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.

Oswald and Winkelmann (2019) on Lottery Wins and Happiness

Andrew J. Oswald and Rainer Winkelmann, “Lottery Wins and Satisfaction: Overturning Brickman in Modern Longitudinal Data on Germany.” In: Rojas M. (ed.) The Economics of Happiness. Springer, Cham., 2019.

• The "Brickman" in the title refers to an influential 1978 article that first questioned the Easterlin claim that, in cross-section data, higher income leads to greater happiness, and in part used the happiness of lottery winners as evidence. Brickman et al. found almost no improvement in happiness for lottery winners. [The article is Brickman, P., Coates, D., & Janoff-Bulman, R. (1978). Lottery winners and accident victims: Is happiness relative? Journal of Personality and Social Psychology, 36(8), 917–927.]

• The (usual) positive relationship that exists between income and happiness might not be causal. That is, more money might not mean more happiness -- it could be the other way around, that happier people earn more, or there could be some other factor that drives both happiness and income.

• Lottery winners to the rescue! The income windfall of lottery winners has a suggestion of exogeneity, it does not arise from unobserved personal traits.  

• The "rescue" provided by examining lottery winners might be limited, in part by the small numbers of such winners, and in part because lottery players might share relevant characteristics that are not possessed to the same degree by the rest of the population. This latter issue can be addressed by comparing only lottery winners, looking to see if winners who win more money are happier than those who win less money.  

• Another problem in terms of generalizing claims about money and subjective wellbeing (SWB) is that it is possible that the source of income, and not just the amount, matters for SWB.

• Lottery winning doesn’t seem to do much for health or for children’s health – perhaps because winners engage more intensely in risky activities like drinking alcohol. Mental health problems and mortality might increase for lottery winners.

• If your neighbor wins the lottery, you are more likely to buy a new car and engage in home renovation -- that is, you make significant expenditures on publicly visible goods. 

• Regular lottery players (in Germany) are drawn disproportionately from the less educated segments of society.

• A (biggish?) lottery win boosts satisfaction with your income, like would occur with a 20% increase in income – but the effect fades within a couple of years. A similar tale, with smaller magnitudes, applies to overall life satisfaction.

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!

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.

Lindqvist, Östling, and Cesarini (2018) on Lottery Wealth and Happiness

Erik Lindqvist, Robert Östling, and David Cesarini, “Long-run Effects of Lottery Wealth on Psychological Well-being.” NBER Working Paper No. 24667, May 2018 [pdf of a similar version here]. 

• Adaptation might suggest that the (exaggerated?) hedonic benefits from a monetary windfall will be short-lived. 

• Lottery data can help us identify the extent to which wealth causes increased happiness or life satisfaction, in both the short and the long run. 

• The authors look at Swedish lottery winners 5 to 22 years after their stroke of good fortune. 

• The estimation undertaken here of how much happiness flows from wealth compares very similar people: they are all lottery winners, but the amounts they won differ. 

• Happiness and Life Satisfaction are reported on an 11-point scale. They are highly positively correlated, though are influenced differently by wealth. Other variables collected are Mental Health, and Financial Life Satisfaction.

• Life Satisfaction is raised by an extra $100,000, and the effect is lasting. 

• The source of the increased Life Satisfaction is improved Financial Life Satisfaction. (Yes, a financial windfall improves one's financial satisfaction!)

• Happiness and Mental Health are not improved (in the long run) by a lottery win. 

• This research was all pre-registered: opportunities to p-hack are minimal; N ≈ 3350 

•  Lottery winners in this sample tend to behave prudently – they don't squander their winnings in a short period of time. 

Koessler, Torgler, Feld, and Frey (2016) on Promising to Pay Your Taxes

Ann-Kathrin Koessler, Benno Torgler, Lars P. Feld, and Bruno S. Frey, “Commitment to Pay Taxes: A Field Experiment on the Importance of Promise.” Tax and Transfer Policy Institute, Australian National University, Working Paper 10/2016, November 29, 2016 [pdf here].

• A natural field experiment (n≈2000) is conducted in Switzerland (in 2013); the subjects, Swiss taxpayers, do not know that they are taking part in an experiment. 

• The experiment concerns whether it is possible to encourage timely tax payments by having taxpayers voluntarily promise to remit their taxes on time. One potentially confounding factor, however, is that a new “dunning” policy for late taxpayers is enacted concurrently with the experiment. 

• There are two “promise” treatments. In both cases, subjects are told that if they fill in and return a postcard promising to pay their taxes on time, and then do pay their taxes on time, they will be entered into a lottery. The differences between these two treatments is that in one case the lottery prize is cash – 1000 Swiss francs – and in the other, the prize is a wellness spa trip for two, worth approximately 1000 Swiss francs. 

• Both promise treatments have parallel treatments that provide the same lottery to punctual payers, but that do not require or provide the option for the non-binding promise. A control treatment with no lottery or promise completes the collection. 

• Almost one-third of the subjects who are given an opportunity to promise to pay on time make the promise. The willingness to promise is a pretty strong signal both of whether you have paid on time in the past, and of whether you will pay on time this year. 

• Those who were in the spa lottery and who made the promise saw a significant jump in their compliance rates. But the lotteries with promise opportunities do not seem to do any better overall than the lotteries without the promise opportunities. 

• My takeaway, perhaps not as optimistic as that of the authors, is that the “promise” intervention is pretty weak tea.

Bühren and Pleßner (2014) on “The Trophy Effect”

Christoph Bühren and Marco Pleßner, “The Trophy Effect.” Journal of Behavioral Decision Making 27: 363-377, 2014 [pre-publication version pdf here].

• For everyday (convenience) goods, the endowment effect is reflected in about a 2-to-1 ratio of willingness-to-accept (payment to relinquish a good) to willingness-to-pay (to acquire the good). But for environmental goods or tickets to a basketball game, the ratio could be much higher. The gap is smaller when folks are in a good mood and larger when folks are in a bad mood, though sadness (as opposed to a bad mood) tends to reduce the gap. 

• The authors conduct a series of experiments involving endowing half of the subjects with a pen, under four treatment conditions. All the subjects know that the pen, though a nice one, could be purchased at a nearby shop for 2.10 euro. 

• In the Baseline treatment, half the subjects are given pens, then, willingness-to-accept (wta) and willingness-to-pay (wtp) are assessed. In the Trophy treatment, there is a 15-minute math quiz. Those who score above the median receive a pen, and become potential sellers in the exchange game to follow. 

• In the Work treatment, sellers are chosen randomly, but then they must take the math quiz before being given their pen. (They worked for their pen, they are told, though their performance on the quiz is immaterial.) In the Lottery treatment, everyone is informed that there is a lottery for pens, and the half who win the lottery are given pens. 

• The baseline treatment results in the usual (but weird!) endowment effect, with wta about twice as high as wtp. The Lottery treatment results in a slightly higher, but statistically equivalent, ratio. (Losers in the lottery don’t have a wtp that is lower than in the baseline treatment.) The Work treatment gives similar results, though the average wta (for those diligent workers!) is enhanced. 

• The broader “winning” condition (Trophy plus Lottery Treatments) yields a higher wta (compared to the other two treatments). The broader “work” condition (Trophy plus Work) yields a jump in wta, too. The Trophy treatment has a huge impact on wta, which went to 4.40 euro – and also dropped wtp from 1 euro to .5 euro; the wta/wtp ratio assessed at the medians is 9.6! It looks like the work element (taking the test) is slightly more important than the winning element in driving the trophy effect. And math quiz “losers” don’t like having the pen around to remind them of their failure. 

• The authors replicate a standard finding, that people do not anticipate the endowment effect. In the Work condition, they expect their wta to be less than 2 euro, but it is over 3.5 euro after the 15-minute quiz. 

• In one study, participants are asked how likely they think it is that their math test had been mis-graded. Trophy winners seem to decrease their wta when doubt of their deserving creeps into their mind. In yet another study, there’s (1) a two-hour delay or (2) a one-week delay before the wta and wtp valuations are assessed. With a one-week delay, we are back at the baseline endowment effect: the trophy effect evaporates. And the two-hour delay is statistically equivalent to the one-week delay.

Datta and Mullainathan (2014) on “Behavioral Design”

Saugato Datta and Sendhil Mullainathan, “Behavioral Design: A New Approach to Development Policy.” Review of Income and Wealth 60(1): 7–35, March 2014.

• Behavioral economics can help us design development policies that will work. There are no guarantees, of course – much of what we have learned comes from small-scale field experiments, and their external validity and ability to scale are not yet proven. 

• The poor are like the rest of us, though their poverty adds to their psychological burdens. 

• A farmer’s failure to use fertilizer might not arise from an underlying preference not to use it; indeed, it can happen even where there is a desire to use fertilizer. People procrastinate, and they do so repeatedly; people also lack self-control to resist temptations, including temptations to use resources for things other than fertilizer. As a result, the timely provision of fertilizer at a small subsidy can have significant impacts on usage; likewise, a commitment savings plan can spur fertilizer use. 

• Four types of mental resources are scarce: (1) self-control; (2) attention; (3) cognitive capacity; and (4) understanding. More information or even financial subsidies may not resolve the problems created by these scarce resources. 

• Datta and Mullainathan argue that development problems might be fairly situation-specific, and that the binding constraint or constraints might implicate behavioral issues. (Compare with Dani Rodrik's work (with co-authors) on "growth diagnostics".) Datta and Mullainathan suggest a behavioral mapping of problems that reveals where these constraints (bottlenecks) might bind. Commitment savings accounts, steady income flows, appropriate defaults, reward lotteries, and reminders: these are some strategies that can help to overcome behavioral bottlenecks.

Mullainathan on Development Economics (2006)

Sendhil Mullainathan, “Development Economics Through the Lens of Psychology.” Proceedings of the Annual Bank Conference on Development Economics, 2006 [pdf].

• Parents claim to value education highly, but kids attend school sporadically. The problem seems to be the short-term decisions by the parents, so it might be best to target those decisions. The provision of meals in schools might help, and perhaps collecting school fees in small, regular payments rather than as one large, annual payment. Policies that increase school attendance also might improve teacher morale.

• ROSCAs serve as savings commitment devices, promoting regular, small deposits. The lottery-like, skewed payoff is a commitment not to spend the savings until there is a major purchase. Holding wealth in illiquid forms such as jewelry or livestock also helps solve commitment problems. If the access to microcredit undermines other savings commitments, then the mere profitability of a micro-lending program is not a good indicator of its social value.

• Making banks available to rural dwellers might make saving, and not spending, the default condition, providing some commitment. 

• Loss aversion suggests that there is a lot to be said for protecting status quo positions in the course of reform. Existing stakeholders might be grandfathered, as a means to avoiding the imposition of losses.

• People look at the world in a biased way, and can perceive failures of reciprocity even where they do not exist. They might conform their behavior in accord with a negative stereotype. 

• Development policies can be aimed at solving internal problems (commitment, self-control, bias) as well as external problems. 

Atalay et al. (2014) on Prize-Linked Savings Accounts

Kadir Atalay, Fayzan Bakhtiar, Stephen Cheung, and Robert Slonim, “Savings and Prize-Linked Savings Accounts [pdf].” Journal of Economic Behavior & Organization 107, Part A: 86-106, November 2014.

• Lotteries are popular in the US, and poorer households tend to spend a relatively larger share of their income on lotteries. 

• A prize-linked savings (PLS) account is one that enters savers in a lottery, while protecting the principal, the amount of funds deposited by savers. The prize for the lottery typically is financed by paying lower interest on savings than would be paid in the absence of a lottery. It is as if a portion of all interest payments are confiscated and turned into a prize that goes to just one of the savers; the lottery usually features a probability of winning proportional to a saver’s share in overall deposits. 

• PLS accounts are common in some countries, but essentially illegal in the US due to anti-gambling laws. The experiments described in this article aim to determine if US residents would find PLS accounts attractive, and whether PLS accounts would raise total savings (as opposed to just diverting savings from standard savings accounts). 

• The experiments are web-based. Participants are asked about how they would allocate $100 between cash (to be received in 2 weeks’ time); standard lottery tickets (not a PLS); and standard savings (available in 10 weeks). The participants receive some recompense but not, for the most part, the actual results of their investment decisions – the starting $100 (largely) is imaginary. Later, they repeat their choices, with a PLS as an additional option. 

• The experimental results suggest that the introduction of PLS accounts would increase total savings markedly. Further, much of the money invested in PLS accounts would be drawn from funds that otherwise would have gone to purchasing standard lottery tickets. These effects are particularly pronounced among lower-income people and those with little savings.

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.

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?