Abstract
The gap between willingness-to-pay (WTP) and willingness-to-accept (WTA) benefit values typifies situations in which reference points—and direction of movement from reference points—are consequential. Why WTA-WTP discrepancies arise is not well understood. We generalize models of reference dependence to identify separate reference dependence effects for increases and decreases in environmental health risk probabilities, for increases and decreases in costs, and reference dependence effects embodying the interaction of two changes. We estimate separate reference dependence effects for the four possible cost and health risk change combinations using data from our choice-based experiment for a nationally representative sample of 4,745 households. The WTA-WTP gap is due largely to the reference dependence effects related to costs. Standard models of reference dependence are not consistent with the results, as there is an interactive effect. Estimated income effects are under a penny and thus cannot account for higher values of WTA relative to WTP.
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Notes
The influence of reference dependence has been extended in subsequent versions of prospect theory such as that by Schmidt et al. (2008). A recent spate of theoretical models have articulated well-developed theories of reference dependence, as exemplified in Sugden (2003), Munro and Sugden (2003), Kőszegi and Rabin (2006), and Loomes et al. (2009).
Kőszegi and Rabin (2006) develop a more general formulation but provide a shopping example similar to the treatment of costs in this model. Below we note how the approach can be generalized to include the functional dependence of μ and λ.
The factor μ- for cost decreases is also consistent with the possibility of a house money effect, as in Thaler and Johnson (1990).
Because costs and risks are both negatively valued, the arrangement of the quadrants differs from that in other treatments, such as Knetsch and Tang (2006) for which the tradeoff among losses and tradeoffs among gains quadrants are reversed from the order in Fig. 1. The WTP and WTA quadrants are standard.
Our use of the Knowledge Networks panel for EPA-funded water benefit studies has been specifically approved by the Office of Information and Regulatory Affairs, U.S. Office of Management and Budget. Viscusi et al. (2011) provide a detailed analysis of the properties of the survey for the WTP case.
This overall risk estimate is between the estimate of the GI illness incidence rates in the literature, as it is a bit lower than the estimate in Messner et al. (2006) and higher than the estimate in Colford et al. (2002). The other risk estimates presented to subjects using the risk ladder were the annual risk of being bitten by a dog, the risk of being involved in a traffic accident, and the chance of catching the flu. Economic studies of water quality include Innes and Cory (2001) and Hensher et al. (2005).
In particular, subjects chose the new treatment option 52% of the time in the WTP survey context. For discussion of the rationale for the equitable tradeoff approach, see Huber et al. (2008).
U.S. Department of Housing and Urban Development (2011) reports that Blacks and Hispanics have greater exposure to unsafe water.
Calculation of the mean estimates is based on the procedure in Train (2003). If a logged distribution has a mean M and a variance S, then the mean of the unlogged distribution is e(M+S/2). In this application M is the mean predicted logged value across respondents, and S is the variance of those predictions.
The mug experiments were first reported in Kahneman et al. (1990).
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This research was supported by EPA Grant #RD-83326401 to Vanderbilt University.
Appendices
Appendix A. Description of the sample
The survey was administered by Knowledge Networks (KN) to members of the KN panel over the 2008–2009 period. The KN panel is a probability sample of the U.S. population. People who do not have internet access are provided with computers or internet service to generate a representative sample. The total survey length of this Web-based survey was under 25 min. The survey response rate was 69%.
Table 4 presents the demographic characteristics of the sample of 4,745 consistent respondents. The second column of statistics presents the U.S. population counterparts. As the data indicate, the sample mix tracks the U.S. population averages quite closely in terms of gender, age, race, education, marital status, and household income.
Table 5 presents the sample characteristics of the variables used in the empirical analysis.
1.1 Sample characteristics
Appendix B. Sample survey text
B.1 Sample survey text for the first question set (cost up, risk down) willingness to pay
Municipal Water Users:
Imagine that your water utility is considering a new treatment for the water that comes to your home faucet. This treatment would increase the yearly cost of your water bill and also reduce the risk of GI illness.
Well Users:
Imagine that you could purchase a new treatment for the water that comes to your home faucet. This treatment would increase the yearly cost for your tap water and also reduce the risk of GI illness.
All Respondents:
The image above shows that with the new treatment, 20 fewer people would get GI illness every year. The green squares are the people who would not become ill with the new treatment.
Remember the national average for GI illness is about 50 of every 1,000 people each year.
Which alternative would you prefer?
New Treatment | No New Treatment | ||
Yearly Risk of GI Illness | 30 of every 1,000 people | 50 of every 1,000 people | |
Additional Yearly Cost of (Water Bill or Tap Water) | + $ 100 Additional Cost | $0 Additional Cost | |
Your Choice | New Treatment | No New Treatment | No Preference |
B.2 Sample survey text for the second question set (cost down, risk down) tradeoff among gains
Municipal Water Users:
Municipal water treatment facilities are always interested in finding cheaper, more effective methods for removing contaminants from drinking water.
In the next series of questions, we will ask you to imagine that your water utility is considering two new treatments for the water that comes to your home faucet.
Imagine that your water utility has developed new technologies for treating the water that comes to your home faucet.
The first treatment option would reduce GI illness risk at the same cost you are paying now.
The second treatment option would reduce the cost of your water bill with no change in the risk of GI illness.
Even if the proposed reduction is greater than the total cost of your water bill, try to imagine that you would receive the reduced cost anyway, either through lower local taxes or lower costs for other goods.
Remember the national average for GI illness is about 50 of every 1,000 people each year.
The image above shows that with the first treatment, you would have a 20 out of 1,000 lower chance of getting GI illness each year. The green squares show the reduction in your risk of becoming ill with the first treatment.
Which treatment would you prefer?
Treatment 1 | Treatment 2 | ||
Yearly Risk of GI Illness | 30 of every 1,000 people | 50 of every 1,000 people | |
Reduction in Yearly Cost of Wells or Water Bill | $ 0 Reduced Cost | −$ 100 Reduced Cost | |
Your Choice | Treatment 1 | Treatment 2 | No Preference |
B.3 Sample survey text for the second question set (cost down, risk up) willingness to accept
Well Users:
Well users were not asked this set of questions.
Municipal Water Users:
Water utilities try to use the most cost effective treatments available to ensure that the water delivered to your home faucet is safe for drinking.
For the next set of questions, we would like for you to imagine that your local water utility is considering a new treatment for the water that comes to your home faucet. This treatment would be less expensive than what is done currently but would be less effective.
This treatment would decrease the yearly cost of your water bill but would increase the risk of GI illness.
Imagine that your water utility is considering a new treatment for the water that comes to your home faucet. This treatment is less expensive but less effective. It would decrease the yearly cost of your water bill but would increase the risk of GI illness.
Even if the proposed reduction is greater than the total cost of your water bill, try to imagine that you would receive the reduced cost anyway, either through lower local taxes or lower costs for other goods.
Remember the national average for GI illness is about 50 of every 1,000 people each year.
The image above shows that with the new treatment, 20 more people would get GI illness every year. The green squares are the additional people who would become ill if the new treatment were used.
Which treatment would you prefer?
Current Treatment | New Treatment | ||
Yearly Risk of GI Illness | 50 of every 1,000 people | 70 of every 1,000 people | |
Change in Yearly Cost of Wells or Water Bill | $0 Reduced Cost | −$ 100 Reduced Cost | |
Your Choice | Current Treatment | New Treatment | No Preference |
B.4 Sample survey text for the third question set (cost up, risk up) tradeoff among losses
Municipal Water Users:
[#1]
Experts believe that the nation’s water utilities will face increased costs in the future to maintain water treatment infrastructure and to ensure that water supplies stay safe. Many facilities are quite old and in need of maintenance, upgrade, or repair.
Though the exact amount of these costs is not certain, if these costs are not paid, GI illness risks from drinking water are likely to increase.
[#2]
An increasing population means increasing demand for clean water. This requires water utilities to find additional sources for drinking water. New sources are more expensive to reach or require more treatment than existing water sources.
If these costs are not paid, water might be delivered with insufficient treatment to completely disinfect it, increasing the risk of GI illness.
[#3]
Increasing levels of pollution from upstream homes and businesses requires water utilities to treat water longer or perform additional kinds of treatments to ensure that it is safe to use.
If these costs are not paid, water might be delivered with insufficient treatment to completely disinfect it, increasing the risk of GI illness.
Well Users:
[#4]
Increasing levels of pollution from upstream homes and businesses sometimes threatens drinking water supplies for well users.
All Respondents:
Such risks could require additional treatment to ensure that it is safe to use. If these costs are not paid, the water could have an increased risk of causing GI illness.
The next questions will ask what increased costs you would be willing to accept to prevent increases in risk of GI illness in drinking water.
Municipal Water Users:
Suppose that your water utility is proposing a rate increase for the water that comes into your home.
If the rate increase is accepted, your yearly water bill would increase by $100.
If the rate increase is rejected, the risk of GI illness would increase by 20 illnesses per 1,000 people each year.
Well Users:
Suppose that pollution in your area is threatening the safety of your well water. Additional treatment would be required to maintain your tap water’s current level of safety.
If the new treatment is accepted, the yearly cost of your tap water would increase by $100.
If the new treatment is rejected, your risk of GI illness would increase by 20 out of 1,000 each year.
All Respondents:
Municipal Water Users:
The image above shows that without the new treatment, 20 out of 1,000 more people would get GI illness every year. The green squares are the additional people who would become ill without the new treatment.
Well Users:
The image above shows that without the new treatment, there is a 20 out of 1,000 higher risk of GI illness every year. The green squares are the additional chances of becoming ill without the new treatment.
All Respondents:
Would you be in favor of accepting or rejecting this treatment?
With New (Rate Increase or Treatment) | Without New (Rate Increase or Treatment) | ||
Yearly Risk of GI Illness | 50 of every 1,000 people | 70 of every 1,000 people | |
Additional Yearly Cost of (Water Bill or Tap Water) | + $ 100 Additional Cost | $0 Additional Cost | |
Your Choice | Accept. I am in favor of this (Rate Increase or Treatment) | Reject. I am opposed to this (Rate Increase or Treatment) | I have no preference for whether this (Rate Increase or Treatment) happens or not |
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Viscusi, W.K., Huber, J. Reference-dependent valuations of risk: Why willingness-to-accept exceeds willingness-to-pay. J Risk Uncertain 44, 19–44 (2012). https://doi.org/10.1007/s11166-011-9132-2
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DOI: https://doi.org/10.1007/s11166-011-9132-2