Willingness To Pay Distribution Research Articles

An empirical investigation of the distribution of travellers’ willingness-to-pay: A comparison between a parametric and nonparametric approach

Understanding the distribution of the willingness-to-pay (WTP) to reduce travel time or other unpleasant travel attributes experienced by travellers is crucial to making well-informed choices about infrastructure investments and the pricing of services. Given multimodality, heavy tails, and the impact of averaging errors in the classical parametric distribution-based analysis of WTP, this study compares WTP distributions across six distinct datasets using a range of model specifications, including multinomial logit (MNL), mixed logit (MMNL) and nonparametric logit mixed logit (LML). The models are estimated directly in willingness-to-pay space, highlighting that WTP is not uniformly distributed with a high likelihood of having a multi-modal distribution across the population. The findings confirm the intuition on the presence of negative WTP for some undesirable travel attributes. This study raises awareness among transport researchers, modellers, and authorities about using the correct WTP distributions in practice. It adds some empirical evidence regarding the true underlying WTP distribution of various travel attributes to the transport literature.

An Estimation of Ecosystem Service Value of Rice Paddy Wetland in Korea Using Contingent Valuation Method

Agricultural land is an important ecosystem that is essential for human life, and rice paddies, in particular, provide many ecosystem services such as food production and the maintenance of biodiversity. Although the value of rice paddy wetlands is high, they are rapidly disappearing due to urbanization and development. This study aims to estimate the monetary value of the rice paddy wetland ecosystem and investigate the proportion of benefits for each rice paddy wetland function to provide policy implications for rice paddy wetland management. To this end, this study conducted a survey with 988 South Korean citizens regarding rice paddy wetlands and adopted the contingent valuation method (CVM) with various approaches (double-bounded dichotomous choice pooled model, double-bounded dichotomous choice panel model, pseudo referendum model, open-ended question model, etc.). Considering the characteristics of each approach, the present value of the total willingness to pay (WTP) per household was estimated to range from 327 to 347 USD. When extrapolated to the entire country, the total WTP of all households in South Korea is estimated from 6.7 to 7.1 billion USD. This study also finds that households have an average WTP distribution ratio by paddy wetlands function as follows: food supply 33.8%, biodiversity 27.2%, disaster and pollution control 24.2%, and cultural services 14.8%. These findings have policy implications by providing valuable insights for decision-making in determining the priority and allocation levels of financial resources in the future design of policies related to paddy wetlands.

Natural area visitors’ willingness to pay for amphibian conservation in a global biodiversity hotspot

Transfer of harmful pathogens from imported pet animals to natural populations of wildlife is a new challenge in protected area management. Understanding visitors’ preferences for, and value they place on, protecting biodiversity from such disturbances is important in developing effective management interventions. By conducting a visitor survey at two natural areas in the Southern Appalachian region of the United States, a global hotspot of amphibian biodiversity, this study examined natural area visitors’ willingness to pay (WTP) to conserve wild amphibian populations under two different assumptions for the distribution of WTP – normal and log-transformed. Results from the retained model assuming a normal distribution for WTP showed that visitors were willing to pay US$10.55 (95% CI US$9.61—US$11.50) per visit in donation to ensure the persistence of healthy amphibian populations. Determinants of individual WTP under both model specifications included the perceived threat to amphibians from pathogen transmission in natural areas they visit, their self-assessed familiarity with general knowledge about amphibians, the level of importance they placed on the benefits to humans from amphibian biodiversity, and annual household income. These findings are useful in understanding the economic value of amphibian diversity to natural area visitors, and in assessing the viability of a visitor-supported mechanism to fund projects mitigating anthropogenic threats to amphibian biodiversity.

Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution

We study revenue management for an online retailer that offers a single product to customers with a time-varying willingness-to-pay (WTP) distribution. When the WTP distribution changes at an unknown time point (i.e., the change point), the original price quoted to customers may not be optimal. The retailer’s objective is to minimize his revenue loss by determining when to quote a new price to incoming customers and what the new price is. We formulate the problem as an optimization model, which is challenging to solve due to the presence of the unknown change point. To overcome this challenge, we first characterize the probability distribution of the estimated change point using maximum likelihood estimation. We then develop two pricing algorithms to solve the model by leveraging the characterized distribution. Lastly, through numerical studies, we illustrate the effectiveness of the proposed algorithms in identifying change points and recommending optimal post-change selling prices. The numerical results suggest that the proposed pricing algorithms significantly reduce the frequency of false change detection in the early stages of a selling season. The proposed pricing algorithms also outperform the benchmark pricing algorithm in reducing the retailer’s revenue loss.

The temporal stability of WTP estimates for the emissions reduction using the contingent valuation survey in Queensland, Australia

The temporal stability of willingness to pay (WTP) estimates, from contingent valuation method (CVM) surveys, is required for reliable benefit transfer. While there have been numerous tests of the temporal stability of WTP estimates over a short time period, the evidence of the stability of WTP estimates over a long time period is limited. In this study, the temporal stability of WTP estimates for the emissions reduction over a ten-year period in Queensland, Australia is assessed. The first survey was conducted in 2009 at the end of the global financial and economic crises. The second survey was conducted in 2018 when the economic background changed significantly. The paper is focused on two main questions: (1) whether WTP is stable over a long time period under the changes in the background economic conditions and (2) if WTP is not stable, whether it is due to changes in socio-economic characteristics or underlying preferences. The results indicate that CVM estimates of WTP for emission reduction are stable over a ten-year period even after changes in underlying socio-economic conditions. However, care should be taken when transferring the estimates under the changes in the business cycle due to possible changes in WTP distribution.

Learning customer preferences and dynamic pricing for perishable products

This research proposes a revenue management framework for perishable products when customer preferences are unknown before the selling season begins. In this research, customer preferences are measured by the distribution of customer willingness to pay (WTP). When the WTP distribution is initially unknown, a long short-term memory (LSTM) neural network is adopted to quickly learn the distribution by using limited selling data in early periods of the selling season. The average LSTM estimation error is less than 5% in the fifth period of the selling horizon and approximately 1% in the 25th period when the WTP follows a Gaussian distribution with an unknown mean. The estimation of WTP distribution is then used by a dynamic pricing model to generate optimal price decisions. To reduce the calculation burden of the pricing model, we present the existence of a lower bound on the optimal price, provided that the coefficient of variation of WTP distribution is bounded by 80%. In our numerical study, the proposed pricing framework is benchmarked against the optimal pricing strategy under a known customer WTP distribution, and the revenue difference caused by the unknown WTP distributions is less than 2% in most cases. This small revenue difference represents the costs to learn the unknown customer preferences. For perishable products without inventory replenishment, such as airline tickets or hotel rooms, the small preference learning costs make the proposed framework especially valuable.

Indirect estimation of willingness to pay for energy technology adoption

Adopting energy-efficient and clean technologies is key to climate change mitigation and meeting long-term sustainability goals because they significantly reduce energy consumption and related carbon emissions. Understanding existing barriers and drivers for the adoption of these energy-efficient and clean technologies will be crucial to meeting ambitious national energy and emissions targets, and the customers’ willingness to pay (WTP) is a key factor in understanding the potential for scaling-up adoption. However, in practice, commonly-used WTP estimation methods such as survey or purchase experiments are not always practical or feasible due to budget, time, labor or data constraints. This study proposes a new constrained optimization-based indirect estimation of WTP for energy technology adoption using customers’ implicit life-cycle cost-benefit analysis and market data. The empirical probability distribution of WTP is estimated using the Monte Carlo methods. This new indirect estimation method provides a deeper understanding of the barriers and customers’ willingness to adopt high efficiency and clean energy technologies, and informs the development of supporting policies and programs needed to accelerate market adoption.

Continuous pricing algorithms for airline RM: revenue gains and competitive impacts

Traditionally, airlines have been limited to a set of fixed fare classes and, in turn, price points, to distribute their fare products. The advent of IATA’s new distribution capability (NDC) will soon enable airlines to quote any fare from a continuous range. In theory, such continuous pricing could increase revenues by extracting more of the consumer surplus, through its ability to offer more granular fares, closer to the customer’s willingness-to-pay (WTP). In this article, we describe several algorithms that lead to the quotation of a single fare from a continuous range. These algorithms either rely on traditional fare classes for the purpose of forecasting and optimization (class-based), or completely abandon the notion of fare classes, instead assuming different WTP distributions within each booking period prior to departure (classless). We describe how these algorithms build upon and differ from their traditional RM counterparts. Performance of these heuristics is then benchmarked against traditional class-based RM, and competitive impacts are analyzed when continuous pricing is adopted by one airline asymmetrically or both airlines symmetrically in a hypothetical 2-carrier network in the passenger origin–destination simulator (PODS). We find that continuous pricing is generally revenue-positive, and the revenue gains can be as high as 2.0% for the first-mover and reach up to 1.2% when both airlines adopt the new method. In addition, we show that these gains depend on the number of fare classes in the traditional fare structure used as a baseline, and that they are smaller under lower demand-to-capacity ratios.

Regional differences in farmers' preferences for a native bee conservation policy: The case of farming communities in Northern and Eastern Thailand.

Evidence points to past bee-mediated crop pollination deficits in Chanthaburi province, Eastern Thailand. Conversely, no such evidence has yet been reported for Chiang Mai province (Northern Thailand), suggesting that wild pollination is delivered there above the requirements of local orchards. Discrete choice experiments (DCE) were conducted to elicit the preferences of pollinator-dependent orchard farmers with regard to three pollinator conservation measures and their possible effects on of native bee populations in each region. We fitted random parameter logit (RPL) models on the resulting data to capture preference heterogeneity and to obtain willingness to pay (WTP) point estimates. To test our results’ robustness, we also inspected for scale heterogeneity by fitting generalized mixed logit (GMXL) models on the pooled and individual datasets. This yielded WTP space estimates (i.e., directly from WTP distributions) and made possible the comparison of farmers’ preferences for a native bee conservation policy in both regions. The results hint at significant WTP differences for some of the conservation policy attributes between both provinces. Furthermore, unobserved contributions to choice seem to have been more random in Chiang Mai. Our analyses also suggest that farmers who engage in bee-related activities are WTP more for a conservation policy that includes bee husbandry.

Estimating discount rates for environmental goods: Are People’s responses inadequate to frequency of payments?

Most stated preference studies estimate discount rates using a split-sample approach. Each sample faces a different payment frequency (for instance, 1, 5, 10) together with a randomly assigned bid vector; both the frequency of payments and the bid are fixed for a specific individual. This paper evaluates whether allowing respondents to choose their preferred payment frequency affects the estimated discount rate. We use data from a contingent valuation survey of a network of marine reserves and estimate discount rates using both an exogenous and endogenous approach. The former calculates the mean of the willingness to pay (WTP) for each sample and then finds the discount rate that makes the present value of each payment frequency equivalent. The latter estimates the WTP and the discount rate jointly. Results show that allowing people to choose the payment schedule significantly reduces the implicit discount rate. We observed the highest reductions in discount rates when we used all the information available from the valuation questions to bound the WTP distribution. Our analysis suggests that the exogenous approach would not be recommended for testing the adequacy of people’s responses to the frequency of payments.

Do consumers value food products containing upcycled ingredients? The effect of nutritional and environmental information

This study was the first to use a ranking experiment to estimate the effect of nutritional and environmental information on UK consumers’ willingness to pay (WTP) for biscuits containing an upcycled ingredient, namely, defatted sunflower cake flour. Informing consumers about the nutritional and/or environmental benefits of the upcycled ingredient resulted in a significant increase in their WTP for this new food. Moreover, we found that nutritional and/or environmental information similarly affected individual WTP distributions for the upcycled ingredient towards more positive values. Our findings have important implications for product development and marketing strategies of upcycled food businesses.

Predicting Transaction Outcomes Under Customized Pricing with Discretion: A Structural Estimation Approach

We consider a company selling heterogeneous products with prices customized for each customer and the final price is set by negotiations between sales agents and customers. This type of pricing modality is referred to as customized pricing with discretion and commonly used in insurance, consumer loans, mortgages, and many business-to-business markets. We assume that each sales agent has a minimum reserve price (RP) and each customer has a maximum willingness-to-pay (WTP) and, if the deal occurs, they agree on a price between these two values, which are not directly observable. Given the outcomes of a series of negotiations, our goal is to estimate the underlying joint distribution of WTP and RP and predict the outcomes of future transactions. We assume that the price that prevails as the outcome of the negotiation can be represented as a generalized Nash bargaining equilibrium. We develop a structural estimation method based on the expectation-maximization algorithm that allows for the WTP and RP distributions to depend on an arbitrary set of covariates. Using both simulated and a real-world data set, we show that our proposed method improves the predictive accuracy of the deals’ final prices by 6.8% and the customers' decision to accept the deal by around 2% compared to standard regression-based approaches. These results are robust to assumptions on the distribution of bargaining power between the two parties in the negotiation. We also show that the estimated distributions can be used to optimize controls on negotiated prices that can significantly increase revenues relative to both unconstrained negotiations and centrally-optimized fixed prices.

A Statistical Matching approach to reproduce the heterogeneity of willingness to pay in benefit transfer

Researchers and policymakers seek a better understanding of the social demand for agri-environmental public goods (PGs), that, being nonmarket goods, are usually valuated by means of stated preference methods by eliciting people's willingness to pay (WTP). In actual policy design, benefit transfer (BT) is often preferred to novel surveys which are expensive and time demanding. Common BT approaches are value and function transfer that can provide good estimates of the mean WTP but disregard the heterogeneity of the individuals' preferences. The WTP distribution is thus flattened, leading to a misrepresentation of the PG demand. The objective of this paper is to improve BT in its ability to reproduce the actual WTP distribution at the policy site by means of the non-parametric micro Statistical Matching. We use this novel approach to transfer individual WTP values for soil erosion and carbon sequestration elicited by contingent valuation on people living in Emilia-Romagna, Italy. Comparing the results with the ones of value and function transfers, our approach outperforms the others, reflecting the actual WTP distribution and lowering the benefit transfer errors. In this way, BT can better support policymakers in designing new agri-environmental policy instruments, more targeted towards specific demand segments and hence with higher cost-effectiveness.

Does angler willingness-to-pay for changes in harvest regulations vary by state? Results from a choice experiment in the Gulf of Mexico

Information on the economic value of changes in harvest regulations such as bag limits is necessary to understand the economic benefits and costs of recreational fishing policies. As fishery managers consider policies that vary across space, time, and angler groups we need information on the distribution of angler willingness-to-pay (WTP) for regulations across these dimensions. In this paper we ask whether angler WTP for changes in bag limits varies by state of license. We estimated an angler choice model using data from a stated preference choice experiment in the Gulf of Mexico. The parameters of the model were used to calculate the distribution of WTP for changes in bag limits for dolphinfish, snapper, red snapper, grouper, and king mackerel. Using the bag limit WTP distributions for each species we examined whether WTP varied by state in a statistically significant and economically meaningful way. We found that anglers with a license to fish in Florida were willing to pay relatively more for grouper bag limits than anglers with a license to fish in Louisiana. We also found that anglers with a license to fish in Alabama or Mississippi were willing to pay relatively more for red snapper bag limits than anglers with a license to fish in Florida. There were not significant differences in the WTP for the bag limits among anglers with a license to fish in Louisiana and anglers with a license to fish in Alabama or Mississippi.

Time equals money? Valuing ecosystem-based adaptation in a developing country context

AbstractTo guide investments in ecosystem-based adaptation (EbA) in developing countries, numerous stated preference valuation studies have been implemented to assess the value of ecosystem services. These studies increasingly use time payments as an alternative to money. There is limited knowledge, however, about how to convert time to money and how the type of payment affects willingness to pay (WTP). In this study, the results of choice experiments using time and money payments are compared in the context of EbA measures in Vietnam. Six, of which five individual-specific, conversion rates are applied. WTP estimates are found to be higher for time payments. Moreover, the type of payment vehicle as well as the conversion rate has substantial effect on mean WTP and WTP distributions. We discuss implications of these results for the conversion of time to money and the use of resulting WTP estimates in cost benefit analyses in developing countries.

Valuing the water supply: ecosystem-based potable water supply management for the Legedadie-Dire catchments, Central Ethiopia

BackgroundThere is a substantial interest in the values that consumers place on drinking water quality and supply. Financial resources are crucial to improving the urban potable water supply in developing countries that are characterized by low-cost recovery rates and a high and rapidly growing demand for more reliable services. This study examined households’ willingness to pay (WTP) for the improvement of water services by identifying their water choice decisions and the mode of water supply that they prefer the water supply authority to use among several alternative water supply options. Stated-preference data were collected from 322 randomly selected households in Addis Ababa, who were presented with three sets of choices (three alternative bundle choices, including the reference scenario). The data were analyzed using the mixed logit WTP space model. Three approaches to modeling the distribution of WTP (fixed, uncorrelated, and correlated) using mixed logit WTP space models were compared.ResultsThree-quarters of the households agreed to contribute money toward ecosystem-based water supply management (EBWSM) intervention programs on a monthly basis. The average contribution that the respondents were willing to pay was 150.5 Ethiopian Birr (ETB) as a one-off lump sum to kick off the EBWSM activities. Most of the respondents chose a bundle of water supply options that provides risk-free and high-quality water with no months of shortages than moderate water quality that is safe to drink and palatable with 1 month shortages annually. This implies that households would need to be supplied with risk-free, high-quality water without interruption at an appropriate flow pressure. The model with correlations fitted the data well with the highest simulated log-likelihoods at convergence and gave the best estimate of the households’ WTP for water improvement. Nearly 46% of the sampled households were willing to pay more than 33 ETB per month, and 49% of the households were willing to pay between 21 ETB and 33 ETB per month for the monthly water bill. Overall, approximately 95% of the sampled households were willing to pay more than 21 ETB.ConclusionCustomers are willing to pay to avoid most types of water supply restrictions. Moreover, WTP is sensitive to the scope of service improvement, income, affixed price, and elicitation method. In summary, mixed logit WTP-space models can help accurately predict household-level WTP, which can be used to select improvements in drinking water access and services in the Legedadie-Dire catchments.

How much will the Chinese public pay for air pollution mitigation? A nationwide empirical study based on a willingness-to-pay scenario and air purifier costs

Willingness to pay (WTP) for clean air is one of the most important indicators of the public's acceptance of air pollution mitigation policies. However, few studies have characterized the spatial distribution of WTP, explored its “hypothetical bias”, or analyzed its relationship with air pollutant concentrations. To address this gap in knowledge, a nationwide empirical study (N = 9744) was conducted from December 2016 to February 2017 in China. The contingent valuation method (CVM) was adopted to assess WTP based on a scenario, and air purifier costs (APCs) incurred by the public were used as an indicator of WTP in the real-life scenario.The results show that the mean value of APCs (243.81 CNY(year⋅person)−1) is lower than WTP (275.39 CNY(year⋅person)−1), which means that the Chinese public may not pay as much money for clean air in the actual scenario as in the WTP scenario. This result is important for predicting and evaluating the feasibility and effectiveness of air pollution economic policies. We also observed significant spatial differences in APCs: the public in more heavily polluted areas such as the eastern coastal region, northern coastal region, Middle Yellow River region and northeast region have higher APCs than the public in other regions, the proportion of people who purchased air purifiers and the distribution of APCs positively correlated with concentrations of particulate matter with aerodynamic diameters less than 2.5 (PM2.5), nitrogen dioxide (NO2), carbon monoxide (CO), and ozone (O3), while no significant spatial difference or correlation relationship was observed for WTP. This result indicates that pollutant concentration is not the main driving factor of WTP but they are driving factors for APCs, which may provide new evidence for the driving factors of WTP and APCs. Finally, the policy implications behind these results are discussed, providing references and scientific support for policy makers and subsequent research.

Potential demand for voluntary community-based health insurance improvement in rural Lao People's Democratic Republic: A randomized conjoint experiment.

IntroductionIn Lao People’s Democratic Republic (PDR), community-based health insurance (CBHI) is the only voluntary insurance scheme; it typically targets self-employed people, most of whom reside in rural areas and are dependent on agricultural activities for subsistence. However, until very recently, the enrollment rate has fallen short and failed to reach a large percentage of the target group. To promote the CBHI scheme and increase demand, some supporting components should be considered for inclusion together with the health infrastructure component.ObjectivesThis paper provides empirical evidence that the benefit package components of hypothetical CBHI schemes have causal effects on enrollment probabilities. Furthermore, we examine the distribution of willingness to pay (WTP) in response to policy changes based on a sample of 5,800 observations.MethodsA randomized conjoint experiment is conducted in rural villages in Savannakhet Province, Lao PDR, to elicit stated preference data. Each respondent ranks three options—two hypothetical alternatives and the CBHI status quo scheme. The levels of seven attributes—insurance coverage for medical consultations, hospitalizations, traffic accidents, pharmaceuticals and transportation; premiums; and prepaid discounts—are randomly and simultaneously assigned to the two alternatives.ResultsThe findings suggest that the average WTP is at least as large as 10.9% of the per capita income of those who live in rural areas, which is higher than the WTP for health insurance averaged across low- and middle-income countries (LMICs) in the literature. The component of round-trip transportation insurance coverage has a significant effect on WTP distribution, particularly increasing the share of the highest bin.ConclusionTherefore, the low CBHI scheme enrollment rate in Lao PDR does not necessarily imply low demand among the targeted population, as the finding from the WTP analysis illustrates potential demand for the CBHI scheme. Specifically, if transportation is addressed, enrollment is likely to significantly increase.

Generalized multinomial probit Model: Accommodating constrained random parameters

Skewed and constrained distributions for model parameters are better suited to provide realistic taste sensitivity and Willingness-To-Pay (WTP) distributions in many empirical applications. In this context of random taste heterogeneity, the standard multinomial probit (MNP) has seen limited applicability largely owing to the normal distributional assumption of model parameters that will invariably result in (a) counter-intuitive taste sensitivities for a significant proportion of the population, and (b) WTP distributions without finite moments. In this paper, a Generalized MNP (GMNP) model that allows constrained random parameters with multivariate truncated normal distribution was developed. The ability of the maximum simulated likelihood inference method to retrieve the model parameters was demonstrated on synthetic data using the GHK simulator with quasi-Monte Carlo sequences. The bias in the parameters of the MNP model that ignores the constraints on model parameters was also demonstrated. Also, the proposed model was used to analyze car parking preferences in Jerusalem while ensuring (a) negative taste sensitivities for cost and time attributes, and (b) finite moments of the WTP measures associated with walk and search times.

Domestic water supply, residential water use behaviour, and household willingness to pay: The case of Banda Aceh, Indonesia after ten years since the 2004 Indian Ocean Tsunami

In this study, we developed a preliminary assessment of current domestic water supply and use in Banda Aceh, Indonesia, a city that was hardest hit by the Indian Ocean Tsunami of 2004. The motivation was to develop understanding of the status and future direction for improvement of domestic water supply after 10 years of post-tsunami reconstruction. For this purpose, we collected primary and secondary information from both water utility and residential households. In particular, we conducted household survey to examine water use behaviour in relation to domestic water supply by local utility, public perception on water supply service, and household willingness to pay (WTP) for reliable water supply. Our study results show that domestic water supply in the city has been improving in service coverage but is subject to high percentages of non-revenue water, financial loss, and poor performance. Despite available tap water, residential households access multiple water sources differentially between drinking and non-drinking purposes. All survey respondents are willing to pay for reliable water supply service, with median WTP estimated at approximately 190% of current household monthly water bill. Most respondents have a concentrated WTP distribution whose mean depends mainly on household income, family size, and water use behaviour. The study findings fill in the knowledge gap in the literature while informing improvement of domestic water supply in Banda Aceh, Indonesia.