Payment Decoupling, Prepurchase, and Credit Card Purchases		55

preferences, we call this a framing effect. In this case, people show a preference for having losses framed in an integrated way and gains framed in a segregated way. We call this a preference for hedonic framing. Although people show a preference for hedonic framing, it appears they either do not have the ability to conduct or a preference for hedonic editing. Thus, they experience integration or segregation based on how the events are presented to them and do not necessarily control this presentation.

Up until now, we have treated the value function much like a standard utility function. More generally, however, the literature on mental accounting acknowledges that people feel some degree of loss or pain for the money traded away in a transaction, and this pain should enter into the value function. Thus, if purchasing a good, one obtains the value of consuming the good and feels the pain of losing the money associated with the price. Together the gain from consumption and loss from paying is the acquisition utility. The person will also experience any transaction utility. If the pain of paying the price is integrated with the consumption value, then acquisition utility may be written as vax − p, where va is the acquisition value function, x is the monetary equivalent value of consuming the good, and p is the price paid. We may consider x to be the amount one would be required to pay for the experience of consumption that would leave one indifferent between consuming and not consuming. If one segregated the pain of payment from the joy of consumption we could write acquisition utility as vax + va− p.

One’s transaction utility could be written as vt − p + pr , where vt is the transaction utility value function and pr is the reference price, or the price one feels is a fair price to pay for the object. It is generally assumed that people integrate consumption and payment, so that the value of purchase can be written as vax − p + vt− p + pr. Alternatively, if sufficient time passes between purchase and consumption, it may be that at the time of consumption the consumer disregards the payment altogether when consuming, called payment decoupling. Such payment decoupling might explain why people feel more indulgent when using credit cards than when using cash for payment. If a person integrates the price and consumption, he or she should purchase the good so long as vax − p + vt− p − pr is greater than the value obtained for the best alternative use of the money. If one disregarded price through payment decoupling, one need only find that vax is greater than the best alternative.

Payment Decoupling, Prepurchase, and

Credit Card Purchases

According to the theory of mental accounting, when an item is purchased, a person figuratively opens a mental account that may be closed when the good is consumed. This account is evaluated through the value functions to determine if the account has a positive or negative balance. Drazen Prelec and George Loewenstein propose that transaction and consumption activities often bring these accounts to mind, causing additional pleasure when the account balance is positive or additional pain when the account balance is negative. Thus, someone who has taken out a loan for a car might recall the outstanding balance on the loan when he drives. Because the loan has not been paid, the framing of the loan and driving events forces him to integrate the debt and the driving, making the experience of driving unpleasant. Alternatively, someone who has

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paid for the car outright does not consider the expense of the car when driving. Rather, he only considers the consumption experience, making driving a much more pleasant experience. Payment decoupling leads one to write off past payment at the time of consumption, while recognizing the weight of future payments. Prelec and Loewenstein speculate that items that provide repeated consumption (such as a clothes washer) allow one to stomach future payments, whereas single-use items (e.g., a vacation) do not. They propose that people prorate future payments over future expected consumption experiences. In other words, consumers consider the number and quality of the anticipated future consumption episodes when considering the number and size of the future payments. Thus, a consumer facing future payments on a durable good might consider the value of the account

v	δt x − p ,	3 7
	t = 0

where x is the value of consumption in any time period, p is the payment on debt for the good in any period, δ is a discount factor, and the index t represents time. If instead the good is consumed once but paid for over time, then after consumption has already taken place, the account is evaluated as

v	δt − p .	3 8
	t = 0

If the consumer anticipates this future dread of payment when consumption no longer occurs, then prorating payment can lead consumers to prefer to prepay for goods that can be consumed only once but potentially prefer to buy durable goods on credit.

By prorating, the consumer considers the future payment and the future consumption when evaluating the account. Thus, if the future consumption is expected to be at least as good as the forgone money, consumers evaluate the account as having a positive balance even if there is outstanding debt. Alternatively, if there is no future consumption, the consumer considers only the future payment, ignoring (or at least discounting) the prior consumption when evaluating the account, which thus has a negative balance. Prelec and Loewenstein asked participants whether they would prefer to prepay for a vacation at $200 a month for six months or to pay upon returning at $200 a month for six months. Additionally they asked participants whether they would prefer to prepay for delivery of a washing machine at $200 a month for six months or pay after delivery $200 a month for six months. On average participants preferred to prepay for the vacation and preferred to buy the washing machine on credit. Thus, Prelec and Loewenstein find support for the notion of payment decoupling together with prorating.

Similar motives can drive credit card spending. Intuitively, credit cards are often used for purchases of single-use goods, which seems counter to the principles outlined by Prelec and Loewenstein. Some evidence suggests that credit cards allow consumers to

Investments and Opening and Closing Accounts		57

ignore the cost of purchase while consuming, much like the prepayment option described above. Perhaps, by aggregating a large number of insignificant purchases in one bill, the credit card serves to effectively decouple payment from consumption, despite the knowledge of future payment. In effect, the bill obscures the costs of each individual purchase, thus eliminating payment from the account. Thus, one may enjoy one’s impulse purchase without the dread of future payment.

Investments and Opening and Closing Accounts

One of the primary suppositions of the mental accounting model is that consumers have a desire to close accounts only when they have a positive or zero balance. Consider a person who makes an investment. The initial cost of the investment sets a natural reference point for the decision maker. Any return above the reference point may be considered a gain, and any return below the reference point may be considered a loss. If people are motivated to close accounts that have a positive or zero balance, they are more likely to sell an investment that has made a gain than one that has made a loss. For example, selling a house that has declined in value forces the seller to realize the money loss he incurred. Alternatively, holding onto the house and waiting for the price to come back up above the purchase price can allow the seller to forgo (for a time) the pain of the loss in investment. Selling the investment would instead close the mental account, solidifying the reality of the losses.

This effect is potentially one of the causes of the sunk-cost fallacy, causing people to continue with investments or activities that are losers in hopes of obtaining a balanced mental account. Were these sunk costs to persist in one’s memory forever, the accounts may be at a loss in perpetuity, and the person would continue with bad investments forever, hoping to eventually balance the account. Luckily, this does not appear to be the case. Rather, people depreciate the cost of investments over time in a process called payment depreciation. Over time, the pain of payment diminishes, and they feel less and less motivated by the initial payment. They get over it. Recall the example from Hal Arkes and Catherine Blumer where subjects were charged different prices for theater ticket subscriptions. Although there was substantial difference in attendance in the first half of the theater season, there was no real difference in the second half of the season. By this time, the additional money spent on tickets had been fully depreciated, and both sets of participants were equally motivated to attend. Suppose a person paid p at time t = 0 for purchase of a durable good (e.g., shoes). Suppose further that value of a consumption incident for the durable good is equal to x. Then, at any point in time, consuming the good would yield utility that may be written as vax − pδt, where δ is a discount factor that is positive and less than 1. Thus, as time passes, the price paid plays less and less of a role in acquisition utility gained from consumption as δt gets smaller and smaller. Further, the price is depreciated in transaction utility as vt− p + prδt, so that eventually accounts may be closed at a minimal mental loss. This can create a motivation for hanging onto more-expensive items as they age, whereas comparably functional items that were cheaper would be thrown away or sold.

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EXAMPLE 3.4 Investment and Divestment

Suppose you hold a portfolio of stock investments. Over time, some of the stocks drop in price and are worth less than you purchased them for, and others increase in price and are worth more. Traditional economic tools suggest that you should make decisions to sell based on the expected future return on investment, not on the history of price. Further, future stock prices are often modeled as a random walk. If stock prices follow a random walk, then the expected future price should be equal to the current price. In this scenario, there may be no particular reason to prefer to sell either stocks that have lost or stocks that have gained value. The past change in value should provide no information about the future performance. Further, tax laws in the United States allow people to reduce tax payments once losses are realized on the stock market. In this case, we might expect people to be motivated to sell losing stocks more often than winning stocks. Mental accounting predicts the opposite. A person behaving according to the theory of mental accounting will hold the stocks that have lost value in the hope of balancing the account. Thus, mental accounting supposes that stocks that have gained in value will be sold more often than those that have lost.

Terrance Odean used transaction data for 10,000 customers of a discount brokerage firm to examine this prediction. He found that customers were much more likely to sell investments that had increased in value rather than those that had decreased in value. Over the course of the year, customers would sell and realize close to 15 percent of the gains in their portfolio. On the other hand, they would sell and realize only 10 percent of the losses in their portfolio. This tendency to realize gains and avoid realizing losses is called the disposition effect. Here, customers selling a stock value the sale as vps − pp, where ps is the price at sale, and pp is the price a purchase. Clearly, this value is larger for a gaining stock than for a losing stock. Thus the customer, hoping to avoid realizing a loss, favors selling the gaining stocks.

Customers who sold the gaining stocks tended not to reinvest their gains, suggesting that they were not simply rebalancing their portfolio after a gain so as to reduce the percentage of value in the particular gaining stock and return to the original mix of investments. It is difficult to discern the customer’s expectations of future returns. However, Odean compared the actual returns of the stocks that were sold after gains against those that were held after losses. The average return on the winning stocks that were sold was about 2.4% over the next 252 trading days after sale. The return over the same period for the losing stocks that were not sold was about −1%. Thus, if individual beliefs mirrored reality, customers should have sold the losers. Interestingly, the trend reverses in the month of December. In December, customers might have been motivated to realize their losses to take advantage of tax deductions for the sale of stock at a loss. The reversal in December, however, is not strong enough to outweigh the strong disposition effect throughout the rest of the year.

Investments and Opening and Closing Accounts		59

EXAMPLE 3.5 More on Paying for Gym Memberships and Attendance

John Gourville and Dilip Soman proposed and tested the notion of payment deprecia- tion—that the price paid for an item has a diminishing effect on consumption behavior as time goes on. They provide several hypothetical and experimental examples of payment depreciation, and the most compelling is a study of the attendance behavior at a gym in Colorado. Membership in the gym was purchased on an annual basis, but payments were made once every six months from the time of enrollment. Thus, a member joining in January would pay in January and June each year. Interestingly, no matter when the month of payment occurred, there was a substantial spike in attendance following payment. Approximately 35 percent of attendance in any six-month window occurs in the month of payment. Alternatively, less than 10 percent of attendance occurs in the fourth or fifth month after payment. First-time members of the gym were excluded from their study so that initial excitement for a gym membership would not bias results.

Imagine a member considering a trip to the gym. He has attended n − 1 times since the last time he paid to renew his membership, and he can attend and obtain a value of vaxn − pδtn+ vt− pδt + prn, where xn is the monetary value to the member of experiencing the n th single attendance event at the gym, p is the price paid once every six months, δ is the monthly rate of depreciation, t is the number of months since the last payment was made, n is the number of times the member has attended the gym since paying (including the attendance event under consideration), and prn is the price the individual considers fair for attending the gym n times. In the acquisition value function, the price paid is divided by n to indicate amortization of costs over the number of times attended. In the first month after paying, the price looms large, being multiplied in both instances by δ0 = 1. Right after payment, the member has not yet attended and n = 1, and thus the value of attending for the first time since paying in the first month after paying is vax1 − p+ vt− p + pr1. Almost certainly the fair price of attending one time, pr1, is much less than the rate for six months of membership. Thus the transaction utility is heavily negative. As well, the value of the experience of attending once is certainly much less than the cost of a six-month membership. Thus, acquisition utility is also heavily negative. Thus, the account is considered a loss at the time of payment and must remain open while the member pursues a balanced account. Still, although attending the first time has a negative value, the value is more than not attending the first time in that month,va− p+ vt− p, because at least the member obtains the value of the single instance of attendance.

Over time, the number of times attended and the number of months increases. Suppose the rate of depreciation is δ = .75. In the fourth month, if the member has attended 11 times, the value of additional attendance is vax12 − 0.002p+ vt− 0.316p + pr12. If the fair price for attending 12 times is more than 0.316 times the price of a six-month membership, then the transaction utility is clearly positive. At this point, the member is no longer motivated to keep the account open by a negative transaction utility. Suppose for now that attending the gym for the twelfth time in four months is actually considered to be of negative value (I feel like I am spending all my