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    Richard Zeckhauser

    Recent medical literature suggests that vitamin D supplementation protects against acute respiratory tract infection. Humans exposed to sunlight produce vitamin D directly. This paper investigates how differences in sunlight, as measured... more
    Recent medical literature suggests that vitamin D supplementation protects against acute respiratory tract infection. Humans exposed to sunlight produce vitamin D directly. This paper investigates how differences in sunlight, as measured over several years within states and during the same calendar month, affect influenza incidence. We find that sunlight strongly protects against influenza. This relationship is driven by sunlight in late summer and early fall, when there are sufficient quantities of both sunlight and influenza activity. A 10% increase in relative sunlight decreases the influenza index in September by 3 points on a 10-point scale. This effect is far greater than the effect of vitamin D supplementation in randomized trials, a differential due to broad exposure to sunlight, hence herd immunity. We also find suggestive evidence, consistent with herd immunity theory, that the protective sunlight effect is strongest with a middle level of population density. David Slusky ...
    Hurricane Katrina did massive damage because New Orleans and the Gulf Coast were not appropriately protected. Wherever natural disasters threaten, the government-- in its traditional role as public goods provider-- must decide what level... more
    Hurricane Katrina did massive damage because New Orleans and the Gulf Coast were not appropriately protected. Wherever natural disasters threaten, the government-- in its traditional role as public goods provider-- must decide what level of protection to provide to an area. It does so by purchasing protective capital, such as levees for a low-lying city. We show that if private capital is more likely to locate in better-protected areas, then the marginal social value of protection will increase with the level of protection provided. That is, the benefit function is convex, contrary to the normal assumption of concavity. When the government protects and the private sector invests, due to the ill-behaved nature of the benefit function, there may be multiple Nash equilibria. Policy makers must compare them, rather than merely follow local optimality conditions, to find the equilibrium offering the highest social welfare. There is usually considerable uncertainty about the amount of inv...
    We consider the interaction of two enemy nations. Nation 1 wants to develop a nuclear bomb (or other weapons of mass destruction). Nation 2 wants to prevent such a development through the deterrence of a threatened attack, or an actual... more
    We consider the interaction of two enemy nations. Nation 1 wants to develop a nuclear bomb (or other weapons of mass destruction). Nation 2 wants to prevent such a development through the deterrence of a threatened attack, or an actual attack if it thought the bomb was produced. 2 has an intelligence system that imperfectly indicates the presence of a bomb. 1, if lacking the bomb, can open its facilities to prevent an attack. A further uncertainty is that nation 2 does not know nation 1’s type. He could be a Deterrer, whose prime goal is to avoid an attack, or he could a Provocateur who prefers an unjustified attack if he does not possess the bomb, so as to build support from inside his nation and the outside world. The game has a unique sequential equilibrium. The qualitative nature of that equilibrium depends on parameters, on preferences and information conditions. A number of initially counterintuitive results emerge. For example, it may sometimes be rational (an equilibrium str...
    There are two players. Player 1 is of one of two types: B, whose capability to build a nuclear bomb is approaching a critical level, and NB, which does not have such a capability. The type is a private information of 1. Let β, 0 < β... more
    There are two players. Player 1 is of one of two types: B, whose capability to build a nuclear bomb is approaching a critical level, and NB, which does not have such a capability. The type is a private information of 1. Let β, 0 < β < 1 be the probability of B. β is commonly known. Player 2 would regard the capability to build the bomb as a severe threat, and has the capability to attack and destroy1’s facilities. (For expositional clarity, we treat Player 1 as male and Player 2 as female.) ∗Ariel University, Israel, artyomj@ariel.ac.il †The Interdisciplinary Center, Herzliya, Israel and Stony Brook University, NY, USA,amty21@gmail.com ‡Harvard University, USA,Richard Zeckhauser@hks.harvard.edu
    Due to betrayal aversion, people take risks less willingly when the agent of uncertainty is another person rather than nature. Individuals in six countries (Brazil, China, Oman, Switzerland, Turkey, and the United States) confronted a... more
    Due to betrayal aversion, people take risks less willingly when the agent of uncertainty is another person rather than nature. Individuals in six countries (Brazil, China, Oman, Switzerland, Turkey, and the United States) confronted a binary-choice trust game or a risky decision offering the same payoffs and probabilities. Risk acceptance was calibrated by asking individuals their " minimum acceptable probability " (MAP) for securing the high payoff that would make them willing to accept the risky rather than the sure payoff. People's MAPs are generally higher when another person rather than nature determines the outcome. This indicates betrayal aversion. (JEL C72, C91)
    Complicated pricing schedules can make it very difficult for consumers to know what price they are paying. Such schedules are in widespread use in important economic domains such as taxation, assistance to the poor, and utility pricing.... more
    Complicated pricing schedules can make it very difficult for consumers to know what price they are paying. Such schedules are in widespread use in important economic domains such as taxation, assistance to the poor, and utility pricing. When people have limited understanding of the actual schedules they face, they are likely to perceive them in a crude fashion. We define the term “schmedule” to be an inaccurately perceived schedule. We call the act of behaving as if one were facing a schmedule rather than the true schedule, “schmeduling.” Our focus is on two forms of schmeduling: ironing and spotlighting. Ironing arises when an individual facing a multipart schedule perceives and responds to the average price at the point where he consumes. Spotlighting occurs when consumers identify and respond to immediate or local prices, and ignore the full schedule, even though future prices will be affected by current consumption. We analyze the welfare implications of ironing in three setting...
    Managers display distinctive word choice styles when they conduct earnings conference calls. Some CEOs and CFOs are straight talkers. Others, by contrast, are vague talkers. Vague talkers routinely use words such as “approximately”,... more
    Managers display distinctive word choice styles when they conduct earnings conference calls. Some CEOs and CFOs are straight talkers. Others, by contrast, are vague talkers. Vague talkers routinely use words such as “approximately”, “probably”, or “maybe”. Analysts and the stock market attend to the style of managerial talk. They find earnings news less informative when managers are vague and respond less and more slowly as a result. Overall, quantitative information and straightforward contextual information are complements. Large firms with vague managers receive lower valuations relative to their book value.
    Money is the prime incentive in economic models. Recent evidence makes it clear that people are also greatly concerned about how their incomes compare with those of others, suggesting that rank may be a strong motivator as well. Three... more
    Money is the prime incentive in economic models. Recent evidence makes it clear that people are also greatly concerned about how their incomes compare with those of others, suggesting that rank may be a strong motivator as well. Three experiments in Vietnam assessed whether students in realworld learning environments were concerned with their performance rankings. The results showed that concern with rank, even when rankings were not publicly revealed, strongly motivated performance on academic tests. Moreover, rank was able to outweigh money as a motivator.
    For decades, the U.S. Air Force has contemplated replacing the A-10 Thunderbolt II “Warthog” with a newer fighter aircraft. However, a quantitative analysis comparing the Warthog’s performance and costs with those of its intended... more
    For decades, the U.S. Air Force has contemplated replacing the A-10 Thunderbolt II “Warthog” with a newer fighter aircraft. However, a quantitative analysis comparing the Warthog’s performance and costs with those of its intended replacement, the F-35 Lightning II Joint Strike Fighter, shows that retiring the Warthog would be operationally unsound and fiscally imprudent. The rationale for the replacement is that it would increase airpower capability while controlling costs. That rationale does not withstand scrutiny. An effectiveness analysis based on results from a survey of joint terminal attack controllers indicates that the A-10 vastly outperforms the F-35 in providing close-air support (CAS), a critical requirement for future conflicts against terrorists and insurgents. A cost analysis demonstrates that replacing the A-10 before its service life ends in 2035 would cost at least $20.9 billion. The replacement plan would waste substantial resources and seriously impair U.S. milit...
    Consumer search serves productive roles in an economy with multiple goods. In equilibrium, search promotes the sorting of consumers among producers, thereby enabling the market for new goods, and potentially increasing welfare and profits... more
    Consumer search serves productive roles in an economy with multiple goods. In equilibrium, search promotes the sorting of consumers among producers, thereby enabling the market for new goods, and potentially increasing welfare and profits above the benchmark case (an economy with a single good, hence, no search). When competitors are few, additional direct competitors may benefit a firm, as more sellers may encourage more consumers to search. In return, consumer search entices producers of new goods to enter. Neither of these externalities, nor the coordination problems faced by consumers and producers, is appropriately recognized in the literature. (JEL D11, D43, D62, D82, D83, G22)
    Behavioural economic research has established that defaults, one form of nudge, powerfully influence choices. In most policy contexts, all individuals receive the same nudge. We present a model that analyses the optimal universal nudge... more
    Behavioural economic research has established that defaults, one form of nudge, powerfully influence choices. In most policy contexts, all individuals receive the same nudge. We present a model that analyses the optimal universal nudge for a situation in which individuals differ in their preferences and hence should make different choices and may incur a cost for resisting a nudge. Our empirical focus is onterminated choosers(TCs), individuals whose prior choices become no longer available. Specifically, we examine the power of defaults on individuals who had enrolled in Medicare Advantage plans with drug coverage and whose plans were then discontinued. Currently, if these TCs fail to actively choose another Medicare Advantage plan, they are defaulted into traditional fee-for-service Medicare (TM) without drug coverage. Overall, the rate of transition of TCs into TM is low, implying that original preferences and status quo bias overpower the default. Increasing numbers of Americans ...
    Massive dollars shuttled back and forth among firms on the twisted path to and passage of the 2017 tax reform. Prices of individual stocks responded to the difference between initial and revised expectations. From the bill's... more
    Massive dollars shuttled back and forth among firms on the twisted path to and passage of the 2017 tax reform. Prices of individual stocks responded to the difference between initial and revised expectations. From the bill's initiation in the House to final passage, high-tax firms gained significantly, given the dramatic cut from 35 percent to 21 percent in the corporate tax rate. Internationally-oriented firms suffered notably, since investors assessed that the surprisingly high repatriation tax outweighed the benefits from territorial taxation. Daily price movements show that the aggregate market responded positively to lower expected taxes.
    The patrons of Raphael, among the most powerful men in Europe, paid far more for his paintings than they did for those by most of his celebrated contemporaries. The present study aims to bring attention to this impressive, albeit rarely... more
    The patrons of Raphael, among the most powerful men in Europe, paid far more for his paintings than they did for those by most of his celebrated contemporaries. The present study aims to bring attention to this impressive, albeit rarely discussed, observation. A combination of approaches from different disciplines provides a methodological framework for analyzing extraordinary compensation for artists in a wide range of areas and time periods. Signaling, risk management, and the superstar model, all concepts from economic theory, together with distinction, a theory from sociology, help to explain this phenomenon and to understand its importance.
    Recollection bias is the phenomenon whereby people who observe a highly unexpected event hold current risk beliefs about a similar event that are no higher than their recollection of their prior beliefs. This article replicates and... more
    Recollection bias is the phenomenon whereby people who observe a highly unexpected event hold current risk beliefs about a similar event that are no higher than their recollection of their prior beliefs. This article replicates and extends the authors' previous study of recollection bias in relation to individuals' perceptions of the risks of terrorism attacks. Over 60% of respondents in a national U.S. sample of over 900 adults believe that the current risk of a future terrorist attack by either an airplane or in a public setting is no higher than they recall having believed, respectively, before the 9/11 attack and before the Boston Marathon bombing. By contrast, a rational Bayesian model would update to a higher currently assessed risk of these previously uncontemplated events. Recollection bias is a persistent trait: individuals who exhibited this bias for the 9/11 attack exhibited it for the Boston Marathon bombing. Only one-fifth of respondents are free of any type of ...
    A pioneering game theorist who made the world a safer place
    Traditional decision theory distinguishes between risk and uncertainty. With risk, the probabilities of possible outcomes are known; with uncertainty, those outcomes are known, but not their probabilities. We introduce the concept of... more
    Traditional decision theory distinguishes between risk and uncertainty. With risk, the probabilities of possible outcomes are known; with uncertainty, those outcomes are known, but not their probabilities. We introduce the concept of ignorance, a third, less tractable category. With ignorance, even the possible outcomes cannot be identified. Ignorance takes importance when high payoffs are associated with the unidentified outcomes. Thus we focus on consequential amazing developments, or CADs. CADs spring upon societies as well as individuals. In the policy realm, the 2008 financial meltdown and the Arab Spring would represent CADs, major unanticipated events. For an individual, a CAD might be the discovery that a faithful spouse of many years has a secret second family, or that our trusted business partner has been pilfering corporate secrets all along. Authors depict the implications of consequential ignorance in some of the greatest of literary works: Hamlet's ignorance of his father's killer, Macbeth's unawareness of outcomes when he attempts to seize the Scottish crown, Odysseus's journey back to Ithaca involving a series of consequential adventures, all unknowable. Consequential ignorance cannot be studied in a controlled laboratory setting, since its payoffs are high, its time delays often long, and merely introducing the subject tends to give away the game. Thus we study ignorance through great works of literature, from antiquity to the present day, positing that great writers understand how humans make decisions. We distinguish between unrecognized and recognized ignorance. In the latter category, we identify specific cognitive biases at work. We provide a formula for calculating consequential ignorance that incorporates the expected magnitudes and assessed base rates for CADs. Finally, we propose steps towards measured decision making under ignorance.
    The U.S. hospital industry is unusual in that for-profit, private nonprofit, and public entities compete side-by-side. We evaluate alternate theories of the nonprofit form employing three approaches: an historical review, a case study,... more
    The U.S. hospital industry is unusual in that for-profit, private nonprofit, and public entities compete side-by-side. We evaluate alternate theories of the nonprofit form employing three approaches: an historical review, a case study, and an econometric analysis. The metaphor of an ecosystem, bringing to mind disparate organizations in coadapting relationships, helps explain the historical ebbs and flows of ownership structures in the U.S. hospital industry. The entry and exit of for-profit hospitals appears consistent with dynamic efficiency in resource allocation. Our econometric analysis focuses on hospital behaviors in California and Florida during 1982-1990, a period corresponding to a shift in the reimbursement system from cost-pass-through to fixed price. The reimbursement change does not lead to differences in the mix of services provided by different ownership forms. While for-profits reduce their level of uncompensated care, their payer mix of Medicare, Medicaid and private patients continues to be similar to that of nonprofit non-teaching hospitals. No absolute cost advantages to for-profits emerge, not even relative success in cost containment by large-chain for-profits. The main response of large-chain for-profits to reimbursement pressures has been reorganizations.
    Introduction: Joining the Game 1 The History of Early Admissions 2 The State of the Game 3 Martian Blackjack: What Do Applicants Understand about Early Admissions? 4 The Innocents Abroad: The Admissions Voyage 5 The Truth about Early... more
    Introduction: Joining the Game 1 The History of Early Admissions 2 The State of the Game 3 Martian Blackjack: What Do Applicants Understand about Early Admissions? 4 The Innocents Abroad: The Admissions Voyage 5 The Truth about Early Applications 6 The Game Revealed: Strategies of Colleges, Counselors, and Applicants 7 Advice to Applicants Conclusion: The Essence of the Game and Some Possible Reforms Appendix A Median SAT-1 Scores and Early Application Programs at Various Colleges Appendix B Data Sources Appendix C Interview Formats Notes Acknowledgments Tables and Figures Index
    Does independent market adjustment always lead to a less than Pareto optimal supply of goods when there are external economies? The traditional Pigovian conclusion that it did has recently been rejected by some eminent economists. This... more
    Does independent market adjustment always lead to a less than Pareto optimal supply of goods when there are external economies? The traditional Pigovian conclusion that it did has recently been rejected by some eminent economists. This rejection began with a contribution in this Review by James Buchanan and Milton Kafoglis, who produced examples in which independent market adjustment apparently provided optimal or even supra-optimal supplies of goods with external economies, and thus found the orthodox Pigovian conclusion unsatisfactory. Their finding has been accepted by many economists, including William Baumol, who attempted, in a subsequent communication in this journal, to provide a formal, general explanation of their result. This note will show that Buchanan and Kafoglis failed to call attention to the major theoretical point

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