Why rational agents report zero or negative WTPs in valuation experiments

ABSTRACT

In surveys of the willingness-to-pay for different policies, typically there are responses that are classified as protest responses. Such responses appear to defy efforts to address the issue through best practice in the design and testing of survey instruments. The general impression from the literature is that the predominant approach to identifying and handling outliers, including protest responses, is by econometric techniques. In contrast, in this paper we focus on a simple theoretical model of agents equipped with well-behaved (textbook) preferences. The model is used to identify one type of responses that, at first glance, might be characterized as protest responses or possibly as scenario rejection. The novel explanation of the, in fact, perfectly rational behaviour relates to the total tax burden faced by a respondent. A possibly provocative finding is that the agent is searching for the constrained optimum while the survey-designer, intentionally or unintentionally, is trying to induce/convince the agent to value a second-best option. In particular, we don’t have to turn to behavioural economics, i.e. question rational choice theory, to arrive at a plausible theoretical explanation of what could be taken for protest responses.

KEYWORDS:

• Willingness-to-pay
• protest responses
• scenario rejection
• rational agents

1. Introduction

In surveys of the willingness-to-pay (WTP) for different policies, typically there are responses that are classified as protest responses. A protest bid is defined as not stating the true WTP value for the good in question for whatever reason (Frey and Pirscher 2019). Usually, all participants stating zero as willingness to pay and give a reason why they refuse to pay (i.e. do not have a genuine WTP of zero) are labelled as protesters. According to the recent study by Frey and Pirscher (2019) the percentage of protesters in contingent valuation surveys is substantial; around 20 percent across many studies. As Atkinson et al. (2012) observe protest rates appear to ‘defy’ efforts to address the issue through best practice in the design and testing of survey instruments. According to Brouwer and Martin-Ortega (2012), the identification and treatment of protest response in stated preference research such as contingent valuation is an underdeveloped area.

The National Oceanic and Atmospheric Administration (NOAA) expert panel (Arrow et al. 1993) suggests not pushing respondents to choose between ‘Yes’ and ‘No’. An option of ‘No-answer’ should be offered in the discrete choice stage for respondents who cannot clearly decide between ‘Yes’ and ‘No’. The recent follow-up to the Panel by Johnston et al. (2017) addresses the issue of behavioural or response ‘anomalies’ including protest responses. They claim that where clear symptoms of systematic anomalous responses have been identified from similar studies in the literature or during pretesting, stated preference studies should be designed to avoid these anomalies. When this is not possible, the surveys should be designed to investigate anomalous responses and analyses should use the information to investigate the effects. According to Johnston et al. (2017, 364) the main concern for data analysis is how protest responses and outliers should be handled in the estimation of values. Approaches include dropping observations, conducting analyses with and without these observations, and developing models that attempt to control for factors that affect protests (Meyerhoff and Liebe 2010, 2014).

Thus, the general impression from the literature is that the predominant approach to identifying and handling outliers, including protest responses, is by econometric techniques (Meyerhoff and Liebe 2010, 2014). In contrast, in this paper, we focus on a simple theoretical model to identify one type of responses that, at first glance, might be characterized as protest responses or possibly as scenario rejection (Johnston et al. 2017, 363). The novel explanation of the, in fact, perfectly rational behaviour relates to the total tax burden faced by a respondent.

Thus, we do not need to draw on behavioural economics (Thaler 2016). Such an approach would point at the possibility that humans are incapable of making rational decisions when faced with involved survey designs. We do not question that such human failures could be important explanations of actual behaviour. We just argue that it is not necessary to take that step to understand why agents come up with seemingly irrational responses.

We consider an agent equipped with well-behaved (‘textbook’) preferences. The commodity to be evaluated is a well-defined pure public good. Thus, we consider a case which corresponds to an incentive-compatible (consequential) survey; refer to Carson and Groves (2007, 2011). We show that what might be interpreted as a protest bid in fact is a logical response by a rational agent facing an overwhelming tax burden.

The paper is structured as follows. In Section 2 the model is developed and used to derive the results. Section 3 adds a few concluding remarks. An appendix deriving one of the results used in Section 2 is added.

2. Model and results

Consider an individual paying t percent of her fixed income in taxes in exchange for z⁰ units of the commodity under consideration and G⁰ units of other services provided by the public sector. The project under evaluation is an increase in the provision of z from z⁰ to z¹; for simplicity, we interpret z as a pure (environmental) public good, but the analysis is valid also for other types of commodities that are not priced in markets, such as health quality and life expectancy. Furthermore, let us assume that the individual feels that she does not get bang for the buck in the initial or pre-project situation. Hence, it holds that:(1) $V(p,m\cdot (1-t),z^0,G^0)=V(p,m-\mathrm{\Delta }T,z^0,G^0)<V(p,m,z^0,0),$(1) where V(.) denotes a well-behaved indirect utility function, and p denotes a vector of goods prices. Because pre-tax income m is fixed, the tax payment, denoted ΔT, is easily calculated. To simplify notation without any loss of generality, it is throughout assumed that z⁰ = 0 but the symbol z⁰ is kept for the sake of clarity; recall that the focus is on the change in the provision of z.

According to Equation (1), the individual is worse off than without any public services. Nevertheless, the individual has to accept whatever taxes the government imposes. However, there is a strictly positive tax rate, denoted t^G , such that the individual is indifferent between having (z⁰, G⁰) and having (z⁰, 0):(2) $V(p,m\cdot (1-t^G),z^0,G^0)=V(p,m-\mathrm{\Delta }{T}^G,z^0,G^0)=V(p,m,z^0,0),$(2) where t^G < t, and ΔT^G denotes the tax payment that makes the individual indifferent between the two options. It is straightforward to demonstrate that the amount ΔT^G corresponds to an area under an income-compensated (Hicksian) WTP-curve for G between 0 and G⁰. (Whether G⁰ exceeds the Samuelson level for the efficient provision of G or not depends on the cost structure in providing the services.)

Next, consider an increase in z, assuming that the marginal utility of the commodity is strictly positive on the considered range. Then, there is a tax rate t^Gz > t^G such that:(3) $V(p,m\cdot (1-t^{Gz}),z^1,G^0)=V(p,m\cdot (1-t^G),z^0,G^0)=V(p,m,z^0,0).$(3) Note that z = z¹ (z = z⁰) in the left-hand side (middle) utility function.

Next, convert the change in the tax rate to an amount of money:(4) $\begin{array}{rl}& V(p,m\cdot (1-t^{Gz}),z^1,G^0)=V(p,m-\mathrm{\Delta }{T}^G-C{V}^z,z^1,G^0)=\\ & V(p,m-\mathrm{\Delta }T-C{V}^{\mathrm{\Delta }z},z^1,G^0)=V(p,m,z^0,0),\end{array}$(4) where CV denotes a compensating variation.¹ The measure CV^z evaluates the change in z, conditional on paying a ‘fair’ tax for other public services. In contrast, CV^{Δ z} evaluates the change, conditional on the actual initial tax payment for G⁰. Because disposable incomes, after paying for the extra provision of z, must be the same in both of the associated middle expressions in Equation (4), CV^{Δ z}  = CV^z  + ΔT^G – ΔT. Therefore, CV^{Δ z} ⋛ 0; the sign depends on the magnitude of the ‘excess tax’ ΔT – ΔT^G ; see Equation (4’) below for a numerical illustration.

Hence, it is not necessarily true that the individual reports a positive WTP although, by assumption, the marginal utility of the public good is strictly positive. This is not due to a ‘preference failure’, nor to a poorly designed valuation experiment. The reason is that in evaluating Δz she looks at the total ‘package’ of goods and services delivered by the government. Therefore, she first deducts her overpayment of taxes before paying for Δz. Typically, the project under evaluation is very small relative to the total tax payment. This implies that even if t exceeds t^G by a tiny fraction, CV^{Δ z} could be strictly negative.

A simple numerical illustration is provided by the following (Stone-Geary type of) indirect utility function:(4\prime) $V(.)=ln(m\cdot (1-t\left)\right)+ln(G+1)+ln(z+1),$(4\prime) where the price of the single private good is set equal to unity (and any constant associated with the utility provided by this good is suppressed). Both G and z are equal to zero in the status quo. Set m = 10³, G⁰ = 1, and z¹ = 1/100. Then, t^G  = 1/2, and t^Gz  = 51/101. Thus, CV^z is around 49,5 and according to this comparison the agent is willing to pay for the extra provision of the public good. However, if the agent faces an initial tax rate t equal to 51/101, she reports a zero WTP, i.e. CV^{Δ z}  = 0. If t > 51/101, she reports CV^{Δ z} < 0. For example, if t = 6/10, then CV^{Δ z} ≈ – 950,5. Nevertheless, the marginal utility of z is strictly positive also when evaluated at z¹. (Trivially, the WTP would be negative if the agent considers z as a public bad for which ∂V/∂z < 0.)

Nevertheless, the researcher might classify the strategy as an example of scenario adjustment or rejection, in which respondents do not interpret scenarios as intended and thus value something different from the intended item or outcome; see Johnston et al. (2017, 327). To elaborate upon this issue, suppose the respondent can be convinced to pay for Δz conditional on her initial tax rate and G. Now, she makes the following estimation:(5) $V(p,m\cdot (1-t^z),z^1,G^0)=V(p,m-\mathrm{\Delta }T-CV,z^1,G^0)=V(p,m\cdot (1-t),z^0,G^0),$(5) where t^z > t, and t·m = ΔT in the middle expression. CV is the conventional WTP-measure. It assumes that the respondent can be convinced to disregard whether she is paying too much in taxes or not. In any case, CV > CV^{Δ z} because the right-hand side utility in Equation (5) falls short of the right-hand side utility in Equation (4) when t > t^G ; see also Equation (1). Moreover, CV^z ≥ CV, with the equality holding if preferences are quasi-linear; see the appendix for details. With this exception, CV^z > CV > CV^{Δ z} . However, if the agent, in contrast to the maintained assumption, perceives that t = t^G , then CV^z  = CV = CV^{Δ z} .²

3. Concluding remarks

This paper points at a theoretical reason, in contrast to many ad hoc suggestions or econometric analyses, why what might be taken for a protest bid instead is a logical response to WTP-questions when the respondent already perceives she is paying too much in taxes. Non-participation, i.e. reporting a zero WTP, occurs as a special case of our model. Reporting a large negative WTP is another possibility, depending on the magnitude of the perceived excess burden of taxes. Thus, to understand such responses in surveys it is not necessary to invoke a ‘preference failure’.

Even if Equation (5) provides the intended scenario (comparison between project and baseline) in a survey, it remains to show that this is the relevant one from a policy perspective. What researchers might overlook is the fact that the scenario considered in Equation (4) represents a constrained optimal allocation of scarce resources; we speak of constrained because G (and z) may differ from their optimal levels. In contrast, it can be claimed that Equation (5) takes the economy further away from its optimum. It is far from self-evident that it is good practice to classify a (constrained) optimal strategy as scenario rejection and hence consider ‘strange’ responses as protest responses.

Obviously, in designing a valuation scenario focus is on providing an accurate and detailed description of the considered project and its properties. Seemingly, the status quo is familiar to respondents. This paper illustrates that this is far from self-evident; rather, the baseline is open to different interpretations. Therefore, the discussion here underscores the importance of carefully designing also the baseline or status quo; this is also emphasized by, for example, Johnston et al. (2017). In any case, even if the baseline in Equation (5) is designed according to best practices, one cannot rule out that some agents oppose or ignore this baseline, given that they perceive that they already are paying too much for the services provided by public sector.

There is a further important twist that is worthwhile to point out. It is often observed that respondents are unable to report a unique WTP. A common suggestion is that this outcome is due to preference uncertainty. Hence, it is argued, a respondent is only able to report an interval for her WTP. A large and growing literature is devoted to developing payment vehicles for this case and to determining the width of the interval. For recent applications, the reader is referred to Angelov and Ekström (2017) and Mahieu et al. (2017). However, a respondent who does not experience preference uncertainty but is faced with the option to report a payment interval might choose to report CV^{Δ z} as the lower and CV as the upper endpoint of the interval.

The outcome observed in this paper should not be confused with hypothetical bias in stated preference studies. It arises when respondents report a willingness to pay that exceeds what they actually pay using their own money in laboratory or field experiments (Loomis 2011). Such a bias does not occur because agents are equipped with well-behaved textbook preferences, and come up with unique numbers, conditional on scenario specifications.

The approach used here has empirically testable implications. These could help researchers to detect and handle the kind of responses discussed in this paper. In surveys, let the respondent assess (on a scale) whether she gets bang for the buck. This could provide some evidence on what might seem to be protest bids or outliers. Such a variable could possibly also enter as an explanatory variable when estimating a WTP-function, although there could be an endogeneity problem. Another option is to allow the respondent to locate a fair tax payment, i.e. the tax rate denoted t^G or the corresponding number of tax dollars. Then, given this tax or the corresponding amount of money, ask the respondent to pay for the considered policy proposal. In a second phase, the respondent is asked to value the proposal, conditional on what she currently pay in taxes, i.e. the tax rate denoted t or the corresponding number of tax dollars. Possibly, in order to avoid ‘anchoring’ on the initial amount (Johnston et al. 2017, 347), split samples, where one sample is asked to value Equation (4) and the other sample Equation (5).

In experiments researchers could let agents face a bundle of two commodities, one capturing the commodity/project to be evaluated, the second commodity representing other public services. Let participants pay a fixed amount for the second commodity, then pay for the commodity under evaluation. The amount paid for the rest of public services could randomly range from what agents perceive is a fair price to ‘forcing’ them to pay too much. The maintained hypothesis is that the outcome will reflect the WTP-measures derived in this paper.

Acknowledgements

We are grateful for detailed comments and suggestions by an anonymous referee. Kriström acknowledges support from the Marianne & Marcus Wallenberg Foundation, Project MMW 2017.0075 ‘The right question – new ways to elicit quantitative information in surveys.’

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Marianne and Marcus Wallenberg Foundation [grant number MMW 2017.0075].

Notes

1 Thus, the valuation question is intended to be stated in monetary units, not as an increase in the tax rate.

2 In terms of the example in Equation (4’), all three measures coincide for t = 1/2. For t above it holds that CV^z > CV > CV^Δz.

3 Quasi-linear example: v = m·(1 – τ) + ln(z + 1) + ln(G + 1). Set m = 5, and the remaining parameters as below Equation (4’). Then, t^G = ln(2)/5, and CV = CV^z = ln(101/100). If τ = t = 2/10, then CV^Δz ≈ –0,3. If t = t^G = ln(2)/5, then CV^z =CV = CV^Δz.

Appendix

In order to sign the difference between CV and CV^z , add k>0 to CV to obtain:(A.1) $\begin{array}{rl}& V(p,m\cdot (1-t)-CV+k,z^1,G^0)=V(p,m\cdot (1-t^G)-C{V}^z,z^1,G^0)=\\ & V(p,m,z^0,0)>V(p,m\cdot (1-t),z^0,G^0).\end{array}$(A.1) Suppose ∂V/∂m = V_m is constant (quasi-linear preferences). Then, it is easily verified that k adds m·t and deducts m·t^G to increase utility from its initial level in the second line. Hence CV = CV^z .³ If ∂V_m/∂m < 0, then k < m·(t – t^G ) and CV < CV^z ; recall that k is evaluated at a lower disposable income than, for example, m·t^G in line one.