Signature
MWTP_k = -beta_k / beta_c
| Inputs | Definition | Unit |
|---|---|---|
beta_k | Estimated coefficient on attribute k, or the difference between the coefficients of the two levels compared | utility per unit of attribute k |
beta_c | Estimated coefficient on the cost attribute, negative when a higher cost lowers the utility of an alternative | utility per unit of currency as coded |
MWTP_k | Money a respondent would give up for a one-unit improvement in attribute k, or for a move between two of its levels | currency in which the cost attribute is coded |
|---|
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.
Try this function
Implementations
Excel
Marginal WTP from model coefficients
With the attribute coefficient in AttributeCoef and the cost coefficient in CostCoef, Excel returns marginal WTP, or #N/A when the cost coefficient is not negative.
=IF(CostCoef<0,-AttributeCoef/CostCoef,NA())
Assumptions
Utility linear in cost
The cost attribute enters the utility function linearly, so the marginal utility of money is constant across the cost range. Estimates outside the range of costs shown to respondents are extrapolations.
Coefficients on the same scale and model
beta_k and beta_c come from the same estimated model. Scale differences between respondents cancel in the ratio, so WTP is comparable across groups when the coefficients are not.
Worked examples
Individual rather than group consultation for type 2 diabetes
In a discrete choice experiment on lifestyle programmes, individual consultation had a coefficient of 0.50 and groups of 10 patients minus 0.46, a difference of 0.96, and the cost coefficient was minus 0.75 per 100 euros, or minus 0.0075 per euro. Marginal WTP for individual consultation is 128 euros a year, as reported by Veldwijk and colleagues.
beta_k = 0.96; beta_c = -0.0075; MWTP_k = 128
Ten kilograms of anticipated weight loss
The same study estimated a coefficient of 0.72 for an expected outcome of 10 kg weight loss. From the rounded coefficients, marginal WTP is 96 euros a year; the authors report 97 euros from unrounded estimates.
beta_k = 0.72; beta_c = -0.0075; MWTP_k = 96
Common errors
Dropping the minus sign
Dividing 0.96 by minus 0.0075 without the leading minus gives minus 128 euros, which reads as a payment needed to accept the preferred level. The negative cost coefficient is divided into the negative of the attribute coefficient.
Ignoring the unit of the cost attribute
When cost is coded in hundreds of euros, minus 0.96 divided by minus 0.75 gives 1.28, meaning 128 euros, not 1.28 euros. The coding of the cost attribute sets the unit of the result.
Sources
DCE willingness to pay as a ratio to the cost coefficient
Veldwijk J, Lambooij MS, van Gils PF, Struijs JN, Smit HA, de Wit GA. Type 2 diabetes patients' preferences and willingness to pay for lifestyle programs: a discrete choice experiment. BMC Public Health. 2013;13:1099. Methods (negative of the out-of-pocket cost coefficient used as the marginal utility of money; ratio of an attribute estimate to it gives WTP), table 4 panel mixed logit estimates (individual consultation 0.50, groups of 10 minus 0.46, expected outcome 0.72, out-of-pocket costs per 100 euros minus 0.75) and reported WTP of 128 euros and 97 euros a year.
Textbook on discrete choice experiments in health
Ryan M, Gerard K, Amaya-Amaya M, editors. Using Discrete Choice Experiments to Value Health and Health Care. Dordrecht: Springer; 2008. Estimation of marginal rates of substitution and willingness to pay from the coefficients of a random utility model with a cost attribute.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0