Public Goods and Impure Altruism

1. Public Goods and Impure Altruism Presentation by Peter McHenry September 23, 2004

2. Why Public Goods Experiments? • Test our theory (Nash equilibrium, etc.) • Describe interactions of people in groups • Do people behave cooperatively? • Does this behavior vary across environments? • Inform policy • Do taxes crowd out charitable donations? • Will people provide public goods on their own?

3. Major Experiments in Public Goods • Drawing from John Ledyard chapter in The Handbook of Experimental Economics • Several disciplines: • Sociology (Marwell at Wisconsin) • Psychology (Dawes at Oregon) • Political Science (Orbell at Oregon and Carnegie-Mellon) • Economics (Isaac and Walker at Arizona and Indiana)

4. What a Public Goods Experiment Looks Like • 4 subjects around a table • Each has 2 envelopes: private and public • Each is given $5 and asked to distribute it between envelopes, secretly • Subjects keep there private envelope; the public funds are collected, doubled, and distributed evenly among subjects • Highlighted outcomes: • Dominant strategy to contribute $0 to public good (free-ride) • Pareto-optimum play is to contribute $5 to public good

5. Major Experimental Findings • In one-shot games mixture of Pareto and free-riding (Nash) • Contributions decline with repetition • Face-to-face communication increases contribution

6. Bohm (1972) • Perhaps the first public goods experiment • Requested the willingness to pay to see two Swedish comedians on TV • Only see the show if your group’s stated willingness to pay covers the production costs • Result: plenty of willingness to pay (little free riding). Little difference between those forced to pay and others.

7. Dawes, McTavish, and Shaklee (1977) • Members of groups choosing O (cooperate) or X (deviate) based on payoff tables. Varying types of communication. • Communication increases cooperation (about 72 percent cooperation with unrestricted communication)

8. Marwell and Ames (1979, 1980) • Teenagers on the phone, given tokens, investing in public or private goods • About 50 percent of resources to public goods  theoretical free-riding is weak • Prompted economists to get involved (defending the theory predicting more free-riding)

9. Kim and Walker (1984); Isaac, McCue, and Plott (1985) • Public and private contributions as before • Add repetition • Contribution declines with repetition • Roughly 50% in round 1 to 10% by round 5 • But why the reduction in contributions? (not controlled) • Learning about strategies • Learning about the payoff tables • Punishing

10. Isaac, Walker, and Thomas (1984) • More systematic study • Undergraduates at computer terminals • Vary four characteristics • Repetition: less contribution from repetition • Group size: not much of an effect • Marginal payoff: big effect • Experience: more experience yields less contribution

11. “Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence” James Andreoni, 1989, JPE

12. Motivation • Free riding is not pervasive • In experiments, players tend to cooperate • Charity is pervasive (2.3 percent of GDP in the U.S. in 2002, American Association of Fundraising Counsel) • Crowding out is not complete • Taxes tend to increase public good allocation • Contrary to theoretical neutrality results

13. Andreoni’s Gimmick • Add public good contribution as an argument in the utility function • This implies a “warm glow” from giving, beyond its indirect effect of increasing public goods • This will help explain: • Cooperation in public goods allocation • Incomplete crowding out

14. A Little Vocabulary • Pure altruism • Just like previous models • Utility depends on private consumption and total public goods available • Impure altruism • Andreoni’s focus here • Utility depends on private consumption, total public goods, and own public contribution (warm glow) • Pure egoism • For comparisons • Utility depends on private consumption and own public contribution

15. The Model (of Impure Altruism) • n agents • Agent i, endowed with wi, chooses private goods (xi) and public good contribution (gi), and pays tax (i) • Total public goods: Y = G + T • i’s total giving to public goods: yi = gi + i • Y-i = others’ (voluntary and involuntary) public goods contributions • Utility depends on xi, Y, and gi

16. Optimization • Agent i solves:

17. Unconstrained problem • Assuming interiority (Inada conditions for xi and gi are sufficient) • After substitutions:

18. Decision Rule • Find First Order Condition and Solve for Y • The decision rule is: • Choosing total contribution (gi + I)

19. Substitutability • Under pure altruism, the decision rule is: • Hence, gi and i are perfect substitutes (only their sum, yi, matters) • Under impure altruism, agents are less willing to substitute gi for i, sincei is in the second argument of fi

20. Intuition about Neutrality • Pure altruism (previous models with neutrality) • Increase i by $1 • Optimizing consumer shifts gi down $1 to maintain equilibrium (assuming interiority) • Hence, Y=0, ie, neutrality • Impure altruism (Andreoni’s model) • Increase i by $1 • Consumer shifts down gi, but by less than $1, since gi and i are imperfect substitutes. The consumer cares about gi in and of itself (warm glow). • Hence, Y > 0, ie, incomplete crowding out

21. A bit more formally. . . . • Decrease wi by $1. How much does Y-i need to increase to maintain constant Y? • Totally differentiate the decision rule and set dY=0, di=0. • Rearranging yields:

22. Altruism Index • i is an index of altruism • Relatively high values of i correspond with a high willingness to substitute gi and Y-i • j >i implies j is more altruistic than i

23. Change the Tax on Agent 1 • Assume demand for goods is normal with respect to “social wealth”: wi + Y-i • Totally differentiate donation function, holding wealth constant and varying only 1

24. Neutrality Breaks Down • With normality assumptions, • Hence, • In the neutral case, taxes do not change Y at all. Here, imperfect substitution between voluntary (gi) and involuntary (i) contributions yields Keynesian effects in general.

25. Relative Altruism and Taxation • Consider two agents, i and j, with i > j • i is more altruistic than j • Taxing i leads to more crowding out than taxing j, since i is more willing to substitute own and others’ contributions than j. • So, to increase aggregate public goods, tax the less altruistic agent (j).

26. The Big Ideas • Warm glow (own contribution in the utility function) may explain cooperation in experiments, and donations to charity. • Empirically, taxation does not appear to be neutral, as some theory predicts. Theory with warm glow captures this non-neutrality (incomplete crowding out).

27. A Criticism • Treatment of corner solutions seems sloppy • Interiority assumed • This is relaxed eventually, but • Still working with the same first order condition, which needed the interiority assumption to be derived • Would seem better to follow Bergstrom, Blume, and Varian (1986) in treating corner solutions

28. Experimental Support for the Warm Glow • James Andreoni “Warm-glow versus Cold-prickle: The Effects of Positive and Negative Framing on Cooperation in Experiments” QJE 1995. • An experiment with endowments contributed either to private or public goods • Two treatments: positive and negative frame. Both groups share identical incentives.

29. Framing • Positive frame • Emphasis on others not being affected by one’s own private consumption • But public contribution yields positive externality to others • Negative frame • Emphasis on one’s own private consumption depriving others of public consumption • But public contribution does not affect others • Recall: identical incentives in either frame.

30. Results • On average, subjects in the positive frame contributed about twice as much to public consumption as did those in negative frame. • Since payoffs are identical between frames, more than pure altruism is needed to explain contribution differences between frames. • Warm glow (impure altruism) is a possible explanation: subjects enjoy helping others.