Concept Architecture
Concept
Theoretically, Willingness to Accept (WTA) is the minimum monetary compensation an individual requires to accept the loss of a good, service, health state or reduction in welfare. It is grounded in welfare economics and consumer theory and is based on compensating variation, whereby compensation is sufficient to maintain an individual's initial level of utility following a loss. In health economics, WTA is used to value health risks, adverse health outcomes and reductions in health-related quality of life.
Mathematically, willingness to accept is represented as the monetary amount that equates utility before and after a change in welfare. It is estimated by solving for the level of compensation that leaves the individual indifferent between retaining the original state and accepting the loss with financial compensation.
In practice, willingness to accept is estimated using stated preference methods, including contingent valuation and discrete choice experiments, or inferred from revealed preference data where appropriate. It is applied in cost-benefit analysis, environmental health economics, occupational health, valuation of health risks and estimation of compensation for health losses.
Purpose
Used to estimate the monetary compensation required for reductions in health or welfare, value adverse health outcomes, support cost-benefit analysis, assess compensation policies and quantify preferences for avoiding health losses.
Mathematical Formulae
Primary Formula
U(Y,H) = U(Y + WTA, H?)
where:
- U = utility function
- Y = initial income
- H = initial health state
- H? = health state after the loss
- WTA = minimum compensation required to maintain the original level of utility
Supporting Formulae
There is no universally recognised canonical mathematical formula.
Related Mathematical Methods
- Compensating variation
- Utility maximisation
- Welfare economics
- Contingent valuation
- Discrete choice experiments
- Revealed preference analysis
- Econometric estimation
Example
Individuals are asked the minimum compensation they would require to accept an increase in the annual probability of a medication side effect.
A respondent states that they would require �2,500 to accept the increased risk while remaining indifferent between the two alternatives.
The estimated willingness to accept for that respondent is therefore:
WTA = �2,500
Population estimates are obtained by aggregating individual responses using appropriate econometric methods.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(B2:B501) | Calculate the mean willingness to accept across respondents |
| MEDIAN | =MEDIAN(B2:B501) | Estimate the median willingness to accept |
| PERCENTILE.INC | =PERCENTILE.INC(B2:B501,0.95) | Estimate the upper distribution of compensation values |
| LINEST | =LINEST(B2:B501,C2:F501,TRUE,TRUE) | Estimate determinants of willingness to accept using regression analysis |
VBA (Optional)
Automate the calculation of summary willingness-to-accept statistics and sensitivity analyses across multiple respondent datasets.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Freeman AM, Herriges JA, Kling CL. The Measurement of Environmental and Resource Values: Theory and Methods. Routledge.
- Hanemann WM. Willingness to Pay and Willingness to Accept: How Much Can They Differ? American Economic Review. 1991.
- OECD. Cost-Benefit Analysis and the Environment.
- ISPOR Good Practice Reports.
Related Concepts (2)
Library
Publications
1
Conjoint Analysis Applications in Health — A Checklist: A Report of the ISPOR Good Research Practices for Conjoint Analysis Task Force — Bridges, Hauber, Marshall, Lloyd, Prosser, Regier, Johnson & Mauskopf, Vol. 14, No. 4 ed., 2011 (Value in Health)
The ISPOR good-practice checklist for conjoint analysis and discrete-choice experiments in health — the stated-preference methods used to elicit patient and public preferences over treatment attributes for value assessment and priority-setting.
Journal ArticleView source →
Frequently Asked Questions (6)
What is willingness to accept?
The minimum compensation an individual would require to voluntarily give up a good or accept a worse outcome.
Source: Hanemann 1991
What does willingness to accept measure?
Willingness to accept is the smallest sum of money an individual would require to give up a good voluntarily, or to tolerate a worse outcome. It measures the value of a loss from the individual's own standpoint, framed as the compensation that would leave them no worse off than before. In valuation it is the counterpart to willingness to pay, applied where the relevant change is a loss of something held rather than the gain of something new.
Source: Hanemann 1991
Why does willingness to accept often exceed willingness to pay?
For the same good, the compensation demanded to give it up commonly exceeds the amount that would be paid to obtain it. Part of the gap reflects that willingness to pay is bounded by income while willingness to accept is not. A larger part is attributed to loss aversion, whereby a loss is felt more strongly than an equivalent gain, and to the good having few close substitutes, which widens the divergence. The difference can be substantial rather than negligible.
Source: Hanemann 1991
When is willingness to accept the appropriate measure?
Willingness to accept fits situations framed as a loss of an entitlement the individual already holds, such as giving up an existing service, accepting a new risk, or losing access to a resource. The choice between it and willingness to pay depends on the assumed direction of the change and on who holds the property right. Because the two can diverge widely, stating which measure is used, and why, matters for how a valuation should be read.
Source: Hanemann 1991
What are the difficulties in measuring willingness to accept?
Willingness to accept is harder to elicit reliably than willingness to pay. Because it is not constrained by income, stated amounts can be very large or open-ended, and respondents may reject the premise of being compensated for a loss they consider unfair. Hypothetical framing can inflate answers further. These difficulties lead many stated preference studies to elicit willingness to pay even where willingness to accept would be the more fitting measure, which can understate the value of losses.
Source: Hanemann 1991
How does willingness to accept relate to economic welfare measures?
Willingness to accept and willingness to pay correspond to different theoretical welfare measures, the compensating and equivalent variations, which value a change relative to different reference points. Which applies depends on whether the individual is assumed to have a right to the situation before or after the change. Standard theory predicts the two should be close for small changes and for goods with substitutes, so the large gaps often observed indicate that these conditions do not hold in practice.
Source: Hanemann 1991
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 5 Aug 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EE-CBA-055
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