Preference Elicitation Methods and Equivalent Income: An Overview

4.1. Contingent valuation data

The contingent valuation method employs a direct survey question to collect the data required to compute equivalent incomes, i.e., the individual WTPs to attain the reference levels in the nonincome dimensions.⁵

Respondents are first presented with a description of a hypothetical situation. In the context of estimating equivalent incomes this consists of a description of a hypothetical life situation in which the nonincome dimensions are fixed at their reference values (see section 4.5 for an illustration).

They are then asked to state their maximum WTP (or minimum WTA) for a change to that hypothetical situation, using a specified elicitation mechanism. Several alternatives are common in the literature. Open-ended questions directly ask respondents to state their WTP for the change. The single-bounded referendum method presents respondents with a (randomly assigned) payment amount and asks whether they would be willing to pay that amount, with a dichotomous choice (yes/no) response. The double-bounded version follows up with a second question to estimate bounds around an individual’s WTP, improving statistical efficiency. In the bidding game, respondents are given multiple rounds of dichotomous choices, with the final question typically open-ended. Under the payment card method, respondents select the value closest to their WTP from a predefined list. Table 1 summarizes these methods and provides examples.

Finally, contingent valuation surveys usually include debriefing questions to verify respondents’ understanding of the hypothetical situation and assess the validity of the stated valuations.

4.2. Estimation of WTP

Nonparametric and parametric estimation techniques can be employed to analyze the elicited contingent valuation data. Open-ended questions and the bidding game (with a final open-ended question) provide individual WTP values directly, which can then be used to compute equivalent income (see section 4.5). Standard linear regression techniques may also be applied to assess the determinants of the elicited WTP values.⁶

Other mechanisms yield binary or interval-coded responses that can be treated as limited dependent variables in interval regression models, which are based on random utility theory (McFadden et al., 1973). Two approaches are commonly used to analyze binary choice data from single-bounded referendum designs. The first is the utility difference model of Hanemann (1984), which uses a random utility model to monetize the utility change. The second is the bid-function model, which directly specifies a functional form for respondents’ WTP.

Since random utility models are discussed in the next section, we illustrate here how the bid-function can be employed to estimate WTP. Let $r_i=1$ if the individual answers “yes”, and $r_i=0$ if the individual answers “no” to a randomly assigned bid amount $w_i$ in the referendum survey. The WTP function for a sample can be recovered by specifying the probability that an individual gives an affirmative response to the bid amount as:

where ${\text{WTP}}_i(x_i,{\epsilon }_i)$ is a function that depends on a set of observed characteristics $x_i$, such as nonmonetary dimensions of well-being (and possibly also personal characteristics of the respondent), and an error term ${\epsilon }_i$. By specifying this function as linear in parameters $\beta$, we obtain:

Assuming different distributions for the unobserved factors ${\epsilon }_i$ leads to various econometric models. For instance, assuming ${\epsilon }_i\sim N(0,{\sigma }^2)$, i.e., that ${\epsilon }_i$ follows a normal distribution, yields an expression close to the standard probit model:

where $\Phi$ denotes the standard normal cumulative distribution function. The parameters $\beta$ and $\sigma$ can be estimated using maximum likelihood. The estimation of preferences for the double-bounded referendum method extends this approach to the case of interval data (see Hanemann et al., 1991).

4.3. Advantages and disadvantages of the contingent valuation method

A key advantage of the contingent valuation method for estimating equivalent incomes is that it provides a direct measure of WTP at the individual level. This is particularly useful when studying how WTP values vary across different individuals. The contingent valuation method is also flexible enough to value a wide range of goods, including those that are considered as an indivisible whole and cannot readily be valued as a function of multiple attributes (Johnston et al., 2017).⁷ Some elicitation mechanisms, such as the bidding game or referendum method, mimic familiar, real-world valuation mechanisms, which reduces the cognitive burden on respondents and may enhance the validity of the estimates. Finally, the method is relatively easy to administer and understand. This applies particularly to elicitation mechanisms like open-ended questions and payment cards, which do not require complex experimental designs.⁸ The ease of understanding enhances respondent engagement, potentially increasing the credibility of the WTP estimates.

The popularity of different elicitation mechanisms has evolved over the years in response to the advantages and disadvantages of each approach, some of which are listed in Table 1. Early studies relied on an open-ended question, which is by far the most straightforward approach and has the advantage of yielding individual-level WTP estimates. However, this method has become less popular over time due to the difficulty of answering open-ended questions and hypothetical and strategic biases that might arise, leading to implausibly high WTP values or large numbers of protest votes. More recent studies have opted for the referendum method, which mitigates these issues to some extent. The method became particularly popular following the endorsement of the National Oceanic and Atmospheric Administration (NOAA) panel of experts, chaired by Kenneth Arrow and Robert Solow, which highlighted that the single-bounded method reduces strategic bias, by providing incentives for respondents to answer truthfully (Arrow et al., 1993). Carson and Groves (2007) caution that this is only the case if the referendum is single-bounded and perceived by the respondent as consequential.⁹ Yet, the core limitation of the single-bounded referendum approach is that it provides very limited information about an individual’s preferences. It may also be subject to anchoring (or starting point) bias, whereby individuals interpret the bid amount as providing information on what is reasonable or expected. The bidding game approach is one alternative that provides more information on preferences by narrowing down the bounds around an individual’s WTP and is cognitively easier than the standard open-ended question. Still, the method is subject to starting point bias as well as the phenomenon of “yes-saying” (i.e., false affirmative answers). Payment cards avoid the latter by providing individuals with a visual set of payment options to choose from. However, the intervals between the payment cards, their position, and the upper and lower limits may still lead to some degree of bias (Hausman, 2012).¹⁰

Some studies have used variations of contingent valuation designs to reduce such biases. Chanel et al. (2017), for instance, experiment with a circular payment card wheel. Respondents are first asked to think about their maximum WTP and then presented with a pie chart wheel that has different segments with payment amounts. Respondents then move the wheel until they find a section that matches their valuation. Chanel et al. (2017) argue that this format reduces starting point bias as each segment is equally likely to be seen first, and reduces middle-point bias because there is no predetermined start or end points on the wheel. Champonnois et al. (2018) find that this format reduces anchoring bias in a multiple elicitation format. Others have introduced formats that incorporate respondent uncertainty to avoid the problem of “yes-saying.” For instance, Dubourg and Loomes (1997) ask using a disc that they rotate back and forth between different values to elicit the largest amounts the respondent would definitely pay and smallest amounts they would definitely not pay. Welsh and Poe (1998) propose multiple response options to payment card questions ranging from: “Definitely no,” “Probably no,” “Not sure,” “Probably yes,” and “Definitely yes.” Wang and Whittington (2005) introduce a stochastic payment card mechanism in which respondents can state their likelihood to pay different amounts on a numeric scale (0%, 25%, 50%, 75%, and 100%).

4.4. Reliability and validity of the contingent valuation method

There has been a long-running debate among economists regarding the validity of WTP estimates derived from contingent valuation studies. This debate was mainly centred on the evaluation of environmental damages. The contingent valuation method initially gained some form of legitimacy after the NOAA panel of experts, concluded that, given a set of best practices, contingent valuation studies “convey useful information” and could provide “estimates reliable enough to be the starting point of a judicial process of damage assessment” (Arrow et al., 1993, p. 43). However, Portney (1994), a member of the panel, notes that this conclusion was made reluctantly, which motivated the panel members to construct a set of best-practice guidelines for future contingent valuation studies. These included stipulations that researchers should: i) use personal instead of mail interviews; ii) elicit WTP instead of WTA; iii) utilize the referendum format; iv) accurately describe the valuation scenario; iv) remind respondents of their budget constraints and substitutes for the good in question; and v) include follow-up questions to measure respondent understanding. Since the NOAA report, economists have remained divided on the validity of the contingent valuation method. Notable examples are provided in two symposia of the Journal of Economic Perspectives in 1994 and 2012, which featured articles from prominent proponents and critics of the contingent valuation method. Generally, proponents argue that when contingent valuation methods are carefully applied they provide meaningful measures of value (see Kling et al., 2012; Carson, 2012). Critics, in contrast, contend that the method is subject to numerous biases and inconsistencies that cast doubt on the elicited WTP values (see Hausman, 2012). While the debate is far from settled, it is important to consider the weight of empirical evidence concerning the validity of the approach and the consequences for the elicitation of equivalent incomes.

Various studies have attempted to assess criterion or convergent validity by comparing estimates from stated and actual scenarios (i.e., using real money payments).¹¹ Differences are typically interpreted as evidence of hypothetical bias. Existing evidence, principally from the field of environmental economics, suggests that contingent valuation estimates of WTP are generally upwardly biased (List and Gallet, 2001; Murphy et al., 2005; Kling et al., 2012; Hausman, 2012). For instance, the most recent meta-analyses suggest that the mean and median ratio of stated to actual values across studies is around 2 and 1.4, respectively (Foster and Burrows, 2017; Penn and Hu, 2018). However, these findings are not always consistent across fields. In the field of health economics, stated preference estimates of the value of statistical life, i.e., the marginal rate of substitution between income and mortality risk, are typically lower than those derived from revealed preference studies (Alberini, 2019). For instance, Viscusi and Masterman (2017) report a mean value of statistical life of $13.5 million from their meta-analysis of 953 revealed preference studies. In a follow-up review of stated preference estimates, they report an average value of $10.3 million (Masterman and Viscusi, 2018). It remains an open question how the discrepancies between the results in different fields can be explained.

The existence of hypothetical bias has been the subject of considerable debate, particularly regarding whether it reflects the nature of the question or rational responses to the incentives embedded in surveys. Several authors argue that interpreting hypothetical bias from meta-analyses is difficult without considering the incentive structure and the consequentiality of the surveys (Carson and Groves, 2007; Kling et al., 2012; Haab et al., 2013). Carson and Groves (2007) argue that what is often perceived as hypothetical bias may actually be a rational response to the incentives present in the survey design. For example, they note that referendum surveys for hypothetical public goods may incentivize respondents to overstate their WTP if they believe that a government agency will not be able to enforce payment if the good is provided.¹² In this regard, Carson and Groves (2007) assert that only incentive-compatible and consequential surveys can reliably predict how rational agents will respond. Haab et al. (2013) further observes that several studies meeting these criteria have shown no evidence of hypothetical bias.

Various ex ante survey methods have been developed to mitigate different forms of hypothetical bias in contingent valuation (see Loomis, 2011). One common approach, known as cheap talk, involves reminding respondents of the tendency to overstate values before they answer the contingent valuation question (see Cummings and Taylor, 1999). Budget reminders ask respondents to consider their budget constraints when stating their WTP, while honesty oaths require respondents to pledge truthfulness prior to answering (see Jacquemet et al., 2013). Another method, consequentiality scripts, emphasizes the potential importance of their responses, particularly in relation to policy changes that may affect their personal well-being. Evidence on the effectiveness of these approaches is mixed, with some studies finding limited reductions in hypothetical bias and improvements in validity (Johnston et al., 2017). Recent meta-analyses suggest that methods like cheap talk, consequentiality scripts, and uncertainty analysis may reduce hypothetical bias to a degree, though generally by only a small margin (Foster and Burrows, 2017; Penn and Hu, 2018).

Construct validity has primarily been assessed through tests of scope sensitivity. These tests follow the recommendation of the NOAA panel that scope effects—where respondents’ WTP increases with the scale of the good provided—should be “adequate” (Arrow et al., 1993). However, the NOAA panel members do not define what constitutes adequate effects, leading to an ongoing debate within the literature. Kling et al. (2012) and Carson (2012), for example, review the literature and conclude that scope effects are present in most well-designed CV studies, which supports the construct validity of the method. Conversely, Hausman (2012) argues that the magnitude of these effects is rarely substantial enough to affirm validity. He thus advocates for a more stringent version of the scope test, i.e., the adding-up test proposed by Diamond and Hausman (1994), as a benchmark for meeting the NOAA panel’s adequacy criterion. In the adding-up test, a composite nonmarket good is divided into two components, A and B, and respondents are asked to value each part incrementally and then as a whole (C = A + B).¹³ The test is passed if ${\text{WTP}}_A+{\text{WTP}}_{B|A}={\text{WTP}}_C$, where ${\text{WTP}}_{B|A}$ is the incremental WTP for B. Hausman points out that many studies lack this test, and those that include it frequently fail, citing the findings of Desvousges et al. (2012).¹⁴

Haab et al. (2013) argue that the conclusions of Hausman (2012) rely on selective evidence and that the magnitude of scope effects may reflect diminishing marginal utility. They critically reassess the findings of Desvousges et al. (2012) and broaden their review of the literature to show that many studies do indeed pass the scope test. They also point out that the adding-up test imposes restrictions on preferences and requires additional assumptions for empirical assessment, specifically that respondents believe A has already been provided when valuing $B|A$. Desvousges et al. (2016) reply to the arguments of Haab et al. (2013), emphasizing that passing the scope test alone does not confirm validity. They assert that scope effects should also demonstrate adequacy, which they believe can only be evaluated using an adding-up test.¹⁵ Citing a memo from the NOAA panel members, Whitehead (2016) contends that NOAA intended contingent valuation estimates to be judged on their “plausibility” rather than strict adequacy. He proposes the scope elasticity test as an alternative to the adding-up test, finding that many existing studies yield elasticities within a plausible range.

Evidence on the reliability of contingent valuation estimates remains mixed. Bishop and Boyle (2019) review the available test-retest literature, concluding that well-conducted contingent valuation studies tend to yield reliable estimates of value. Nevertheless, estimates from such studies are often sensitive to the question format and other subtle aspects of survey design (Champ and Bishop, 2006; Lichtenstein and Slovic, 2006a). These differences may reflect the unique incentives (e.g., strategic underreporting) and behavioral factors (e.g., anchoring) associated with each elicitation mechanism (Bateman et al., 2002). Vossler and Zawojska (2020) test the effects of behavioral factors across four different elicitation formats (single/double-bounded referendum, payment cards, and open-ended) while controlling for economic incentives.¹⁶ They find that the distributions of WTP are similar across each format, suggesting that behavioural factors alone may not account for the elicitation effects observed in prior studies. Nonetheless, they underscore that the interaction between behavioural factors and economic incentives could still play a role in the contingent valuation context.

4.5. Contingent valuation and the estimation of equivalent income

Typically, empirical applications of the contingent valuation method in the context of equivalent income first elicit information about the respondent’s actual life situation and then ask for their WTP to move to a hypothetical life situation with reference values in the nonmonetary dimensions. For example, in the context of health, Fleurbaey et al. (2013) first ask:¹⁷

“If no health problems had occurred in the past 12 months and you would therefore have been in perfect health, you would have saved the health expenditures that you stated earlier. Moreover, you would have benefited from a better quality of life. Without accounting for health expenditures, would you have preferred a lower income in the last 12 months without any of the health problems that you had?” (yes/no/do not know)

Respondents answering “yes” were then asked the following valuation question:

“Indicate the monthly decrease in your personal consumption in the last 12 months that you would have accepted, to be in perfect health (during the same period), on top of the health expenditures that you would have saved.”

Responses to the valuation question provide a direct measure of WTP, as illustrated in Figure 1. By subtracting this value from actual income (or consumption), a direct estimate of equivalent income is obtained. When using the referendum elicitation mechanism, the expected equivalent income can be estimated as discussed previously.

If multiple life dimensions are involved, one can either ask for the WTP to transition to the overall reference situation or, if more detailed information is desired, first elicit WTP values for each dimension separately. In the latter case, a scope issue arises, as discussed before. For instance, when focusing on two dimensions, one would generally expect the overall WTP to move to the reference situation, $\text{WTP(}{z}_{1i}\to {\overline{z}}_1,z_{2i}\to {\overline{z}}_2\text{)}$, to be larger than each of the individual values, $\text{WTP(}{z}_{1i}\to {\overline{z}}_1\text{)}$ and $\text{WTP(}{z}_{2i}\to {\overline{z}}_2\text{)}$. Moreover, if separability between dimensions cannot be assumed, it is essential to clarify how the individual WTP values for one dimension depend on the implicitly assumed levels of the other dimensions.

In policy applications, simulations of equivalent incomes in counterfactual scenarios are often required. For such simulations, information about individuals’ entire indifference maps is essential. However, these maps cannot be directly obtained from a contingent valuation survey, as one can only infer that the life situations $(y_i,z_i)$ and $(y_i^{\star },{\overline{z}}_i)$ lie on the same indifference curve (see equation (1)). Nevertheless, by making parametric assumptions about the shape of the indifference curves and accounting for preference heterogeneity across sociodemographic subgroups, it is possible to estimate indifference maps at the group level. Examples of this approach are provided by Schokkaert et al. (2013) and Samson et al. (2018).

4.6. The Adaptive Bisectional Dichotomous Choice method

Some recent studies have advanced the contingent valuation method to address limitations in eliciting preferences for estimating equivalent incomes. One such proposal is the Adaptive Bisectional Dichotomous Choice (ABDC) method, introduced by Decancq and Nys (2021). The ABDC method can be viewed as an extension of the standard bidding game, presenting respondents with a choice between two life situations, each described by two dimensions (income and health), one of which reflects their actual life situation and the other being a hypothetical one.¹⁸ By systematically adjusting the levels of each dimension in the hypothetical life situation, nonparametric bounds around each individual’s indifference sets can be obtained.

An illustration of the ABDC method is provided in Figure 3 for individual $i$, who is assumed to have incomplete preferences. Their upper contour set (UC) and lower contour set (LC) are indicated in the figure. The area between these two sets represents the noncomparable set, life situations that the individual cannot rank relative to their actual situation, ${\ell }_i=(y_i,h_i)$. The ABDC method begins by presenting the respondent with a pair of life situations: their actual life situation, ${\ell }_i=(y_i,h_i)$, and a hypothetical life situation $\left(\frac{1}{2}{y}_i,\overline{h}\right)$ (at point A). If they prefer the hypothetical life situation over their own, then their indifference set is located below point A. Subsequently, they choose between their own life and $\left(\frac{1}{4}{y}_i,\overline{h}\right)$ (point B). If they now prefer their own life, the indifference set lies above point B. The next hypothetical life for comparison is positioned at point C, or $\left(\frac{3}{8}{y}_i,\overline{h}\right)$, which is halfway between points A and B. This iterative algorithm continues until the respondent is either unable to make a choice or a maximum number of choices is reached.¹⁹ The process can then be repeated with different reference levels, such as $\frac{1}{2}\overline{h}$, to estimate bounds around other areas of the indifference set.

Figure 3.

There are several novelties in this method compared to standard contingent valuation methods. First, the ABDC method captures more detail about individuals’ indifference curves by fixing the level of one dimension in the hypothetical life situation and varying the other. This approach allows for a more flexible analysis of preferences using nonparametric techniques from demand analysis (Varian, 1982), enabling tests of specific aspects such as monotonicity and the validity of commonly used functional forms, while relaxing assumptions about completeness. Second, the ABDC method employs a bisectional algorithm to progressively narrow the bounds around the indifference set. After each choice, the algorithm halves the level of one dimension in the hypothetical life, keeping the other fixed, which increases the precision of the estimates. Third, the ABDC method allows individuals to indicate that they cannot compare two alternatives by selecting an “I don’t know” option. This option may enhance the validity of estimates compared to methods that force respondents to make a choice, which may lead to phenomena as “yes-saying” or other heuristics. Offering the “I don’t know” option aligns furthermore with behavioral versions of equivalent income that relax the assumption of completeness. (see Fleurbaey and Schokkaert, 2013).

Table 2 provides an overview of some advantages and disadvantages of the ABDC method. As an extension of the bidding game elicitation mechanism, the ABDC method is potentially subject to starting-point biases that could influence the elicitation of equivalent income. Evidence from the contingent valuation literature suggests that this may impact both the point estimates and uncertainty intervals derived. For example, Dubourg and Loomes (1997) find that the starting bid influenced the best estimate of the respondents’ WTP, as well as uncertainty intervals in an iterated bidding game experiment similar to the ABDC. Additionally, eliciting preferences across more than two dimensions (i.e., constructing an indifference surface) is complicated by the large number of dichotomous choices required, which can lead to respondent fatigue and is likely less efficient than multi-attribute valuation methods (e.g., choice experiments) that are discussed in the next section. Nevertheless, the ABDC method may be valuable for researchers interested in measuring equivalent income directly rather than the trade-offs between the different well-being dimensions. For example, one can elicit the WTP for attaining the reference levels across multiple dimensions at once.²⁰

By combining data generated by the ABDC method with standard assumptions about preference relations, such as transitivity, monotonicity, and convexity, the method can be employed to map individual indifference sets in a nonparametric manner. In their study, based on an online survey of 2,575 respondents from the United States, Decancq and Nys (2021) provide bounds on indifference sets through the individual’s actual life situation. Alternatively, data from the ABDC method can also be employed to test these preference assumptions and to assess consistency with commonly used functional forms in the literature. Decancq and Nys (2021) find that 17.5% of respondents make choices that violate monotonicity and transitivity, while approximately 9.5% fail tests of transitivity and convexity. About one third of respondents display choices inconsistent with a constant elasticity of substitution between income and health; inconsistency rates are higher for linear (95.4%), Cobb-Douglas (71.8%), Leontief (48.7%), and kinked linear (70%) preferences. Burone and Decancq (2023) apply the ABDC method to a representative sample of 2,048 individuals in the Netherlands to measure equivalent incomes in the three-dimensional income-health-social interactions space directly, without mapping the full indifference surface. Their study also allows for a comparison between the ABDC method and other approaches, results to which we will return in section 7.

5.1. Data from multiattribute methods

The design and implementation of the multiattribute methods involves several stages. First, researchers must select the relevant attributes and corresponding levels for the good being valued. This selection process typically draws on theoretical insights and pretesting to ensure that the attributes and levels are realistic. In the context of equivalent incomes, these attributes correspond to relevant life dimensions. Next, researchers construct a set of alternatives from these attributes and levels, aiming for precise and efficient estimation of each attribute’s relative contribution. This often requires an experimental design that is orthogonal (i.e., uncorrelated attribute levels) and balanced (i.e., each attribute level appears an equal number of times across the experiment). Such designs can be created using orthogonal arrays or statistical software.²¹ Following this, alternatives are grouped into choice sets using various methods (see Johnson et al., 2013) or presented directly. Finally, the survey is conducted to elicit individuals’ preferences for the different attributes.

There are two broad categories of multiattribute methods: choice experiments and conjoint analysis. Choice experiments can be subdivided into two main forms. The first, discrete choice experiments, present individuals with sets of two or more alternatives, one of which is often a status quo option. In these experiments, respondents are typically asked to make a series of choices between the presented alternatives, allowing researchers to capture detailed information on their preferences. The second form, rank-order choice experiments, requires respondents to rank the presented alternatives according to their (ordinal) preference relation.

Conjoint analysis, by contrast, incorporates cardinal aspects of preference intensity. One popular approach in this category is the contingent rating method, where respondents rate hypothetical scenarios on a semantic or numerical scale (usually from 1 to 10) based on their preferences. Another approach, pairwise comparisons, is similar to discrete choice experiments in presenting two alternatives, but it asks individuals to rate the strength of their preference for one alternative over the other (e.g., “somewhat prefer” or “strongly prefer”) on a scale. This approach thus combines elements of discrete choice experiments and contingent rating, capturing both choice and the intensity of preference.

5.2. Estimation of preferences

Data from choice experiments and conjoint analysis are typically analyzed with parametric methods. Yet, the two categories rely on different theoretical frameworks. Decisions in a choice experiment are mostly modelled using random utility theory, which assumes that respondents’ preferences can be represented by a specific parametric functional form based on observable attributes of an alternative plus a random error component, capturing unobservable factors that influence choice (McFadden et al., 1973). This approach is related to the method described in section 4.2, with the main difference being that two alternatives are compared in choice experiments, whereas a reported WTP is compared with a deterministic benchmark in the earlier method. Different assumptions regarding the distribution of random error terms in a random utility model yield different discrete choice models. For instance, assuming normally distributed errors leads to a multinomial probit model, while assuming errors follow an extreme value distribution results in the conditional (or rank-order) logit model. The parameters of these models are estimated from observed choices or rankings using maximum likelihood and can provide WTP estimates if a monetary attribute (e.g., income or cost) is included.

We illustrate how preferences can be estimated with a basic discrete choice model. Suppose individuals are presented with choices between two or more hypothetical life situations, as has been used in previous empirical studies. Under the assumptions of random utility theory, the probability of individual $i$ choosing a hypothetical life $j$ is given by:

where $V_{ij}$ is a function that specifies how an individual’s utility depends on observable factors and ${\epsilon }_{ij}$ captures a set of random unobservable factors that influence choice but are not included within $V_{ij}$. These unobservable factors are particularly salient in stated preference studies as individuals may vary in the attention they give to the choice task or in how they account for unlisted attributes (Train and Weeks, 2005). The welfare interpretation of the model depends on whether ${\epsilon }_{ij}$ represents optimization errors or idiosyncratic preference factors. Assuming an extreme value distribution of these unobservable factors leads to the logit case, in which a closed form for the choice probability is obtained:

Further assuming that $V_{ij}$ is linear, we have:

where $y_{ij}$ is the income level of a hypothetical life and $z_{ij}$ includes all other nonmonetary aspects of the described life, such as health and social interactions. The coefficients of equation (4) can be estimated via maximum likelihood. Marginal rates of substitution can be computed by taking the ratio of these coefficients.

Preference heterogeneity can be introduced via interaction terms or by specifying more complex models. Advances in simulation methods enable researchers to estimate both the distribution of preferences within a population and individuals’ positions within this distribution, based on their sequence of choices, using mixed logit models (see McFadden and Train, 2000; Train, 2009). However, these models require the researcher to specify the shape of the preference distribution from the outset, the parameters of which are estimated from respondents’ choices. The problem is that this distribution is unknown and assumptions regarding it are likely to be arbitrary.²²

Unlike choice experiments, where respondents are asked to rank life situations and express ordinal preferences, conjoint analyses elicit the intensity of preference. WTP values can be estimated from contingent rating or pairwise comparison data in various ways. In the contingent rating method, one can estimate a linear preference function and take the ratio of the dimension coefficients to estimate marginal rates of substitution (Roe et al., 1996). Pairwise comparison data can be analyzed similarly, with the right-hand side of the model containing differences between the dimensions across alternatives rather than levels (see Magat et al., 1988). Hanley et al. (2001) notes that many pairwise comparison studies respecify the ratings as ordinal variables indicating choice, allowing analysis within a random utility theory framework, although this discards the additional preference intensity information. Nevertheless, this information can be incorporated as follows.

Assume that individual $i$ indicates their strength of preference $R_{i,l}$ on a cardinal scale from 0 to 10 between a pair of hypothetical life situations $l$. The lower and upper bounds of this scale reflect a strong preference for either one of the hypothetical life situations. Denote the differences in the income and nonmonetary dimensions across pairs of life situations $l$ as $\Delta y_{i,l}$ and $\Delta z_{i,l},$ respectively. The researcher estimates the following equation using ordinary least squares:

where the ratio of two coefficients ($-\gamma \text{}\text{}/\text{}\beta$) is equal to the respondent’s marginal rate of substitution between income and the nonmonetary dimension. The model is flexible enough to capture group-level preference heterogeneity by introducing interaction terms between the coefficient and sociodemographic variables. The pairs of life situations could also be varied using an algorithm to calculate individual-level marginal rates of substitution (see Magat et al., 1988).

5.3. Advantages and disadvantages of multiattribute methods

Choice experiments have been argued to have several advantages over other preference elicitation methods (see Hanley et al., 2001). First, they provide a theoretically grounded framework with which to identify trade-offs between different attributes of nonmarket goods. While contingent valuation methods can also be used to estimate the value of different attributes (i.e., through a series of valuation questions), the process is usually more costly, cumbersome, and inefficient. Second, the outputs of choice experiments are more generalizable to other scenarios, given that the method focuses on valuing attributes rather than the nonmarket good as a whole. For instance, the estimated coefficients can be used to predict choices across other alternatives with similar attributes. Third, they provide opportunities for learning and preference discovery via repeated choices. Discrete choice models are flexible enough to account for this process (e.g., mistakes during preference formation) through the inclusion of the random utility term (Lancsar and Louviere, 2006). Lastly, choice experiments avoid the use of explicit money valuations, which may be subject to phenomena such as protest votes, as described in the case of contingent valuation methods in the previous section.

Nevertheless, choice experiments face several limitations:

• Cognitively demanding: The overall precision of choice experiment estimates depends not only on the statistical efficiency of the underlying experimental design but also on the response efficiency, i.e., the degree of measurement error resulting from respondents’ mistakes or nonoptimal choice behavior (Johnson et al., 2013). Choice experiments can be cognitively demanding for respondents to answer if they have to consider many different attributes or alternatives simultaneously when making a choice. They may also have to make these choices a number of times. The overall complexity of the choice experiment may therefore lead to respondent fatigue or the use of heuristics, i.e., simplifying strategies that are not in line with the principle of utility maximising behavior. Such effects may contribute to the error term of the model (i.e., lower response efficiency), thereby reducing the precision of the parameter estimates. On the other hand, making choices seems to be more natural and less cognitively demanding than looking for indifference between two situations (as is often required for contingent valuation applications). For instance, Attema and Brouwer (2013) find that choice tasks yield more internally consistent responses than matching (i.e., searching for indifference) tasks.

• Nonattendance bias: A key underlying assumption in a choice experiment is that respondents consider all the attributes of each alternative when making a choice or ranking. In practice, however, choice experiments may be susceptible to nonattendance bias, whereby respondents make their choices based on a subset of the attributes presented. There are several possible reasons why this might occur. Respondents might use simplifying strategies to make choices if the number of alternatives or attributes is too large to process. Alternatively, respondents may consider only one attribute of the alternatives to be important, leading to lexicographic orderings.²³ Several methods have been proposed to correct for this bias. Hole (2011), for instance, proposes an endogenous attribute attendance model that adjusts the standard conditional logit formula for nonattendance bias (based on a set of observable respondent characteristics). These corrections are tricky, however, as it is difficult to distinguish between nonattendance bias and genuine lexicographic preferences.

• Restrictive preference assumptions: The estimation methods are parametric and therefore impose some structure on individual preferences over observable attributes. Several challenges are relevant in this regard. First, there may be complex interactions between attributes that cannot be adequately modelled using standard choice models. Second, there may be attributes that are omitted from the experiment but are important determinants of choice. Respondents may also infer changes in these omitted attributes from the presented alternatives, which could lead to bias in the parameter estimates and reduce precision. In addition, these challenges make it difficult for researchers to measure the total value of a change in the provision of a nonmarket good. This is because choice models often assume that the value of an alternative is equal to the sum of its parts, i.e., the observed attributes (Atkinson and Mourato, 2015). Hanley et al. (2001) argue that this additive framework may be problematic as certain attributes may be missing and respondents may not value “whole” goods in this way. They point to evidence from several studies indicating that discrete choice experiments provides larger estimates of total value than contingent valuation. Such concerns are particularly relevant for the measurement of well-being using the equivalent income.

• Preference heterogeneity: Unlike contingent valuation methods, choice experiments are unable to provide direct measures of WTP at the individual level.²⁴ In standard conditional logit models, preference heterogeneity can be captured at the grouplevel via interaction terms. Mixed logit models offer more flexibility in the modeling of preference heterogeneity but only provide estimates of individual parameters based on strong parametric assumptions about the functional form of individual preferences as well as how these preferences are distributed across the population.

We summarize some advantages and disadvantages of specific multiattribute methods in Table 3. The key advantage of choice experiments (in row 1 and 2) over conjoint analysis (in row 3 and 4) is that they provide estimates of WTP that are consistent with random utility theory. Meanwhile, conjoint analysis methods can provide more information, i.e., intensity of preference, than standard choice or ranking tasks. However, they also rely on relatively strong assumptions about inter- and intrapersonal scale use. It is perhaps for this reason that conjoint analysis has failed to garner popularity with economists (Hanley et al., 2001).

5.3. Reliability and validity of multiattribute methods

In contrast to contingent valuation, evidence on the reliability and validity of discrete choice experiments remains relatively limited and mixed. Haghani et al. (2021) provide a review of criterion and convergent validity in discrete choice experiments by examining hypothetical bias across four fields: consumer, environmental, health, and transport economics. Their review covers 57 peer-reviewed studies, more than half of which report significant hypothetical bias. The authors identify two key issues complicating hypothetical bias testing across studies. First, a true benchmark preference is often missing, making it challenging to assess hypothetical bias. Second, hypothetical bias likely varies with the choice context. Notably, the field of health economics reflects a different perspective on the extent of this bias compared to other fields, likely due to differences in perceived importance. For example, health-related surveys may prompt respondents to take choice tasks more seriously than questions about consumer goods, such as foods or beverages. Conversely, protest responses seem more frequent in health contexts. Additionally, health-focused choice experiments often examine private goods, while environmental surveys tend to concern public goods, which may be more vulnerable to other biases (e.g., warm glow and free-rider effects).

In their systematic review of 107 studies within environmental economics, Rakotonarivo et al. (2016) assess the reliability and validity of choice experiments. For reliability, they examine studies that incorporate test-retest trials (repeating the same survey at different times), as well as variations in framing, the provision of additional deliberation or information, and experimental design changes (including adjustments to attributes, levels, and design parameters). Nearly half of the estimates (45%) showed sensitivity to minor design changes. Regarding validity, the authors evaluate studies testing for criterion ($n$ =11), convergent ($n$ =13), and construct validity ($n$ =30), with construct validity assessments including conformity with standard rational choice axioms and attribute non-attendance. The results are mixed at best: no criterion validity evidence was found, and only limited convergent validity with other methods. While most respondents passed monotonicity tests, high levels of self-reported attribute nonattendance were reported. Additionally, only two of six studies testing for scope effects found evidence supporting these effects.

There are various other studies testing the convergent validity of choice experiments within the field of health economics. For instance, several studies find that the WTP values elicited from discrete choice experiments are much higher than those obtained from contingent valuation (Ryan et al., 2004; van der Pol et al., 2008; Ryan and Watson, 2009; Bijlenga et al., 2011; Danyliv et al., 2012). Danyliv et al. (2012) review this literature in more detail and highlight potential causes of this difference, including restrictive assumptions regarding the linearity of the utility function (as discussed earlier), the absence of substitutes (e.g., opt-out alternatives), and specific aspects of the experimental design (e.g., the range of the price attribute). Comparisons between other forms of choice experiment and contingent valuation are less common in health economics. A rare example is provided by Magat et al. (1988), who find that morbidity valuations obtained from the pairwise comparison and contingent valuation methods differ considerably, with the former yielding higher WTP estimates.

These findings also connect to evidence on preference reversals observed between matching and choice tasks within the behavioral economics literature (Tversky et al., 1988; Lichtenstein and Slovic, 2006b). In a matching task, respondents adjust a single dimension of an alternative to achieve equivalence between two alternatives, similar to contingent valuation when a monetary attribute is adjusted. In a choice task, respondents’ preferences are inferred from their choices between two alternatives, one of which is iteratively varied until a point of indifference is reached. Tversky et al. (1988) argue that the discrepancy between preferences obtained from these two methods can be explained by the prominence effect, whereby respondents focus more on the most important (or prominent) attribute when making choices rather than matching. Attema and Brouwer (2013) demonstrate that this effect is also prevalent when eliciting preferences over health states and life span, in the form of QALYs. Pinto-Prades et al. (2018) find that the prominence effect may be mitigated to some extent by using nontransparent methods that hide the underlying objective of an iterated choice task. Such findings may also affect the elicitation of equivalent income using variations of these methods: open-ended/payment cards in the case of matching and ABDC (see section 4.6) in the case of choices.

5.4. Multiattribute methods and the estimation of equivalent income

In multiattribute approaches, the good to be valued is viewed as a function of various attributes. In the context of estimating equivalent incomes, the good to be valued is a life situation that can be described using several life dimensions.²⁵ While multiattribute methods have not yet been used in the literature to estimate equivalent incomes, the relevant preferences can be estimated based on comparisons or valuations of descriptions of hypothetical life situations, sometimes referred to as vignettes.

When relying on a choice experiment, respondents are asked to compare several life situations of which the attribute level in the life dimensions are experimentally varied. Recall that the actual life situation of individual $i$ is denoted by ${\ell }_i=(y_i,z_i)$ and the reference life situation ${{\ell }^{\prime }}_i=(y_i^{\star },{\overline{z}}_i)$. Using the estimated preference parameters from the linear model in equation (4), for instance, the actual and the reference life situation are equivalent if:

where ${\overline{z}}_i$ represents, as before, the reference level of the nonmonetary dimensions and $y_i^{\star }$ the equivalent income. By rearranging this equality, we can easily obtain an expression for the equivalent income:

Preference heterogeneity can be accommodated by including interaction terms with sociodemographic variables in the specification of $V_{ij}$ in equation (4). We will return to this procedure when describing the life satisfaction method in section 6.2.

When using the contingent rating (or factorial survey) method, respondents rate several vignettes, i.e., hypothetical life situations described across various life dimensions. These ratings allow the straightforward estimation of (group-level) preferences.²⁶Van Loon and Decancq (2022), for instance, present each respondent with seven vignettes, each describing a hypothetical life situation across six dimensions. The respondents, 800 older adults, are given an 11-point satisfaction scale for their response.

“Please read the following life description carefully.

You have [moderately severe] physical or mental health problems.

You have [several times per week] contact with family or friends.

The total net household income is [€5,000.00].

You do [once per week] a hobby or leisure activity.

You do [several times per week] a useful or meaningful activity.

You spend [less than once per week] time on religion or spirituality.

How satisfied would you be if you were in this situation?”

The bracketed words indicate levels that varied experimentally across vignettes. Van Loon and Decancq (2022) employ a multilevel model to estimate preferences based on the ratings of the vignettes, incorporating error terms at both the vignette and respondent levels. Although the authors do not compute equivalent incomes, this could be done with the estimated parameters using equation 6. A total of 154 respondents rated vignettes across five waves, from May to December 2020, enabling a test of the temporal reliability of the estimated preferences. In 6 of 10 cases, the hypothesis of parameter stability could not be rejected.

6.1. Self-reported well-being data

A relatively recent literature explores the potential of using self-reported well-being measures (SWB) to inform policymaking decisions. An example is the life satisfaction question from the European Social Survey:

“All things considered, how satisfied are you with your life as a whole nowadays? Please answer using this card, where 0 means extremely dissatisfied and 10 means extremely satisfied.”

Data on SWB have by now been collected for thousands of respondents throughout the world with large-scale surveys. The literature analyzing this data has followed two distinct paths. One path interprets the responses as cardinal measures of utility (e.g., Layard et al., 2008), while the other seeks to recover information about ordinal preferences from the responses (as in the previously discussed contingent rating method). These preferences can then be used to value nonmarket goods (e.g., Clark and Oswald, 2002; Ferrer-i-Carbonell and Van Praag, 2002) or to construct measures of well-being (e.g., Decancq et al., 2015a).²⁷ Typically, researchers regress life satisfaction scores on income and nonmonetary dimensions of well-being, controlling for other personal characteristics of the respondents. The estimated coefficients can then be used to derive the marginal rate of substitution between income and a selected life dimension.

From a theoretical perspective, responses to the life satisfaction question capture experienced rather than decision utility. The former reflects an ex post evaluation of one’s situation, that is, after experiencing the consequences of different choices. In contrast, decision utility is based on choices made ex ante and reflects individuals’ beliefs about their consequences. We have already seen that choices can only be considered reliable indicators of well-being if they are made under ideal conditions, characterized by full information, correct beliefs, and an absence of behavioral distortions, among other factors (Hausman, 2011; Bernheim, 2016). Given that these conditions are rarely met in practice, some have argued that experienced utility (equivalently, SWB measures) may serve as a better indicator of informed preferences and, therefore, well-being (Decancq et al., 2015b).

6.2. From life satisfaction scores to equivalent income

To illustrate the estimation of preferences using the life satisfaction method, assume the existence of a satisfaction function $S(\cdot )$ that maps a life situation into a self-reported life satisfaction score, typically measured on a scale from 0 to 10. While this life satisfaction score is a cardinal value, it may also be informative about the underlying ordinal preferences, provided a consistency assumption holds (Decancq et al., 2015a).

Consistency assumption: $S_i({\ell }_i)\ge S_i({{\ell }^{\prime }}_i)$ if and only if ${\ell }_i{R}_i{{\ell }^{\prime }}_i^{}$ for each individual $i$.

Under this assumption, the marginal rates of substitution between dimensions can be estimated using a life satisfaction regression. The functional form of this regression can be flexibly chosen, but a common specification is a log-linear one:

where $S_{it}$ is the life satisfaction score given by individual $i$ in period $t$, $y_{it}$ is their income (in logarithm), $z_{it}$ is a vector of nonmonetary life dimensions, ${\alpha }_i$ and ${\mu }_t$ capture individual fixed effects and time effects, respectively, and $x_{it}$ is a set of sociodemographic control variables that capture how individuals use the reporting scales. The marginal rates of substitution depend on the coefficients $\beta$ and $\gamma$. Differences in scale use are captured by the fixed effects ${\alpha }_i$, time-varying control variables $x_{it}$, and idiosyncratic error terms ${\epsilon }_{it}$. These scaling differences reflect variations in ambitions and adaptation (Sen, 1985), or cultural differences in scale use (Johnson et al., 2005), and should not influence the equivalent income. Equivalent incomes are based solely on marginal rates of substitution, not on the specific cardinalization of the preferences. Indeed, equivalent income can be calculated, starting from the equivalence between the actual and the reference life situation:

Solving this equation for $y_{it}^{\star }$ yields:

The value of the equivalent income depends on the actual income and the WTP, which depend on the estimated coefficients $\beta$ and $\gamma$ and the difference between the actual nonmonetary dimensions and the reference values $(z_{it}-{\overline{z}}_i)$. It does not depend on any of the scaling variables.

More flexible forms (e.g., using Box-Cox transformations) of the model in equation (7) can be adopted to account for nonlinearities (see, e.g., Decancq and Schokkaert, 2016; Decancq et al., 2019). Group-level preference heterogeneity can be introduced by including interaction terms between the dimensions of life and sociodemographic variables indicating group membership in equation (7) (see, e.g., Decancq et al., 2015a; Decancq and Schokkaert, 2016). Because it is based on interactions in a regression analysis, the life satisfaction method can capture group-level preference heterogeneity, but not individual-level heterogeneity.

6.3. Advantages and disadvantages of the life satisfaction method

An important advantage of the method is that life satisfaction data are relatively inexpensive and easy to collect, as only one additional survey question is required. Major life satisfaction surveys (e.g., Gallup) target a representative sample in each country, allowing researchers to capture the preferences of the entire population. Although results from these large surveys may be affected by low response rates (Heffetz and Rabin, 2013; Benjamin et al., 2023a), such large samples are often unavailable for other methods that require more resources per respondent (e.g., choice experiments). Additionally, the method may be less susceptible to biases inherent to other stated preference methods (e.g., ordering and framing effects) as well as protest responses.

The life satisfaction approach, however, also has some disadvantages. Most importantly, the consistency assumption that underpins the method is empirically untestable. Researchers must therefore take this assumption as given when inferring preferences from predicted life satisfaction scores. There is a literature comparing hypothetical choices and hypothetical estimates of well-being (Benjamin et al., 2012, 2014b), which is providing indirect evidence. A key issue is that people may not maximize their own satisfaction with life but take account of their relatives in their choices, whether real or hypothetical. This means that choices and self-centred preferences may not be completely aligned, and therefore, consistency between life satisfaction and preferences cannot be directly assessed through the relation between life satisfaction and decisions.

The preference information derived with the life satisfaction method ultimately depends on the factors an individual considers when responding to a life satisfaction question and how those factors are weighted. It remains unclear which utility concept respondents apply in formulating their responses (Benjamin et al., 2023a).

Furthermore, there is an ongoing debate on whether self-reported well-being scores should be interpreted as a measure of an individual’s happiness (in which case they could be considered an important life dimension and thus a component of the preferences; see Benjamin et al., 2012; Adler et al., 2017) or as a reflection of underlying preferences (Decancq et al., 2015a). Fleurbaey and Schwandt (2016) provide evidence supporting the latter view.

In addition, there are several econometric challenges posed by the estimation of the life satisfaction regression in equation (7). Perhaps the two most important are:

• Endogenous regressors and measurement errors: More satisfied individuals may earn higher incomes. Prior studies have shown that controlling for this type of bias via instrumental variables increases the income coefficient considerably (Knight et al., 2009; Powdthavee, 2010; Himmler et al., 2021), leading to lower WTP estimates for the nonmonetary dimensions and, thus, higher equivalent incomes. On the other hand, it has also been argued that income is measured with considerable error, which could bias its effect toward zero, bias the WTP estimates for the nonmonetary life dimensions upward and the estimates of equivalent income downward (Himmler et al., 2021).

• Scaling effects: An implicit assumption of equation (7) is that, conditional on the included scaling variables, all individuals use the reporting scale in the same way when rating their life satisfaction. Bond and Lang (2019) refer to this as the assumption of a common reporting function, which they consider to be “unlikely to be correct” (see also Kaiser and Oswald, 2022). Indeed, scale use may depend on various observable (such as the life dimensions themselves) and unobservable factors, the latter of which are problematic if correlated with the variables of interest. One approach to address this bias involves using vignettes that describe hypothetical life situations to anchor the scale on which people report their life satisfactions (King et al., 2004).²⁸ Yet, the use of anchoring vignettes requires that individuals rate the vignettes on the same scale as they evaluate their own life satisfaction (“response consistency”) and that each individual rates the vignettes in the same way (“vignette equivalence”). When preferences are heterogeneous, the latter assumption is strong (see Benjamin et al., 2023b for a recent discussion).

6.4. Reliability and validity of the life satisfaction method

We are unaware of any systematic analyses assessing the validity of marginal rates of substitution derived from the life satisfaction method. Some studies, however, have evaluated convergent validity by comparing WTP estimates obtained from the life satisfaction method with those derived from other methods:

• Dolan and Metcalfe (2008) compare WTP estimates from contingent valuation and the life satisfaction methods within an urban regeneration project in the UK. They find that estimates derived from the life satisfaction method are substantially larger than those obtained via contingent valuation.

• Benjamin et al. (2014b) survey medical students, comparing their choices of residence with anticipated levels of self-reported well-being in each scenario. They estimate marginal rates of substitution across residence dimensions using both data sources and find substantial differences between the two sets of estimates. This result holds across different measures of self-reported well-being, such as happiness and life satisfaction, and the authors note that these findings relate to anticipated, not experienced, subjective well-being.

• Murtin et al. (2017) estimate the WTP for life expectancy gains across OECD countries. Their life satisfaction-based method, using individual-level data, produces WTP values far exceeding those from the value of statistical life literature. They suggest that individual-level measurement error may be influencing these results. When re-estimating the model with country-level data, their results align more closely with values reported in the literature.

• Akay et al. (2020, 2023) estimate indifference maps over income and leisure time using both the life satisfaction method and labor supply choices (i.e., revealed preferences). Constructing money-metric utilities with both methods, they find a high degree of correlation between welfare rankings derived from the two approaches, though some discrepancies persist.

• Humphreys et al. (2020) compare WTP estimates for Olympic gold medals derived from the life satisfaction and contingent valuation (referendum) methods. They report that the life satisfaction-based estimates significantly exceed those obtained via contingent valuation.

Regarding construct validity, the consistency assumption remains problematic since it cannot be empirically tested. Thus, we cannot verify whether individuals’ life satisfaction scores correspond with their underlying ordinal rankings of life situations. This links to a broader issue of whether life satisfaction scores reflect any standard economic notion of utility. Benjamin et al. (2023c) present evidence on this front using an online survey that probes respondents on how they interpret and answer different self-reported well-being questions. Their findings suggest that respondents’ answers do not clearly correspond to notions such as lifetime, forward-looking, or period utility, nor do they align with self-centred utility. Instead, many respondents incorporate other-regarding preferences, including considerations for family members. However, their research indicates that minor adjustments in the wording of self-reported well-being questions may improve alignment with specific utility concepts.

8.1. Contingent valuation

Empirical studies using the contingent valuation method to elicit preferences have primarily focused on life situations defined in the income (or consumption) and health domain.

Fleurbaey et al. (2013) elicit WTP values for perfect health using a payment card format. They ask individuals to state the absolute decrease in personal consumption they would have accepted over the last year to be in perfect health (in addition to the health expenditures already incurred). Response cards range from “0 euros” to “more than 1500 euros” per month. Their pilot study was carried out with 542 respondents from the Marseille area, of which 20% either refused to answer the question or did not know how to answer. They distinguish between “severe” and “less severe” health problems and estimate indifference maps at the group level.

Building on this study, Schokkaert et al. (2013) and Samson et al. (2018) carry out a payment card contingent valuation study with 2,413 French respondents, with a focus on the valuation of health outcomes for individuals with hypertension. Self-assessed health is measured on a 0-100 scale and respondents are asked how much income they would be willing to give up to have been in perfect health over the past 12 months. The focus in Samson et al. (2018) is on the application of the equivalent income for priority setting in health insurance.

Abasolo et al. (2018) use a similar payment card method to elicit equivalent income with respect to health and relationship problems. Instead of using absolute amounts, the authors use cards with percentage decreases in consumption. Their online sample is relatively small with only 52 respondents. However, their qualitative debriefing questions yield important insights. For instance, some individuals were puzzled that consumption would go down after health has improved (i.e., they believed better health would allow them to increase their spending).

In their book, Capéau et al. (2020) analyze 1,857 respondents in the Measuring Equivalent Income (MEqIN) dataset, which includes contingent valuation questions regarding individuals’ WTP for health, housing, and ideal job characteristics. The question asks respondents how much they would be willing to reduce their monthly consumption over the next year to enjoy the reference level of the non-monetary dimension. The survey utilizes a payment card method with options ranging from “0 euros” to “more than 1500 euros”. The nonmonetary dimensions are presented to individuals on a scale ranging from 0 to 100.

Decancq and Nys (2021) apply the ABDC method in an online survey of 2,260 respondents in the United States. Because the framework allows for incomplete preferences, respondents can indicate that certain life situations are not comparable. The authors assess comparability across individuals by examining whether the extended upper contour set of the better-off respondent and the extended lower contour set of the worse-off respondent intersect.³¹ If these sets do not intersect, the pair can be ranked. Using this criterion, approximately one fifth of all respondent pairs can be ordered. In about half of the pairs, the intervals containing the equivalent incomes do not overlap, allowing for a robust comparison of their equivalent incomes.

8.2. Multiattribute methods

Published studies employing multiattribute methods to elicit preferences for computing equivalent income remain scarce. A notable exception is the recent work by Ta et al. (2024), who use an online survey of about 7,000 UK respondents to elicit preferences across seven well-being dimensions: physical and mental health, loneliness, income, employment, housing, and neighborhood safety. The authors further investigate preference heterogeneity by gender, age, and income and assess the temporal stability of preferences.³²

Nonetheless, a number of studies have applied multiattribute methods to assess the relative importance of different well-being dimensions, outside the equivalent income framework. We briefly review some examples later.

Adler and Dolan (2008) ask a small group of students in the US and UK to rank hypothetical life situations (which they call the “different lives” method) that differ in terms of income, life expectancy, health, and self-reported well-being. They find that respondents place greater weight on health and happiness than income and life expectancy.

Benjamin et al. (2012) present about 2,700 respondents in the US with pairs of “possible lives” that differ in many aspects, such as the amount of sleep one has due to a job and the level of income that job provides. They ask individuals to state which life would make them more satisfied and which one they would choose. Their results indicate a high degree of correlation between the responses to the two questions.

Benjamin et al. (2014a) ask 4,600 respondents to make pairwise comparisons of different aspects of well-being. They use a rating scale that asks individuals whether they “Much prefer,” “Somewhat prefer,” or “Slightly prefer” one of two options. They use OLS to analyze the relative marginal utilities associated with each aspect of well-being.

Adler et al. (2017) present large samples of respondents in the US and UK (total sample size of about 13,000 respondents) with choices between life situations described by income, health, family life, career goals, and knowledge. They also include measures of life satisfaction within the hypothetical life situations to see whether respondents prefer life situations with higher levels self-reported well-being. The results suggest that people often choose the life with higher levels of satisfaction and that health is also an important factor.

Watson et al. (2019) derive dimension weights for the Oxford Index of Multiple Deprivation using a discrete choice survey with a sample of 1,000 respondents in the UK. They ask respondents to compare hypothetical life situations with different levels of, e.g., income, employment, health, and housing quality and to state which life requires most support from the government. The results show that individuals place more weight on health, and housing quality relative to employment.

Fujiwara (2021) asks 282 respondents to compare the life situations of two hypothetical individuals and rate which would be more satisfied with their life situations. Following this, he prompts the respondent to record the level of satisfaction on a scale between 1 and 7. The study considers several dimensions: health, household income, unemployment, and ability to rely on family and friends.

Deyshappriya and Feeny (2021) use a variation of a standard discrete choice experiment, the so-called Potentially All Pairwise RanKings of all possible Alternatives (PAPRIKA) method to elicit the dimension weights of the Human Development Index in Sri Lanka. This method is an adaptive type of a discrete choice experiment that invokes the assumption of transitivity to identify and minimize the number of comparisons an individual is required to make. The weights from the method are derived using linear programming. McGillivray et al. (2023) use the same method to elicit weights in the UK.

Van Loon and Decancq (2022) ask 800 respondents to consider vignettes of possible life situations and rate their SWB in each. These vignettes describe various levels of different dimensions of life (health, income, social relations, leisure, engagement and religion) and are generated using a fractional factorial design. Once individuals have rated different vignettes, they estimate the relative weight of each dimension.

8.3. Life satisfaction method

A third strand of the literature has adopted the life satisfaction approach. Likely due to the widespread availability of life satisfaction data across countries, this strand has grown in recent years.

Decancq et al. (2015a) proposed the use of life satisfaction data to construct the equivalent income measure. They utilize the Russia Longitudinal Monitoring Survey (RLMS) from the period 1995-2003 to estimate trade-offs between income, health, housing, and wage arrears, using equation (7). They correct for unobservable heterogeneous scale use, by including individual fixed effects in their regressions.³³ Their results indicate that social welfare depends on the chosen well-being measure, with various measures (e.g., income, life satisfaction, and equivalent income) all yielding different distributions of well-being. They also document some degree of preference heterogeneity among different sociodemographic groups.³⁴

Over the past decade, a series of studies have relied on the life satisfaction method to estimate preferences for well-being measurement. These studies often compare the correlations between preference-based measures and standard well-being indicators such as income or life satisfaction, or examine the individuals identified as worst-off under different well-being measures. Decancq and Neumann (2016), for instance, compare across different well-being measures (including equivalent incomes and von Neumann-Morgenstern utilities) using cross-sectional data from the 2010 German Socio-Economic Panel (GSOEP), focusing on three dimensions: income, health, and labor status. They find strong correlations among well-being measures aggregating the three dimensions, whether preference-based or not, and weak correlations of such measures with life satisfaction or income. Decancq and Schokkaert (2016) adopt the life satisfaction method using two waves of the European Social Survey to estimate equivalent incomes across several European countries, incorporating dimensions such as health, social interactions, unemployment status, and safety. Again, they find that the choice of well-being measure matters, with some countries showing large shifts in rankings once nonmonetary dimensions are incorporated into the equivalent income. Defloor et al. (2017) compare results across different notions of subjective well-being as explained variable in equation (7) (life satisfaction, happiness, and perceived life value) and show that achievements in the dimensions of well-being matter more for equivalent incomes than individual preference heterogeneity. Yang (2018) use the life satisfaction method to estimate preferences for the dimensions of the Human Development Index based on data from the British Household Panel Survey (BHPS). These estimated preferences are then used in a “preference index,” which resembles the equivalent income approach but employs a different method to label indifference curves and enable interpersonal well-being comparisons. Ledić and Rubil (2019) estimate equivalent incomes using data from the European Quality of Life Survey (EQLS) and decompose the difference in inequality between income and equivalent income into two components: one reflecting the correlation between income and nonincome dimensions (and between income and individual preferences) and another arising from individuals’ differing positions in the equivalent income and income distributions. Decancq et al. (2020) interpret the equivalent income measure of well-being through the lens of the capability approach and apply the life satisfaction method to estimate preferences using Colombian data. They compare the identification of the worst-off under the equivalent income approach with alternative approaches, such as the Colombian Multidimensional Poverty Index (MPI) and find substantial differences. Finally, Mori and Sakamoto (2024) compare equivalent incomes with three well-being measures (income, life satisfaction, and the MPI) from the perspective of human dignity. Using data from an Indian Slum Survey in Delhi, the study finds that the life satisfaction method yields relatively low valuations for education and health.

A few studies have used the life satisfaction method to estimate preferences and compute equivalent incomes for addressing policy questions. Jara and Schokkaert (2017) assess the effects of different policy scenarios on income, self-reported well-being and the equivalent income, using an (ex ante) microsimulation tool. Their results indicate that the ranking of different policies depends on the well-being measure used. Decancq et al. (2025) use the life satisfaction approach to study the (ex post) impact of the introduction of a noncontributory social pension program (Pension 65) in Peru, highlighting its varying effects on the three main ethnic groups: Mestizo, Quechua, and Aymara. As welfare criterion they check whether the program has lifted recipients to a higher indifference curve.

Applications of the life satisfaction method illustrate how the equivalent income concept can be extended to domain-specific measures of well-being or applied in specific contexts. Schokkaert et al. (2011) and Ledić and Rubil (2021) use the life satisfaction method to estimate so-called equivalent wages, a concept that is designed to capture heterogeneous working conditions and job quality, in similar fashion as equivalent income captures differences in quality of life. Decancq and Michiels (2017) apply the life satisfaction approach to measure the concept of successful aging and compare it with objective and subjective measures of successful aging.

Reconnecting with the early literature, some recent studies have compared living standards by constructing equivalent incomes that combine information from revealed preference studies with estimates from life satisfaction regressions. Murtin et al. (2017), for example, construct equivalent incomes incorporating life expectancy and unemployment; see also Veneri and Murtin (2019) and Boarini et al. (2022). Trade-offs for the former are recovered from revealed preference studies on the value of statistical life while preferences for the latter are estimated using the life satisfaction method. The resulting equivalent income measure is utilized to measure the welfare loss from the Great Recession. They find that welfare decreased by a much larger rate for equivalent incomes than GDP per capita.

9.1. Challenges for equivalent income elicitation

Several theoretical challenges extend to empirical implementation:

• Dimensions for inclusion: Respondents may not only make different trade-offs between life dimensions but may also hold varying views on which dimensions are essential to a good life. Comprehensively listing these dimensions is likely challenging. For instance, Benjamin et al. (2014a) identify over 100 aspects of well-being in the literature that they randomly assign to respondents. Benjamin et al. (2017) suggest that this number could be closer to 2,000 aspects. With so many dimensions, evaluation becomes cognitively demanding, requiring separability assumptions to aggregate detailed aspects into a smaller set of higher-level dimensions. However, if the dimensions become too abstract, they may lose relevance to respondents’ lived experiences, reducing evaluation salience. Additionally, respondents may implicitly consider changes in dimensions not included in the stated preference task, potentially increasing error term variance and introducing systematic bias into the estimated coefficients.

• Measurement of nonmonetary dimensions: The equivalent income approach often requires quantitative measurement of nonmonetary dimensions such as health, social interactions, and environmental quality. Accurately conveying changes in these concepts in a way that avoids varied interpretations is challenging. For instance, individuals may interpret ambiguous terms such as “high,” “medium,” and “low” differently, which can add error variance and bias in estimated random utility models.³⁵ Additionally, the use of indices or arbitrary scales may introduce scaling effects, as respondents may interpret these scales differently (see Benjamin et al., 2017). This issue is particularly evident when health is measured as “self-perceived health status.”

• Interactions between nonmonetary dimensions: Interactions between dimensions can complicate the estimation of their individual contributions to well-being. For instance, Abasolo et al. (2018) report that respondents struggled with the concept of sacrificing income to attain optimal physical or mental health, as improved health might enable higher earnings or better job prospects. Respondents in their study also highlighted these interdependencies when ranking hypothetical life scenarios. Another example is the link between health and social interactions: a housebound individual may be unable to attain their ideal social situation, even if the scenario asks them to imagine otherwise. This suggests that respondents may have difficulty distinguishing between their opportunity sets and preferences.

• Monetary trade-offs: Some respondents may reject the idea of trade-offs between income and nonmonetary dimensions of life, which can lead to a high incidence of protest responses in contingent valuation surveys. Evidence on this issue within equivalent income surveys is limited. However, Fleurbaey et al. (2013) found that 20% of their 435 respondents reported they would not accept a lower income, even if it meant avoiding health issues experienced in the past 12 months.

• Selecting reference levels: Within the equivalent income approach, WTP values are elicited with respect to a reference level of each life dimension. Though this reference level is ultimately a normative choice, a practical challenge arises if the level should align with respondents’ conceptions of an “ideal” situation. This can be complex if individuals have varying views on what is the “ideal” level of a dimension. Figure 4 illustrates a scenario where an individual’s “ideal” level of social interactions ($\overline{s_i}$) is lower than the reference level set by the researcher ($\overline{s_i^{\circ }}$). If the WTP is elicited for $\overline{s_i^{\circ }}$ (i.e., $\text{WTP(}s\to \overline{s_i^{\circ }}\text{)}$) through an open-ended contingent valuation question, the researcher may not capture the maximum WTP for social interactions, which is actually $\text{WTP(}s\to \overline{s_i}\text{)}>\text{WTP(}s\to \overline{s_i^{\circ }}\text{)}$. This issue highlights challenges in defining reference levels and raises questions about the relevance of standard validity tests, such as scope sensitivity. Methods that capture more details about an individual’s indifference curve, such as ABDC, could be useful in this regard.

Figure 4.

A more fundamental challenge in eliciting equivalent income is raised by insights from behavioral economics. Accumulating evidence suggests that respondents often construct rather than retrieve well-defined preferences during the elicitation process, especially when faced with goods they have little prior experience with. This constructive process is highly sensitive to contextual cues within the survey, such as anchors and question framing (Lichtenstein and Slovic, 2006b). Payne et al. (2000) argue therefore that stated preference practitioners should view themselves as architects, aiding respondents in constructing “defensible” preferences, rather than as archaeologists unearthing pre-existing preferences.

This constructive view raises two challenges for stated preference researchers. The first is to establish the “best possible” context for respondents to elicit preferences. There is an ongoing debate within the field on this context, which we do not attempt to resolve here. Nevertheless, previous calls for a more constructive approach to contingent valuation, for instance via the use of multiattribute utility theory and decision analysis (Gregory et al., 1993), seem to have fallen short within the field in favor of shorter and more efficient multiattribute methods, such as discrete choice experiments.³⁶

The second challenge is ensuring that the theoretical concept being elicited is adaptable enough to accommodate context-dependent preferences (Bernheim, 2021). The equivalent income approach can account for context dependency to some extent by relaxing the completeness assumption (Fleurbaey and Schokkaert, 2013). This essentially implies that if A is preferred over B in one genuine choice context, but B is preferred over A in another, we lack sufficient information to establish a definitive ranking between A and B. Some studies have demonstrated how this can be operationalized using nonparametric techniques (Decancq and Nys, 2021; Burone and Decancq, 2023).

9.2. Avenues for future research

Based on this discussion, we propose several promising avenues for future research on equivalent incomes. First, there are variations of existing methods that have been relatively unexplored within the literature on equivalent income and well-being measurement more broadly:

• Nonparametric methods: Methods like the ABDC approach could be extended to accommodate multiple nonmonetary dimensions. This is relatively straightforward for measuring well-being directly, as introducing additional dimensions does not require a greater number of choice sets than those currently used. Indeed, researchers would only need to elicit the equivalent income itself: the point that is the intersection between the indifference surface and a reference vector of dimensions (see, e.g., Burone and Decancq, 2023). However, challenges may arise with the curse of dimensionality if the objective is to estimate marginal rates of substitution or entire indifference maps.

• Pivot designs: To our knowledge, aside from the small-scale study by Abasolo et al. (2018), choice experiments have not been widely employed to elicit equivalent income. This may reflect concerns that these methods do not yield individual-level preferences, a limitation shared by the life satisfaction method, which has nonetheless seen broader application in the literature. Future research could explore the potential of pivot designs. Typically, discrete choice experiments present alternatives preselected by the researcher, assuming that all individuals face the same choice situations. This may, however, be suboptimal from cognitive and contextual standpoints. For instance, respondents may struggle to relate to hypothetical scenarios far removed from their own experiences. Pivot designs, which have been used to reduce cognitive load and enhance realism in discrete choice experiments (see Rose et al., 2008), involve first identifying a respondent-specific reference alternative (e.g., their actual life situation). Attributes in the choice situations are then generated relative to this reference alternative (i.e., pivoted). For equivalent income elicitation, hypothetical life situations could be pivoted around respondents’ actual life situations. This follows a similar approach taken in contingent valuation studies on equivalent income, which compare respondents’ actual life situation to a reference situation. We foresee two advantages here: first, this approach allows efficient elicitation of marginal rates of substitution, thereby avoiding the curse of dimensionality; second, with careful experimental design, equivalent income could also be estimated nonparametrically.

• Contingent rating: Traditional applications of conjoint analysis may conflict with the assumptions of equivalent income, but some variants could leverage the ordinal nature of respondents’ ratings. For instance, as proposed by Benjamin et al. (2017), individuals could be asked to predict their life satisfaction levels in various hypothetical scenarios. Marginal rates of substitution could then be estimated for the dimensions within these scenarios.³⁷ This method extends the life satisfaction approach discussed earlier, relying on the same core assumption – namely, that ordinal preferences can be inferred from stated life satisfaction scores, known as the consistency assumption. Equivalent incomes could also be estimated nonparametrically based on these scores.

• Constructive preferences: Developing elicitation techniques that aid respondents in forming their preferences represents a particularly promising area, with both empirical and ethical benefits. Empirically, preference estimations may be more robust when respondents are supported in refining incomplete preferences and mitigating cognitive biases. Ethically, these techniques are likely to yield preferences that are more authentic and thus more deserving of consideration in policy applications. This will be the focus of a follow-up paper.

Additionally, mixed surveys that combine and compare different preference elicitation techniques may yield valuable insights. For instance, Burone and Decancq (2023) administered both ABDC and contingent valuation methods to respondents in varying sequences, comparing responses both between and within groups. They found that respondents with precise (complete) preferences gave consistent answers across methods, while those with more incomplete preferences showed less consistency. This suggests that combining different approaches may be an effective strategy for helping respondents refine their preferences during the survey process.