A note on identification in discrete choice models with partial observability

TY - JOUR

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

AU - Fosgerau, Mogens

AU - Ranjan, Abhishek

PY - 2017/8/1

Y1 - 2017/8/1

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 -