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 -