Oliver (2021) on Prospect Theory and Risk Preferences

Adam Oliver, “Reflecting on Reflection: Prospect Theory, Our Behaviors, and Our Environment.” Behavioural Public Policy, 1-11, 2021.

• A full-blown version of prospect theory includes both diminishing sensitivity in both the gains domain and the loss domain, as well as probability weighting, where low probability outcomes tend to be overweighted in valuing prospects and high-probability outcomes tend to be underweighted.

• Diminished sensitivity on its own implies risk averse behavior in the gains domain and risk seeking behavior in the loss domain.

• But, adding probability weighting to diminished sensitivity leads to what is called the "fourfold pattern" of risk preferences, or, the reflection effect. 

• For high probability gains, diminishing sensitivity and underweighting combine to produce risk averse behavior. But for low-probability gains, overweighting tends to more than offset diminishing sensitivity, leading to risk loving behavior (as with the appeal of lotteries). 

• For low probability losses, probability (over)weighting counters diminishing sensitivity, leading to risk averse behavior, while for high probability losses, (under)weighting combines with diminished sensitivity to lead to risk seeking behavior. 

• Oliver examines whether the fourfold pattern of risk preferences is displayed with respect to life expectancy prospects, as well as to monetary prospects. For monetary  prospects, a thirty-question interview protocol is administered to 60 university-affiliated people, with the (incentivized) questions focusing on eliciting certainty equivalents for prospective risky investment decisions.

• "the respondents generally became more averse to risk as probability increased in the domain of gains and as probability declined in the domain of losses, which... is consistent with the predictions of the prospect theory reflection effect [p. 4]."  

• So for monetary decisions, the fourfold pattern holds up pretty well in the interview results, though less well when looking at low probability gains or losses.

• A second set of 60 interviews with different (though still university-affiliated) people is used to look at preferences in the health domain. Now it is certainty equivalents in terms of lifetime duration that are elicited. Again, the results are largely consistent with the fourfold pattern.

• Risk seeking in the case of high probability losses – money or life expectancy – seems to be the most intense of the risk preferences.

• Though the results are consistent with prospect theory, Oliver is skeptical of the notion that prospect theory explains these results. Instead, he offers an evolutionary story (involving abundance v. scarcity) for why the fourfold pattern might emerge even without full-on prospect theory-style preferences.

• That is, evolution might have favored a pattern of behavior, a heuristic, that calls for risk seeking with high-probability losses. For some people in some circumstances, such a "bias" might still be sensible.

• Two other articles that point to useful heuristics that might be interpreted as irrational biases come to mind: Chen and Schonger on ambiguity aversion and the heuristic not to transact with folks who know a lot more than you do about the transaction; and Smitizsky, Liu, and Gneezy on endowment effects and the heuristic that as a buyer you try to understate your willingness-to-pay and as a seller you tend to exaggerate the value of the good to you.

White and Perfors (2022) on Ambiguity Aversion in Vignettes

Joshua P. White and Andrew Perfors, “Ambiguity Aversion in Qualitative Contexts: The Role of Prior Beliefs,” May 22, 2022; available here.

• The idea is to test for ambiguity aversion in more-or-less familiar risky situations that are not about money, such as blind dates or election outcomes. Further, the issue of whether ambiguity aversion arises from people holding pessimistic beliefs about the actual odds facing them in ambiguous situations is explored.

• The three lab experiments employ Amazon Mechanical Turk (overall n>2000) and the analysis is pre-registered, including the data exclusion criteria.

• The 24 vignettes: Would you rather be in the risky situation or the ambiguous situation? Half of the vignettes concern potential gains (e.g., new job) and half concern potential losses (e.g., losing a job). 

• The results: ambiguity aversion is typically present on average in both the gain and loss framings; ambiguity aversion is greater, however, in the gain scenarios, and the amount of aversion varies quite a bit across scenarios. 

• The scenario that tracked an Ellsberg urn problem showed (easily) the highest ambiguity aversion. 

• For some individuals, the aversion to ambiguity seems to derive from pessimistic feelings about how ambiguity would be resolved. (The Ellsberg-style urn vignette – which involved a casino! – is particularly likely to be affected by pessimism.) But there remains a good deal of ambiguity aversion that does not derive from pessimistic beliefs (nor from "comparative ignorance," the concern that a decision maker is up against better informed folks – such as casino owners, perhaps?).

Beine, Charness, Dupuy, and Joxhe (2020) on Earthquakes and Preferences

Michel Beine, Gary Charness, Arnaud Dupuy, and Majlinda Joxhe, “Shaking Things Up: On the Stability of Risk and Time Preferences.” IZA Discussion Paper No. 13084, March 2020. 

• It seems as if most economists believe that an individual’s risk and time preferences are pretty stable. 

• Patient people and the risk averse would seem to be less likely to migrate, and some empirical evidence supports this view. 

• Albanian per-capita GDP of just over $4000 per year is 30% of the EU average, despite recent high growth in Albania 

• The researchers converge on Tirana, where the currency is the Albanian lek, worth a bit less than one cent. Participants on average get about 12 dollars for a 20-minute or so interview, more than a day’s pay. 

• The 9 enumerators conducting the interactions speak Albanian. Geolocation data for the interviews is automatically collected, with n≈1500. 

• The first choice, aimed at gauging risk preferences: you have 100 coins, each worth 10 lek. You can put some of them in a bag. With probability .5, you will get triple what you put in; with probability .5, you will get nothing. How many coins will you put in the bag? (You keep the coins that you choose not to put in the bag). 

• For time preferences, the question concerns whether you would rather have 1000 lek today or some larger amount of money one month from today. The goal is to see how much more people will have to be paid to induce them to wait one month for their money. 

• The study started on August 31, 2019, and lasted through the end of the year. But on September 21 and November 26, 2019, two major earthquakes hit Tirana. 

• The control group in this (re-imagined post-quake) study is those people whose preferences were tested prior to the first earthquake. The two treatment groups are (1) those who experienced one earthquake, and (2) those who experienced two earthquakes, prior to their testing. 

• “the first earthquake reduces the amount invested in a risky asset (versus a safe asset) by about 25%, while the second one leads to an additional similar effect [p. 3].” Why the big change after the second one, when earthquakes have lost the element of surprise? And why should any changes in risk aversion be reflected in incentivized laboratory games with fixed probabilities? 

• Migration intentions share no connections with risk preferences among the study population, until after the second quake. (But pre-earthquake, already 70% of Albanians intend to migrate.) More exposure to the quakes makes more risk averse people more likely to migrate. More patience also means a lower intention to emigrate. 

• Before the first earthquake, about 42 coins are invested on average in the risk preferences situation: 144 people invest zero, 102 invest all 100 coins. (Aren’t there anti-gambling laws in Albania?) The number of coins risked falls from 42 to 34 to 23 with the earthquakes. 

• Would you take 2590 lek one month from now instead of 1000 lek today? Almost half of the participants would take the immediate 1000 lek. Patience (limited as it is) is cut in half with the first quake, and almost halved again with second. 

• Being exposed to heavier shaking (the geo data proxy for exposure) seems to be connected with a bigger change in risk and time preferences. 

• The earthquakes affect migration intentions indirectly, through their influence on risk and time preferences: the earthquakes mean that the now more risk averse people become willing to emigrate. More impatient people also are more interested in emigration.

Golman, Gurney, and Loewenstein (2020) on Information Gaps

Russell Golman, Nikolos Gurney, and George Loewenstein, “Information Gaps for Risk and Ambiguity.” Psychological Review 128(1): 86–103, 2021; http://dx.doi.org/10.1037/rev0000252 

• The authors argue that risk and ambiguity aversion arise from the desire to avoid unpleasant thinking about unanswered questions. (Risk and ambiguity loving, alternatively, is associated with the prospect of being spurred to think about pleasant matters.) 

• If you have a question with an unknown answer, you have an information gap. The attention that this gap attracts from you depends on salience (contextual factors which highlight the gap) and importance. 

• Gambling raises the importance of certain information gaps – which team will win? – and hence, directs our attention towards them. We therefore like to gamble when we welcome the increased attention, and are dissuaded from gambling on topics we don’t like to think about. 

• A key information gap concerns uncertain outcomes. Risk aversion (even with minimal stakes) can arise from our desire to avoid thinking about the uncertainty. Compound lotteries, er, compound the uncertainty, and the aversion. 

• The previous two bullet points offer new explanations for (1) betting on your favorite team and (2) low-stakes risk aversion. (A risk averse person presumably would want to bet against their favorite team, as a way of buying insurance against the bad outcome that arises if the preferred team loses.) 

• When shown risky prospects one-at-a-time, people seem to respond similarly to more and less ambiguous situations. When there is a choice between prospects, however, ambiguity aversion emerges. The comparison among alternatives presumably makes the information gaps (not knowing the precise probabilities) more salient. 

• People with relevant expertise enjoy ambiguity, as in racetrack betting. But those who feel uninformed find the ambiguity unsettling. 

• Study 1: Pittsburgh Pirates fans choose how much to bet on either their team’s hits or the number of strikeouts suffered by batters on their team. These bets involve no ambiguity – once the fans choose a bet size, their probability of being assigned the “winning” side of the bet is .5. Nevertheless, the fans bet more when hits are the relevant subject. Presumably they do not enjoy having to think about the strikeouts that the players on their team will suffer. 

• Study 2: Carnegie Mellon University alumni are given the opportunity to bet on the future relative rankings of two excellent CMU computer science departments – or on the relative future prospects of two not-so-good natural science departments. In this case, objective probabilities are not known, there is ambiguity in the prospects. The alumni display aversion to the ambiguity; however, they show a lot less aversion to that ambiguity when betting on the great departments. It seems that thinking about the future success of CMU star departments is a happy thought that they, to some extent, welcome.

Vosgerau and Peer (2019) on Preference Malleability

Joachim Vosgerau and Eyal Peer, “Extreme Malleability of Preferences: Absolute Preference Sign Changes Under Uncertainty.” Journal of Behavioral Decision Making 32(1): 38-46, January 2019.

• The evidence on the extent to which preferences are constructed as opposed to revealed has been challenged. Much of the evidence is based on a person preferring option A to option B in one condition, and then, preferring option B to option A in a somewhat different condition -- where the conditions differ only with respect to supposedly irrelevant factors. 

• The best evidence of preference malleability would be where a person evaluates the same prospect (just A, no B) in opposite directions – is it a good or a bad, is it desirable or undesirable? – in different conditions. 

• The authors conduct two experiments (the second experiment is a near replication of the first with a larger sample size and some other improvements) where subjects indicate whether they have to be paid to accept a prospect (it’s bad), and also whether they would pay for the opportunity to obtain the same prospect (it’s good). If they are both willing to pay and need to be paid for the prospect, then it seems that their preferences are quite malleable. 

• One lottery: you win 30 NIS (Israeli New Shekels) if heads and lose 20 NIS if tails; second lottery: you win 30 NIS if a die toss brings an odd number and lose 20 NIS if the toss yields an even number. These lotteries are thus identical in terms of payoffs and probabilities. 

• The experimenters ask how much subjects would need to be paid (“compensation amount”) for one of the lotteries and how much they would be willing to pay for the other lottery. 

• Most people are willing-to-pay, and even more people demand compensation -- but about half (experiment 1) or about 84% (experiment 2) do both. People do not seem to know whether the lottery is desirable or undesirable or both: they do not seem to possess some underlying, stable preference concerning this lottery. 

• In experiment 1, the more people were willing to pay for the lottery, the more they also required to be compensated to receive the lottery.

•  The experimental design also allows some inferences to be made concerning risk preferences; for instance, if your willingness-to-pay for a lottery is less than the lottery's expected value, that is evidence that you are risk averse. Risk preferences, too, are not clear or stable: about 34% of the participants in experiment 1 (and 61%+ in experiment 2) indicate that they are both risk averse and risk seeking/neutral!

Lowenstein (2019) Responds to Duckworth, Milkman, and Laibson (2019)

George Loewenstein, “Self-Control and Its Discontents: A Commentary on Duckworth, Milkman, and Laibson.” Psychological Science in the Public Interest 19(3): 95-100, 2019.

• Much to admire in Duckworth, Milkman, and Laibson (2019), especially the categorization of strategies to bolster self-control into situational v. cognitive and self-deployed v. other-deployed.

• Two (sort of) implicit assumptions seem to hover around the analysis, however, and I [Loewenstein] want to challenge those assumptions (assumptions which the authors themselves do not accept).

• One assumption that readers might come away with is that worsening problems such as lack of savings or obesity are brought about by self-control shortcomings, and that the strategies presented in Duckworth, Milkman, and Laibson (2019) are appropriate means to solve those problems. But inadequate self-control is not the source of (relatively recent) problems like rises in obesity and declines in savings. Rather, these problems have other, large causes, and thus, other solutions.

• A second assumption that readers might adopt is that self-control is about trying to get people to take a longer-term perspective. But many people suffer from being excessively future-minded (they are "hyperopic") -- these people need enhanced self-control to limit their future focus, to increase their current indulgence.

• The US has only become an outlier among nations with respect to undersaving and obesity in the past 40 years or so -- these problems do not reflect a new wave of a lack of self-control that swept across the land. What has changed is, for instance, a growth in income inequality and in the availability of snack foods and credit cards.

• Self-control is not about the present versus the future; it is about affect (System 1) versus more considered thinking (System 2) – this is why some people indulge insufficiently (“tightwaddism” and workaholism). (Look at the substantial investments people make in education -- do these evince present bias?) Mental accounting (like establishing an entertainment account) can help with future bias, too!

• Behavioral economics research might have a puritanical (or "Calvinist") bias.

O’Donoghue and Somerville (2018) on Risk Aversion

Ted O’Donoghue and Jason Somerville, “Modeling Risk Aversion in Economics.” Journal of Economic Perspectives 32(2): 91-114, Spring, 2018.

• As Rabin and Thaler (2001) indicate, expected utility (EU) maximization seems incapable of explaining people’s risk preferences – even though it does suggest some nice measures of the degree of risk aversion. 

• Other models of risk aversion, however, might prove more empirically sound, while maintaining tractability. That is, we might not need expected utility to analyze problems involving risk aversion, as alternative models could replicate current standard, EU-based results, while offering still more or avoiding the shortcomings associated with the assumption of EU maximization. 

• Consider standard findings associated with insurance: (1) A more risk averse person is willing to pay more for insurance (than is a less risk averse person); and (2) at a fixed price per dollar of insurance (fixed in excess of the actuarially fair price), a more risk averse person will purchase more insurance (than will a less risk averse person). 

• Consider standard findings associated with financial investments: (1) In a world with one safe (riskless) and one risky asset, more risk averse people invest less in the risky asset; and (2) if the population as a whole becomes more risk averse, the price of the risky asset must fall (equivalently, the expected return from holding the risky asset must rise). 

• Consider standard findings of principal/agent analysis, say, when a risk neutral principal hires a risk averse agent: (1) if the agent’s effort is not observable, then to encourage effort, the agent will have to bear some risk (so that lower output leads to less pay); and (2) the unobservability of effort is costly to the principal, who would prefer to contract on effort directly. 

• The various claims made concerning risk aversion in the three previous bullet points do require risk aversion – but they do not require expected utility maximization. That is, many of the ideas that have been developed around the concept of risk aversion – developed in the context of expected utility maximization – remain valid even when expected utility maximization is not descriptively accurate.

• Consider loss aversion as an alternative approach, one where outcomes are judged against a reference point and “losses loom larger than gains.” For prospects with some loss and some gain outcomes, loss aversion can generate risk averse behavior. (This style of loss aversion does not require "diminished sensitivity," the feature of prospect theory that leads to risk averse behavior in the gains domain and risk seeking behavior in the losses domain.)

• A second alternative, also featured in prospect theory, is probability weighting. The general notion is that, in practice, decision weights might not equal objective probabilities. Specifically, probability weighting typically involves the overweighting of low probability events and the underweighting of high probability events. This type of probability weighting can generate, depending on the options, either risk seeking or risk averse behavior. Lotteries, for instance, might be attractive (induce risk seeking behavior) due to the overweighting of the low-probability outcome of a large win. 

• Finally, consider contextual features and salience. Extreme or vivid outcomes (like deaths in terrorist attacks) might garner intense attention, leading to higher decision weights on those outcomes. The contextual feature of the available (although unchosen) options can exert influence by shifting the salience of other outcomes. Again, choices displaying risk aversion can arise from these factors. Expected utility maximization is neither necessary nor sufficient for explaining risk-averse behavior.

Vis and Kuijpers (2018) on Prospect Theory and Foreign Policy

Barbara Vis and Dieuwertje Kuijpers, “Prospect Theory and Foreign Policy Decision-Making: Underexposed Issues, Advancements, and Ways Forward.” Contemporary Security Policy 39(4): 575-589, 2018.

• Risk, in both prospect theory and in useful foreign policy applications, involves outcome uncertainty—so risk considerations are important in the gains domain as well as the loss domain. 

• Probability weighting often is ignored in applications of prospect theory, but it can override the usual “risk averse for gains, risk loving for losses” result. 

• In particular, low probability gains might see risk loving behavior, and low probability losses might be met with risk averse behavior. 

• And in foreign policy applications, low probabilities for unusual events are common. 

• Multiple dimensions are relevant in foreign policy decisions, so there can be multiple reference points, and outcomes might involve gains with respect to some reference points but losses with respect to other reference points. 

• When (to whom and for what decisions) might prospect theory apply? What decisions are better described by expected utility theory? 

• Oddly, ambiguity goes unmentioned in this article.

Rouyard et al. (2018) on Prospect Theory and Chronic Disease

Thomas Rouyard, Arthur Attema, Richard Baskerville, José Leal, Alastair Gray, “Risk Attitudes of People with ‘Manageable’ Chronic Disease: An Analysis Under Prospect Theory.” Social Science & Medicine 214: 144-153, 2018.

• Many patients are non-compliant with recommended medical treatments, at a cost to their health. Is it possible that their choices reflect risk-loving behavior in the loss domain?

• Two outcomes are examined in this study, longevity and quality of life. The usable sample size is n=110; 52 members of this sample have Type 2 diabetes mellitus.

• The empirical approach is aimed at identifying the prospect theory “value function” (in both the loss and gain domains) and the probability weighting (of an objective probability of .5). The estimation of the value function includes an estimation of the extent of loss aversion.

• Many questions are of the nature: Your status quo is to live 20 more years with an excellent quality of life. You must choose between option A, which would give you (with certainty) an additional 3 years of life with a pretty good quality of life, or option B, which offers a 50% chance of gaining 6 years of life, 3 years of high quality and 3 years of low quality, and a 50% chance of remaining with the status quo.

• For loss aversion, the relevant question is of the nature: The status quo is to live 20 more years with an excellent quality of life. A risky prospect available to you involves a 50% probability of gaining an additional 10 years of life with a pretty good quality of life, and a 50% probability of losing L years of life. What is the L that makes you indifferent between the risky prospect and the status quo?

• The authors find that most folks are risk averse in both the loss and gains domains. Older people tend to be more risk averse. Loss aversion is significant (median λ=1.19).

• It probably isn’t risk seeking that leads to medical noncompliance.

Clark and Lisowski (2017) on Prospect Theory and Moving

William A. V. Clark and William Lisowski, “Prospect Theory and the Decision to Move or Stay.” Proceedings of the National Academy of Sciences of the United States of America 114(36): E7432–E7440, September 5, 2017.

• Clark and Lisowski examine residential moves (of 70 kilometers or more) in Australia between 2010 and 2014. 

• The analysis assumes that the status quo residence represents the reference point. 

• The authors argue that the endowment effect in housing occurs because residents learn more about advantages and disadvantages of their housing, and that this raises “use values” relative to “exchange values.” 

• Previous empirical evidence indicates that the probability of moving decreases with the duration of living in the current residence; the authors, therefore, include a duration variable, as well as an indicator for owning versus renting, among their independent variables. 

• Clark and Lisowski also possess a variable that captures the extent of self-reported risk aversion on the part of the surveyed individual. It turns out that people who don’t move are quite likely to be in the top half of the population in terms of this measure of risk aversion. 

• Movers tend to be younger, and they tend to be renters in their initial residence. Couples with kids are less likely to move.  

• Both duration and home ownership are associated with decreased re-location, which the authors interpret as an endowment effect -- but are these endowment effects?

Hermann and Musshoff (2016) on Measuring Time Preferences

Daniel Hermann and Oliver Musshoff, “Measuring Time Preferences: Comparing Methods and Evaluating the Magnitude Effect.” Journal of Behavioral and Experimental Economics 65: 16-26, December 2016.

• Two different approaches to measuring discount rates in the past have revealed similar rates for US students – but what about for entrepreneurs, and for German students?

• This article consist of a web-based experiment with German farmers (n=111) and students (n=178); farmers are standing in for entrepreneurs, as farmers must make significant investment decisions that only yield results in the long-term.

• The experiments are conducted with both 100 and 300 euro benchmark amounts; the idea is to test for the “magnitude effect,” in which revealed discount rates fall as monetary amounts rise.

• Further, some previous estimates of discount rates might be skewed by the assumption of risk neutrality.

• The Coller and Williams (CW) task: You can receive €100 in three weeks. Or, you can receive more than €100 in twelve weeks. How much more than €100 do you need before you are willing to wait the extra nine weeks? This experiment is repeated for amounts 3 times as high.

• The Holt and Laury (HL) task: Lottery A offers prizes of either €180 or €144, while lottery B offers the outcomes €346.50 or €9. The higher prize has the same probability of occurring in both lotteries. How high does the probability of the higher prize have to be to get you to choose Lottery B?

• The p task, from Laury et al. (2012): Lottery A pays out zero half the time and €100 half the time, with the prize collected in three weeks. Lottery B pays out zero or €100 too, but doesn’t pay out until 12 weeks from now. How much greater than .5 does the probability of winning €100 have to be to get you to choose Lottery B, and thus wait the additional nine weeks? As with CW, this experiment is replicated with payouts three times as high.

• For farmers, the estimated average discount rate from CW is 12.9% for €100 tests, and 8.8% for €300 tests. For the p task, rates are significantly higher, at 30.6% for the €100 test, and 28.6% for the €300 test. 

• In the joint estimation, student discount rates are similar to the farmers’. For the p-test on students, while this method still led to higher discount rates (significantly so for the €300 version) compared to the joint estimation, the increase was not nearly as a great as it was for farmers. 

• For both students and farmers, raising the stakes to €300 lowers discount rates significantly in the joint estimation – the decline is greater for students. In the p-test approach, the fall in discount rates associated with higher stakes is not significant. This non-result suggests that for risky alternatives, the magnitude effect might not exist.

Larson, List, and Metcalfe (2016) on Myopic Loss Aversion and the Equity Premium Puzzle

Francis Larson, John A. List, and Robert D. Metcalfe, “Can Myopic Loss Aversion Explain the Equity Premium Puzzle? Evidence from a Natural Field Experiment with Professional Traders.” August 31, 2016; available here.

• The puzzle: the real return on US equities is about 8% per annum, versus about 1% for riskless assets. This spread cannot easily be explained as a risk premium. 

• One hypothesis: traders display myopic loss aversion (MLA), and hence the frequent downticks (short-term declines in asset value) are psychologically costly – people will only put up with these costs if there is an offsetting premium in the monetary return. If MLA can explain the equity premium puzzle, then it must be present in the “marginal” trader. 

• Laboratory experiments have found that myopic loss aversion is common. The standard design involves varying the rate at which price information is delivered to traders. Those who receive information at high frequency are exposed to more revelations of downticks, and hence, if they display MLA, they will underinvest in the risky asset, the one that is subject to lots of downticks. 

• The Larson, List, and Metcalfe paper employs a (natural?) field experiment, where traders do not know they are taking part in an experiment; they think they are beta-testing a new online trading platform. 

• The traders' recompense is to be paid eventually in-kind based on the profits that they accrue during their two weeks of testing. They can “buy” a risky asset whose return is tied (in a not-fully-obvious way) to the US dollar exchange rate. The tying is such as to bias the return to the asset to be positive. 

• The experiment reveals MLA – traders who are given infrequent (once per 4 hours) price updates keep more of their stake in the risky asset, and earn considerably more, than those traders who receive second-by-second updates. 

• Traders tend to desire more frequent price updates, but perhaps that information degrades their performance. 

• Since both the Frequent (n=73) and Infrequent (n=78) groups of traders can trade at any time, this experiment avoids a confounding feature of past laboratory experiments, that both information and trade opportunities are altered among conditions.

Viscusi and Gayer (2015) on Reasons to Distrust Government Nudges

W. Kip Viscusi and Ted Gayer, “Behavioral Public Choice: The Behavioral Paradox of Government Policy.” Harvard Journal of Law & Public Policy 38(3): 973-1007, 2015 [pdf].

• Behavioral departures from full rationality are often used as justifications for government interventions in markets. But the resulting government policies can institutionalize, not rectify, the rationality shortfalls.

• Regulators themselves possess rationality shortfalls, and there are features of the environment in which regulators operate that push them away from pursuing first-best policies.

• If the median voter possesses biases, then a democratic government is likely to share those biases.

• Less-than-rational individuals tend to bear the costs of their errors themselves – not so with regulators. Further, individuals might have enhanced incentives (relative to bureaucrats) to acquire relevant information. Regulators, like all of us, can be overconfident in their abilities.

• Can we trust the claims that people are less-than-rational, or at least the universality of the claims? People are heterogeneous, and what looks like a mistake might reflect specific, reasonable preferences.

• Many consumer durables now have energy efficiency mandates, justified by internalities. But the energy-efficiency misjudgment is far from a proven problem. The claims of energy savings tend to be engineering-based, unavailable in practice, while individual circumstances can rationalize seemingly myopic choices.

• We could be more confident in an even-handed use of behavioral economics if a lot of pre-existing mandates were being replaced by non-coercive nudges. But instead, we see behavioral economics being used to tighten regulation, not to loosen it. Notice that the less-than-complete (narrow) self-interest that behavioralists often emphasize implies that even externalities might be internalized without government policy.

• The EPA instituted a fuel economy labelling requirement that seems intended to remedy all the problems that their later efficiency mandates also targets – don’t they trust their own labelling regulation?

• In dealing with health and safety risks, government does not seem to be more rational than individuals. In practice, worst-case scenarios are over-weighted in regulatory policy; EPA methodology leads to cascading of conservative estimates so that extremely low-likelihood problems can dominate policy. Further, the number of people exposed to a risk, which should be central in formulating policy, is ignored.

• Increases in risk are a sort of loss, and loss aversion kicks in – in the form of alarmist regulatory responses to ebola, terrorism, etc.

• The FDA fears errors of commission much more than errors of omission. [Nonetheless, the evidence base is weak – look how often risks are revealed only after approval; then there are off-label uses, which are quite legal, despite not having been tested in the usual sorts of controlled trials.]

• If organic veggies carry less risk than non-organic vegetables, but they cost more, it could still be better health-wise for people to eat more, non-organic veggies.

• For people to accept a small increase in risk often involves a payment some six times larger than they would pay for the same reduction in risk – a reflection of loss aversion. The “first, do no harm” principle leads to a similar effect in policy. It is often hard to identify victims of the FDA’s failure to approve a useful drug.

• Agencies can have tunnel vision, treating their issue in isolation. In OSHA, for example, regulators are not even allowed to look at the costs of fixing a hazard. One result: costs per life saved vary widely across domains, in ways that seem to be far from optimal.

People are Not Exponential Discounters, and That’s OK

Some Notions Drawn, as I Recall, from Rabin (2002) and Frederick, Loewenstein, and O'Donoghue (2002)

• Would you rather have $20 now or $21 one week from now? If you choose the immediate $20 – a perfectly reasonable choice – then you discount monetary rewards by at least 5 percent per week. Would you rather have $20 now, or $250 one year from now? If you are an exponential discounter, and you preferred the immediate $20 in the initial situation, then you must prefer the immediate $20 to $250 one year hence, as 1.05 to the 52nd power is more than 12.6. If the question concerned two years from now, you would turn down $3100 in two years’ time for an immediate $20.

• Would you rather have $20 now or $22 one week from now? If you chose the immediate $20, then you discount by at least 10 percent per week. Would you rather have $20 now, or $2800 one year from now? If you are an exponential discounter, you must still want the $20, as 1.10 to the 52nd power is more than 140. In two years’ time, you’d turn down $400,000 (1.1 to the 104th power is more than 20,000) for an immediate $20. 

• Rabin showed that the sort of risk aversion over small-stakes gambles that most people display is inconsistent with expected utility theory, because such behavior would necessitate crazy choices for higher stakes gambles. What is demonstrated above is rather analogous, that the sort of time preference that people display for small stakes, short time-frame situations is not consistent with exponential discounting, because it would necessitate crazy choices for longer time-frame choices.

Barberis (2013) on 30 Years of Prospect Theory

Nicholas C. Barberis, “Thirty Years of Prospect Theory in Economics: A Review and Assessment.” Journal of Economic Perspectives 27(1): 173-96, 2013.

• Prospects are evaluated with decision weights not equal to probabilities, and with valuation tied not to overall wealth, but to gains and losses relative to a reference point. Besides probability weighting and reference dependence, prospect theory also invokes loss aversion and diminishing sensitivity. 

• Diminishing sensitivity with respect to losses is equivalent to risk seeking: the pain of losing $900 is more than 90 percent of the pain of losing $1000. 

• The probability weighting function overweights low probabilities and underweights high probabilities. These weights are not interpreted (within prospect theory) as mistakes. 

• What is the relevant reference point? Koszegi and Rabin (and others) take the reference point to be recent expectations. People then gain when consumption is larger than expected consumption; therefore (perhaps), I do not like to hear praise for a book that I intend to read. 

• The overweighting of low probability, good outcomes, helps to explain the interest in lotteries, and the low average return to some positively skewed financial securities. 

• Prospect theory is carried over to riskless choice via the endowment effect. The endowment effect comes in two forms, exchange asymmetries and willingness-to-pay/willingness-to-accept gaps; both can follow from loss aversion. 

• Some behaviors that looks like contradictions of prospect theory (such as the eroding of the endowment effect among experienced traders) could reflect different reference points.

Kahneman (2011) on Prospect Theory

Daniel Kahneman, “Prospect Theory.” Chapter 26, pages 278-288, in Thinking, Fast and Slow, New York: Farrar, Straus and Giroux, 2011.

• Outcomes (the carriers of utility) often seem to be associated with gains or losses relative to some reference point, not to overall states of wealth. Many people can’t generate a precise estimate of their wealth. 

• Consider choosing between the prospects (+$900; 1) and (+$1000, $0; .9, .1). They have the same expected value, but we would expect that most people would choose the certainty of gaining $900 to the risky option. 

• Now consider choosing between the prospects (-$900; 1) versus (-$1000, $0; .9, .1); many people would choose the risky prospect over the certainty of losing $900. People who are risk averse with respect to gains become risk loving with respect to losses. 

• In physical sensations and in many other ways we respond to differences from a reference point. Is a bowl of water warm? The answer depends on the environment, holding the temperature of the water constant. 

• Might loss aversion be an evolutionary adaptation, in that threats to the status quo are more urgent than are improvements? 

• Consider the prospect (+$x, -$100; .5, .5); how much does x have to be for you to be willing to accept this gamble? For most people, it is between $150 and $250, indicating a “loss aversion ratio” of 1.5 to 2.5. 

• Prospect theory ignores anticipated disappointment and regret, though these seem to matter in many actual choices.

Loewenstein, John, and Volpp (2013) on Leveraging Behavioral Biases to Help People

George Loewenstein, Leslie John, and Kevin G. Volpp, “Using Decision Errors to Help People Help Themselves.” Chapter 21, pages 361-379, in The Behavioral Foundations of Public Policy, Eldar Shafir, editor, Princeton: Princeton University Press, 2013.

• The oddly named “Theory of the Second Best” indicates that if there are some number n of conditions that must hold for things to be fully optimal (first best), then that is no reason to believe that moving from n-2 of those conditions holding to n-1 of the conditions holding represents an improvement. Perhaps your “first best” is to go to the cinema with your special friend to watch a touching romantic comedy. But if your special friend is not available (or perhaps has found someone new), then going to a romantic comedy might not be an improvement over the status quo of wallowing at home.

• Loewenstein, John, and Volpp apply the notion of the second best to fight behavioral fire with behavioral fire: harnessing departures from rationality to counteract other departures from rationality. Maybe overoptimism can be used to cancel out excessive risk aversion? 

• Asymmetric paternalism is an intervention that helps “irrational” people make better decisions, without imposing in a serious way upon the decisions of rational people. 

• The self-serving fairness bias: what favors me is fair. This bias can prevent the settlement of disputes between two parties. It can be used to promote a settlement, however, because both parties might be willing to trust a “neutral” mediator who can impose a settlement. 

• The stickiness of default options and the attractiveness of lotteries are two biases that can be used to promote weight loss, exercise, medical compliance, public transport use, and charitable contributions. 

• Lottery prizes are good motivators thanks in part to the overweighting of small probabilities. A daily lottery that lets you know if you won or not, but only pays if you were in compliance with the desired behavior on the day you won, also adds anticipated regret into the mix. 

• Some commercial entities (e.g. casinos) have significant pecuniary incentives to appeal to our less-than-rational impulses. But some firms, such as health insurers or employers who gain from our better compliance with medical protocols, have monetary incentives to make our decision making more “rational.” 

• Loewenstein, John, and Volpp note a number of biases that many people seem to display in their decisionmaking. These biases include narrow bracketing; the hot-cold empathy gap; projection bias; and present bias. 

• “Narrow bracketing” occurs when decisions are examined in isolation (perhaps as potential changes from the status quo) rather than holistically. 

• The “hot-cold empathy gap” refers to our inability to predict how we will behave in the “hot” state (perhaps when we are very hungry or angry) when we are examining our behavior while in the “cold” state. 

• “Projection bias” is the idea that people predict that their future preferences will be pretty much the same as their current preferences. But there might be hedonic adaptation, or a change in visceral factors. Projection is one explanation underlying the advice not to go grocery shopping on an empty stomach. 

• People save too little not because the rate of return to savings is too low, but (in part?) because of a “present bias” or an interest in instant gratification. The “Save More Tomorrow” plan allows people to (semi-)commit to savings increases at a later date, and this program has been quite successful in spurring savings.

• Is it distasteful or unethical to take advantage of common decision errors for paternalistic purposes?

Some Material Connected to Machina (1987)

Mark Machina, “Choice under Uncertainty: Problems Solved and Unsolved.” Journal of Economic Perspectives 1(1): 121-154, Summer 1987.

• A short review of choice under uncertainty: The general prospect (or lottery) is (x1, x2, …, xn; p1, p2, …, pn), where the xi’s are monetary outcomes and the pi’s are the associated probabilities.


• The expected value of the prospect (x1, x2, …, xn; p1, p2, …, pn) is p1x1+p2x2+…+pnxn = Σ pixi. 


• The expected utility of the prospect (x1, x2, …, xn; p1, p2, …, pn) is p1 U(x1) + p2 U(x2) +…+ pn U(xn) = Σ pi U(xi), where U(x) is the von Neumann-Morgenstern utility function defined over monetary outcomes xi. The standard model of choice under uncertainty is that a person will choose among prospects in such a manner as to maximize her expected utility.


• A person is risk averse if, when endowed with a riskless prospect, she always declines fair bets (bets that offer her the same expected value as her riskless prospect) – and this is equivalent to diminishing marginal utility of income.


• Machina (1987) and the Triangle Diagram: Fix the (three) dollar outcomes at x1, x2, x3; let x1<x2<x3. 


• With outcomes fixed but probabilities variable, every prospect (x1, x2, x3; p1, p2, p3) can be represented by a point in the unit simplex, which can be graphed as a triangle on p1-p3 axes (because p2 must equal 1-p1-p3, we only need a two-dimensional graph to indicate every prospect).


• Indifference curves for an expected utility maximizer will be linear in this space. Iso-expected value lines also will be linear. 


• We can use the diagram to speak about stochastic dominance; mean-preserving spreads; and risk preferences.


• Expected utility maximization requires that individual choices adhere to the "independence axiom": If the prospect P* is preferred to the prospect P, then the compound prospect aP* + (1-a)P’ is preferred to aP + (1-a)P’, for all prospects P’ and for all 0<a<1. 


• The independence axiom implies indifference curves that are linear in the probabilities, and hence, are straight, parallel lines within the triangle diagram. Nonetheless, many different choices seem to indicate that people have indifference curves that “fan out,” as opposed to being parallel lines.


• One common departure from the independence axiom (and hence from expected utility maximization) is the Allais Paradox (which can be neatly illustrated within the Triangle Diagram). Here's the setting:
  
  
                       Alternative 1                 Alternative 2
  
  
  Situation A:         ($1M;1)                           ($5M, $1M, $0; .1,.89,.01)
  
  
  Situation B:         ($1M,$0; .11,.89)          ($5M,$0; .1,.9)
  
  
  The "M" indicates that all dollar payoffs above involve millions of dollars. People typically choose alternative 1 in situation A, and alternative 2 in situation B. These two choices are inconsistent with expected utility maximization. [Why? To prefer alternative A1 to alternative A2, as an expected utility maximizer, you must have EU(A1) > EU(A2). This inequality can be rewritten as 1u($1) > .1u($5) + .89u($1) + .01u($0), and this inequality can be further simplified to .11u($1) > .1u($5) + .01u($0)*. If you also prefer  alternative B2 to alternative B1, then, as an expected utility maximizer, EU(B2) > EU(B1). This inequality can be rewritten as .1u($5) + .9 u($0) > .11u($1) + .89u($0), and this inequality can be further simplified to .1u($5) + .01u($0) > .11u($1), or equivalently, .11u($1) < .1u($5) + .01u($0). Compare this with inequality *; they contradict each other. Therefore, you cannot be an expected utility maximizer: there are no values for u($5), u($1), and u($0) such that your choices could be consistent with expected utility maximization.]

Rabin and Thaler (2001) on Risk Aversion and the Failures of Expected Utility

Matthew Rabin and Richard H. Thaler, “Risk Aversion,” Journal of Economic Perspectives 15(1): 219-232, Winter 2001.

·  In the expected utility (EU) model, risk aversion is equivalent to diminishing marginal utility of income.

·  Any meaningful risk aversion over small stakes is inconsistent with EU maximization, as it requires a crazy unwillingness to take on risk at larger stakes. In other words, EU maximizers must be effectively risk neutral for small stakes, such as those in laboratory experiments. Nonetheless, people display risk aversion at small stakes.

·  Extended warranties and rental car insurance are purchased by many people, though the small stakes (relative to lifetime wealth) and high prices involved imply that they should be unattractive to expected utility maximizers.

·  Small-scale risk averse behavior is consistent with loss aversion, where the status quo is the reference point, and with mental accounting (narrow bracketing), a failure to look at the situation in the bigger picture.

·  Even the money pump argument offers more support for loss aversion and narrow bracketing than for expected utility maximization, as people are not reliably turned into money pumps. They are more likely to purchase those ill-advised warranties, for instance, when the warranties are tied to the purchase of the good itself, thereby promoting an isolated view of the transaction; for most decisions, consumers will not be so misled. An expected utility maximizer who bought such a warranty, however, would then necessarily agree to all sorts of ridiculous purchases.

·  The rate-of-return on stocks (as opposed to bonds, say) seems to be excessive, even though there should be some premium for holding stocks because stocks are riskier than bonds. This “equity premium puzzle” might be due to loss aversion and narrow bracketing. The day-to-day fluctuations in stock prices cause many short-term losses for shareholders. The equity premium comes from the fact that loss-averse investors require compensation to put up with all of the short term (mental accounting) losses.

Rabin (2002) on Psychology and Economics

Matthew Rabin, “A Perspective on Psychology and Economics.” European Economic Review 46: 657 – 685, 2002.
 

• “Ceteris paribus, the more realistic our assumptions about economic actors, the better our economics [page 658].” Rabin is implicitly taking on Milton Friedman’s discussion in his 1953 essay “The Methodology of Positive Economics,” where Friedman suggests that the realism of assumptions is not a test of the value of a theory; rather, theories should be judged on their ability to predict the data or explain the evidence.

• The departures of behavior from traditional economics assumptions are both common and systematic. We are not fully rational, fully self-controlled, or fully self-interested.

• Three important behavioral regularities are loss aversion, the endowment effect, and an interest in behaving in a reciprocal fashion. Further, people seem to have preferences not over final outcomes alone, but over changes from a reference point – standard economics assigns utility only over final outcomes.

• The standard economics assumption of exponential discounting of future costs and benefits has never had any empirical justification. The “behavioral” assumption of a present bias not only is more realistic, but it also explains common behaviors such as undersaving and procrastination that are hard to square with exponential discounting. Further, the standard approach to risk aversion is like the standard approach to discounting, obviously wrong and incapable of explaining common behavior.

• The argument that markets would punish irrational behavior doesn’t mean we shouldn’t study such behavior – rather the opposite, actually. The fact that in some settings a bias dissipates is not to say that people do not have such a bias or that it cannot have meaningful implications.