Dynamic choice, multistate duration models and stochastic structure

An important problem in the analysis of intertemporal choice processes is how to justify the choice of mathematical structure of the transition probabilities. A related and delicate identification problem is to separate the effect of unobserved variables from the influence on preferences from past choice behavior (state dependence). The present paper proposes a particular behavioral assumption to characterize the stochastic structure of intertemporal discrete choice models under the absence of state dependence. This assumption extends Luce axiom; "Independence from Irrelevant Alternatives", to the intertemporal context. Under specific regularity conditions the implication of these assumptions is that the individual choice process is a Markov chain with a particularly simple structure of the transition probabilities. By drawing on results obtained by Dagsvik (1983, 1988) it is demonstrated that this structure is consistent with an intertemporal and life cycle consistent random utility model where the utilities are independent extremal processes in time. Finally, the framework is extended to allow for state dependence and time varying choice sets.