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on Discrete Choice Models |
| By: | Rub\'en Loaiza-Maya; Didier Nibbering |
| Abstract: | The multinomial probit model is often used to analyze choice behaviour. However, estimation with existing Markov Chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice data sets. This paper proposes a variational inference method that is fast, even when a large number of choice alternatives and observations are considered. Variational methods usually require an analytical expression for the unnormalized posterior density and an adequate choice of variational family. Both are challenging to specify in a multinomial probit, which has a posterior that requires identifying restrictions and is augmented with a large set of latent utilities. We employ a spherical transformation on the covariance matrix of the latent utilities to construct an unnormalized augmented posterior that identifies the parameters, and use the conditional posterior of the latent utilities as part of the variational family. The proposed method is faster than MCMC, and can be made scalable to both a large numbers of choice alternatives and a large number of observations. The accuracy and scalability of our method is illustrated in numerical experiments and real purchase data with one million observations. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.12495&r= |
| By: | Herrera-Araujo, Daniel; Rheinberger, Christoph; Hammitt, James K. |
| Abstract: | Many stated-preference studies that seek to estimate the marginal willingness-to-pay (WTP) for reductions in mortality or morbidity risk su˙er from inadequate scope sensitivity. One possible reason is that the risk reductions presented to respondents are too small to be meaningful. Survey responses may thus not accurately reflect respondents’ preferences for health and safety. In this paper we propose a novel approach to estimating the value per statistical life (VSL) or the value per statistical case (VSC) based on larger risk reductions measurable as percentages. While such non-marginal risk reductions are easier to understand, they introduce well known biases. We propose a methodology to de-bias VSL and VSC estimates derived from the evaluation of non-marginal risk reductions and present a proof of concept using simulated stated preference data. |
| Keywords: | Value per Statistical Life; Value per Statistical Case; non-marginal risks reductions; scope sensitivity |
| JEL: | D10 D81 I1 Q51 |
| Date: | 2022–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:126887&r= |
| By: | Takeshi Fukasawa (Graduate School of Economics, The University of Tokyo and Junior Research Fellow, Research Institute for Economics and Business Administration, Kobe University, JAPAN) |
| Abstract: | This study investigates in what cases a firm's dynamic price-setting behavior can be approximated as static under dynamic demand, by developing a dynamic discrete choice model. Under dynamic demand with random utility shock following Gumbel distribution, this study shows that an oligopolistic firm's optimal price-setting behavior is well approximated by the static one with no strategic consideration, when consumers' conditional choice probabilities (CCPs) of choosing the firm's product are small for all consumer types and state variables. If the condition does not hold, the firm's behavior might be far from static. |
| Keywords: | Dynamic demand; Dynamic price-setting behavior; Static approximation; Monopolistic competition; Dynamic discrete choice |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2022-19&r= |
| By: | Jason Soria; Shelly Etzioni; Yoram Shiftan; Amanda Stathopoulos; Eran Ben-Elia |
| Abstract: | On-demand mobility platforms play an increasingly important role in urban mobility systems. Impacts are still debated, as these platforms supply personalized and optimized services, while also contributing to existing sustainability challenges. Recently, microtransit services have emerged, promising to combine advantages of pooled on-demand rides with more sustainable fixed-route public transit services. Understanding traveler behavior becomes a primary focus to analyze adoption likelihood and perceptions of different microtransit attributes. The COVID-19 pandemic context adds an additional layer of complexity to analyzing mobility innovation acceptance. This study investigates the potential demand for microtransit options against the background of the pandemic. We use a stated choice experiment to study the decision-making of Israeli public transit and car commuters when offered to use novel microtransit options (sedan vs. passenger van). We investigate the tradeoffs related to traditional fare and travel time attributes, along with microtransit features; namely walking time to pickup location, vehicle sharing, waiting time, minimum advanced reservation time, and shelter at designated boarding locations. Additionally, we analyze two latent constructs: attitudes towards sharing, as well as experiences and risk-perceptions related to the COVID-19 pandemic. We develop Integrated Choice and Latent Variable models to compare the two commuter groups in terms of the likelihood to switch to microtransit, attribute trade-offs, sharing preferences and pandemic impacts. The results reveal high elasticities of several time and COVID effects for car commuters compared to relative insensitivity of transit commuters to the risk of COVID contraction. Moreover, for car commuters, those with strong sharing identities were more likely to be comfortable in COVID risk situations, and to accept microtransit. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.01974&r= |
| By: | Bhavook Bhardwaj; Siddharth Chatterjee |
| Abstract: | The standard economic model of choice assumes that a decision maker chooses from sets of alternatives. A new branch of literature has considered the problem of choosing from lists i.e. ordered sets. In this paper, we propose a new framework that considers choice from infinite sequences. Our framework provides a natural way to model decision making in settings where choice relies on a string of recommendations. We introduce three broad classes of choice rules in this framework. Our main result shows that bounded attention is due to the continuity of the choice functions with respect to a natural topology. We introduce some natural choice rules in this framework and provide their axiomatic characterizations. Finally, we introduce the notion of computability of a choice function using Turing machines and show that computable choice rules can be implemented by a finite automaton. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.00070&r= |
| By: | Yuki Oyama |
| Abstract: | Although the recursive logit (RL) model has been recently popular and has led to many applications and extensions, an important numerical issue with respect to the evaluation of value functions remains unsolved. This issue is particularly significant for model estimation, during which the parameters are updated every iteration and may violate the model feasible condition. To solve this numerical issue, this paper proposes a prism-constrained RL (Prism-RL) model that implicitly restricts the path set by the prism constraint defined based upon a state-extended network representation. Providing a set of numerical experiments, we show that the Prism-RL model succeeds in the stable estimation regardless of the initial and true parameter values and is able to capture positive utilities. In the real application to a pedestrian network, we found the positive effect of street green presence on pedestrians. Moreover, the Prism-RL model achieved higher goodness of fit than the RL model, implying that the Prism-RL model can also describe more realistic route choice behavior. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.01215&r= |
| By: | Lixiong Li; Marc Henry |
| Abstract: | We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test statistic is a discrete analogue of a new optimal transport characterization of the sharp identified region. Both test statistic and critical values rely on simulation drawn from the distribution of latent variables and are computed using solutions to discrete optimal transport, hence linear programming problems. We also propose a fast preliminary search in the parameter space with an alternative, more conservative yet consistent test, based on a parameter free critical value. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.00473&r= |
| By: | Anton J. Kleywegt; Hongzhang Shao |
| Abstract: | Finding the optimal product prices and product assortment are two fundamental problems in revenue management. Usually, a seller needs to jointly determine the prices and assortment while managing a network of resources with limited capacity. However, there is not yet a tractable method to efficiently solve such a problem. Existing papers studying static joint optimization of price and assortment cannot incorporate resource constraints. Then we study the revenue management problem with resource constraints and price bounds, where the prices and the product assortments need to be jointly determined over time. We showed that under the Markov chain (MC) choice model (which subsumes the multinomial logit (MNL) model), we could reformulate the choice-based joint optimization problem as a tractable convex conic optimization problem. We also proved that an optimal solution with a constant price vector exists even with constraints on resources. In addition, a solution with both constant assortment and price vector can be optimal when there is no resource constraint. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.04774&r= |
| By: | Felix Brandt; Chris Dong |
| Abstract: | We introduce a new notion of rationalizability where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of rationalizing relations such that a strict preference between two alternatives in some feasible set is preserved when removing other alternatives. We then show that a choice function is locally rationalizable if and only if it satisfies Sen's $\gamma$ and give similar characterizations for local rationalizability via transitive, PIP-transitive, and quasi-transitive relations. Local rationalizability is realized via families of revealed preference relations that are sandwiched in between the base relation and the revealed preference relation of a choice function. We demonstrate the adequacy of our results for analyzing and constructing consistent social choice functions by giving simple characterizations of the top cycle and the uncovered set using transitive and quasi-transitive local rationalizability. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.05062&r= |
| By: | Cun, W.; Pesaran, M. H. |
| Abstract: | This paper develops and solves a spatiotemporal equilibrium model in which regional wages and house prices are jointly determined with location-to-location migration flows. The agent’s optimal location choice and the resultant migration process are shown to be Markovian, with the transition probabilities across all location pairs given as non-linear functions of wage and housing cost differentials, endogenously responding to migration flows. The model can be used for the analysis of spatial distribution of population, income, and house prices, as well as for spatiotemporal impulse response analysis. The model is estimated on a panel of 48 mainland U.S. states and the District of Columbia using the training sample (1976-1999), and shown to fit the data well over the evaluation sample (2000-2014). The estimated model is then used to analyze the size and speed of spatial spill-over effects by computing spatiotemporal impulse responses of positive productivity and land-supply shocks to California, Texas, and Florida. Our simulation results show that states with a lower level of land-use regulation can benefit more from positive state-specific productivity shocks; and positive land-supply shocks are much more effective in states, such as California, that are subject to more stringent land-use regulations. |
| Keywords: | location choice, joint determination of migration fl‡ows and house prices, spatiotemporal impulse response analysis, land-use deregulation, population allocation, productivity and land supply shocks, California, Texas and Florida |
| JEL: | E00 R23 R31 |
| Date: | 2022–04–09 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2225&r= |