Discrete Choice Prox-Functions on the Simplex

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps. As illustration, we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming adjusts demand within a consumption cycle.

Nonparametric Analysis of Random Utility Models: Computational Tools for Statistical Testing

Kitamura and Stoye (2018) recently proposed a nonparametric statistical test for random utility models of consumer behavior. The test is formulated in terms of linear inequality constraints and a quadratic objective function. While the nonparametric test is conceptually appealing, its practical implementation is computationally challenging. In this paper, we develop a column generation approach to operationalize the test. These novel computational tools generate considerable computational gains in practice, which substantially increases the empirical usefulness of Kitamura and Stoye's statistical test.

Assessing Social Carrying Capacity of Tourism Destinations with Random Utility Models*

Some local visitors or tourists avoid visiting resorts because they have experienced or anticipate overcrowding. Hence, policymakers are concerned to monitor congestion levels. The paper proposes the use of the elasticity of the probability of visiting a destination with respect to increases in congestion, from a random utility framework. More precisely, random parameter logit model is estimated. The advantage of this approach is that it captures not only the current level of congestion but other aspects, such as the sensitivity of different destinations towards crowding and different visitors’ concern about congestion and their probabilities of visiting alternative destinations. It is shown that the rate of change of the elasticity increases with the number of visitors, capturing the expected underlying non-linear relationship such that, when the number of visitors is low, the index is also low but increases exponentially with the influx of new visitors.