A dual approach to nonparametric characterization for random utility models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916292699619328 |
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| author | Koida, Nobuo Shirai, Koji |
| author_facet | Koida, Nobuo Shirai, Koji |
| contents | This paper develops a novel characterization for random utility models (RUM), which turns out to be a dual representation of the characterization by Kitamura and Stoye (2018, ECMA). For a given family of budgets and its "patch" representation á la Kitamura and Stoye, we construct a matrix $Ξ$ of which each row vector indicates the structure of possible revealed preference relations in each subfamily of budgets. Then, it is shown that a stochastic demand system on the patches of budget lines, say $π$, is consistent with a RUM, if and only if $Ξπ\geq \mathbb{1}$, where the RHS is the vector of $1$'s. In addition to providing a concise quantifier-free characterization, especially when $π$ is inconsistent with RUMs, the vector $Ξπ$ also contains information concerning (1) sub-families of budgets in which cyclical choices must occur with positive probabilities, and (2) the maximal possible weights on rational choice patterns in a population. The notion of Chvátal rank of polytopes and the duality theorem in linear programming play key roles to obtain these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A dual approach to nonparametric characterization for random utility models Koida, Nobuo Shirai, Koji Theoretical Economics Econometrics This paper develops a novel characterization for random utility models (RUM), which turns out to be a dual representation of the characterization by Kitamura and Stoye (2018, ECMA). For a given family of budgets and its "patch" representation á la Kitamura and Stoye, we construct a matrix $Ξ$ of which each row vector indicates the structure of possible revealed preference relations in each subfamily of budgets. Then, it is shown that a stochastic demand system on the patches of budget lines, say $π$, is consistent with a RUM, if and only if $Ξπ\geq \mathbb{1}$, where the RHS is the vector of $1$'s. In addition to providing a concise quantifier-free characterization, especially when $π$ is inconsistent with RUMs, the vector $Ξπ$ also contains information concerning (1) sub-families of budgets in which cyclical choices must occur with positive probabilities, and (2) the maximal possible weights on rational choice patterns in a population. The notion of Chvátal rank of polytopes and the duality theorem in linear programming play key roles to obtain these results. |
| title | A dual approach to nonparametric characterization for random utility models |
| topic | Theoretical Economics Econometrics |
| url | https://arxiv.org/abs/2403.04328 |