components of utilities to choice probabilities is surjective. In other words, any vector of choice probabilities can be obtained by selecting suitable utilities for alternatives. This result has implications for at least three areas of interest to econometricians: the Hotz and Miller (1993) estimator for structural dynamic discrete choice models, nonparametric identification of multinomial choice models, and consistency of conditional density estimators based on co- variate dependent mixtures. Keywords. Multinomial choice models, identification, Hotz and Miller estimator, covariate dependent mixtures. JEL classification. C35, C61.