374		COMMITTING AND UNCOMMITTING

Over the range of δ 0.850, 0.865 Kerry continually postpones, hoping he will eventually perform task x2. By always procrastinating, he obtains utility 0. The highreward task has a large upfront cost but a much larger potential reward 201 − δ > 133. The immediate cost and his time-inconsistent preferences lead him not to do the smaller-reward activity now but to continually postpone the larger-reward activity. If the larger-reward activity were not available (i.e., x1 did not exist), Kerry would anticipate performing x1 in the second period. In this case, the choice in the first period would be between u1, 11 and u1, 21. Kerry would always choose to perform x1 immediately because u1, 21 = δu1, 11. In this case, having a high-reward option available that is not immediately attractive can induce infinite procrastination, leading Kerry to be much worse off. Partial naïfs are not always better off when given more choices.

Uncommitting

Sophistication when possessing time-inconsistent preferences can be a double-edged sword. Although a person always wants to commit to a future consumption path to maximize his current perception of utility, when the future finally arrives, he will be willing to pay a premium to break that commitment. Consider Robin, a sophisticate who has trouble making it to the gym.

Let us consider an infinite-horizon decision problem in which each period represents a week. Exercising in any period yields an immediate cost of c and a reward in all subsequent periods of v. Moreover, suppose that Robin must pay k0 each week as part of his gym membership, and that he cannot easily rescind his membership. In the first period, Robin anticipates that in any period t he will solve

maxxt ,xt + 1,	− k0	− xtc + β	δi − k0	− xt + i + 1c + t + i xjv ,	13 70
		i = 0		j = 1

where xt are dummy variables taking a value of 1 if Robin chooses to exercise in period t and a value of 0 otherwise. Robin will decide not to exercise in period t if the additional discounted utility of doing so is less than that of not exercising, or (using the properties of geometric series again; see footnote 2)

β
1 − δ v − c < 0.	13 71

Let us suppose that this is the case. Thus, without commitment, Robin would always choose not to exercise. The would-be athlete in period t will instead wish he will exercise in the next period (and each period thereafter) if the utility of doing so is greater than not doing so, or if

	δ
β	1 − δ v − c	> 0.	13 72

If this is the case, then the sophisticate in the first period must decide whether to exercise then, (and never again), or not to. Equation 13.71 implies that he will forgo exercising forevermore.

Uncommitting		375

Now suppose that the gym offers two gym memberships, one that results in a weekly cost of k0, and another that adds k1 to the weekly cost (thus charging the member k0 + k1 > k0 for the membership). For this additional fee, the gym agrees to fine gym members k2 > 0 after any week in which they do not use the gym. Under this system, equation 13.70 becomes

maxxt ,xt +1						−k0 −k1 −xtc − 1 −xt k2					13 73
	,	+β	i =0 δ	i	−k0	−k1 −xt +i +1c − 1 −xt +i +1			k2 +	t +i
										j =1 xjv
so that the athlete now forgoes the gym in period t only if
							β
								v − c < − k2.			13 74
							1 − δ

If k2 is large enough, the threat of the penalty will act as a commitment mechanism, and Robin will plan to exercise in period t and not procrastinate. By participating in the commitment mechanism, Robin pays k1 every week into the infinite future. This results,

by the properties of geometric

series, in a net present

value of

the cost

given by

k1 1 − δ . The additional utility of exercising every week is given by

− c + β

δi − c +

t + i v = β

δi iv − c 1 +

β

.

13 75

− δ

i = 0

j = 1

i = 0

1

Robin will buy the commitment mechanism and begin to exercise every week if

β

δi iv − c 1 +

β

>

k1

.

13 76

1

−

δ

− δ

i = 0

1

By offering the commitment mechanism, the gym is able to make more money from the sophisticated gym user, potentially increasing their profits (given that the cost of maintaining gym equipment does not increase too much). But this also creates another opportunity. Suppose Alex, an enterprising person who loves to exercise, sees that he can now make some money from the would-be athlete. In any period, while Robin would like to make a commitment for future gym use, he would also be willing to pay some amount to break his commitment. So Alex offers to pose as Robin, exercising for Robin and signing in at the gym under Robin’s name. In return, Alex asks that Robin pay him k3 < k2. In this case, equation 13.74 now becomes

−k0 −k1 −xtc −1 −xtk3

maxxt ,xt +1	,	+β	i	−k0 −k1 −xt +i +1c − 1 −xt +i +1 k3 +	t +i
			i =0 δ		j =1 xjv

1377

and Robin will decide not to exercise if

β

1

− δ v − c − k1 < − k3. 1378

So long as k3 is small enough that equation 13.78 is satisfied, Robin will break his commitment and Alex will be paid to go to the gym.

	376		COMMITTING AND UNCOMMITTING

In fact, any time time-inconsistent decision makers are willing to pay to enter a commitment mechanism, they will also be willing to pay to break the commitment at some future when it binds. This preference reversal leads to a money pump of the sort described in the first section of this book. We can pump all of the money out of sophisticates by first charging them to commit, then charging them to uncommit, and repeating. Some companies actually use such models. For example, time-share vacations allow users to commit themselves to vacations in advance by offering very low prices. Then, when the users cannot bring themselves to meet the commitment (work or other more important responsibilities encroach), they allow the members to pay a fee to cancel. Of course, such a money pump only works so long as sophisticates are not aware of the possibility to uncommit at the time they enter the commitment device. Once they get wise to this option, the pump is dead. Alternatively, partial naïfs might enter and sustain a money pump even with this knowledge. This happens because they do not fully recognize how likely they will be to pay to opt out of the commitment.

EXAMPLE 13.5 Quitters, Inc.

A short story by Stephen King, dramatized as one part of the movie The Cat’s Eye, illustrates our willingness to enter into commitment devices and our lack of ability to control our own future behavior. The main character, Dick Morrison, finally wants to quit smoking, and, based on the testimonial of an old college friend, decides to try Quitters, Inc. Upon visiting Quitters, Inc., he finds that the company was originally founded by a mob boss who was losing the fight with lung cancer due to his own habit. The counselor he meets with openly tells him that the company had served as a front for the Mafia but that they still care very deeply about getting people to quit. In fact, his counselor guarantees that by the completion of their program, Dick will never smoke again.

Their plan illustrates a severe commitment device. Those who enroll will be under surveillance constantly. Those caught smoking will face severe and increasingly horrid penalties. For the first cigarette, associates of the program will kidnap Dick’s wife and torture her in front of Dick. If he gives in to temptation again, Dick will be captured and tortured. Other family members would follow and suffer more-severe versions of torture. If Dick gives in to temptation a tenth time, a Quitters, Inc., associate will be sent to kill him, guaranteeing he will never smoke again. At once, knowing that such steep penalties face us, we would almost certainly find it much easier to keep the commitment to abstain from such indulgent but destructive activities as smoking.

In fact, many programs to help people quit addictions rely on addicts having friends or others who check up on them regularly. Although most of these do not include threats to personal well-being, they certainly include threats of embarrassment, but they also include support for those who are facing temptation. Such mechanisms seek to alter the cost and benefit associated with the behavior. If we truly had full control of our actions, no one fully intending to quit would be the least bit reluctant to join a Quitters, Inc.–style program. Our reluctance reveals quite a lot about the amount of control we truly feel we have over ourselves and the strength of our resolve. Thankfully for Dick, he was able to kick the habit with very few slip-ups. Now if he can only maintain his weight.

Uncommitting		377

EXAMPLE 13.6 Illiquid Assets, Liquid Assets, and the U.S. Savings Rate

U.S. consumers hold the lion’s share of their assets in illiquid assets, such as a 401k retirement account, or other assets that are difficult at best to access in the short term. Households keep an average of two thirds of their wealth in accounts that cannot be accessed immediately. We tend to hold very small amounts of money in savings accounts, CDs, or even mutual funds or stocks that could be sold in the short run. When our assets are in illiquid investments, we effectively limit our own ability to access and use our money.

Although holding such illiquid assets seems unintuitive generally, David Laibson notes that people with time-inconsistent preferences might seek such illiquid assets to prevent themselves from spending the money they should really be saving. Thus, illiquid assets function as a commitment mechanism for sophisticated (or at least partial naïf) savers. Given the opportunity to place their money either in an account that can be easily accessed or one that requires notifying the bank at least one period ahead of when they will need the money, a sophisticate might prefer the illiquid account even if the expected return on investment is lower than with the liquid account.

This is a simple application of the sophisticate model to savings decisions, but it is one that has some impressive implications. From 1947 to 1983 the average American had saved between 8 percent and 12 percent of every dollar he or she received. Then the savings rate began a long and rapid decline, bottoming out close to 1 percent in 2007. Several competing theories have tried to explain America’s long trend toward living paycheck to paycheck. One potential explanation lies in the increasing amount of innovation within the financial sector.

Over the years since 1983, potential savers have increased their access to money through the wider distribution of credit cards, the introduction of automated teller machines (ATMs), and the introduction of assets that had properties of long-term investment accounts but that could be accessed more quickly and easily. For example, home equity lines of credit became much more prevalent, with people charging items to the increasing value of their home. Once approved for the line of credit, homeowners could simply start borrowing up to their limit, often using checks or a plastic card. Internet banking has further liquefied what would have been illiquid assets.

Without ATMs and Internet banking, one would almost certainly have to go to the bank to conduct almost any transaction. Such travel time and waiting in line creates a certain cost to access your money. Now money may be accessed at anytime from anywhere. Perhaps this introduction of additional liquidity contributed the eroding of the U.S. savings rate. After the recession of 2008, the savings rate started to rebound, at the same time that stock returns plummeted and consumer credit began to evaporate. One alternative explanation for the decline in savings is the expectation that stock returns would allow people to increase wealth without the hard work of saving. This expectation disappeared in 2008. The simultaneous evaporation of U.S. credit might make it difficult for economists to completely disentangle these competing explanations for wide swings in U.S. savings behavior.