2.1. Mental accounting

Thaler (Reference Thaler1985) first proposed mental accounting theory as a possible explanation for non-standard behavior. According to this theory, agents have different mental accounts for topically and temporally separate purchases. This idea implies that even if agents have a rational preference, their choices can be different from those of a standard, neoclassical agent due to use of mental accounts.

In this paper, we consider a model of mental accounting with only topical separation of psychological accounts.Footnote ¹ For example, consumers can have different mental accounts for food, recreation, and education. The critical assumption of the model is that money is not fungible in these different mental accounts.

Consider an agent who maintains $n$ mental accounts that are topically separate. For simplicity, assume that $\mathbf{x}_{i}$ denotes the vector of goods in account i, and $u_{i}(\mathbf{x}_{i})$ denotes the utility function for account $\textit{i}$. Suppose that the total utility is additive on all accounts and is given by

(1)\begin{equation} U(\mathbf{x}_{1} ,\dots, \mathbf{x}_{n}) = \sum_{i=1}^{n}u_{i}(\mathbf{x}_{i}). \end{equation}

Let $M$ be the total income of the agent in a given period, and $\theta_{i}$ denotes the proportion of income they have set aside for account $i$, that is, $\theta_{i}M$ denotes the budget for account $i$.Footnote ² Thus, the budget constraint of the agent with a mental account would be different from the same for a neoclassical agent. Let $\mathbf{p}_{i}$ denote the price vector in account $i$ and $\mathbf{x}_{i}$ denote the consumption vector. Then we can rewrite the budget constraints as follows:

(2)\begin{align}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\ NC: \quad \sum_{i}\mathbf{p}_{i}\mathbf{x}_{i} \leq M \end{align}

(3)\begin{align} MA: \quad \mathbf{p}_{i}\mathbf{x}_{i}\leq \theta_{i}M \quad \forall i\in\left\lbrace 1, \dots, n\right\rbrace, \end{align}

where $\mathbf{p}_{i}\mathbf{x}_{i}$ denotes the total expenditure in account $i$. Inequality (2) denotes the budget equation for a neoclassical agent (NC), and the second set of inequalities (Equation (3)) refers to an agent with mental accounting (MA).

We extend this model to incorporate non-market goods for which prices are not available. Suppose that the account $j$ contains only two goods, a non-market good $x_{j}$ and a composite good $x_{-j}$. For simplicity, we write the utility function for account $j$ as

(4)\begin{equation} u_{j}(\mathbf{x}_{j}) = v(x_{j}) + x_{-j}. \end{equation}

That is, the utility function in account $j$ is quasi-linear in the non-market good $x_{j}$.Footnote ³ Instead of a price, we assume that the consumer is offered a choice of a given amount $\bar{x}_{j}$ of the non-market good $x_{j}$. The agent can respond “yes” or “no” to the offered bid $b$ for $\bar{x}_{j}$. Let $v(\bar{x}_{j})$ and $v(0)$ denote the levels of utility when the consumer chooses “yes” or “no”, respectively. Under the neoclassical paradigm, the agent would be willing to opt for $\bar{x}_{j}$ if and only if

(5)\begin{equation}\sum_{i\neq j} u_{i}(\hat{\mathbf{x}}_{i}) + v(\bar{x}_{j}) + \hat{x}_{-j} \geq \sum_{i\neq j} u_{i}(\hat{\mathbf{x}}_{i}^{\prime}) + v(0) + \hat{x}_{-j}^{\prime} \end{equation}

(6)\begin{equation} \sum_{i\neq j} \mathbf{p}_{i}\hat{\mathbf{x}}_{i} + b + p_{-j}\hat{x}_{-j} = \sum_{i\neq j} \mathbf{p}_{i}\hat{\mathbf{x}}_{i}^{\prime} + p_{-j}\hat{x}_{-j}^{\prime}\leq M, \end{equation}

where $\hat{\mathbf{x}}_{i}$ and $\hat{\mathbf{x}}_{i}^{\prime}$ in Equations (5) and (6) denote the optimal choices for all other accounts $i\neq j$; $\hat{x}_{-j}$ and $\hat{x}_{-j}^{\prime}$ denote the optimal choices in account $j$, excluding the non-market good under “yes” or “no” options, respectively; and $p_{-j}$ refers to the price in account $j$ excluding the non-market good. Thus, the NC agent would say “yes” to bid $b$ if the non-market good improves their total utility, subject to their overall budget constraint.

However, the agent faces a different choice problem under the mental accounting framework. Note that the choice of “yes” or “no” in account $j$ does not affect the choices in any other account, since the MA agent has separate mental accounts for different types of expenditure. Thus, the MA agent would be willing to opt for $\bar{x}_{j}$ if and only if

(7)\begin{equation} v(\bar{x}_{j}) +x_{-j} \geq v(0) + x_{-j}^{\prime} \end{equation}

(8)\begin{equation} b+ p_{-j}x_{-j} \leq \theta_{j}M;\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \end{equation}

(9)\begin{equation} p_{-j}x_{-j}^{\prime} \leq \theta_{j} M,\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\end{equation}

where $x_{-j}$ and $x_{-j}^{\prime}$ denote the optimal levels of all other goods except the non-market good $x_{j}$ in account $j$ under “yes” or “no” choices, respectively. The inequality in Equation (7) implies that the net value of opting for the non-market good in account $j$ is better than not opting for it. The inequality in Equation(8) ensures that the budget constraint for account $j$ is satisfied. Thus the MA agent would say “yes” to bid $b$ if the non-market good improves their total utility, subject to the budget constraint in the relevant mental account $j$.

To explore these inequalities further, assume that $p_{-j} =1$.Footnote ⁴ If $x_{-j}^{\prime}-x_{-j}\geq b$, then we can rewrite Equation (7) for the MA agent as

(10)\begin{equation} v(\bar{x}_{j}) + \theta_{j}M -b \geq v(0) + \theta_{j}M. \end{equation}

Upon simplification, we can rewrite the optimization condition of MA agents as

(11)\begin{equation} \quad\quad v(\bar{x}_{j}) -b \geq v(0) \end{equation}

(12)\begin{equation} b \leq \theta_{j}M - x_{-j} \equiv M_{j}. \end{equation}

Combining the two inequalities in Equations (11) and (12), we find that the agent would be willing to opt for “yes” if and only if the following inequality holds:

(13)\begin{equation} b \leq \min \left\lbrace M_{j}, v(\bar{x}_{j})-v(0) \right\rbrace. \end{equation}

Using this framework, we want to investigate the scope sensitivity of an MA agent. In this model, we only consider the external scope. To define the external scope, we consider two different levels of the environmental good offered in account $j$, such that one level is strictly higher than the other. Proposition 1 explains the impact of mental accounts on the sensitivity of external scope.

Proof. Consider two possible levels of the non-market environmental good $\bar{x}^{1}_{j}$ and $\bar{x}^{2}_{j}$ and a bid $b$. If $\bar{x}^{1}_{j}$ denotes a strictly higher amount of environmental good, then by strict monotonicity of $v(x_{j})$,

(14)\begin{equation} v(\bar{x}^{1}_{j}) \gt v(\bar{x}^{2}_{j}). \end{equation}

Thus, if $v(\bar{x}^{2}_{j}) - v(0) \gt b$, then with probability 1 we have $v(\bar{x}^{1}_{j}) -v(0) \gt b$.

However, we also need to consider the budget constraint of the MA agent here. Suppose that $M_{j}$ is sufficiently small such that

(15)\begin{equation} b \gt \theta_{j}M -x_{-j} \equiv M_{j}. \end{equation}

This can happen if either $\theta_{j}$ is sufficiently small, i.e., the consumer has allotted a small budget for account $j$, or $x_{-j}$ is sufficiently large, i.e., the consumer has already spent a significant amount out of account $j$.

Under Equation (15), the optimal choice for the MA agent would be “no” under both offers $\bar{x}^{1}_{j}$ and $\bar{x}^{2}_{j}$ as given in Equations (16) and (17),

(16)\begin{equation} b \gt \min \left\lbrace M_{j}, v(\bar{x}^{1}_{j})-v(0) \right\rbrace \end{equation}

(17)\begin{equation} b \gt \min \left\lbrace M_{j}, v(\bar{x}^{2}_{j})-v(0) \right\rbrace. \end{equation}

Thus, the probability of choosing “yes” would be zero in both cases when $M_{j}$ is sufficiently small, i.e., when Equation (15) is satisfied.

This shows that, even if $v(\bar{x}^{1}_{j}) \gt v(\bar{x}^{2}_{j})$, the probability of choosing “yes” is not strictly higher when $v(\bar{x}^{1}_{j})$ is offered for bid $b$. Hence, proved.

Note that the same would not be valid for an NC agent. Since they do not use separate mental accounts, they would be willing to choose “yes” if the benefit of doing so is higher than the cost, assuming that the budget constraint is not binding. That is, if $M$ is sufficiently high compared to $b$.

2.2. An illustrative example

Consider an agent who decides whether to pay for a non-market good in a single bounded dichotomous choice questionnaire. The agent chooses whether to pay a bid $b$ based on two principles: first, the standard neoclassical argument, given by Equation (18) as

(18)\begin{equation} w \geq b, \end{equation}

where $w$ denotes the marginal value of the environmental good, that is, $v(x_{j})-v(0)$, and $b$ denotes the bid price. If $w \lt b$, that is, if the agent’s WTP is less than the proposed bid, they would not contribute. Second, whether the total expenditure, that is, the bid amount $b$ exceeds the amount $M_{j}$ (that is, $\theta_{j}M-x_{-j}$, the residual budget for the environmental good) specified by the mental account $j$ that contains the environmental good, given as

(19)\begin{equation} b \leq M_{j}. \end{equation}

Motivated by our specification, consider an external scope test in this questionnaire, where subjects are offered one of the two scopes. The large scope is one unit of the environmental good, and the small scope is one-third of the environmental good.

Note that if $w$ is sufficiently higher than the bid, but $M_{j}$ (the residual budget of the environmental good) is sufficiently small, the second constraint is binding, while the first is not. For example, suppose that a respondent has a marginal value of $ w = 900$ for one unit of the environmental good. This implies that if offered to restore only one-third unit of the environmental good, their marginal valuation would be $w=300$. Consider now a bid price of $ b=250$. If the respondent does not have mental account constraints, they would be willing to pay regardless of how much environmental good is offered. In summary, for any $b\in (300, 900)$, the NC respondents will only pay for one unit, not a one-third unit of the environmental good. Using similar logic, for any $b \lt 300$, the NC respondent will pay for both; and, if $b \gt 900$, the NC respondent will pay for neither.

Now consider a respondent who has a residual budget of $M_{j} = 150$ for the environmental good in question. If $b=250$, they will not pay, irrespective of the amount of the environmental good offered, whereas if $M_{j}=300$, they will pay for both amounts, again irrespective of the amount of the good offered. Thus, a strict mental accounting constraint can create sensitivity to the external scope.

3.1. Survey design and data collection

Data from the Sardana (Reference Sardana2019) field experiment was used for empirical estimation. The field experiment was based on an on-site survey sample of 1,027 visitors. Tourists visiting three adjoining sites (National Park and Wildlife Sanctuaries that are declared protected areas) to the coffee plantations, namely Nagarhole National Park, Iruppu Falls, and Mandalpatti, in the Kodagu district of Karnataka, India, were intercepted. A random sample composed of an equal number of observations from the three sites was collected. The survey was conducted on weekends in January 2016. The respondents were randomly selected at the ticket counter or at the exit gate. The policy described to the respondents was to raise revenue to restore native trees in private coffee plantations. For this purpose, a coercive payment was introduced, in the form of a surcharge on the entrance fee to protected areas, which would be levied on all respondents above the age of 18 years, if they voted in favor of the restoration program. The survey instrumentFootnote ⁵ was randomized according to seven bids and two split samples. There were a total of 14 schedules for every instrument that were randomized among respondents.

Fifty-six per cent of respondents said “yes” to paying the surcharge and forty-four percent said “no”. The binary response to the WTP question is the dependent variable in our analysis. Additionally, information on socio-economic variables and site-specific variables was collected. Table 1 in Section 3.4.2 describes the variables used in our analysis and their summary statistics.

Table 1.

Description of variables used for statistical analysis ( $n=1027$)

3.2. Measuring mental accounts

In the study, respondents’ valuations for restoring native trees is measured using the CV method. The respondents were asked if they would be willing to pay the offered bid (in the form of a surcharge above the entrance fees). In split sample I, for every visitor who paid the higher entrance fee, one native tree would be restored. In split sample II, for every visitor who paid the higher entrance fee, one-third of a native tree would be restored. Therefore, split sample I is the larger scope (with more of the environmental good) and split sample II is the smaller scope (with less of the environmental good) in our study.

To apply the mental accounting model in this context, we need to measure the relevant mental accounts that respondents might be using when deciding how much to pay for a restoration program in the form of a surcharge. Since the surcharge will be paid on the entrance fees to the national park, we assume that the subjects put the expenditure for it in their recreational budget. In the absence of a direct measure of the recreational budget, we use the spending data, namely total trip expenditure (amount spent during their trip, excluding entrance fees to the park) and the entrance fees paid by the respondents. Using their spending data, we can show that subjects who are more likely to be constrained by their mental account for recreational goods are less likely to pay for the restoration program.

Egan et al. (Reference Egan, Corrigan and Dwyer2015) tested the mental accounting hypothesis in a CV model by providing a split sample treatment where payment schedules differ. They found evidence that mental accounting explains a modest difference between one-time and annual WTP when presented with ongoing payments. Since in our study, the time dimension across the split sample is irrelevant, a similar analysis would not be informative. To implement the idea of mental accounting in our empirical model, we need to know the mental account that the subject had assigned for the environmental good and how to estimate it. Unfortunately, these data were not collected in the original survey (Sardana, Reference Sardana2019). To avoid this issue, we instead considered data regarding the actual financial decision that we can observe in the data.

In the survey, subjects were asked to report their payment of the entrance fee to the national park. Since the environmental good in question (native tree restoration) enhances the recreational experience of visiting national parks, we assume that both these expenditures – the entrance fee and the contribution to restoring native trees (as a surcharge above the entrance fee) – would belong to the same mental account, which we refer to as $R$ (for recreation). In addition, in the field experiment, subjects were asked about their WTP to restore native trees through a surcharge on the entrance fee, which further strengthens our argument.

Suppose that an agent has a residual budget of $M_{j} = 400$ for the account $R$ before paying the entrance fee. If they now paid the entrance fee of $f = 250$, they would have only $150$ remaining in the account and would not be willing to contribute for the restoration program if the bid-amount (for the restoration program in the form of surcharge) was $b=250$. On the other hand, they might be willing to contribute to the restoration program if they pay only $f = 75$ and are left with $325$. Assuming that both types of expenditures are part of the same account, we can use the heterogeneity of one to learn about the other, assuming $R$ is known.Footnote ⁶

We argue that the total trip expenditure, called $T$, can proxy for the unobserved value of $R$. For each respondent, we measure the ratio of the entrance fee paid ( $f$) to the total trip expenditure ( $T$).Footnote ⁷ Conceptually, the residual budget left to pay the surcharge would be given by $R-T-f$; alternatively, it would be $\frac{R}{T}-1-\frac{f}{T}$. If we assume $\frac{R}{T}$ to be constant for our subjects (as we assume $T$ is a good proxy for $R$), a higher $\frac{f}{T}$ would imply a lower residual budget left to pay the surcharge.Footnote ⁸

Based on this ratio ( $\frac{f}{T}$), we divide the entire sample into seven expenditure classes with a range of subjects who spend from 1–8 per cent to more than 40 per cent of their trip expenditures on visits to the national park.Footnote ⁹

3.3. Predictions

We conjecture that agents for whom the proportion of entrance fee to the total trip expenditure is high, that is, who belong to a higher expenditure class would be more likely to be constrained by the mental account, that is, $R-T-f$. Consequently, the probability of choosing “yes” would be more likely to be lower for the higher expenditure classes. Since MA constraints directly affect WTP for agents, we would instead consider the probability of choosing “yes” for a random $b$ offered to agents. Thus, using Proposition 1, we make the following predictions.

Note that standard neoclassical arguments cannot explain this decreasing pattern.Footnote ¹⁰ If we argue that agents in a higher expenditure class have a higher valuation for recreational activities, then they will be more likely to say “yes”. Moreover, Proposition 1 also shows the impact of mental accounting on scope insensitivity. If mental accounting constraints are binding, that is, $M_{j} \leq w(x_{j})$, then the probability of saying “yes” would not increase monotonically for $x_{j}$ offered, implying the following prediction.

Following Proposition 1, when respondents are subject to binding mental accounting constraints for the environmental good, the relevant inequality for decision making becomes whether $b\leq M_{j}$. Thus, even if the value of the offered good is higher than the bid amount, the agent will not choose “yes”.