Funding Public goods with Lotteries: Experimental Evidence John Morgan; Martin Sefton Heriberto Gonzalez October, 2007

Outline I. Introduction II. Motivation III. Theoretical Model IV. Experiments a. Penn State experiment b. Iowa experiment V. Results and Analysis Predictions VI. Conclusions

I. Introduction An effective means of raising funds through voluntary contributions is essential to provide public services Charitable gambling is a significant revenue generating instrument In Britain private charities raise 8% ( 500 millions) of their income through lotteries In 1992, in the US about $6 billion was raised by private charities through lotteries.

II. Motivation Will risk-neutral expected utility maximizers ever have an incentive to purchase lottery tickets with negative expected values? How effective are lotteries in financing public goods? When are lotteries more effective than other voluntary schemes for providing public goods?

II. Motivation Morgan (2000) develops a model of equilibrium wagering in lotteries whose proceeds are used to finance public goods We want to focus in three predictions of this model: the lottery provide (strictly) more of the public good than direct solicitations public good provision increases with the size of the lottery prize wagers vary with the return from the public good

III. Theory Morgan (2000) introduces a theory of demand for lottery tickets. Agents are risk-neutral expected utility maximizers with heterogeneous preferences and quasi-linear utility functions. In equilibrium, the gamble is unfair The amount of public good provision depends upon the rate of return from the public good and the size of the lottery prize Ticket purchases more than cover the cost of awarding prizes iff public good provision is efficient

III. Theory: simple model A linear homogeneous version of Morgans model N individuals; e endowments; R fixed prize The lottery is allowed to provide negative amounts of the public good. is the constant marginal per capita return of public good provision

If x i =0 If N >1 joint-payoffs are maximized at x i =e => VCM results in under-provision With R>0 equilibrium wagers are positive Extreme free-riding does not constitute an equilibrium in the lottery as it does in a VCM III. Theory: simple model N ==>

G L is increasing in R Taking limits a per capita payoff of lottery exceeds the per capita utility of e that is attained (in equilibria) under voluntary contributions The introduction of lottery alleviates the free-rider problem but does not eliminate it. III. Theory: simple model

Summarizing, The model implies particular levels of wagering given group size, prize level, and The model implies that wagers and public good provision increase with the size of the lottery prize The model predicts that wagers and public good provision increase with III. Theory: simple model

IV. Experiments: Penn State Two sets of parallel sessions In each set, one session used VCM and the other one LOT incentives 40 subjects were randomly allocated between two rooms Two more sessions were conducted in parallel, using identical procedures but different subjects (checking replicability)

IV-a. Experiments: Penn State Each session consisted of two phases Phase I: subjects were anonymously paired and played a 10-stage game Phase II: subjects were rematched and played a single- stage game against another anonymous partner Decisions in phase I as well as phase II are considered independents In each session, only possible communication between subjects is via their formal decisions

IV-a. Experiments: Penn State In every round subjects were endowed with 10 tokens They had to divide between a private and group account A token placed in the private account returned 100 points A token placed in the group account returned 75 points to the subject and his partner In the VCM treatment 8 tokens were placed directly in the group account yielding each subject 600 points In the LOT treatment, 8 tokens worth of points provided a prize of 800 to the winner of the lottery In this experiment were used two-person groups instead of 4 or more as usual in this kind of experiments

IV-a. Experiments: Penn State PREDICTIONS The Nash equilibrium calls for each subject to place either 0 tokens in the group account for VCM; or 8 tokens in the group account for LOT

IV-b. Experiments: Iowa Test the prediction that lotteries alleviate free-riding in a more traditional public good environment Eight sessions conducted in fall; each session 20 different subjects, visually isolated Each session consisted of 20 rounds, first five of which were designated as a practice rounds Subjects were randomly divided into four-person groups; they did not know who were in his group and the integrants in that group changed every round Each subject were endowed with 20 tokens

IV-b. Experiments: Iowa At the end of the session one of rounds was chosen at random to determine earnings Subjects received 25 cents for every 50 points Two sessions used the VCM treatment A token placed in the private account yielded 100 points A token placed in the group account yielded 75 points to everyone in the same group In the VCM treatment subjects received 600 points every round In the LOT treatment the lotterys winner received 800 points

IV-b. Experiments: Iowa Two sessions for the LOT treatment In the LOT treatment the lotterys winner received 800 points To investigate the effect of size of prize two more identical sessions to LOT treatment were used; the new prize was 1600 points To investigate the effect of linking lottery proceeds to public good provision two more identical sessions to LOT treatment were used; subjects received zero points from the group account

IV-b. Experiments: Iowa PREDICTIONS In theory, each subject should place 0 tokens in the group account for VCM 6 tokens in the group account for LOT 12 tokens in the group account for BIGLOT 1.5 tokens in the group account for BADLOT

V. Results The results from VCM sessions are similar to those from other public good experiments Figure 1 (Penn) and 2 (Iowa) reveals excessive contributions (relative to equilibrium) declining in later rounds

V. Results Despite that the equilibrium in the P-VCM treatment is supported by dominant strategies, the equilibrium is a superior predictor of behavior in the P-LOT treatment The average wagers in the I-LOT treatment do not converge to the Nash prediction, and in fact they remain excessive throughout both sessions.

V. Results By comparing LOT, for the BIGLOT the equilibrium is more efficient BADLOT is relatively efficient

V. Results When the Nash equilibrium prediction is more efficient, as in the P-LOT, BIGLOT or BADLOT, average wagers conform to the prediction quite well. When the prediction is less efficient, as in the I-LOT, there is excessive giving.

V. Results Averaging round by round, LOT increase contributions LOT increase public good provision

V. Results Comparing round-by-round Iowa treatments

V. Results We fail to reject the null hypothesis that the distributions are the same across sessions.

V. Results Figures 1-6 suggests that repetition has important effects in at least some of the sessions Wilcox matched-pairs test is used to determine whether the median contribution amounts vary across rounds in each of the treatments

V. Results Mean final round contributions to the group account are close to theoretical predictions except in the VCM and I-LOT treatments.

V. Results Agreement between actual and predicted contributions occurs when the equilibrium of the mechanism is relatively efficient, while actual contributions are excessive when the equilibrium is relatively inefficient.

V. Results When the public good is socially undesirable, contributions are significantly reduced

VI. Conclusions When individuals account for he benefits from public good provision it becomes rational for risk-neutral individuals to participate in such a lottery For relatively efficient lotteries wagering behavior is well predicted by the theory, while for less efficient we observe excessive wagering Despite excessive generosity in the VCM, lotteries increase the provision of the public good Large prize lotteries will be more successful fund-raising devices than smaller scale endeavors

V. Results When the equilibrium of the lottery is relatively efficient, average wagers are well predicted by the model Lotteries with a relatively efficient equilibrium generate higher levels of public good provision than VCM Lotteries are less successful in funding a socially undesirable public good