FIGURE 4. View of the World from 9th Avenue. Saul Steinberg, cover of The New Yorker, March 29, 1976 © The Saul Steinberg Foundation / Artists Rights Society (ARS), New York. Cover reprinted with permission of The New Yorker magazine. All rights reserved.
The technical term for discounting of this general form that starts out high and then declines is quasi-hyperbolic discounting. If you don’t know what “hyperbolic” means, that shows good judgment on your part in what words to incorporate in your vocabulary. Just keep the faulty telescope in mind as an image when the term comes up. For the most part I will avoid this term and use the modern phrase present-biased to describe preferences of this type.
To see why exponential discounters stick to their plans while hyperbolic (present-biased) discounters do not, let’s consider a simple numerical example. Suppose Ted and Matthew both live in London and are avid tennis fans. Each has won a lottery offering a ticket to a match at Wimbledon, with an intertemporal twist. They can choose among three options. Option A is a ticket to a first-round match this year; in fact, the match is tomorrow. Option B is a quarterfinal match at next year’s tournament. Option C is the final, at the tournament to be held two years from now. All the tickets are guaranteed, so we can leave risk considerations out of our analysis, and Ted and Matthew have identical tastes in tennis. If the matches were all for this year’s tournament, the utilities they would assign to them are as follows: A: 100, B: 150, C: 180. But in order to go to their favorite option C, the final, they have to wait two years. What will they do?
If Ted had this choice, he would choose to wait two years and go the final. He would do so because the value he puts right now on going to the final in two years (its “present value”) is 146 (81% of 180), which is greater than the present value of A (100) or B (135, or 90% of 150). Furthermore, after a year has passed, if Ted is asked whether he wants to change his mind and go to option B, the quarterfinal, he will say no, since 90% of the value of C (162) is still greater than the value of B. This is what it means to have time-consistent preferences. Ted will always stick to whatever plan he makes at the beginning, no matter what options he faces.
What about Matthew? When first presented with the choice, he would also choose option C, the final. Right now he values A at 100, B at 105 (70% of 150) and C at 113 (63% of 180). But unlike Ted, when a year passes, Matthew will change his mind and switch to B, the quarterfinal, because waiting one year discounts the value of C by 70% to 126, which is less than 150, the current value of B. He is time-inconsistent. In telescope terms, referring back to the New Yorker cover, from New York he couldn’t tell that China was any farther than Japan, but if he carried that telescope to Tokyo, he would start to notice that the trip from there to Shanghai is even farther than it was from New York to Chicago.
It bothered Samuelson that people might display time inconsistency. Econs should not be making plans that they will later change without any new information arriving, but Samuelson makes it clear that he is aware that such behavior exists. He talks about people taking steps equivalent to removing the bowl of cashews to ensure that their current plans will be followed. For example, he mentions purchasing whole life insurance as a compulsory savings measure. But with this caveat duly noted, he moved on and the rest of the profession followed suit. His discounted utility model with exponential discounting became the workhorse model of intertemporal choice.
FIGURE 5
It may not be fair to pick this particular paper as the tipping point. For some time, economists had been moving away from the sort of folk psychology that had been common earlier, led by the Italian economist Vilfredo Pareto, who was an early participant in adding mathematical rigor to economics. But once Samuelson wrote down this model and it became widely adopted, most economists developed a malady that Kahneman calls theory-induced blindness. In their enthusiasm about incorporating their newfound mathematic rigor, they forgot all about the highly behavioral writings on intertemporal choice that had come before, even those of Irving Fisher that had appeared a mere seven years earlier. They also forgot about Samuelson’s warnings that his model might not be descriptively accurate. Exponential discounting just had to be the right model of intertemporal choice because Econs would not keep changing their minds, and the world they now studied no longer contained any Humans. This theory-induced blindness now strikes nearly everyone who receives a PhD in economics. The economics training the students receive provides enormous insights into the behavior of Econs, but at the expense of losing common-sense intuition about human nature and social interactions. Graduates no longer realize that they live in a world populated by Humans.
Intertemporal choice is not just an abstract concept used in theoretical economics. It plays a vital role in macroeconomics, where it underlies what is called the consumption function, which tells us how the spending of a household varies with its income. Suppose a government has seen its economy plunge into a deep recession and decides to give everyone a one-time tax cut of $1,000 per person. The consumption function tells us how much of the money will be spent and how much will be saved. Economic thinking about the consumption function changed quite dramatically between the mid-1930s and the mid-1950s. The way in which models of the consumption function evolved illustrates an interesting feature about how economic theory has developed since the Samuelson revolution began. As economists became more mathematically sophisticated, and their models incorporated those new levels of sophistication, the people they were describing evolved as well. First, Econs became smarter. Second, they cured all their self-control problems. Calculate the present value of Social Security benefits that will start twenty years from now? No problem! Stop by the tavern on the way home on payday and spend the money intended for food? Never! Econs stopped misbehaving.
This pattern in the evolution in economic theory can be seen by examining the models of the consumption function proposed by three economist heavyweights: John Maynard Keynes, Milton Friedman, and Franco Modigliani. We can begin with Keynes, who famously advocated just the sort of tax cut used in this example. In his masterwork, The General Theory of Employment, Interest and Money, he proposed a very simple model for the consumption function. He assumed that if a household received some incremental income, it would consume a fixed proportion of that extra income. The term he used to describe the proportion of extra income that would be consumed is the marginal propensity to consume (MPC). Although Keynes thought that the marginal propensity to consume for a given household was relatively constant if its income did not change dramatically, he agreed with his contemporary Irving Fisher that the MPC would vary considerably across socioeconomic classes. Specifically, he thought the propensity to spend would be highest (nearly 100%) for poor families, and decline as income rises. For the rich, a windfall of $1,000 would barely affect consumption at all, so the MPC would be close to zero. If we take the case of a middle-class family that saves 5% of any additional income earned, then Keynes predicts that the MPC from a $1,000 windfall would be 95%, or $950.
A couple of decades later, in a book published in 1957, Milton Friedman made the plausible observation that households might have the foresight to smooth their consumption over time, so he proposed the permanent income hypothesis. In his model, a family that is saving 5% of its income would not spend $950 extra in the year of the windfall, but instead would spread it out. Specifically, he proposed that households would use a three-year horizon to determine what their permanent income is, so would divide the extra spending evenly over the next three years. (This implies a discount rate of 33% per year.) That means that in the first year, the family would spend about $950/3, or $317.†
The next move up in sophistication came from Franco Modigliani, writing with his student Richard Brumberg. Although his work was roughly contemporaneous with Friedman’s, his model was one step up the economic ladder toward the modern conception of an Econ. Rather than focus on short-term periods such as a year or even three years, Modigliani based his model on an individu
al’s total lifetime income, and his theory was accordingly called the life-cycle hypothesis. The idea is that people would determine a plan when young about how to smooth their consumption over their lifetime, including retirement and possibly even bequests.
In keeping with this lifetime orientation, Modigliani shifted his focus from income to lifetime wealth. To make things simple and concrete, let’s suppose that we are dealing with someone who knows that he will live exactly forty more years and plans to leave no bequests. With these simplifying assumptions, the life-cycle hypothesis predicts that the windfall will be consumed evenly over the next forty years, meaning that the marginal propensity to consume from the windfall will be just $25 per year ($1000/40) for the rest of his life.
Notice that as we go from Keynes to Friedman to Modigliani, the economic agents are thinking further ahead and are implicitly assumed to be able to exert enough willpower to delay consumption, in Modigliani’s case, for decades. We also get wildly different predictions of the share of the windfall that will be immediately spent, from nearly all to hardly any. If we judge a model by the accuracy of its predictions, as advocated by Friedman, then in my judgment the winner among the three models’ ability to explain what people do with temporary changes to their income would be Keynes, modified somewhat in Friedman’s direction to incorporate the natural tendency to smooth out short-run fluctuations.‡ But if instead we choose models by how clever the modeler is, then Modigliani is the winner, and perhaps because economists adopted the “cleverer is better” heuristic, Modigliani’s model was declared best and became the industry standard.
But it is hard to be the smartest kid in the class forever, and it is possible to take the model up one more level in sophistication, as shown by Robert Barro, an economist at Harvard. First, he assumes that parents care about the utility of their children and grandchildren, and since those descendants will care about their own grandchildren, their time horizon is effectively forever. So Barro’s agents plan to give bequests to their heirs, and realize that their heirs will do likewise. In this world, the predictions about how much money will be spent depend on from where the money comes. If the $1,000 windfall had come from a lucky night at the casino, Barro would make the same prediction as Modigliani about consumption. But if the windfall is a temporary tax cut that is financed by issuing government bonds, then Barro’s prediction changes. The bonds will have to be repaid eventually. The beneficiary of the tax cut understands all this, and realizes that his heir’s taxes will eventually have to go up to pay for the tax cut he is receiving, so he won’t spend any of it. Instead he will increase his bequests by exactly the amount of the tax cut.
Barro’s insight is ingenious, but for it to be descriptively accurate we need Econs that are as smart as Barro.§ Where should one stop this analysis? If someone even more brilliant than Barro comes along and thinks of an even smarter way for people to behave, should that too become our latest model of how real people behave? For example, suppose one of Barro’s agents is a closet Keynesian, an idea that Barro would abhor, and he thinks that the tax cut will stimulate the economy enough to pay off the bonds from increased tax revenues; in that case, he will not need to alter his planned bequests. In fact, if the tax cut stimulates the economy enough, he might even be able to reduce his bequests because his heirs will be the beneficiaries of the higher economic growth rate. But notice now we need Econs who are fully conversant with both economic theory and the relevant empirical tests of effects of fiscal policy in order to know which model of the economy to incorporate in their thinking. Clearly, there must be limits to the knowledge and willpower we assume describe the agents in the economy, few of whom are as clever as Robert Barro.
The idea of modeling the world as if it consisted of a nation of Econs who all have PhDs in economics is not the way psychologists would think about the problem. This was brought home to me when I gave a talk in the Cornell psychology department. I began my talk by sketching Modigliani’s life-cycle hypothesis. My description was straightforward, but to judge from the audience reaction, you would have thought this theory of savings was hilarious. Fortunately, the economist Bob Frank was there. When the bedlam subsided, he assured everyone that I had not made anything up. The psychologists remained stunned in disbelief, wondering how their economics department colleagues could have such wacky views of human behavior.¶
Modigliani’s life-cycle hypothesis, in which people decide how much of their lifetime wealth to consume each period, does not just assume that people are smart enough to make all the necessary calculations (with rational expectations) about how much they will make, how long they will live, and so forth, but also that they have enough self-control to implement the resulting optimal plan. There is an additional unstated assumption: namely, that wealth is fungible. In the model, it does not matter whether the wealth is held in cash, home equity, a retirement plan, or an heirloom painting passed on from a prior generation. Wealth is wealth. We know from the previous chapters on mental accounting that this assumption is no more innocuous or accurate than the assumptions about cognitive abilities and willpower.
To relax the assumption that wealth is fungible and incorporate mental accounting into a theory of consumption and savings behavior, Hersh Shefrin and I proposed what we called the behavioral life-cycle hypothesis. We assume that a household’s consumption in a given year will not depend just on its lifetime wealth, but also on the mental accounts in which that wealth is held. The marginal propensity to consume from winning $1,000 in a lottery is likely to be much higher than a similar increase in the value of a household’s retirement holdings. In fact, one study has found that the MPC from an increase in the value of retirement saving can even be negative! Specifically, a team of behavioral economists showed that when investors in retirement plans earn high returns, making them richer, they increase their saving rates, most likely because they extrapolate this investment success into the future.
To understand the consumption behavior of households, we clearly need to get back to studying Humans rather than Econs. Humans do not have the brains of Einstein (or Barro), nor do they have the self-control of an ascetic Buddhist monk. Rather, they have passions, faulty telescopes, treat various pots of wealth quite differently, and can be influenced by short-run returns in the stock market. We need a model of these kinds of Humans. My favorite version of such a model is the subject of the next chapter.
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* I once gave a talk about self-control to a group of economists at the Hebrew University in Jerusalem. At one point I used the word “temptation,” and one of the audience members asked me to define it. Someone else in the audience jumped in to say, “It’s in the Bible.” But it was not in the economists’ dictionary.
† Here, and in what follows, I will also assume for simplicity that interest and inflation rates are zero, or, if you like, that they equal each other and all numbers are adjusted for inflation.
‡ If we take a longer-run problem, such as saving for retirement, then the story gets more complicated, and I would move a bit further toward Modigliani. See the discussion of the behavioral life-cycle hypothesis just below.
§ When Robert Barro and I were at a conference together years ago, I said that the difference between our models was that he assumed that the agents in his model were as smart as he was, and I assumed they were as dumb as I am. Barro agreed.
¶ Or, as my Cornell colleague and good friend Tom Gilovich said to me: “I never cease to be amazed by the number of convenient null hypotheses economic theory has given you.”
12
The Planner and the Doer
When I starting thinking seriously about self-control problems, there was little in the economics literature upon which to draw. Like most graduate students, I knew nothing about the early scholars whose work was discussed in the previous chapter. Graduate students rarely read anything written more than thirty years ago. And there was not much new going on either. However, I did find myself motiv
ated by the work of three scholars: one economist and two psychologists.
Robert Strotz, an economist at Northwestern University, wrote the only economics paper on self-control I found. Although many economists had been using the discounted utility model Samuelson had formulated, few aside from Strotz had paid any attention to his warnings about time inconsistency.
In this paper, published in 1955, Strotz took a deep dive into the problem, investigating the mathematical properties a person’s preferences had to satisfy to ensure that once he makes a plan, he will not want to change it. We need not dwell on the technical details of the paper. Suffice to say that there was only one highly specific case (exponential discounting) in which one could be sure that people would be time-consistent, and, like Samuelson, Strotz worried that these conditions would not be met.
These worries led Strotz to engage in what has become an obligatory discussion of Homer’s tale of Odysseus and the Sirens. Almost all researchers on self-control—from philosophers to psychologists to economists—eventually get around to talking about this ancient story, and for once, I will follow the traditional path.
Recall the setup. The Sirens were an ancient version of an all-female rock band. No sailor could resist the call of their songs. But any sailor who submitted to the temptation of trying to steer his ship close to the rocks would find himself shipwrecked. Odysseus wanted to both hear the music and live to tell about it. He devised a two-part plan to succeed.* The first part was to make sure that his crew did not hear the Sirens’ call, so he instructed them to fill their ears with wax. The second part of the plan was to have his crew bind him to the mast, allowing Odysseus to enjoy the show without risking the inevitable temptation to steer the ship toward the rocks.
Misbehaving: The Making of Behavioral Economics Page 11
