Signature
WTP_mean = sum_(i=1)^n [w_i] / n; B = N_pop * sum_(i=1)^n [w_i] / n
| Inputs | Definition | Unit |
|---|---|---|
w_i | WTP of respondent i, the amount stated or marked, zero for genuine zero responses | currency per person |
n | Number of respondents included, after any exclusion of protest responses | count of people |
N_pop | Number of people in the population whose WTP is aggregated | count of people |
WTP_mean | Average stated WTP of the respondents included in the analysis | currency per person |
|---|---|---|
B | Sum of WTP over the population, estimated as mean WTP multiplied by population size | currency in the stated price year |
Function
Willingness-to-pay estimation function
Maps stated or modelled preferences for a change in health or health care to a sum of money: the marginal value of an attribute from the coefficients of a discrete choice model, or the mean of individual valuations from a contingent valuation survey, scaled to the affected population. Aggregate WTP is the monetary benefit that cost-benefit analysis sets against the present value of costs.
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Implementations
Excel
Mean WTP and aggregate benefit
With stated values of the included respondents in StatedValues and the population in Population, the first formula returns mean WTP and the second the aggregate benefit.
=AVERAGE(StatedValues); =AVERAGE(StatedValues)*Population
Assumptions
Representative simple random sample
Scaling mean WTP by population size is valid when the sample is a simple random sample of the population with complete responses. Otherwise responses are weighted to the population before aggregation.
Protest responses classified before averaging
Follow-up questions separate protest zeros, which reject the scenario or payment vehicle, from genuine zeros. Excluding protesters assumes their values resemble those of other respondents; counting them as zeros understates mean WTP. Both results are commonly reported.
One valuation per person and consistent units
Each w_i values the same change, paid through the same vehicle and period, such as a one-off payment through local taxation, and N_pop counts the same units as the sample, such as people or households.
Worked examples
Payment card survey with protest zeros counted
Ten respondents mark 0, 0, 0, 10, 20, 20, 50, 100, 100 and 200 pounds; two of the zeros are protests. Counting all ten gives mean WTP of 50 pounds and, for a population of 100,000, an aggregate benefit of 5,000,000 pounds, below the programme's present value cost of 5,500,000 pounds. The figures are illustrative, as in the article.
w_i = [0,0,0,10,20,20,50,100,100,200]; n = 10; N_pop = 100000; WTP_mean = 50; B = 5000000
Payment card survey with protest zeros excluded
Excluding the two protest zeros leaves eight respondents, a mean of 62.5 pounds and an aggregate benefit of 6,250,000 pounds, above the cost. The sign of net benefit turns on the treatment of two respondents.
w_i = [0,10,20,20,50,100,100,200]; n = 8; N_pop = 100000; WTP_mean = 62.5; B = 6250000
Common errors
Aggregating median WTP
In the example the medians are 20 and 35 pounds, giving 2,000,000 or 3,500,000 pounds. The median indicates what a majority would support, but only the mean multiplied by the population estimates total benefit for cost-benefit analysis.
Choosing the protest treatment that favours the programme
Reporting only the exclusion of protesters, the more favourable result in the example, hides an assumption the follow-up answers cannot confirm. The treatment of protest responses is reported as a sensitivity analysis.
Sources
Mean and median WTP and aggregation to the population
Pearce D, Özdemiroglu E, et al. Economic Valuation with Stated Preference Techniques: Summary Guide. London: Department for Transport, Local Government and the Regions; 2002. Paragraphs 12.23 to 12.25 (mean WTP is relevant for cost-benefit analysis, median WTP for public choice, both reported) and 15.03 to 15.08 (aggregate WTP as mean or median WTP multiplied by the number of people in the population for a simple random sample; weighted sums otherwise), and table 9.7 on valid and protest responses.
Textbook on cost-benefit analysis in health care
Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015. Chapter on cost-benefit analysis: willingness to pay as the monetary valuation of benefits and its elicitation by contingent valuation.
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