Discrete and Continuous Choice, Max-Stable Processes, and Independence from Irrelevant Attributes

Abstract

The Generalized Extreme Value Model was developed by McFadden for the case with discrete choice sets. The present paper extends this model to cases with both discrete and continuous choice sets and choice sets that are unobservable relative to the analyst. We also propose behavioral assumptions that justify random utility functions (processes) that have a max stable structure i.e., utility processes where the finite dimensional distributions are of the multivariate extreme value type. Finally we derive non-parametrically testable implications for the choice probabilities in the continuous case.

Sectoral labour supply, choice restrictions and functional form

“…A justification for the structure (2.3) is given in Dagsvik (1994). There it is demonstrated that under Assumption 2, if the choice among jobs satisfies the IIA property then particular structure on the particular structure of the marginal intensity measure of ε(z), ε -2 dε, in (2.3) follows.…”

“…In other words, g(h, w)dhdw yields the probability that a market opportunity with Dagsvik, 1994). The term θ 1 can be interpreted as the fraction of the feasible opportunities that are market opportunities.…”

“…In Dagsvik (1994) it is demonstrated that the set of Poisson points for which the utilities lie above any given positive level is finite (with probability one). Thus the set of "interesting" feasible jobs is (almost surely) finite, and it varies from one agent to another.…”

“…In this paper the distributional properties of the agents' preferences, in the presence of latent choice sets of jobs, follow from an assumption; "Independence from Irrelevant Attributes", proposed by Dagsvik (1994).…”

Statistical properties of consideration sets

“…That is, a low probability will be indicated for goods with undesirable X j and/or small ε ij . The issue of individual C i 's is perhaps even clearer here as different 14 Considerable more flexibility with respect to needing to observe actual choice sets is possible, if one makes the assumption that an individual's utility from an alternative has a true random component (Dagsvik, 1994). 15 It is always useful to allow the possibility that the two parameter vectors are statistically equivalent.…”