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We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to…
We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.
Questionnaire measures of consumers’ willingness to pay (WTP) and price sensitivity are biased, yet these declarative methods can aid managerial decision-making…
Questionnaire measures of consumers’ willingness to pay (WTP) and price sensitivity are biased, yet these declarative methods can aid managerial decision-making. Additional choices involve which question formats to use (open-ended or discrete choice) and how many questions (unique versus multiple). This paper aims to inform such choices for online data collection with an empirical evaluation of the size of the bias induced by four methods (price acceptability, price judgements, multiple discrete choices and single discrete choices) in a realistic choice context.
An experimental framework collects online data about a staple product whose price should be well known. Price sensitivity, WTP and their confidence intervals are derived from a logistic binary model of acceptability, then ranked to evaluate the size of the bias of each method, relative to an indirect benchmark.
Online data collections with self-administrated questionnaires lower respondents’ involvement and create substantial bias; hypothetical methods overestimate WTP and underestimate price sensitivity, especially with methods using unique questions (both discrete choice and price acceptability). Multiple questions (price judgements and repeated random discrete choices) increase attention to price information and reduce the bias. The round price effect also is notable in data collected by open-ended methods.
To measure declarative WTP and price sensitivity with online data collections, researchers should use a random discrete choices method. Price acceptability questions and split tests are not recommended. Price judgements provide reliable information about consumer reactions to prices, but the strong round price bias is problematic.
This study adds to marketing and economic literature by comparing actual measurement methods used by firms, rather than hypothetical versions, and offers strong external validity.
Patients and health professionals often make decisions which involve a choice between discrete alternatives. This chapter reviews the econometric methods which have been…
Patients and health professionals often make decisions which involve a choice between discrete alternatives. This chapter reviews the econometric methods which have been developed for modelling discrete choices and their application in the health economics literature. We start by reviewing the multinomial and mixed logit models and then consider issues such as scale heterogeneity, estimation in willingness to pay space and attribute non-attendance.
Advertisers frequently use social media for interactive and customer-oriented relationship marketing (RM) purposes. Moreover, sports clubs and players have been using…
Advertisers frequently use social media for interactive and customer-oriented relationship marketing (RM) purposes. Moreover, sports clubs and players have been using their social media accounts to post content of their sponsors and other advertising companies. Such posts create visibility and have value for these advertising companies, something which has not been empirically quantified in the existing literature. Hence, this paper's purpose is to identify the factors or attributes that influence the value of such advertisement posts.
A discrete choice approach is used to empirically estimate the utility that sponsorship managers derive from a post advertising their company or product on football clubs' and players' social media.
The results indicate that more followers, better on-field performance and a lower price significantly increase the advertising company's utility. Moreover, the used social media channel has a significant influence too, since Facebook and Instagram are preferred over Twitter, due to the latter's limited degrees of freedom for advertisers.
Considering additional factors such as the image fit between sponsor and sponsee and presence on the Chinese social media market offers an interesting avenue for future research.
The empirical estimates allow commercial managers of clubs and players to derive companies' relative willingness to pay (WTP) for changes in characteristics of advertisements on their social media from the calculated utilities. This information can be used in the pricing decision when social media posts are sold or included in sponsorship packages.
This is the first study applying discrete choice modelling to link social media marketing (SMM) and sports marketing.
The search for flexible models has led the simple multinomial logit model to evolve into the powerful but computationally very demanding mixed multinomial logit (MMNL…
The search for flexible models has led the simple multinomial logit model to evolve into the powerful but computationally very demanding mixed multinomial logit (MMNL) model. That flexibility search lead to discrete choice hybrid choice models (HCMs) formulations that explicitly incorporate psychological factors affecting decision making in order to enhance the behavioral representation of the choice process. It expands on standard choice models by including attitudes, opinions, and perceptions as psychometric latent variables.
In this paper we describe the classical estimation technique for a simulated maximum likelihood (SML) solution of the HCM. To show its feasibility, we apply it to data of stated personal vehicle choices made by Canadian consumers when faced with technological innovations.
We then go beyond classical methods, and estimate the HCM using a hierarchical Bayesian approach that exploits HCM Gibbs sampling considering both a probit and a MMNL discrete choice kernel. We then carry out a Monte Carlo experiment to test how the HCM Gibbs sampler works in practice. To our knowledge, this is the first practical application of HCM Bayesian estimation.
We show that although HCM joint estimation requires the evaluation of complex multi-dimensional integrals, SML can be successfully implemented. The HCM framework not only proves to be capable of introducing latent variables, but also makes it possible to tackle the problem of measurement errors in variables in a very natural way. We also show that working with Bayesian methods has the potential to break down the complexity of classical estimation.
In this chapter, we describe how random utility maximization (RUM) discrete choice models are used to estimate the demand for commodity attributes in…
In this chapter, we describe how random utility maximization (RUM) discrete choice models are used to estimate the demand for commodity attributes in quality-differentiated goods. After presenting a conceptual overview, we focus specifically on the conditional logit model. We examine technical issues related to specification, interpretation, estimation, and policy use. We also discuss identification strategies for estimating the role of price and non-price attributes in preferences when product attributes are incompletely observed. We illustrate these concepts via a stylized application to new car purchases, in which our objective is to measure preferences for fuel economy.
Discrete choice models are widely used for estimating the effects of changes in attributes on a given product's likely market share. These models can be applied directly…
Discrete choice models are widely used for estimating the effects of changes in attributes on a given product's likely market share. These models can be applied directly to situations in which the choice set is constant across the market of interest or in which the choice set varies systematically across the market. In both of these applications, the models are used to determine the effects of different attribute levels on market shares among the available alternatives, given predetermined choice sets, or of varying the choice set in a straightforward way.
Discrete choice models can also be used to identify the “optimal” configuration of a product or service in a given market. This can be computationally challenging when preferences vary with respect to the ordering of levels within an attribute as well the strengths of preferences across attributes. However, this type of optimization can be a relatively straightforward extension of the typical discrete choice model application.
In this paper, we describe two applications that use discrete choice methods to provide a more robust metric for use in Total Unduplicated Reach and Frequency (TURF) applications: apparel and food products. Both applications involve products for which there is a high degree of heterogeneity in preferences among consumers.
We further discuss a significant challenge in using TURF — that with multi-attributed products the method can become computationally intractable — and describe a heuristic approach to support food and apparel applications. We conclude with a summary of the challenges in these applications, which are yet to be addressed.
Research on strategic choices available to the firm are often modeled as a limited number of possible decision outcomes and leads to a discrete limited dependent variable…
Research on strategic choices available to the firm are often modeled as a limited number of possible decision outcomes and leads to a discrete limited dependent variable. A limited dependent variable can also arise when values of a continuous dependent variable are partially or wholly unobserved. This chapter discusses the methodological issues associated with such phenomena and the appropriate statistical methods developed to allow for consistent and efficient estimation of models that involve a limited dependent variable. The chapter also provides a road map for selecting the appropriate statistical technique and it offers guidelines for consistent interpretation and reporting of the statistical results.
This paper introduces a behavioral framework to model residential relocation decision in island areas, at which the decision in question is influenced by the…
This paper introduces a behavioral framework to model residential relocation decision in island areas, at which the decision in question is influenced by the characteristics of island regions, policy variables related to accessibility measures, and housing prices at the proposed island area, as well as personal, household (HH), job, and latent characteristics of the decision makers.
The model framework corresponds to an integrated choice and latent variable (ICLV) setting where the discrete choice model includes latent variables that capture attitudes and perceptions of the decision makers. The latent variable model is composed of a group of structural equations describing the latent variables as a function of observable exogenous variables and a group of measurement equations, linking the latent variables to observable indicators.
An empirical study has been developed for the Greek Aegean island area. Data were collected from 900 HHs in Greece contacted via telephone. The HHs were presented hypothetical scenarios involving policy variables, where 2010 was the reference year. ICLV binary logit (BL) and mixed binary logit (MBL) relocation choice models were estimated sequentially. Findings suggest that MBL models are superior to BL models, while both the policy and the latent variables significantly affect the relocation decision and improve considerably the models' goodness of fit. Sample enumeration method is finally used to aggregate the results over the Greek population.