A note on identification in discrete choice models with partial observability

Mogens Fosgerau; Abhishek Ranjan

doi:10.1007/s11238-017-9596-x

A note on identification in discrete choice models with partial observability

Mogens Fosgerau^*, Abhishek Ranjan

^*Corresponding author af dette arbejde

Økonomisk Institut

Abstract

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility U_j+ m_j to each alternative in a finite set j∈ {1 , … , J} , where U= {U₁, … , U_J} is unobserved by the researcher and random with an unknown joint distribution, while the perturbation m= (m₁, … , m_J) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→ (Pr (1 | m) , … , Pr (J| m)). Previous research has shown that the choice probability system is identified from the observation of the relationship m→ Pr (1 | m). We show that the complete choice probability system is identified from observation of a relationship m→∑j=1sPr(j|m), for any s< J. That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on m. This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.

Originalsprog	Engelsk
Tidsskrift	Theory and Decision
Vol/bind	83
Udgave nummer	2
Sider (fra-til)	283-292
Antal sider	10
ISSN	0040-5833
DOI	https://doi.org/10.1007/s11238-017-9596-x
Status	Udgivet - 1 aug. 2017

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10.1007/s11238-017-9596-x

Citationsformater

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abstract = "This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility Uj+ mj to each alternative in a finite set j∈ {1 , … , J} , where U= {U1, … , UJ} is unobserved by the researcher and random with an unknown joint distribution, while the perturbation m= (m1, … , mJ) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→ (Pr (1 | m) , … , Pr (J| m)). Previous research has shown that the choice probability system is identified from the observation of the relationship m→ Pr (1 | m). We show that the complete choice probability system is identified from observation of a relationship m→∑j=1sPr(j|m), for any s< J. That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on m. This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.",

keywords = "ARUM, Discrete choice, Identification, Random utility",

author = "Mogens Fosgerau and Abhishek Ranjan",

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doi = "10.1007/s11238-017-9596-x",

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T1 - A note on identification in discrete choice models with partial observability

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AU - Ranjan, Abhishek

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N2 - This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility Uj+ mj to each alternative in a finite set j∈ {1 , … , J} , where U= {U1, … , UJ} is unobserved by the researcher and random with an unknown joint distribution, while the perturbation m= (m1, … , mJ) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→ (Pr (1 | m) , … , Pr (J| m)). Previous research has shown that the choice probability system is identified from the observation of the relationship m→ Pr (1 | m). We show that the complete choice probability system is identified from observation of a relationship m→∑j=1sPr(j|m), for any s< J. That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on m. This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.

AB - This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility Uj+ mj to each alternative in a finite set j∈ {1 , … , J} , where U= {U1, … , UJ} is unobserved by the researcher and random with an unknown joint distribution, while the perturbation m= (m1, … , mJ) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→ (Pr (1 | m) , … , Pr (J| m)). Previous research has shown that the choice probability system is identified from the observation of the relationship m→ Pr (1 | m). We show that the complete choice probability system is identified from observation of a relationship m→∑j=1sPr(j|m), for any s< J. That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on m. This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.

KW - ARUM

KW - Discrete choice

KW - Identification

KW - Random utility

U2 - 10.1007/s11238-017-9596-x

DO - 10.1007/s11238-017-9596-x

M3 - Journal article

AN - SCOPUS:85015766426

SN - 0040-5833

VL - 83

SP - 283

EP - 292

JO - Theory and Decision

JF - Theory and Decision

IS - 2

ER -

A note on identification in discrete choice models with partial observability

Abstract

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