After convincing themselves to spend such an amount on a table, many play several times within the first few months and then grow bored by the game. They still continue to pull out the cue sticks when friends are visiting who may be excited to play. But for the most part, the table just takes up a large amount of space and gathers dust. It is difficult to understand why someone would expend such money for so little use. Nonetheless, it appears to be common.

We have a difficult time determining how we will feel or think in other circumstances. This can lead us to make notoriously bad decisions, albeit with conviction. We purchase items we believe we will want in the future, only to abandon the items as useless at a later date. We might also claim that we should have known better. In this chapter we consider projection bias and hindsight bias. Projection bias deals with predicting how we will feel at some future date. Hindsight bias deals with remembering the information that was available for our judgment at some previous date. In both cases we discuss the evidence for such biases and how they may be modeled.

These biases create time-inconsistent preferences. That is, what we believe we will want at some other time disagrees with what we actually want at that time. We disagree with ourselves. The evidence for such disagreements is convincing. Moreover, we tend to display such disagreements about even the most deliberated and weighty issues—including decisions to go to college, get married, or even to go to war. Within the rational decision framework pervasive in economics, it is difficult to reconcile such systematic regret. Psychologists have shed much light on these internal conflicts and how they can occur. Behavioral economic work sheds further light on the potential impacts of such behavior and potentially how to avoid such impacts.

The Standard Models of Intertemporal Choice

When people make decisions that will affect available choices in the future, economists tend to make a series of simplifying assumptions. These assumptions are not necessary for a person to be rational, per se. Rather, these assumptions seem reasonable, and they allow us to make simple predictions from a complicated problem. Consider first a twoperiod decision-making model (we consider more periods in the following chapters). Originally the person has wealth given by w1. In period 1 the person chooses what portion of w1 to use to buy goods for current consumption, c1, and then consumes these goods. The rest of the wealth is saved until the second period. In the second period, the person uses all remaining wealth, w2 = w1 − c1, to buy goods for consumption, c2, consumes these goods, and then dies. A general model of consumption might suppose that the person solves

where 0 ≤ c1 ≤ w1, and where Uc1, c2 is the utility of consuming c1 in period 1 and c2 in period 2. This model allows consumption in period 1 to be either a complement or substitute for consumption in period 2. In other words, the marginal utility of consumption in period 1 can either increase or decrease when consumption in period 2 increases.

We could, of course, add a few bells and whistles, such as allowing the prices for consumption to change between periods (currently we assume a unit of consumption costs one unit of wealth), allowing savings to accrue interest, or allowing the person to receive additional wealth in the second period. However, with or without these bells and whistles, this model functions exactly like the two-commodity consumer problem presented in Chapter 1, where consumption in period 1 is one good and consumption in period 2 is another good. This general model of intertemporal consumption is presented graphically in Figure 11.1. The budget constraint is depicted by the line where c2 = w − c1. This budget constraint has a slope of negative 1.The convex curves represent indifference curves. Each indifference curve represents all points satisfying Uc1, c2 = k, for some constant k. Thus, the person is indifferent between each consumption bundle along the curve. Utility is assumed to increase as one moves from the origin, in the southwest of the figure, to the northeast portion of the figure. Thus, the problem is solved at the point(s) along the budget constraint that is contained in the northeastern-most indifference curve. In the figure, this occurs at c*1 , c*2, where the slope of the indifference curve is also negative 1.

In this model, people who prefer current consumption over consumption in the next period would have more negatively sloped indifference curves, reflecting that losing one unit of current consumption must be compensated by greater period 2 consumption in order to maintain indifference. Having more negatively sloped indifference curves would also lead the optimal consumption bundle to lie farther to the southeast along the budget constraint. Alternatively, someone who preferred period 2 consumption over current consumption would have indifference curves with a very small negative slope, leading to optimal consumption bundles in the northwest portion of the budget constraint. The slope of the indifference curve could differ by location within the set of choices available. Thus, it could be that someone with relatively high w could have steep indifference curves and opt to consume more in period 1, whereas the same person would have

c2

c2

relatively shallow indifference curves with low wealth and consume more in period 2 (or vice versa). This model offers a lot of flexibility. For many purposes, economists feel this general model omits important information we have about individual preferences over current versus future consumption.

Economists commonly believe that people prefer current consumption to future consumption. Thus a hamburger today is more attractive than a hamburger tomorrow. Moreover, economists tend to believe that people’s within-period preferences over consumption are relatively stable over time. Thus, if I begin to eat a bag of potato chips today, as I eat, my marginal utility declines at about the same rate per chip as it would if I were to instead eat identical chips tomorrow. Thus, in a majority of applications, the economic model of intertemporal choice modifies the model in equation 11.1, assuming

where uc is the utility received within any time period from consumption within that time period (usually called the instantaneous utility function) and δ is a discount factor applied to future consumption. The utility function within each time period is identical except for the discount factor. Generally, 0 < δ < 1, indicating that future utility of consumption is worth less than current utility of consumption. This is commonly called an additive model, because utility of consumption is additively separable across periods. The slope of the indifference curves at any point c1, c2 follows the form

where uci represents marginal utility of consumption in period i.

Thus, increasing δ decreases the slope of the curves, reflecting a preference for period 2 consumption, and decreasing δ increases the slope, reflecting a preference for currentperiod consumption. Many have written about the discount factor, δ, as a measure of patience. If δ is equal to 1, the consumer considers future consumption just as valuable as current consumption. If we assume that the instantaneous utility of consumption is increasing in consumption and displays decreasing marginal utility of consumption, then the consumer optimizes where c1 = c2 = w2. Alternatively, if δ = 0, then the consumer only cares about current consumption and c1 = w and c2 = 0.

This additive form of the intertemporal utility function is used pervasively in modeling investment decisions, use of natural resources, and strategic interactions in bargaining, among many other applications. It is most often used for longer-horizon problems—those involving n > 2 periods. Whether we use the additive model of intertemporal choice or the more general model of intertemporal choice, however, this model relies on the notion that people can predict their utility of consumption function for future time periods. Even if we use these models to consider decisions under risk, economists generally assume the risk is due to not knowing how much consumption will result in future periods, not from any degree of risk or uncertainty regarding the utility of consumption function.

EXAMPLE 11.1 Adapting to Chronic Kidney Disease

Kidney disease affects about one out of every nine adults in the United States and is always a life-altering disease. Milder forms of kidney disease result in reduced function of the kidneys. This generally requires the patient to follow a strict diet, cutting out many desirable foods, counting calories, and limiting liquid intake. Additionally, patients must engage in a strict exercise regimen. In the most serious cases, patients have to undergo kidney dialysis. This usually involves visiting a dialysis center three times a week and sitting in a chair for four hours while the patient’s blood is processed outside the body through a dialyzer. Two needles are inserted into the patient, and tubes are connected to draw blood out and return blood back to the circulation. The dialyzer acts like an artificial kidney, cleaning the blood of foreign substances and reducing the amount of water in the blood. Dialysis patients must undergo this treatment several times a week, or else toxins quickly accumulate in the body, resulting in death. Dialysis patients are typically required to remain close to a home treatment center and cannot travel. Dialysis patients often report feeling weak or nauseated after a treatment. In short, dialysis is an unpleasant treatment, but it is necessary to prolong life. On the surface, one would expect the quality of life to decline substantially if the kidney disease is severe enough to warrant dialysis. Thus, it should be no surprise that when perfectly healthy people are asked, they in fact believe that going on dialysis would significantly reduce their quality of life.

David L. Sackett and George W. Torrance surveyed 189 people about the quality of life they would experience should they contract various diseases. Participants in the study were asked to rate each disease on a scale in which 1 means the respondent is indifferent between living with the disease and being perfectly healthy and 0 means the respondent is indifferent between living with the disease and dying. On average, people believed their quality of life would be 0.32 if they were required to visit a hospital to undergo dialysis for the rest of their life. Alternatively, when current dialysis patients were asked the same question, they rated the quality of life as 0.52 on average. Although 0.52 is a long way from 1, it is also a long way from 0.32. Why would dialysis patients feel so much better off than others might believe them to be? One potential explanation is that people with kidney disease use a different scale for their answers. Perhaps once you have such a reduced quality of life, you cannot remember how good “perfectly healthy” is, and thus your “1” is a healthy person’s “0.6”. This does not appear to be the case. Other studies have compared questions using a vague quality-of-life scale to one that uses a much more explicit scale and find that the more-explicit scale actually generates a wider divergence of values.

In another study, researchers found patients waiting for kidney transplants and asked about the quality of life they would experience if they did or did not receive the transplant within a year. They then tracked down the same patients after one year and found that they displayed similar bias in predicting their own quality of life. Those who had not received transplants were better off than they thought they would be. Those who had received the transplants were worse off than they thought they would be.

One reason people might perform so miserably at predicting their future well-being is that they give a knee-jerk judgment rather than reasoning through what life would really be like. Peter A. Ubel, George Loewenstein, and Christopher Jepson found that if healthy people were asked to think about the ways that they might be able to adapt their

life to kidney disease and dialysis treatment, their predictions of quality of life improves to something that is somewhat closer to that reported by actual patients. Once people begin to consider their ability to adapt, they might realize that some of the things they enjoy most are still possible. People have a hard time predicting how they might adapt to future circumstances, which affects their ability to guess their future utility.

EXAMPLE 11.2 Choosing a College Based upon Weather

Many students are attracted to the warmer climates of Florida or southern California. It is a common theme for students to turn down better educational opportunities for climates that are more amenable to beachgoing or other outdoor sporting activities. One would thus expect that visiting a college in the northeastern United States, a region known for its bad weather, on a day with particularly bad weather, might lead students to question whether they could survive four years of such punishment. However, suppose the school had very little in the way of social or outdoor activities in the first place.

At one academically challenging school, Uri Simonsohn found that visiting on badweather days increases the probability that the potential student will actually enroll. He analyzed the decisions of 562 applicants who had been admitted to the school and who had visited the school before making a decision to enroll. Of the 562 visitors, 259 eventually decided to accept the offer of admission. He then used data from the National Oceanic and Atmospheric Administration collected from the weather station closest to the school on cloud cover for each day students visited the university. Cloud cover is measured on a scale of 0 to 10, with 0 being completely clear skies and 10 being completely overcast skies. Amazingly, he found that an increase in cloud cover by one point increases the probability of accepting the offer of admission by between 0.02 to 0.03, depending on what other control variables are used.

At first glance, one might think this suggests that prospective students are attracted to cloudy places, which seems counterintuitive. Rather, Simonsohn argues that this result occurs because the way people evaluate the options they will face in the future is biased by the options that are currently at hand. When it is sunny, one might wish to spend time outside engaging in recreational activities rather than hunkered down with a textbook. Being taken on a tour of a prestigious university on such a sunny day might underscore the lack of available recreation there. Thus, when students consider the prestigious school versus a school with more recreational options, they might opt for the school with more recreational opportunities, not wanting to be stuck indoors with their textbook when the sun is shining.

Visiting when there is significant cloud cover can make outdoor activities less attractive. In fact, about 78 percent of students polled report that they prefer studying on overcast days than on sunny days. Thus, students who visit the prestigious institution when there is significant cloud cover are in a state in which they prefer studying more than they would otherwise. This experience colors the projection of the utility they anticipate that they will experience in the future when attending the school. In this case, they suppose that they will not mind the lack of outdoor activities and decide to go to the prestigious school. Hence, college admissions officers at academically challenging, yet recreationally challenged, schools across the country regularly hope for rain.