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Funding Public goods with Lotteries: Experimental Evidence John Morgan; Martin Sefton

Funding Public goods with Lotteries: Experimental Evidence John Morgan; Martin Sefton. Heriberto Gonzalez October, 2007. Outline. Introduction Motivation Theoretical Model Experiments Penn State experiment Iowa experiment Results and Analysis’ Predictions Conclusions. I. Introduction.

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Funding Public goods with Lotteries: Experimental Evidence John Morgan; Martin Sefton

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  1. Funding Public goods with Lotteries: Experimental EvidenceJohn Morgan; Martin Sefton Heriberto Gonzalez October, 2007

  2. Outline • Introduction • Motivation • Theoretical Model • Experiments • Penn State experiment • Iowa experiment • Results and Analysis’ Predictions • Conclusions

  3. 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.

  4. 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?

  5. 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

  6. 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

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

  8. III. Theory: simple model • If b<1 and R=0 (VCM) => xi=0 • If Nb>1 joint-payoffs are maximized at xi=e => VCM results in under-provision • With R>0equilibrium wagers are positive • Extreme free-riding does not constitute an equilibrium in the lottery as it does in a VCM N ==>

  9. III. Theory: simple model • GL is increasing in R • Taking limits a per capita payoff of lottery exceeds the percapita 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.

  10. III. Theory: simple model Summarizing, • The model implies particular levels of wagering given group size, prize level, and b • 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 b

  11. 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)

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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 lottery’s winner received 800 points

  17. IV-b. Experiments: Iowa • Two sessions for the LOT treatment • In the LOT treatment the lottery’s 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

  18. 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

  19. 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

  20. 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.

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

  22. 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.

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

  24. V. Results • Comparing round-by-round Iowa treatments

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

  26. 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

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

  28. 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.

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

  30. 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

  31. 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

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