Some issues in the application of closed-ended willingness to pay studies to valuing health goods: an application to antenatal care in Scotland

Limited resources coupled with unlimited demands means that decisions have to be made concerning the allocation of scarce health care resources. The economic instrument of willingness to pay (WTP) is one instrument that can be used to help this decision-making process. Recommendations from the environmental economics literature suggest that the closed end (CE) WTP approach should be used. This approach is just beginning to be used to value health goods. This paper addresses the sensitivity of the closed-ended WTP approach to three issues: the design of the bid vector; the upper and lower limits of integration; and the method of analysis. These are discussed with reference to a study looking at the value of alternative models of ante-natal care in Scotland. The results are discussed and conclusions made concerning the use of the CE WTP instrument for valuing health goods.     

The assumption of equal marginal utility of income: how much does it matter?

In most applied cost–benefit analyses, individual willingness to pay (WTP) is aggregated without using explicit welfare weights. This can be justified by postulating a utilitarian social welfare function along with the assumption of equal marginal utility of income for all individuals. However, since marginal utility is a cardinal concept, there is no generally accepted way to verify the plausibility of this latter assumption, nor its empirical importance. In this paper, we use data from seven contingent valuation studies to illustrate that if one instead assumes equal marginal utility of the public good for all individuals, aggregate monetary benefit estimates change dramatically.     

Willingness to pay for publicly-financed health care: how should we use the numbers?

This paper addresses the question of how willingness to pay (WTP) values in health care evaluation can be used by policy makers. The way in which WTP values are used depends on from whom values are elicited and whether the good concerned is privately-financed or publicly-financed through taxation. Thus, four possible uses of WTP values are identified. The focus is on the two uses which arise in the publiclyfinanced situation. ‘Conventional’ use of WTP values, where the decision as to whether or not to provide a service depends upon whether or not WTP values are greater than total cost, applies only in the privately-financed, and not publiclyfinanced situations. The situations with publicly-financed goods are more complex. The use of WTP values for publicly-financed goods is justified and illustrated.     

Willingness‐to‐pay for parallel private health insurance: evidence from a laboratory experiment

Abstract Debate over the effects of public versus private health care finance persists in both academic and policy circles. This paper presents the results of a revealed preference laboratory experiment that tests how characteristics of the public health system affect a subject's willingness‐to‐pay (WTP) for parallel private health insurance. Consistent with the theoretical predictions of Cuff et al. (2010), subjects’ average WTP is lower and the size of the private insurance sector smaller when the public system allocates health care based on need rather than randomly and when the probability of receiving health care from the public system is high.     

Marginal Valuation of Charismatic Species: Implications for Conservation

Most contingent valuation studies focus on total willingness to pay (WTP) as a measure of welfare change. For policy involving species preservation, however, it is important to distinguish between the benefits of preventing a species from going extinct and the benefits of preserving numbers above the minimum viable population (MVP) level. Once MVP is exceeded, marginal WTP becomes relevant. These propositions are illustrated for the case of one charismatic species whose management is much debated, minke whales in the Northeast Atlantic Ocean. It is shown that, for a given estimate of total preservation value, strict conservation and extinction can both be optimal. This finding highlights the importance of collecting marginal values in contingent valuation surveys.     

Home equity commitment and long-term care insurance demand

This paper shows how home equity may substitute for long-term care insurance (LTCI). The elderly commonly hold substantial wealth in the form of home equity that is rarely spent before death, except for after moves to long-term care facilities. Absent strong bequest motives implies that marginal utility fluctuates less across health states than one would predict based on a standard model without wealth tied up in housing. Numerical examples show that this “asset commitment” may substantially weaken LTCI demand.     

Temporal stability of preferences and willingness to pay for natural areas in choice experiments: A test–retest

The main objective of this paper is to test the temporal stability of stated preferences and willingness to pay (WTP) values from a Choice Experiment (CE) in a test–retest. The same group of participants was asked the same choice tasks in an internet-based CE, conducted twice with a time interval of one year without interviewer interference. We examine choice consistency at individual choice task level and transferability of the underlying indirect utility function and associated WTP values. The results show that choices are consistent in 57 percent of the choice occasions. Comparison of the choice models over time shows that the estimated preference and scale parameters are significantly different, suggesting that choice behaviour changed between the two surveys. Differences between marginal WTP estimates for individual choice attributes are statistically significant only at the 10 percent level. However, we show that this can result in significantly different WTP values for policy scenarios. The instability of estimated mean WTP values for different policy scenarios asks for caution when including WTP values in cost-benefit analysis.     

Willingness to Pay for Car Safety: Evidence from Sweden

This study estimates a marginal willingness to pay (WTP) function for a road-mortality risk reduction. Observed marginal WTP from the Swedish car market is used and found to be positively correlated with the baseline risk of the cars. No statistically significant relationships between examined owner attributes, e.g. wealth and background risk, and marginal WTP are found. When comparing the estimated monetary value of a non-marginal risk reduction derived from the integral of the marginal WTP-function with an estimate based on marginal WTP we find, in line with expectations, that the difference between the estimates is negligible for smaller risk reductions and small, 4–10%, also for relatively large risk reductions.      

Validity of discrete-choice experiments evidence for health risk reduction

There is growing interest in discrete-choice experiment (DCE) as a method to elicit consumers’ preferences in the health care sector. Increasingly this method is used to determine willingness to pay (WTP) for health-related goods. However, its external validity in the health care domain has not been investigated until now. This paper examines the external validity of DCE concerning the reduction of a health risk. Convergent validity is examined by comparing the value of a statistical life with other preference elicitation techniques, such as revealed preference. Criterion validity is shown by comparing WTP values derived from stated choices in the experiment with those derived from actual choices made by the same individuals. Both tests provide strong evidence in favour of external validity of the DCE method.     

The Aggregation of Climate Change Damages: a Welfare Theoretic Approach

The economic value of environmental goods is commonly determined using the concepts of willingness to pay (WTP) or willingness to accept (WTA). However, the WTP/WTA observed in different countries (or between individuals) will differ according to socio-economic characteristics, in particular income. This notion of differentiated values for otherwise identical goods (say, a given reduction in mortality risk) has been criticized as unethical, most recently in the context of the 'social cost' chapter of the IPCC Second Assessment Report. These critics argue that, being a function of income, WTP/WTA estimates reflect the unfairness in the current income distribution, and for equity reasons uniform per-unit values should therefore be applied across individuals and countries. This paper analyses the role of equity in the aggregation of climate change damage estimates, using basic tools of welfare economics. It shows one way of how WTP/WTA estimates can be corrected in aggregation if the underlying income distribution is considered unfair. It proposes that in the aggregation process individual estimates be weighted with an equity factor derived from the social welfare and utility functions. Equity weighting can significantly increase aggregate (global) damage figures, although some specifications of weighting functions also imply reduced estimates. The paper also shows that while the postulate of uniform per-unit values is compatible with a wide range of 'reasonable' utility and welfare specifications, there are also cases where the common-value notion is not compatible with defensible welfare concepts.     

Eliciting preferences for collectively financed health programmes: the ‘willingness to assign’ approach

Improving public involvement in health system decision making stands as a primary health policy goal. However, still limited guidance is available on how best to elicit preferences for health care programmes. This study examines a contingent choice technique to elicit preferences among health programmes, and named ‘willingness to assign’ (WTAS). WTAS reveals relative (monetary-based) values of a set of competing public programmes under a hypothetical healthcare budget assessment. Experimental evidence is reported from a deliberative empirical study valuing ten health programmes in the context of the Catalan Health Service. Evidence from this experimental study reveals that within the context of multiple programmes, preferences are internally more consistent and slightly less affected by ‘preference reversals’ as compared to values revealed from an adapted technique eliciting the willingness to pay (WTP) extra taxes. Another finding suggests that although programmes promoting health received the higher relative valuation, those promoting other health benefits were valued highly.     

Spatial discounting of ecosystem services

The impact of conservation efforts targeted at preserving ecosystem services largely depend on the welfare implications associated with spatial variations in the provision of ecosystem services. While there is ample empirical evidence of spatial discounting or decay of the valuation of ecosystem services, there are still few underpinnings based on welfare economic theory. We establish a theory of spatial discounting that closely follows the concept of time discounting pertaining to climate change, and show spatial discount rates in the consumption, ecosystem service, and willingness to pay (WTP) numeraires. We consider the role of key parameters such as pure rate of spatial preference, consumption change, ecosystem services change, population density, and elasticity of marginal utility. We find that the spatial discount rate of WTP for ecosystem services that frequently appears in the empirical literature is the difference between the ecosystem service discount rate and consumption discount rate, where the ecosystem service discount rate includes both physical distance decay and welfare effects. Finally, we use numerical simulations to illustrate how the three different spatial discount rates vary with the spatial distance from the source of ecosystem services and with consumption patterns, implying many more possible spatial variations of WTP.     

Public-good valuation and intra-family allocation

I derive values of marginal changes in a public good for two-person households, measured alternatively by household member i’s willingness to pay (WTP) for the good on behalf of the household, WTP _i (H), or by the sum of individual WTP values across family members, WTP(C). Households are assumed to allocate their resources in efficient Nash bargains over private and common household goods. WTP _i (H) is then defined by trade-offs between the public good and the household good, and WTP(C) by trade-offs of between the public good and private goods. WTP _i (H) is found to be higher (lower) than WTP(C) when member i has a relatively high (low) marginal valuation of the public good, but tends on average to equal WTP(C). As a consequence, individuals tend to represent households correctly on average when questioned about the household’s WTP for a public good, even when they are purely selfish and answer truthfully. Adding all members’ WTP answers on behalf of the household then leads to double counting. Pure and paternalistic altruism (the latter attached to consumption of the public good) move each member’s WTP on behalf of the household closer to the true sum of individual WTP, but only paternalistic altruism raises this sum.      

Marginal WTP and Distance Decay: The Role of ‘Protest’ and ‘True Zero’ Responses in the Economic Valuation of Recreational Water Quality

We evaluate the sensitivity of distance decay in individuals’ stated willingness to pay (WTP) for water quality improvements in eutrophied lakes. We extend the standard model of contingent valuation (CV) by allowing individuals to adopt a sequential evaluation process consisting of two decision stages. In the first stage respondents decide whether they are ‘protesters’, have a WTP   \(=\)   ‘true zero’ or a \(\hbox {WTP}>0\) . Conditioned on a strictly positive WTP, we use Lee’s selectivity-corrected model to determine the magnitude of their WTP in the second stage. Using CV survey data from Norway we find significant distance decay in the first stage classification of respondents as ‘protesters’, ‘true zero’ WTP, or positive WTP. In the second stage model for positive WTP responses, we find little or no significant relationships when correcting for selection. Results suggest that previous findings of significant distance decay in contingent valuation of lake and river water in Europe may be driven by the definition of ‘protest’ and ‘true zero’ respondents. We find that WTP for water quality may be more useful as a qualitative indicator of political support for user financed water quality measures, than as a cardinal measure of marginal utility of water quality improvements.     

External Tests of Scope and Embedding in Stated Preference Choice Experiments: An Application to Endangered Species Valuation

A criticism often levied against stated preference (SP) valuation results is that they sometimes do not display sensitivity to differences in the magnitude or scope of the good being valued. In this study, we test the sensitivity of preferences for several proposed expanded protection programs that would protect up to three US Endangered Species Act-listed species: the Puget Sound Chinook salmon, the smalltooth sawfish, and the Hawaiian monk seal. An external scope test is employed via a split-sample SP choice experiment survey to evaluate whether there is a significant difference in willingness to pay (WTP) for protecting more species and/or achieving greater improvements in the status of the species. The majority of 46 scope tests indicate sensitivity to scope, and the pattern of scope test failures is consistent with diminishing marginal utility with respect to the amount of protection to each species. Further tests suggest WTP may be proportional to the number of species valued.     

The choice of environmental policy instruments under correlated uncertainty

This paper analyzes how the presence of correlated uncertainty between the cost and benefit of environmental pollution control can affect the choice of policy instruments. It is shown that the superiority of the nonlinear-tax instrument in which the corrective tax coincides with the expected schedule of marginal benefit may break down in favor of a linear-tax or a quantity instrument when the policy environment shifts from the case of independently distributed to the case of correlated uncertainties. With various combinations of parameter values of the two probability distributions, we also construct three distinct ranges in each of which one instrument turns out to be superior to the other two.     

The Design of Pension Pay Out Options When the Health Status during Retirement Is Uncertain

This paper examines the optimal design of pension plans when the health status during retirement is uncertain. Assuming that the health status affects both life expectancy and the marginal utility of consumption, choice between a lump-sum payment and an annuity can be welfare-enhancing if the health status is not observable by pension plan providers. This result holds if the marginal utility of consumption and life expectancy are negatively correlated. On equity grounds, a lump-sum option can be justified even if the marginal utility of consumption is independent of life expectancy.     

Joint Estimation of Multiple CVM Scenarios under a Double Bounded Questioning Format

Contingent valuation surveys frequently ask the same respondent for willingness to pay (WTP) for either different programs or different levels of provision of a single program. When multiple scenarios are considered by the respondent, the errors in the estimates of WTP are likely to be correlated across scenarios. Failing to account for correlation may lead to erroneous inferences concerning differences in WTP. This paper presents a technique that can be used to jointly estimate WTP for multiple scenarios proposed within a survey when the double-bounded questioning format is used. Monte Carlo simulations are employed to show that estimates derived from the joint model provide lower parameter variances as well as tighter confidence intervals surrounding WTP. The model is used to estimate WTP values for data collected in telephone interviews of California residents concerning WTP for fire reduction programs in Oregon and California. Variance properties of these estimates are shown to be similar to those estimated using simulated data.     

Is the Income Elasticity of the Willingness to Pay for Pollution Control Constant?

How willingness to pay for environmental quality changes as incomes rise is a central question in several areas of environmental economics. This paper explores both theoretically and empirically whether or not the willingness to pay (WTP) for pollution control varies with income. Our model indicates that the income elasticity of the marginal WTP for pollution reduction is only constant under very restrictive conditions. Our empirical analysis tests the null hypothesis that the elasticity of the WTP for pollution control with respect to income is constant, employing a multi-country contingent valuation study of eutrophication reduction in the Baltic Sea. Our findings reject this hypothesis, and estimate an income elasticity of the WTP for eutrophication control of 0.1–0.2 for low-income respondents and 0.6–0.7 for high-income respondents. Thus, our empirical results suggest that the elasticity is not constant but is always less than one. This has implications for how benefits transfer exercises, and for theoretical explanations of the environmental Kuznets curve.     

Optimal pollution taxation in a Cournot duopoly

It is well known that the optimal pollution tax in a competitive industry is equal to the marginal damage inflicted by the pollution. It has also been shown that the optimal pollution tax on a monopoly is less than the marginal damage. In this paper, I derive the optimal pollution tax for a Cournot duopoly. If firms have different production costs, the optimal tax rate may exceed the marginal damage. This is so because the tax may be an effective instrument for allocating production from the less to the more efficient firm. It is also shown that, if one firm has a positive most preferred pollution tax, the sum of consumer and producer surpluses will be declining in the tax at this level.