Reducing ambiguity in lotteries: evidence from a field experiment

Ambiguity about the chances of winning represents a key aspect in lotteries. By means of a controlled field experiment, we exogenously vary the degree of ambiguity about the winning chances of lotteries organized to incentivize the contribution for a public good. In one treatment, people have been simply informed about the maximum number of potential participants (i.e. the number of lottery tickets released). In a second treatment, this information has been omitted as in all traditional lotteries. Our general finding shows that simply reducing the degree of ambiguity of the lottery leads to a sizable and significant increase (67%) in the participation rate. This result is robust to alternative prize configurations.     

Financing Public Goods by Means of Lotteries

When viewed as taxes, lotteries are routinely criticized as being both inequitable and inefficient. But is this an entirely fair comparison? Frequently lotteries are used in lieu of voluntary contributions by private charities and governments when taxes are not feasible. When heterogeneous individuals with quasi-linear preferences participate in lotteries whose proceeds will be used to fund a public good, we find that, relative to voluntary contributions, wagers in the unique lottery equilibrium (a) increase the provision of the public good, (b) are welfare improving, and (c) provide levels of the public good close to first-best as the lottery prize increases.     

Funding Public Goods with Lotteries: Experimental Evidence

Why do individuals participate in charitable gambling activities? We conduct a laboratory investigation of a model that predicts risk-neutral expected utility maximizers will participate in lotteries when they recognize that lotteries are being used to finance public goods. As predicted by the model, we find that public goods provision is higher when financed by lottery proceeds than when financed by voluntary contributions. We also find support for other comparative static predictions of the model. In particular we find that ticket purchases vary with the size of the fixed prize and with the return from the public good: lotteries with large prizes are more effective, and ticket purchases drop dramatically when the public good is not valued by subjects.     

The economic analysis of lotteries

This paper considers policy issues arising in the design, regulation and taxation of lotteries, focusing on the market for an on-line lottery game. Demand determines who buys lottery tickets and in what quantities. The design of lotteries affects the terms on which tickets are supplied.
UK data suggest that its lottery may be priced too high to maximize lottery revenue – more revenue might be raised if the proportion of sales allocated to tax and other levies were smaller.
Having established the positive economics of lotteries, the paper then assesses their welfare implications. Pari-mutuel lotteries enjoy scale economies and, as natural monopolies, are invariably run either by government agencies or a regulated licensee. I estimate consumer surplus and identify the excess burden that arises from existing (over)taxation of lotteries. The large price elasticity of demand implies that revenue raised from the lottery is raised very inefficiently. Moreover, the demand for lottery tickets is inferior (and there is some evidence that such games are contagious and addictive). So using lotteries as a vehicle for raising revenue is extremely regressive. Finally, I consider other policy implications: induced effects on charitable giving and on other forms of gambling; the impact on the government budget; perceptions of risk; and distributional considerations.     

An International Comparison and Analysis of Lotteries and the Distribution of Lottery Expenditures

Lotteries are found in nearly half of the world's countries, with annual worldwide lottery ticket sales topping $115 billion. Despite the global presence of lottery games, there has been little research conducted on any international aspect of lotteries. This paper presents the first-ever examination and comparison of lottery games from around the world. Differences in both absolute and relative lottery expenditures are presented. Estimates for the income elasticity of demand for lottery tickets provide evidence on the distributional burden of lottery expenditures. These estimates consider each country by continental location and country income level. Further analysis reveals that lower income countries could adopt Lotto games in order to increase revenues. Recognizing that the distributional impact of lottery games is one of the greatest concerns surrounding lotteries, it is shown that the introduction of Lotto games does not significantly affect the distributional burden of lottery ticket expenditures. Given the international scope of lotteries and the availability of international lottery game data, the paper concludes by discussing future research on international lottery games.     

Poverty and probability: aspiration and aversion to compound lotteries in El Salvador and India

Some experimental participants are averse to compound lotteries: they prefer simple lotteries that depend on only one random event, even when the simple lotteries offer lower expected value. This paper proposes that many behavioral “investments” represent more compound risk for poorer people—who often face multiple dimensions of deprivation—than for richer people. As a result, identical aversion to compound lotteries can prevent investment among poorer people, but have no effect on richer people. The paper reports five studies: two initial studies that document that aversion to compound lotteries operates as an economic preference, two “laboratory experiments in the field” in El Salvador, and one Internet survey experiment in India. Poorer Salvadoran women who choose a compound lottery are 27 percentage points more likely to have found formal employment than those who chose a simple lottery, but lottery choice is unrelated to employment for richer women. Poorer students at the national Salvadoran university choose more compound lotteries than richer students, on average, implying that aversion to compound lotteries screened out poorer aspirants but not richer ones. Poorer and lower-caste Indian participants who choose compound lotteries are more likely than those who choose simple lotteries to have a different occupation than their parents, which is not the case for better-off participants. These findings suggest that the consequences of aversion to compound lotteries are different in the context of poverty and disadvantage.     

THE EFFECT OF CASINO PROXIMITY ON LOTTERY SALES: EVIDENCE FROM MARYLAND

The continued expansion of the casino industry has caused increasing concern regarding the cannibalization of other industries, and in particular, state lotteries. For example, Maryland Lottery sales flattened shortly after casinos began opening in the state. Although previous papers have found that casinos and lotteries have a negative relationship with each other, no previous research has analyzed the impact of casino proximity on lottery sales or has examined the relationship between casinos and different types of lottery games. In this paper, we examine ZIP code‐level monthly lottery sales data from Maryland between July 2009 and February 2014, in order to test the impact of casino proximity on lottery sales, by type of game. Our findings indicate that aggregate lottery sales decline more in closer proximity to casinos, but that casinos affect different lottery products differently. We discuss the consumer behavior and public finance implications of the findings. (JEL H27, H4, L83)     

Lottery expenditures in Canada: a regional analysis of determinants and incidence

This article examines two issues; first, it evaluates the statistical significance of a number of socio-economic and demographic variables on the level of household lottery expenditures in the six regions of Canada. While some household characteristics vary in the extent to which they significantly affect the level of lottery expenditures across regions (wealth, age, occupation, mother tongue and urban location, for example), others are significant in every region. Regional consistency exists in the statistical significance of after tax household income, sex and education of the head of household – lottery expenditures increase as incomes increase; lottery expenditures are significantly lower for female heads of households than for their male counterparts; lottery expenditures decline as the education level of the head of household increases. Second, lottery expenditures are found to be regressive, although the degree of regressivity is less than for lotteries in the United States.     

Experiments on lotteries for shrouded and bundled goods: Investigating the economics of fukubukuro

Fukubukuro (or lucky bag) is a familiar institution in Japan and elsewhere in which the exact contents of a New Year sales item are hidden from the consumer before purchase. Motivated by the fukubukuro example and the lack of evidence on risk attitudes in lotteries involving goods, we conduct a laboratory experiment in which the outcomes are bundled or unbundled goods. The implied gains to a monopoly seller for marketing goods in lottery form rather than separately are only clearly positive for lotteries where there is a higher probability of obtaining the more highly valued good.     

On the Evaluation of Options on Lotteries: An Experimental Study

We present the results of a comparative experimental study of the evaluation of simple lotteries and call/put/insurance options on these lotteries. The main findings and conclusions are:

(a) The observed bidding patterns depend on the type of asset under evaluation. In particular, subject behavior when buying or selling a basic lottery seems much more cautious than their behavior when buying or selling options on that lottery.

(b) The observed bidding patterns also depend on subject positions with respect to the underlying asset. In particular, the bids for buying lotteries and options long are statistically uncorrelated with the bids for selling the same lotteries and options short.

(c) Subjects with extreme risk attitudes are more inclined to violate basic no-arbitrage conditions (like the call-put parity) when bidding for the different lotteries.

We demonstrate that it is difficult to reconcile the experimental evidence with mainstream theories on individual decision and choice (although we find strong support for prospect theory in some parts of the data). We conclude that the evaluation of options on lotteries is context-dependent and subtler than perceived by existing theories.     

Economic shocks and lottery sales: an examination of Maine State lottery sales

ABSTRACT

Most U.S. states earn significant amount of revenues from lottery sales. However, they are also criticized for promoting the lotteries because they have been seen as taking advantage of poor populations. The purpose of this study is to identify the impact of various economic factors on lottery sales by using zip-code level sales within the state of Maine. The results show that an increase of 1% in unemployment rate results in a 0.38% increase in draw lottery sales, but it has no significant impact on instant lottery sales. This highlights the importance of differentiating between two major types of lotteries.     

Lottery or waiting-line auction?

This paper studies the efficiencies of the two most widely used non-price allocation mechanisms: lotteries and waiting-line auctions. As our analysis suggests, in addition to the fairness of the mechanism, the use of lotteries in lieu of waiting-line auctions can be also justified from an efficiency point of view. In particular, we show that the less dispersed consumers’ time valuations are, the more efficient is a lottery relative to a waiting-line auction. In addition, we identify four conditions under which a lottery dominates a waiting-line auction in expected social surplus preserving. Furthermore, the numerical simulations we conduct indicate that over a predominantly wide range of circumstances, a lottery is more socially efficient than a waiting-line auction as an allocative mechanism in the absence of a conventional price system.     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

Lottery expenses and charitable contributions – Taiwan's experience

Individuals’ contributions are affected by their lottery outlays if they consider their spending of lottery funds on charities to be a substitute for or a complement to their direct charitable contributions. This study investigates the effect of lottery outlays on charitable contributions based on the experience of lottery introduction in Taiwan. The estimates reveal that lottery outlays exert a positive effect on charitable contributions while the quantitative impact is significant. This study thus provides evidence ameliorating the pessimistic prospect that people may reduce their direct charitable contributions when they spend more on lotteries. Possible explanations for the positive effect are also discussed.     

A fundraising mechanism inspired by historical tontines: Theory and experimental evidence

The tontine, which is an interesting mixture of group annuity, group life insurance, and lottery, has a peculiar place in economic history. In the seventeenth and eighteenth centuries it played a major role in raising funds to finance public goods in Europe, but today it is rarely encountered outside of a dusty footnote in actuarial course notes or as a means to thicken the plot of a murder mystery. This study provides a formal model of individual contribution decisions under a modern variant of the historical tontine mechanism that is easily implemented by private charities. Our model incorporates desirable properties of the historical tontine to develop a mechanism to fund the private provision of a public good. The tontine-like mechanism we derive is predicted to outperform not only the voluntary contribution mechanism but also another widely used mechanism: charitable lotteries. Our experimental test of the instrument provides some evidence of the beneficial effects associated with implementing tontine-like schemes. We find that the mechanism has particular power in cases where agents are risk-averse or in situations where substantial asymmetries characterize individual preferences for the public good.     

Lotteries, Group Size, and Public Good Provision

We analyze the effect of group size on public good provision under the Morgan (2000) lottery mechanism. For a pure public good, the lottery performs quite well as public good provision is found to increase in group size, even when the lottery prize is held constant. By contrast, for fully rival public goods, per capita provision is found to decrease in group size, even when the lottery prize is proportional to group size. Further, the per capita level of provision will approach zero when group size is sufficiently large.     

Nash consistent representation of effectivity functions through lottery models

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model—i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries—which has a Nash consistent representation. The latter means that there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions satisfying the minimal requirement of respecting first order stochastic dominance among lotteries. No additional condition on the original effectivity function is needed.     

Free riders and the optimal prize in public‐good funding lotteries

We prove the existence and uniqueness of an equilibrium in a game where players, whose preferences exhibit constant absolute risk aversion or constant relative risk aversion, contribute to a public good via lottery‐ticket purchases. Contrasting models with risk neutrality, we show that an equilibrium with a strictly positive amount of the public good may not exist without a sufficient number of participants who are not too risk‐averse. We show that players who are more risk‐averse purchase fewer lottery tickets and are more likely to free ride in equilibrium. In fact, it is possible for free riders to place a larger value on the public good than do those who contribute. In a symmetric equilibrium, we show that an upper bound exists for the amount of the public good, even though there are infinitely many participants. Furthermore, we derive a lottery prize that maximizes the amount of the public good in a symmetric equilibrium and find that such a prize always results in an overprovision of the public good.     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

On Bargaining for an Indivisible Good

This note studies contracts involving lotteries for the purpose of trading an indivisible good. Lottery contracts allow players to reach agreements for trading the good even if the reservation price of the potential buyer is below that of the potential seller. When certainty exchanges are possible, lottery contracts often dominate them. An interesting feature of the contracts is that the probability of trading the good depends on the players' bargaining powers, but the payments do not.Journal of Economic LiteratureClassification Numbers: C78.