Abstract

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility Uj+mj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{j}+m_{j}$$\end{document} to each alternative in a finite set j∈1,…,J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j\in \left\{ 1,\ldots,J\right\} $$\end{document}, where U=U1,…,UJ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {U}=\left\{ U_{1},\ldots,U_{J}\right\} $$\end{document} is unobserved by the researcher and random with an unknown joint distribution, while the perturbation m=m1,…,mJ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {m}=\left $$\end{document} is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→Pr1|m,…,PrJ|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf { m\rightarrow }\left,\ldots,\Pr \left \right) $$\end{document}. Previous research has shown that the choice probability system is identified from the observation of the relationship m→Pr1|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf {m}\rightarrow \Pr \left $$\end{document}. We show that the complete choice probability system is identified from observation of a relationship m→∑j=1sPrj|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {m}\rightarrow \sum _{j=1}^{s}\Pr \left $$\end{document}, for any s

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