A note on identification in discrete choice models with partial observability

This note establishes a new identification result for additive random utility discrete choice models (ARUM). 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=1}^{s}Pr(j|m), for any s