- •Brief Contents
- •Contents
- •Preface
- •Who Should Use this Book
- •Philosophy
- •A Short Word on Experiments
- •Acknowledgments
- •Rational Choice Theory and Rational Modeling
- •Rationality and Demand Curves
- •Bounded Rationality and Model Types
- •References
- •Rational Choice with Fixed and Marginal Costs
- •Fixed versus Sunk Costs
- •The Sunk Cost Fallacy
- •Theory and Reactions to Sunk Cost
- •History and Notes
- •Rational Explanations for the Sunk Cost Fallacy
- •Transaction Utility and Flat-Rate Bias
- •Procedural Explanations for Flat-Rate Bias
- •Rational Explanations for Flat-Rate Bias
- •History and Notes
- •Theory and Reference-Dependent Preferences
- •Rational Choice with Income from Varying Sources
- •The Theory of Mental Accounting
- •Budgeting and Consumption Bundles
- •Accounts, Integrating, or Segregating
- •Payment Decoupling, Prepurchase, and Credit Card Purchases
- •Investments and Opening and Closing Accounts
- •Reference Points and Indifference Curves
- •Rational Choice, Temptation and Gifts versus Cash
- •Budgets, Accounts, Temptation, and Gifts
- •Rational Choice over Time
- •References
- •Rational Choice and Default Options
- •Rational Explanations of the Status Quo Bias
- •History and Notes
- •Reference Points, Indifference Curves, and the Consumer Problem
- •An Evolutionary Explanation for Loss Aversion
- •Rational Choice and Getting and Giving Up Goods
- •Loss Aversion and the Endowment Effect
- •Rational Explanations for the Endowment Effect
- •History and Notes
- •Thought Questions
- •Rational Bidding in Auctions
- •Procedural Explanations for Overbidding
- •Levels of Rationality
- •Bidding Heuristics and Transparency
- •Rational Bidding under Dutch and First-Price Auctions
- •History and Notes
- •Rational Prices in English, Dutch, and First-Price Auctions
- •Auction with Uncertainty
- •Rational Bidding under Uncertainty
- •History and Notes
- •References
- •Multiple Rational Choice with Certainty and Uncertainty
- •The Portfolio Problem
- •Narrow versus Broad Bracketing
- •Bracketing the Portfolio Problem
- •More than the Sum of Its Parts
- •The Utility Function and Risk Aversion
- •Bracketing and Variety
- •Rational Bracketing for Variety
- •Changing Preferences, Adding Up, and Choice Bracketing
- •Addiction and Melioration
- •Narrow Bracketing and Motivation
- •Behavioral Bracketing
- •History and Notes
- •Rational Explanations for Bracketing Behavior
- •Statistical Inference and Information
- •Calibration Exercises
- •Representativeness
- •Conjunction Bias
- •The Law of Small Numbers
- •Conservatism versus Representativeness
- •Availability Heuristic
- •Bias, Bigotry, and Availability
- •History and Notes
- •References
- •Rational Information Search
- •Risk Aversion and Production
- •Self-Serving Bias
- •Is Bad Information Bad?
- •History and Notes
- •Thought Questions
- •Rational Decision under Risk
- •Independence and Rational Decision under Risk
- •Allowing Violations of Independence
- •The Shape of Indifference Curves
- •Evidence on the Shape of Probability Weights
- •Probability Weights without Preferences for the Inferior
- •History and Notes
- •Thought Questions
- •Risk Aversion, Risk Loving, and Loss Aversion
- •Prospect Theory
- •Prospect Theory and Indifference Curves
- •Does Prospect Theory Solve the Whole Problem?
- •Prospect Theory and Risk Aversion in Small Gambles
- •History and Notes
- •References
- •The Standard Models of Intertemporal Choice
- •Making Decisions for Our Future Self
- •Projection Bias and Addiction
- •The Role of Emotions and Visceral Factors in Choice
- •Modeling the Hot–Cold Empathy Gap
- •Hindsight Bias and the Curse of Knowledge
- •History and Notes
- •Thought Questions
- •The Fully Additive Model
- •Discounting in Continuous Time
- •Why Would Discounting Be Stable?
- •Naïve Hyperbolic Discounting
- •Naïve Quasi-Hyperbolic Discounting
- •The Common Difference Effect
- •The Absolute Magnitude Effect
- •History and Notes
- •References
- •Rationality and the Possibility of Committing
- •Commitment under Time Inconsistency
- •Choosing When to Do It
- •Of Sophisticates and Naïfs
- •Uncommitting
- •History and Notes
- •Thought Questions
- •Rationality and Altruism
- •Public Goods Provision and Altruistic Behavior
- •History and Notes
- •Thought Questions
- •Inequity Aversion
- •Holding Firms Accountable in a Competitive Marketplace
- •Fairness
- •Kindness Functions
- •Psychological Games
- •History and Notes
- •References
- •Of Trust and Trustworthiness
- •Trust in the Marketplace
- •Trust and Distrust
- •Reciprocity
- •History and Notes
- •References
- •Glossary
- •Index
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Prospect Theory and Risk Aversion in Small Gambles |
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History and Notes
One complaint often lodged against research into the violations of expected utility theory is that they are based on somewhat contrived experiments. People seldom deal with the types of simple gambles presented in laboratory experiments. Laboratory experiments often involve small amounts of money that might not motivate well-reasoned responses. Further, most gambles presented in a laboratory setting involve a small number of possible outcomes with stated probabilities (such as those that can be represented in a Marschak–Machina triangle). Real-life risky choices are often not characterized by known probabilities but maybe by some general understanding of what might be possible. For example, one cannot know the probability that a certain stock will increase in value in the future. Instead, we are left to guess based upon previous experience and data from prior returns. Further, choices are often not between two possible gambles, but along a continuum. For example, I may purchase any number of shares (even fractions of shares) of a particular mutual fund. Thus it may not be a “this or that” type of question but a “how much” type of question. Finally, the choice experiments that have been used to examine nonexpected utility models are specifically designed to create choices that violate expected utility theory. In many real-world instances, the person is not presented with options that clearly violate expected utility theory. Thus, there may be some bounds to when behavioral models would be useful.
Nonetheless, several themes have developed from this stream of literature that have clear and practical applications. Among these are regret aversion, the systematic misperception of probabilities, and the use of choice heuristics when gambles are similar in some respect. Although these might not be applicable to every study of behavior under risky choice, they certainly make a substantive contribution in many circumstances. Kahneman and Tversky’s prospect theory model of choice under risk has gained wide use because it embodies so many of the anomalies that are found most often in an experimental setting. In many ways, prospect theory has become the most visible face of behavioral economics in the general economics discipline.
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PROSPECT THEORY AND DECISION UNDER RISK OR UNCERTAINTY |
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Biographical Note
Peter P. Wakker (1956 –)
Photo Courtesty of Peter P. Wakker
M.S., Nijmegen University, 1979; Ph.D., Tilburg
University, 1986; held faculty positions at Leiden
University, Tilburg University, University of Amsterdam,
University of Maastricht, and Erasmus University
Peter Wakker obtained his first training in the fields of mathematics that focus on probability, statistics, and optimization. From there it was a very short hop to the study of economic decision making under risk. Wakker is one of the leading theorists in the world regarding decision under risk and uncertainty. He has written dozens of articles using
mathematical theory to examine risky behavior, earning his position as one of the most highly cited economic theorists. His research has won several awards including the Career Achievement Award for the Society of Medical Decision Making. Among his most-cited articles are those examining the use of various probability or decisionweighting schemes, development of the cumulative prospect theory model and several other models of risky decision behavior, and explorations of cardinal measures of utility. Wakker has written two books, one providing a thorough treatment of the use of prospect theory for decisions under risk as well as uncertainty. He has an encyclopedic knowledge of the research literature on risk and uncertainty. As a service to the field, he publishes an annually updated annotated bibliography of risk research that is of vital use to anyone entering the field.
T H O U G H T Q U E S T I O N S
1.Consider that Kim has a choice among the following prospects
Gamble A: |
Gamble B: |
$60 with probability 0.24 |
$65 with probability 0.25 |
$33 with probability 0.24 |
$30 with probability 0.25 |
$0 with probability 0.52 |
$1 with probability 0.50 |
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(a)Rewrite these gambles after applying each of the steps of the editing phase. Does the result depend upon the order in which you apply these steps?
(b)Calculate the value of both gambles using the cumulative prospect theory functions estimated
by Tversky and Kahneman and appearing in equations 10.6 and 10.7, including their parameter estimates. Which gamble would the model predict would be chosen? Does this depend on the order of the steps applied in editing?
2.Stock market investments are inherently risky. Suppose that Sasha is heavily invested in a high-tech firm with a positive earnings outlook. Then reports come out that the firm’s primary technology is under a legal challenge from a competitor. If they should successfully repel the legal challenge, they will make the spectacular profits that everyone had been expecting, creating the expected returns on investment. If they fail, their business model will be irreparably broken
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References |
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and their stock will be worthless. Legal experts give the legal challenge a 60 percent chance of being successful. In the meantime, stock prices have plummeted in response to the news. Sasha previously had $1 million invested, and it is now worth only $400,000. What does prospect theory have to say about Sasha’s likely reaction to the news and devaluation of the stock? What has happened to the level of risk? What is Sasha’s likely reference point? Describe the change in risk aversion. Is Sasha likely to sell out now or hold the stock? Why? How might this explain behavior in a stock market crash?
3.You have a collection of valuable artwork worth $400,000. Suppose that you have preferences represented by the cumulative prospect theory model presented in Example 10.3. You are considering an insurance policy that will pay you the value of your collection should anything destroy it. Suppose that the probability of your artwork being damaged is 0.03.
(a)Considering that the current value of your artwork is your reference point, what is the most you would be willing to pay for the coverage? Express this as a percentage of $400,000.
(b)Now, suppose while you are filling out the paperwork, you are informed that a freak accident
R E F E R E N C E S
Ali, M.M. “Probability and Utility Estimates for Racetrack Bettors.”
Journal of Political Economy 85(1977): 803–815.
Kahneman, D., and A. Tversky. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica 47(1979): 263–292.
Loomes, G. “Evidence of a New Violation of the Independence Axiom.” Journal of Risk and Uncertainty 4(1991): 91–108.
Neilson, W. “Calibration Results for Rank-Dependent Expected Utility.” Economics Bulletin 4(2001): 1–4.
has destroyed half of your collection, leaving you with only $200,000 worth of rare artwork. If we consider $400,000 to be the reference point, now what is the maximum percentage of $200,000 you would be willing to pay to buy insurance that will replace $200,000 should the remaining art be destroyed?
4.Consider the contract problem in Example 10.5. Suppose that when considering whether to take the con-
tract or not, the worker tries to maximize the function
U
b
+ maxi
h, l
Vi, where U
b
= b0.88, the value b is the base level of pay in the contract, and Vi is as given in equations 10.12 through 10.17. Consider that if the
worker takes no contract, she will receive $0.
(a)What is the minimum level of base pay the worker
will accept for a contract with a high base pay and penalties for poor performance (so b = rh)? What are the resulting rl, rh?
(b)What is the minimum level of base pay the worker
will accept for a contract with low base pay and rewards for good performance (so b = rl)? What are the resulting rl, rh?
(c)Suppose the firm can sell high-quality pizza for $10 and low-quality pizza for $7. Which contract will the firm offer in order to maximize their profits?
Rabin, M. “Risk Aversion and Expected-Utility Theory: A Calibration Theorem.” Econometrica 68(2000): 1281–92.
Snydor, J. “(Over)insuring Modest Risks.” American Economic Journal: Applied Economics 2(2010): 177–199.
Tversky, A., and D. Kahneman. “Advances in Prospect Theory: Cumulative Representation of Uncertainty.” Journal of Risk and Uncertainty 5(1992): 297–323.
TIME DISCOUNTING AND THE |
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LONG AND SHORT RUN |
PART3 |
Society often classifies certain actions as tempting, sinful, or indulgent. These are odd concepts within the standard economics framework. If rational decision makers decide to do something, it is because they feel it is the best for them when all things are considered. But then why does society look with disdain on the youth who has taken up smoking or drug use? Obesity has become a substantial policy issue, and many suppose we should take action to curb the ability of people to eat the food they would like to. Some externalities are associated with obesity, though these are primarily due to publicly funded medical care (e.g., Medicare and Medicaid). The public seems to be much more willing to ban or tax certain foods than to simply exclude care for complications resulting from obesity from publicly funded medical care.
Behavioral economists have developed a comprehensive theory of how people make decisions that might have short-term benefits but longer-term costs. In many cases, people appear to be willing to commit themselves to behavior that appears to hurt them in the short term in the hope of providing longer-term benefits. For example, people often prefer to receive monthly installments rather than a single lump sum, citing the possibility that they would waste the money or fail to save enough for future expenses. In each of these cases it seems that people are in conflict with themselves. One course of action provides a short-term benefit but could have disproportionately negative effects in the future, and the person would be better off to forgo the short-term benefit to retain the long-term welfare. In some situations the wise course of action seems so clear that we wish to restrict others’ ability to take the wrong path. Even with all the information necessary to understand the tradeoffs, we might face difficulty in choosing the path that would appear to make us better off.
In this section, we discuss models of time discounting that give rise to time-inconsistent preferences. These models predict familiar behavior with respect to temptation and indulgence. Depending on how much people understand their own tendencies toward indulgence, discounting may might lead them to seek out commitment devices. Along with models of decision under risk, these models have become some of the most visible and widely used among all behavioral economics models.
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Disagreeing with Ourselves: |
11 |
Projection and Hindsight Biases |
On March 19, 2003, President George W. Bush announced that the United States was invading Iraq. This followed months of protracted arguments to the American people and to the world that Iraq had a chemical and biological weapons program that was in violation of their 1991 cease-fire agreement with the United States. Iraq had committed several other blatant violations of the cease-fire agreement, including firing on U.S. airmen. Nonetheless, the Bush administration had set as the centerpiece of its argument for invasion the existence of a thriving chemical and biological weapons program that presented a threat to the region.
Perhaps the most memorable of these arguments was given by the U.S. Secretary of State Colin Powell to the U.N. Security Council on February 5, 2003. Here he presented satellite photos of supposed mobile chemical weapons factories and bunkers for storage of chemical weapons, and he presented other intelligence that appeared to provide solid evidence that Iraq was building the capability to threaten stability in the Middle East. At one point he played tapes of Iraqi military communications in which the order is given to “remove the expression
‘nerve agent’ wherever it comes up in wireless communications” just before a U.N. inspection team arrived. The U.S. House of Representatives, several of the leading nations in the world, and the United Nations eventually took the intelligence argument as sufficient to warrant military action.
When the United States invaded, however, no such weapons were ever found. Moreover, the United States found no evidence to suggest that any such weapons had ever been there. Soon after it became clear that no chemical or biological weapons would be found, hundreds of blogs and much political commentary claimed, in fact, that the intelligence before the war conclusively showed that they did not exist. But if it were really so easy to see through the case that was made at the time, how could so many have been so blind? At one point before invasion the director of the Central Intelligence Agency had called the case a “slam-dunk.” How could he have been so certain if the case was as weak as many claim it was?
Our circumstances often influence our judgment. Consider the purchase of a pool table. Those without such amenities in their homes might visit friends who possess one and find great pleasure in playing a few games of nine-ball. These tables can be a large investment, with new tables often costing between $3,000 and $10,000. After visiting friends and playing pool several times, you might convince yourself that the high price tag is worth it. Yet throughout basements in America, thousands of pool tables sit dormant.
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