Econ 2230: Public Economics. Lecture 15: Fundraising: Lotteries

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1 Econ 2230: Public Economics Lecture 15: Fundraising: Lotteries

2 Lotteries 1. Overview of lotteries 2. Theory of voluntary provision through lotteries (Morgan, 2000) 3. Experimental evidence of lottery effect (Morgan and Sefton, 2000) 4. Revenue dependent vs. fixed prize lottery (Dale 2004) 5. One vs. multiple prizes 6. Field experiment (Lange et al 2006)

3 2. Theory of voluntary provision through lotteries (continued) Morgan (2000) model: Set of betors/donors N={1,,n} x i contribution to public good/ wagers in lottery z i consumption of private good X(N) = i x i X(N\i) = X(N) - x i G provision of public good Consumer s objective Max U i = z i + h i (G), h i >0, h i >0 S.t. z i + x i = w i

4 Morgan Model Fixed prize raffle: Prize R, won with probability x i /X(N) Provision of public good G = X(N) R An equilibrium has a set of bettors N R N and lottery purchases {x 1R, x 2R,,, x nr ) Consumer s objective Max U i = w i x i + R x i /X(N) + h i (X(N) R) F.O.C R [X(N) - x i ]/ [X(N)] 2 + h i =0-1 + R X(N/i)/ [X(N)] 2 + h i =0

5 Morgan Results shown last Despite a negative expected return from winning - risk neutral individuals place bets that exceed the value of the prize Fixed prize raffle provides more of the public good than voluntary contributions Fixed prize raffles are welfare improving How close to efficiency can the raffle get us?

6 Morgan, 2000 Theorem 2: suppose that all individuals have quasi-linear preferences, then given any ε>0 there exists an economy of size i w* i and a raffle with prize R* such that the public goods provision induced by the raffle lies within ε of the first-best outcome, i.e., G R [G*-ε,G*] Pf: Recall x i > 0 if Ψ i (G;R) = R /[R+G] + h i >0 Let G i such that Ψ i (G i ;R) = 0 WOLG G 1 > G 2 > > G n Let R solve Ψ n (G* ;R ) = 0 Let G be the provision i that t results under R Since G < G* then Ψ i (G ;R ) Ψ n (G ;R ) > 0 i Thus, x i >0, i

7 Morgan, 2000 At R>R, x i >0, i i F.O.C. =0 i [ R X(N/i)/ [X(N)] 2 + h i (X(N)-R)]=0 - n + R (n-1) (R+G) / [R+G] 2 + i h i (G) =0 - n+r (n1)/[r+g]+ R (n-1) + i h i (G) =0 As R note that i h i (G) 1 Thus G G* for R With G/ R >0 for some G R [G*-ε,G*] there exists an R* such that - n+r* (n-1) / [R*+ G R ]+ h R i i (G ) =0

8 Morgan, 2000 Theorem 3: A fixed prize raffle provides a positive amount of the public good if and only if the public good is socially desirable Proof: Show that bets will fund the public good only when socially desirable Socially desirable: i h i (0) >1 Suppose n <n bettors i n h i (X(N)-R) n + (n -1) R/X(N) = 0 Suppose fund the public good, i.e. X(N)>R i n h i (0) > n (n -1) = 1 i.e., the public good is socially desirable n h (0) > n i i i h i(0) >1 Suppose socially desirable and does not fund the public good Socially desirable i n h i (0) >1 and does not fund i n h i (0) < 1 contradiction

9 Risk of fixed prize raffle? Not raising sufficient funds to cover prize What are other options? Pari-mutuel raffle where the prize R is determined as a percentage (p) of wagers, e.g., the prize from winning the raffle px(n) and the public good (1-p)X(N) Will that work? Max U i = w i x i +p X(N) x/x(n) i + h i ((1-p) X(N)) Max U i = w i x i + p x i + h i ((1-p) X(N)) FOC -1 +p + (1-p) h i ((1-p) X(N)) =0 FOC h i ((1-p) X(N)) =1

10 Pari-mutuel Raffles FOC h i ((1-p) X(N)) =1 What is the effect of a pari-mutuel raffle on provision of the public good? The equilibrium public goods provision in a pari-mutuel raffle is exactly the same as that obtained through voluntary contributions Intuition? Increase in giving by others Decreases the probability of winning Increases the prize of winning For a risk neutral individual, these two effects counteract each other, as contributions by others give the participant a smaller chance of winning i a larger prize, with exactly the same expected value. With no compensating externality arising from the gamble, the Parimutuel raffle has only the positive externality associated with additional provision of the public good.

11 3: Experimental evidence of lottery effect (Morgan and Sefton, 2000) Use lab experiments to examine behavior in VCM and lottery Experiments conducted at Penn State and Iowa Penn State experimental design N=2 Endowment 10 tokens to divide between private consumption and public good/wagers VCM: π i = 10 - x i (x i +x j + 8) Lottery: π i = 10 -x i + 8 x i /( (x i + x j ) (x i + x j ) Comparable? VCM: MPCR = 0.75, bonus of 6 Lottery: MPCR = 0.75, prize of 8

12 Morgan and Sefton, 2000 Penn State Equilibrium predictions: VCM: π i = 10 - x i (x i +x j + 8) j x i * = 0 Lottery: π i = 10 - x i + 8 x i /(x i + x j ) (x i + x j ) FOC: (x i + x j -x i ) / (x i + x j ) = 0 Symmetry: x i / (2x i ) = 0 8/4 4x i = x i * = 8

13 Morgan and Sefton, 2000 Penn State, 4 sessions, paper and pencil experiment Penn State Two phases: Phase I: 10 stage repeated game with 1 fixed partner Phase II: Single stage with new partner How does this differ from standard VCM? N=2 No random matching Loss of anonymity y and repeated game effects

17 Is this sufficient for a comparison of the two fundraising mechanisms?

19 Penn State findings Behavior in lottery consistent with equilibrium prediction Contributions greater than predicted in VCM Noteworthy that Nash equilibrium prediction in the lottery does so well when the dominant strategy equilibrium in the VCM does so poorly Maybe because the equilibrium is more efficient in the lottery treatment consider cases where the equilibrium is further from being efficient

20 Iowa sessions 8 sessions (computer) N=4 Random rematching at beginning of each round Endowment 20 VCM: MPCR = 0.75, bonus point 6 (=8 0.75) x i * = 0 LOT: MPCR = 0.75, Prize = 8 x i * = 6 BIGLOT: MPCR = 0.75, Prize = 16 x i * = 12 BADLOT: MPCR = 0, Prize = 8 x i* = 3/2 What is different about the LOT treatment relative to Penn State? Purpose of BIGLOT? Purpose of BADLOT?

21 Iowa sessions

24 Iowa sessions

25 Morgan and Sefton (2000) Findings Lotteries with relatively efficient equilibrium average wagers are well predicted by the model generate higher levels of public good provision than VCM s [Lotteries with relatively inefficient equilibrium average wagers are not well predicted by the model do not generate higher levels of public good provision than VCM s] Lotteries are less successful in funding socially undesirable public goods i.e. results are not driven by love of gambling (the prize is barely covered in the BADLOT

26 4: Revenue dependent or fixed prize lottery (Dale, 2004) Charitable Lottery Structure and Fund Raising: Theory and Evidence Do fixed-prize charitable lotteries generate more net revenue than do revenue-dependent lotteries? Revenue-dependent lottery (RDL): prize is a function of the total wagers received. In the simplest form of a revenue-dependent lottery, the raffle, the holder of the winning ticket receives 50% of the revenue raised while the charitable institution receives the other 50%. Compares fixed prize lottery (FPL), revenue dependent lottery (RDL) and VCM

27 VCM, FPL, RDL VCM U i = w i g i + β i G where β i <1 and i β i >1 g i * = 0 RDL let p be the percentage of total contributions used for the lottery prize U i = w i g i + [g i / i g i ] p i g i + β i (1-p) i g i U i = w i g i + g i p+ β i (1-p) i g i U i = w i (1-p) g i + β i (1-p) i g i g i * = 0 With no compensating externality arising from the gamble, the RDL has only the positive externality associated with additional provision of the public good.

28 VCM, FPL, RDL FPL: let F be the fixed prize U i = w i g i + F [g i / i g i ] + β i [ i g i F] FOC: -1 + F [ i g i -g i ] / [ i g i ] 2 + β i =0 (1- β ) [ g ] 2 i i i = F j i g j g i *= [ F j i g j / (1- β i ) ] j i g j Suppose identical donors β i = β g= [ F (n-1) g / (1- β ) ] 0.5 (n-1) g g n = [ F (n-1) g / (1- β) ] 0.5 (g n) 2 =F(n1) g/(1 β) (g n) 2 = F (n-1) g / (1- β) g n 2 = F (n-1) / (1- β) g i *= F(n-1) / n 2 (1- β) > 0

29 Dale Design Treatments: VCM, RDL, FPL 3 sessions of each treatment 20 rounds (incl. 5 for practice) Groups of 4, re-matched each round Endowment of 20 tokens VCM: MPCR = RDL: 50% of raffle tickets used for prize, 50% for public good with MPCR = 0.75 FPL: If contribution at least 19 tokens: Winner received 20 tokens Each individual received 75 points for each token in the group account in excess of 20 tokens. If contribution less than 19 tokens Lottery was called off Each individual kept 20 token endowment

30 Dale equilibrium prediction Equilibrium prediction: g VCM = g RDL = 0 g FPL = F(n-1) / n 2 (1- β) = 20 3 / ( ) = 15

37 Dale (2004) findings fixed-prize lottery induces significantly greater participation and a significantly higher level of public good funding than does a revenue- dependent d lottery.

38 5: One vs. multiple prizes? Effect of splitting the fixed prize into multiple smaller prizes? Under risk neutrality should have no effect Farravelli (2006) and Lange, List and Price (2007, IER) examine the effect of single and multiple prize lotteries Lange et al (2007) assume risk averse bidders. Optimal fund-raising mechanism depends critically on the risk postures of potential contributors and preference heterogeneity. When multiple prizes assumes that bidders can only win one prize

39 Single vs. multiple prizes (Lange, et al, 2007) 1. When agents are risk neutral and have symmetric marginal valuations for the public good, contributions in the single-prize lottery are greater than those in an equivalent-valued l multiple-prize l i lottery (can only win one prize) 2. When agents have symmetric marginal valuations for the public good, there exists a level of individual risk aversion above which contributions in the multiple-prize lottery are greater than those in an equivalent-valued single-prize lottery 3. With sufficient asymmetry in the marginal valuations for the public good, risk-neutral agents contribute more to the public good under the multiple-prize lottery than an identical set of agents contribute under an equivalent-valued valued single-prize lottery (can only win one prize)

40 Experimental design Groups of 4 12 rounds ( 2 for practice) Strangers design (re-matched every round) Follow Morgan and Sefton design of adding prize to value of public good in VCM Only one prize could be won by each individual Elicited risk attitudes at the end of experiment

45 Findings First, average contributions under both the single- and multiple prize lotteries are larger than under the VCM. Second, total provision of the public good is largest under the singleprize lottery. Third, optimal fund-raising mechanism depends crucially on individual risk posture and heterogeneity.

46 For examination of heterogeneous endowments and incomplete information Faravelli, The Important Thing Is not (Always) Winning but Taking Part: Funding Public Goods with Contests, Journal of Public Economic Theory, 13 (1), 1-22 (2011). Corazzini Faravelli and Stanca 2010 A Prize to Give for: An Corazzini, Faravelli, and Stanca, 2010, A Prize to Give for: An Experiment on Public Good Funding Mechanisms Economic Journal,120,

47 6: Field experiment (Lange et al,qje 2006) Door-to-door fundraising solicitation for Center for Natural Hazards Mitigation Research at East Carolina University Lottery: chances of winning based upon their ticket purchases relative to the number of tickets purchased by other households in Pitt County Single-prize lottery treatment: each dollar contributed provided them with one ticket for a raffle where the winner would receive a $1000 prepaid credit card. Multiple-prize lottery treatment: each dollar contributed would provide one chance in a raffle that would award four $250 prepaid credit cards as prizes. Households were informed that they were eligible to win only one of the four prepaid credit cards.

56 Lange et al (2006) Lottery treatments raised roughly 50 percent more in gross proceeds than VCM. Largely driven by greater participation rates in the lotteries: lotteries increase participation i rates by roughly 100 percent. No effect of having multiple versus one prize Accounting for the $1,000 prize when is the lottery preferred: Single-prize lottery treatment: average gift per household approached $0.71 VCM treatment: average gift per household approached $0.38 Need to approach roughly 3030 households in each treatment for the single-prize lottery to net more in proceeds than the VCM.

57 Next - Auctions Goeree, J.K., E. Maasland, S. Onderstal and J.L. Turner (2005). How (Not) to Raise Money, Journal of Political Economy, 113(4): Orzen (2008) Fundraising through Competition: Evidence from the Lab Ath Arthur Schram and dsander Onderstal (2009) Bidding to Give: An Experimental Comparison of Auctions for Charity International Economic Review 50, pp Carpenter, Holmes, and Matthews (Charity Auctions: A Field Experiment, Economic Journal, 118(January): (2008). Sander Onderstal, Arthur J.H.C. Schram, and Adriaan R. Soetevent (2011) Bidding to Give in the Field: Door-to-Door Fundraisers Had it Right from the Start

Public Goods Provision: Lotteries, Provision Point Mechanisms and Voluntary Contribution Schemes

Public Goods Provision: Lotteries, Provision Point Mechanisms and Voluntary Contribution Schemes Srajal Nayak EC 426 - Public Economics March 19, 2018 rajal Nayak (EC 426 - Public Economics) Public Goods