Efficiency and the logit model

Abstract

This paper discusses model building for discrete choice problems in the simplest case - the logit model. General model building principles are formulated and used in evaluatingways of deriving logit choice probabilities. The principles include that models should representhuman behavior, and that the basic assumptions should be testable and refutable againstobservations. Three ways of deriving the logit model are considered; the Luce model, theadditive random utility maximizing approach, and the efficiency approach. The equivalenceof the logit formula and the independence of irrelevant alternatives assumption (the Lucemodel) is well known. It is also well known that the assumption of additive random utilitymaximization with extreme value distribution for the unobservable stochastic componentsimplies the logit formula. The opposite implication does not hold. The principal merit ofadditive random utility maximizing is its coherence with standard economic theory. Itsprincipal weakness is that the basic assumptions can not be tested, since the stochasticcomponents cannot be observed. The efficiency assumption - samples with higher totalobservable utility are more probable - is equivalent to the logit formula. The advantage ofthe efficiency approach lies in its simple, testable basic behavioral assumptions. The independenceof irrelevant alternatives assumption is equivalent to the efficiency assumption.The additive random utility maximization approach and the efficiency approach are notequivalent.