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

Public Goods and Impure Altruism

Presentation by Peter McHenry

September 23, 2004

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?

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)

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

Major Experimental Findings

• In one-shot games mixture of Pareto and free-riding (Nash)

• Contributions decline with repetition

• Face-to-face communication increases contribution

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.

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)

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)

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

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

“Giving with Impure Altruism: Applications to Charity and

Ricardian Equivalence”James Andreoni, 1989, JPE

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

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

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

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

Optimization

• Agent i solves:

€

max

x i,Y,gi

U i(x i,Y,gi)

s.t. x i + gi = wi − τ i

G−i + gi + T = Y

Unconstrained problem

• Assuming interiority (Inada conditions for xi and gi are sufficient)

• After substitutions:

€

max

YU i(wi + Y−i −Y , Y ,Y −Y−i − τ i)

Decision Rule

• Find First Order Condition and Solve for Y

• The decision rule is:

• Choosing total contribution (gi + I)

€

y i = f i(wi + Y−i , Y−i + τ i) −Y−i

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

€

y i = f i(wi + Y−i) −Y−i

€

y i = f i(wi + Y−i , Y−i + τ i) −Y−i

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

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, di=0.

• Rearranging yields:

€

−dY−i

dwi Y

=f ia

f ia + f ie

, defined as α i

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

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

€

dY = c(1−α 1)dτ 1

where c = (1+1− f ia − f ie

f ia + f ie

)−1

i=1

n

∑

f ia and f ie are partial derivatives

and α 1 indexes altruism

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.

€

0 < c ≤1 and 0 < α 1 ≤1

€

0 ≤ dY /dτ 1 <1

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).

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).

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

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.

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.

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.