On ordinal utility, cardinal utility, and random utility

Though the Random Utility Model (RUM) was conceived  entirely in terms of ordinal utility, the apparatus throughwhich it is widely practised exhibits properties of  cardinal utility.  The adoption of cardinal utility as a  working operation of ordinal is perfectly valid, provided  interpretations drawn from that operation remain faithful  to ordinal utility.  The paper considers whether the latterrequirement holds true for several measurements commonly  derived from RUM.  In particular it is found that  measurements of consumer surplus change may depart from  ordinal utility, and exploit the cardinality inherent in  the practical apparatus.

Nonparametric Analysis of Random Utility Models

This paper develops and implements a nonparametric test of Random Utility Models. The motivating application is to test the null hypothesis that a sample of cross-sectional demand distributions was generated by a population of rational consumers. We test a necessary and sufficient condition for this that does not rely on any restriction on unobserved heterogeneity or the number of goods. We also propose and implement a control function approach to account for endogenous expenditure. An econometric result of independent interest is a test for linear inequality constraints when these are represented as the vertices of a polyhedron rather than its faces. An empirical application to the U.K. Household Expenditure Survey illustrates computational feasibility of the method in demand problems with 5 goods.Comment: 54 pages, 2 figure

Heterogeneity and the nonparametric analysis of consumer choice: conditions for invertibility

This paper considers structural nonparametric random utility models for continuous choice variables. It provides sufficient conditions on random preferences to yield reduced- form systems of nonparametric stochastic demand functions that allow global invertibility between demands and random utility components. Invertibility is essential for global identifcation of structural consumer demand models, for the existence of well-specified probability models of choice and for the nonparametric analysis of revealed stochastic preference

Independence, homoskedasticity and existence in random utility models

Introduction Random utility models are often characterised by descriptions such as ‘homoskedastic’ or ‘independent’ in the utilities of the alternatives. However these descriptions do not have meaning in any absolute sense and must therefore be used with care. It is the main aim of this paper to demonstrate this point and discuss the issues it raises. In particular, the discussion leads into a consideration of the circumstances under which the models can be said to exist. The paper gives a definition of random utility models and goes on the define a large sub-class of those models, the additive stimulus models, on which the main discussion of the paper is focussed. The area of discussion is further specified by relating the probability statement, which is the main form in which the model is estimated and used, to the utility and utility difference distributions. New concepts are introduced of indistinguishability and almost-indistinguishability, which can be used in assessing discrete choice models. The paper then shows how a reasonable notion of model structure can be interpreted in terms of utility difference distributions for a class of indistinguishable models. The discussion of the independence of the utility distributions of the alternatives is based on the concepts introduced in the early parts of the paper. This discussion shows that many indistinguishable models exist for which the correlation of the utility functions is radically different. A following discussion goes on to show that the notion of heteroskedasticity is similarly incapable of clear definition, even within classes of indistinguishable models. The final main section discusses the issue of existence, finding that it is quite difficult to ensure that models actually represent a ‘real’ situation, although it is seen as important that the models actually ‘exist’ in some sense.. An error components approach, whether using purely probit models or substituting a logit kernel appears a useful approach to maintaining the ‘reality’ of the model

Overview of utility-based valuation

We review the utility-based valuation method for pricing derivative securities in incomplete markets. In particular, we review the practical approach to the utility-based pricing by the means of computing the first order expansion of marginal utility-based prices with respect to a small number of random endowments

Valuing trout angling benefits of water quality improvements while accounting for unobserved lake characteristics: An application to the Rotorua Lakes

Trout angling is one of the most popular water-based recreational activities in the Rotorua Lakes. Despite the high demand for trout angling and other recreational purposes, water quality in some of these lakes has been declining over the past decades and initiatives to try to restore the lakes are underway. To compliment these efforts, this study uses the travel cost random utility models to explore how changes in water quality would impact upon angler’s choice of fishing destinations. The welfare impacts due to water quality changes and possible lake closures are also explored. These findings highlight the importance of discrete choice random utility models as a policy decision making tool for recreational-based natural resource managers in New Zealand. Additionally, this study represents one of the unique cases in travel cost random utility applications that accounts fully for unobserved site effect

Epstein-Zin Utility Maximization on a Random Horizon

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed-horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies

Tests for the consistency of three-level nested logit models with utility maximization.

This paper provides necessary conditions for testing the local consistency of three-level nested logit models with random utility maximization. We find that for a model with two sub-nests per nest the conditions can lead to a substantial increase in the range of acceptable dissimilarity parameters, irrespective of the number of alternatives per sub-nest.Nested logit, Discrete choice, Random utility maximization