Revealing Differences in Willingness to Pay due to the Dimensionality of Stated Choice Designs: An Initial Assessment

Stated choice (SC) methods are now a widely accepted data paradigm in the study of the choice responses of agents. Their popularity has spawned an industry of applications in fields as diverse as transportation, environmental science, health economics and policy, marketing, political science and econometrics. With rare exception, empirical studies have used a single SC design, in which the numbers of attributes, alternatives, choice sets, attribute levels and ranges have been fixed across the entire design. As a consequence the opportunity to investigate the influence of design dimensionality on behavioural response has been denied. Accumulated wisdom has promoted a large number of positions on what design features are specifically challenging for respondents; and although a number of studies have assessed the influence of subsets of design dimensions, there exists no single study (that we are aware of) that has systematically varied all of the main dimensions of SC experiments. This paper reports some initial findings on what influences, in aggregate, specific design configurations have on the mean willingness to pay for specific attributes using a Design of Designs (DoD) SC experiment in which the ‘attributes’ of the design are the design dimensions themselves. The design dimensions that are varied are the number of choice sets presented, the number of alternatives in each choice set, the number of attributes per alternative, the number of levels of each attribute and the range of attribute levels. The empirical evidence, using a sample of respondents in Sydney choosing amongst trip attribute bundles for their car commuting trip, suggests that, within the boundaries of design dimensionality investigated, mean estimates of WTP for travel time savings in the aggregate cover a range that is appropriate for reporting a global mean and a set of meaningful values for sensitivity testing in project appraisal and demand prediction. When these aggregated mean estimates are conditioned on all design dimensions we do not find any systematic differences due to specific design dimensions; however when each design dimension is assessed without controlling for the other dimensions we find evidence to support differences in aggregate mean WTP attributable to the number of attributes per alternative and the number of alternatives in a choice set. Research funded under the Australian Research Council Large Grants Scheme, Grant A00103962.     

Convergent Validity of Attribute-Based,Choice Questions in Stated-Preference Studies

The application of attribute-based choice questions is well established in the marketing literature, but there are unique aspects of the design that warrant investigation to assess their validity for economic welfare estimation. Three design issues are investigated in this paper: (1) the placement of the monetary stimulus (policy cost to respondents) in the sequence of attributes, (2) the number of policy alternatives respondents are asked to consider in choice questions (two versus three), and (3) the inclusion, versus exclusion, of a status-quo alternative in choice questions. The data used to implement these investigations are from a survey designed to estimate the value Maine residents place on a farmland conservation easement program. Tests of convergent validity indicate that the placement of the monetary stimulus, first versus last in the list of attributes, did not affect estimates of preference parameters, significant differences between questions with three versus two alternatives did occur, and the inclusion/exclusion of a status-quo alternative did not affect preference parameters.     

A unifying impossibility theorem

This paper identifies and illuminates a common impossibility principle underlying a number of impossibility theorems in social choice. We consider social choice correspondences assigning a choice set to each non-empty subset of social alternatives. Three simple axioms are imposed as follows: unanimity, independence of preferences over infeasible alternatives, and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our axioms is serially dictatorial. A number of known impossibility theorems—including Arrow’s Impossibility Theorem, the Muller–Satterthwaite Theorem, and the impossibility theorem under strategic candidacy—follow as corollaries.     

The Effect of Consumers’ Real-World Choice Sets on Inferences from Stated Preference Surveys

For stated preference (SP) studies, we develop a model that assesses the influence of choice set misspecification arising from the omission of perceived substitutes among real-world alternatives in the same class of goods. This problem is most likely to be present when individuals are allowed to select a “no purchase” option instead of being forced to choose from an explicit set of SP alternatives with hypothetical attribute levels. A convenient feature of our model is that researchers do not need to know exactly which omitted real substitute the individual most prefers, only the set of real substitutes that exists. In our empirical illustration, a comparison of rival models suggests researchers who overlook the presence of perceived real alternatives related to an SP experiment can end up with noticeably biased welfare estimates. Our more-general model suggests that it may be prudent for future SP researchers to anticipate, then test and possibly correct for, distortions in utility parameter estimates that result from this problem.      

How Much is Too Much?

In a split sample design, we examine how the number of choice sets, design of the first choice set (context dependence), and the choice of attribute levels in the cost attribute affect the precision in the elicited preferences in otherwise completely identical choice experiment surveys. These issues are investigated for Swedish households’ marginal willingness to pay to reduce power outages. Our results indicate that neither the number of choice sets nor the design of the first choice set has a significant impact on estimated marginal willingness to pay, while the effect was significant for the additive scaling of the cost vector. At the end of the article we discuss the implications of our results on future developments and applications of choice experiments.      

Response Strategies and Learning in Discrete Choice Experiments

This study explores ordering effects and response strategies in repeated binary discrete choice experiments. Mechanism design theory and empirical evidence suggest that repeated choice tasks per respondent induce strategic behaviour. We find evidence that strategic opportunities provided by the order in which choice sets are presented to respondents affect choice decisions (strategic response). The results suggest, however, that respondents may solely respond to high cost rather than low cost inconsistencies. That is, respondents are more cost sensitive, and thus have a lower willingness to pay (WTP), if the same or a similar level of provision was offered in a previous choice set at a lower cost than if it was not. Yet, the cost sensitivity, and thus WTP, remains unaffected if the same or a similar level of provision was offered in a previous choice set at a higher cost. Our findings further indicate that cost sensitivity increases (and thus WTP decreases), when respondents progress through the choice task, with this increase (decrease) lessening as more choice questions are answered. Possible explanations are value learning and strategic learning.     

Nash Equilibrium and Welfare Optimality

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A , where the subset is interpreted as the set of "welfare optima". A game form (or "mechanism") implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game form (implying, in particular, that a Nash equilibrium exists) and, (ii) all Nash equilibria are welfare optimal. The main result of this paper establishes that any SCR that satisfies two properties—monotonicity and no veto power—can be implemented by a game form if there are three or more individuals. The proof is constructive.     

Should Reference Alternatives in Pivot Design SC Surveys be Treated Differently?

Analysts are increasingly making use of pivot style Stated Choice (SC) data in the estimation of choice models. These datasets often contain a reference alternative whose attributes remain invariant across replications for the same respondent. This paper presents evidence to suggest that respondents react differently to the attributes of these reference alternatives and those of purely hypothetical alternatives. While some such evidence has been reported in the existing literature, this paper goes further and details a number of different departures from a common treatment of the two types of alternatives, relating both to the observed part of utility and the error term.     

Hurdle and Latent Class Approaches to Serial Non-Participation in Choice Models

In repeated choice modelling studies, it is often the case that individuals always select the status quo option. Although this pattern may reflect considered choices, they may also be the result of alternative decisions about whether to participate in the choice process at all. Alternative methods of dealing with this behaviour, each with associated implications for estimates of economic values, are presented. In particular we consider the alternative strategies of excluding such individuals from the data, using hurdle models to explicitly model this group, and propose the use of latent class models to endogenously allow for different preference structures. An advantage of the latent class approach is that the form of the non-participation need not be defined in advance. These approaches are considered using UK choice experiment data on food choices where the attributes include genetic modification of food. The latent class approach reveals the presence of two forms of non-participation in the data. This paper draws work commissioned by UK Department of Environment Food and Rural Affairs (DEFRA). The views presented in this paper are those of the authors alone and should not be regarded as those of DEFRA or of individuals within DEFRA.     

Incorporating Discontinuous Preferences into the Analysis of Discrete Choice Experiments

Data from a discrete choice experiment on improvements of rural landscape attributes are used to investigate the implications of discontinuous preferences on willingness to pay estimates. Using a multinomial error component logit model, we explore differences in scale and unexplained variance between respondents with discontinuous and continuous preferences and condition taste intensities on whether or not each attribute was considered by the respondent during the evaluation of alternatives. Results suggest that significant improvements in model performance can be achieved when discontinuous preferences are accommodated in the econometric specification, and that the magnitude and robustness of the willingness to pay estimates are sensitive to discontinuous preferences.     

TV viewing: application of a formal choice model

Choices of television programs is viewed as a process of deciding among a set of alternative goods with zero prices. A choice model can thus be based purely on individuals' preferences for various characteristics of a set of shows available, incorporating the option of not watching if all shows are too dissimilar to these desires. The shows are first grouped according to salient characteristics and a preferred value for each characteristic is estimated for each potential viewer. A perceived position of each show is similarly estimated and watching is shown to decline as similarity between preferred show and available alternatives declines. The choice model predicts show choice better than simpler models based on aggregate audience measures or on network loyalty, but the explanatory power is weak; some suggestions for improvement are made.     

Valuations of aircraft noise: experiments in stated preference

The aim of this paper is to report new evidence relating to residents’ valuations of aircraft noise in three countries with an emphasis on a comparison of the valuations obtained using two contrasting approaches. One might be regarded as a standard stated choice approach offering pairwise comparisons of two alternatives characterised by a limited number of attributes. The other choice format adopted is innovative in drawing inspiration from the priority evaluator approach to embed aircraft movements alongside a wide range of other local factors that impact on residents’ quality of life. The paper addresses the differences in the results of the two approaches and explores the possible explanations for these variations. Although not conclusive, there is a suspicion that strategic bias may have influenced the results and we urge further research regarding incentives to such bias.     

Numeraire choice in agricultural supply analysis

Should the choice of numeraire price for modelling profit functions be arbitrary, or is more careful study needed? Here, the choice of numeraire is examined using tests for models specification and out-of-sample predictive accuracy based on the crop and livestock data obtained from Iowa. The results of this study indicate that, for this data set and functional form, it does indeed make a difference which numeraire you choose. This is in contrast to previous studies which, in general, indicated that the choice of numeraire equation is arbitrary or, more commonly, offered no justification for the netput chosen.     

Manipulation and the Pareto rule

This paper examines rules that map preference profiles into choice sets. There are no agendas other than the entire set of alternatives. A rule is said to be “manipulable” if there is a person i, and a preference profile, such that i prefers the choice set obtained when he is dishonest to the one obtained when he is honest. It is “nonmanipulable” if this can never happen. The paper indicates how preferences over choice sets might be sensibly derived from preferences over alternatives, and discusses seven different notions of manipulability associated with seven different assumptions about preferences over sets of alternatives. The paper has two sections of results. In the first I show that the Pareto rule, that is, the rule that maps preference profiles into corresponding sets of Pareto optima, is nonmanipulable in four of the seven senses of manipulability, and manipulable in three of them. In the second section, I examine this conjecture: If an arbitrary rule is nonmanipulable and nonimposed, and if indifference is disallowed, then every choice set must be contained in the set of Pareto optima. The conjecture is true under the strongest definition of nonmanipulability.     

Extending the Nash solution to choice problems with reference points

In 1985 Aumann axiomatized the Shapley NTU value by non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives. We show that, when replacing unanimity by “unanimity for the grand coalition” and translation covariance, these axioms characterize the Nash solution on the class of n-person choice problems with reference points. A classical bargaining problem consists of a convex feasible set that contains the disagreement point here called reference point. The feasible set of a choice problem does not necessarily contain the reference point and may not be convex. However, we assume that it satisfies some standard properties. Our result is robust so that the characterization is still valid for many subclasses of choice problems, among those is the class of classical bargaining problems. Moreover, we show that each of the employed axioms – including independence of irrelevant alternatives – may be logically independent of the remaining axioms.     

Using an integrated choice and latent variable model to understand the impact of “professional” respondents in a stated preference survey

Internet panels are increasingly used for stated preference research. Because members of such panels receive compensation for each completed survey, one concern is that over time this creates professional respondents who answer surveys solely for the monetary compensation. We identify professional respondents using data on panel tenure, survey response frequency, completion rate and total number of completed surveys. We find evidence of two types of professional respondents: “hyperactives” who answer surveys frequently and “experienced” who have long panel tenure and a large number of completed surveys. Using an integrated choice and latent variable model on stated preference survey data, we find that “hyperactive” respondents are less likely to choose the 'status quo’ and have a more stochastic choice process as seen from the econometrician's point of view, whereas “experienced” respondents have a relatively more deterministic choice process. Our results show that “hyperactive” respondents significantly impact estimated values.     

Modelling preference heterogeneity for theatre tickets: a discrete choice modelling approach on Royal Danish Theatre booking data

This article analyses the behavioural choice for theatre tickets using a rich data set for 2010–2013 from the sale system of the Royal Danish National Theatre. A consumer who decides to attend a theatre production faces multiple sources of price variation that involves a choice by the consumer among different ticket alternatives. Three modelling approaches are proposed in order to model ticket purchases: conditional logit with socio-demographic characteristics, nested logit and latent class. These models allow us explicitly to take into account consumers’ preference heterogeneity with respect to the attributes associated with each ticket alternative (quality of the seat and day of the performance). In addition, the willingness to pay of choice attributes is estimated. Final results suggest that customers’ characteristics in terms of age and frequency of theatre attendance characterize different patterns of behaviour in the choice of theatre ticket.     

Multivariate Mixed Models for Open-Ended Contingent Valuation Data: Willingness To Pay For Conservation of Monk Seals

Although dichotomous choice (DC) contingent valuation (CV) has been recommended by the US NOAA 'blue-ribbon' panel for large-scale contingent valuation studies, useful information can still be obtained from smaller, open-ended (OE) studies, often undertaken as a precursor to a DC survey. The CV study considered here was carried out in Greece and looked at willingness-to-pay (WTP) for protecting the Mediterranean monk seal (Monachus-monachus) in the Aegean area. This is the most endangered seal in the world, and the application of the CV methodology was the first such application in Greece. The OE data consist of two responses: first, a binary response detailing whether or not respondents were in principle prepared to pay for the protection of this seal; secondly, those respondents who answered 'yes' to the first question were then asked to state their maximum WTP for such protection. A multivariate binomial – log-normal mixture model is used to develop a bid function including explanatory variables such as income, sex, age and education. Such a modelling approach provides an alternative to more commonplace tobit estimation. However, the model is extended to include further information which was collected on:(a) an increased WTP amount given in response to information that the initial WTP amount may not be enough to prevent the extinction of the seal;(b) respondents were asked to divide their final WTP amount between use, option and existence values, the latter requiring a multivariate model with four binary and four continuous responses per individual in the same model.The discussion focuses on the methodological issues raised with some comment on the substantive interpretation of results.     

The Possibility of Issue-Specific Decisions on Multiple Social Choice Issues

This paper considers an aggregation rule when each alternative consists of elements of multiple issues. I assume that each issue-specific aggregation rule can be applied to each issue and explore whether various different issue-specific aggregation rules are compatible. When the set of alternatives has some structure (which we call a set connected by loops), there exists a powerful individual whose preference always coincides with the social ordering in every issue. As a corollary, Arrow's General Possibility Theorem is obtained.