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.     

Charitable Lottery Structure and Fund Raising: Theory and Evidence

Do fixed-prize charitable lotteries generate more net revenue than do revenue-dependent lotteries? I present the results of an experiment designed to test a theoretical prediction of the relationship between the prize structure of a lottery funding a public good and individuals' participation in the lottery. I find that a fixed-prize lottery configuration induces significantly greater participation and a significantly higher level of public good funding than does a revenue-dependent lottery.     

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.     

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.     

Common fate,game harmony and contributions to public goods: experimental evidence

We experimentally study the effects of common fate on voluntary contributions to linear public goods. In each period, earnings are assigned to subjects according to the outcome of a lottery. In ‘common fate’, ‘independent fate’ and ‘rival fate’ treatments, the lottery outcomes of group members are (respectively) positively correlated, stochastically independent and negatively correlated. We observe the highest contributions and strongest reciprocity under common fate. Contrary to the game harmony hypothesis, contributions are not lower under rival fate than under independent fate. Surprisingly, under rival fate, having won the lottery in one period induces higher contributions in the next period.     

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.     

Public Versus Private Provision of Public Goods

It is well known that public goods are underprovided in a static setting with voluntary contributions. Public provision—in a median voter framework with proportional taxation—generally exceeds private provision. This paper compares private and public provision of public goods in a dynamic setting. In a dynamic setting, voluntary donations can result in efficient provision. Also, majority‐rule solutions exist even when taxes are not proportional to income. At low discount factors, public provision tends to exceed private provision. As patience increases, however, private provision may exceed public provision. This occurs because many outcomes with a low level of public good provision—and potentially large targeted transfer payments to particular individuals—become sustainable under public provision. Under private provision, however, large targeted transfers are unsustainable. To finance the public good, private provision tends to result in benefit taxation, and public provision tends to result in progressive taxation.     

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)     

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.     

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.     

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.     

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.     

Politically Determined Income Inequality and the Provision of Public Goods

Political processes may bring about Pareto improvements by increasing income inequality in a society that produces a public good by voluntary contributions. Proportional taxation funds a “governing agent.” The most endowed agent is the Condorcet winner for governing agent. When the tax rate can also be chosen by a vote, the ideal point of the agent with median initial endowment is the Condorcet winner under Cobb–Douglas utility. If Pareto improvements are possible, this ideal point corresponds to Pareto improvement. Pareto improvement may also be possible, even when a Leviathan set taxes, if there is deadweight loss from taxation. Pareto improvements are indeed always possible in “large” societies. On the other hand, no improvements may be possible if the initial distribution of wealth is very unequal in a “small” society, and Condorcet winners may not exist for other utility functions.     

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.     

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.     

On the existence of expected multi-utility representations

We prove the following facts related to the expected multi-utility representation of an affine preorder: If the prize space is not compact and if the lottery set consists of all probabilities on the prize space, standard independence and continuity axioms do not guarantee the existence of a (continuous) representation. If the prize space is σ-compact and lotteries have compact support, a representation exists. When the preorder in question is bounded, this result extends to the set of lotteries that consists of all probabilities on the prize space. For the case of monetary lotteries, the boundedness assumption in this last result can be dropped, provided that the preference relation at hand is monotone and risk-averse.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.     

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.