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"Utility models"
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Variational Inference for Large-Scale Models of Discrete Choice
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact inference is often intractable. Markov chain Monte Carlo techniques make approximate inference possible, but the computational cost is prohibitive on the large datasets now becoming routinely available. Variational methods provide a deterministic alternative for approximation of the posterior distribution. We derive variational procedures for empirical Bayes and fully Bayesian inference in the mixed multinomial logit model of discrete choice. The algorithms require only that we solve a sequence of unconstrained optimization problems, which are shown to be convex. One version of the procedures relies on a new approximation to the variational objective function, based on the multivariate delta method. Extensive simulations, along with an analysis of real-world data, demonstrate that variational methods achieve accuracy competitive with Markov chain Monte Carlo at a small fraction of the computational cost. Thus, variational methods permit inference on datasets that otherwise cannot be analyzed without possibly adverse simplifications of the underlying discrete choice model. Appendices C through F are available as online supplemental materials.
Journal Article
On the Acceptability of Electricity Demand Side Management by Time of Day
Advances in the introduction of fluctuating renewable energies, such as photovoltaics (PV), have caused power-system destabilization. However, stability can be improved if consumers change the way they use power, moving to time slots when the PV output in an area is high. In large cities in developed countries, where the types of distributed energy resources are varied, demand side management (DSM) in which consumers share power supplies and adjust the demand has received considerable attention. Under effective DSM that uses the latest information and communication technology to maximize the use of renewable energy, we believe that sparing use of appliances is not the only solution to address global warming. If behavioral change shifts the use of domestic appliances from one time slot to other time slots, we do not have to abandon the use of these appliances. The aim of this study is to determine the possibility of such behavioral changes in people in order to provide basic information for operating an effective DSM. To that end, we conducted a questionnaire-based survey of 10,000 households in Japan. We investigated the proportion of people responding to a request for a demand response (DR) under the given presented reward in time slots when DSM by DR is required. We also analyzed the factors influencing people’s response to a request for a DR. Furthermore, based on the rewards likely to be achieved in the adjustable power market, we estimated how much adjustable power would be realized.
Journal Article
Underlying Consumer Heterogeneity in Markets for Subscription-Based IT Services with Network Effects
In this paper we explore the underlying consumer heterogeneity in competitive markets for subscription-based information technology services that exhibit network effects. Insights into consumer heterogeneity with respect to a given service are paramount in forecasting future subscriptions, understanding the impact of price and information dissemination on market penetration growth, and predicting the adoption path for complementary products that target the same customers as the original service. Employing a continuous-time utility model, we capture the behavior of a continuum of consumers who are differentiated by their intrinsic valuations from using the service. We study service subscription patterns under both perfect and imperfect information dissemination. In each case, we first specify the conditions under which consumer rational behavior supported by the utility model can explain a general observed adoption path, and if so, we explicitly derive the analytical closed-form expression for the consumer valuation distribution. We further explore the impact of awareness and distribution skewness on adoption. In particular, we highlight the practical forecasting importance of understanding the information dissemination process in the market as observed past adoption may be explained by several distinct awareness and heterogeneity scenarios that may lead to divergent adoption paths in the future. Moreover, we show that in the later part of the service lifecycle the subscription decision for new customers can be driven predominantly by information dissemination instead of further price markdowns. We also extend our results to time-varying consumer valuation scenarios. Furthermore, based on our framework, we advance a set of heuristic methods to be applied to discrete-time real industry data for estimation and forecasting purposes. In an empirical exercise, we apply our methodology to the Japanese mobile voice services market and provide relevant managerial insights from the analysis.
Journal Article
Impact of Shippers' Choice on Transportation System Congestion and Performance
In this research, we show how modeling shippers' responses to congested freight transportation on an important segment of the Upper Mississippi River (UMR) inland navigation system strongly influences the measurement of expected economic benefits attributed to a range of congestion mitigation measures. We present a model of the UMR that integrates a shippers' random utility model with a discrete event simulation model of the most congested 100-mile segment of the UMR system. The random utility model recognizes that waterway shippers may opt out of using the UMR in response to increased congestion and instead utilize alternative transport modes or destinations. Incorporating the dynamic response of shippers to changing operating conditions improves existing simulation models by explicitly accounting for the preferences and values of shippers, thereby providing a consistent estimate of the direct economic benefits associated with measures designed to reduce congestion and improve system performance. The major contributions of our research include demonstrating the importance of using models that capture shippers' responses to congestion in freight transportation systems and illustrating a novel methodology for quantifying the direct economic benefits to users of measures to improve transportation on the UMR.
Journal Article
CAUTIOUS EXPECTED UTILITY AND THE CERTAINTY EFFECT
Many violations of the independence axiom of expected utility can be traced to subjects' attraction to risk-free prospects. The key axiom in this paper, negative certainty independence (Dillenberger (2010)), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy negative certainty independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well defined sense. We show that our representation can also be derived from a \"cautious\" completion of an incomplete preference relation.
Journal Article
STOCHASTIC CHOICE AND REVEALED PERTURBED UTILITY
Perturbed utility functions—the sum of expected utility and a nonlinear perturbation function—provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce's IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across different agents and across decision problems. We also show that these representations correspond to a form of ambiguity-averse preferences for an agent who is uncertain about her true utility.
Journal Article
The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity
The mixed or heterogeneous multinomial logit (MIXL) model has become popular in a number of fields, especially marketing, health economics, and industrial organization. In most applications of the model, the vector of consumer utility weights on product attributes is assumed to have a multivariate normal (MVN) distribution in the population. Thus, some consumers care more about some attributes than others, and the IIA property of multinomial logit (MNL) is avoided (i.e., segments of consumers will tend to switch among the subset of brands that possess their most valued attributes). The MIXL model is also appealing because it is relatively easy to estimate. Recently, however, some researchers have argued that the MVN is a poor choice for modelling taste heterogeneity. They argue that much of the heterogeneity in attribute weights is accounted for by a pure scale effect (i.e., across consumers, all attribute weights are scaled up or down in tandem). This implies that choice behaviour is simply more random for some consumers than others (i.e., holding attribute coefficients fixed, the scale of their error term is greater). This leads to a \"scale heterogeneity\" MNL model (S-MNL). Here, we develop a generalized multinomial logit model (G-MNL) that nests S-MNL and MIXL. By estimating the S-MNL, MIXL, and G-MNL models on 10 data sets, we provide evidence on their relative performance. We find that models that account for scale heterogeneity (i.e., G-MNL or S-MNL) are preferred to MIXL by the Bayes and consistent Akaike information criteria in all 10 data sets. Accounting for scale heterogeneity enables one to account for \"extreme\" consumers who exhibit nearly lexicographic preferences, as well as consumers who exhibit very \"random\" behaviour (in a sense we formalize below).
Journal Article
Stochastic modelling of electricity and related markets
The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives.
eBook
Algorithmic monoculture and social welfare
As algorithms are increasingly applied to screen applicants for high-stakes decisions in employment, lending, and other domains, concerns have been raised about the effects of algorithmic monoculture, in which many decision-makers all rely on the same algorithm. This concern invokes analogies to agriculture, where a monocultural system runs the risk of severe harm from unexpected shocks. Here, we show that the dangers of algorithmic monoculture run much deeper, in that monocultural convergence on a single algorithm by a group of decision-making agents, even when the algorithm is more accurate for any one agent in isolation, can reduce the overall quality of the decisions being made by the full collection of agents. Unexpected shocks are therefore not needed to expose the risks of monoculture; it can hurt accuracy even under “normal” operations and even for algorithms that are more accurate when used by only a single decision-maker. Our results rely on minimal assumptions and involve the development of a probabilistic framework for analyzing systems that use multiple noisy estimates of a set of alternatives.
Journal Article