Toward a Theory of Charitable Fund‐Raising

In Andreoni's threshold public-good model, absent seed money, a Nash equilibrium with zero giving exists.

“in the absence of seed money, there exists a Nash equilibrium with zero charitable giving.”

Seed money commitments can remove the zero-giving equilibrium by reducing the amount still to be raised.

“The zero-contribution equilibrium can be eliminated, however, by initial commitments of seed money, which lower the remaining amount to be raised in the public fund-raising campaign.”

Andreoni's theory implies that publicly announced seed contributions can raise total giving to a capital campaign.

“One testable implication of the theory is that publicly announced seed contributions can increase the total amount of giving to a capital campaign.”

Andreoni's theory indicates a critical seed level above which the zero equilibrium ceases and only a positive equilibrium remains.

“The theory indicates that there exists a critical level of seed money t above which the equilibrium at zero ceases to exist, and only the equilibrium at remains.”

Andreoni proposes that seed money raises contributions by removing the risk of a zero-giving equilibrium.

“Andreoni proposes that seed money influences contributions by eliminating the danger of a zero-giving equilibrium.”

Andreoni's theory, read literally, implies that contributions in this experiment would shift discontinuously from a zero equilibrium to an equilibrium of at least $3,000.

“Andreoni's theory, if taken literally, predicts that contributions in our experiment should jump discretely from an equilibrium of zero to an equilibrium of at least $3,000”

Andreoni's model correctly predicts that seed money raises contributions, but it may give the wrong reason for that effect.

“Though Andreoni's model correctly predicts the positive effect of seed money on contributions, it may be proposing the wrong explanation for this effect.”

The seed money result is consistent with Andreoni's prediction.

“This result is consistent with the prediction of Andreoni (1998).”

The empirical seed money findings are broadly consistent with Andreoni's theoretical prediction.

“Our empirical findings concerning seed money are broadly consistent with the theoretical prediction of Andreoni (1998).”

Andreoni predicts seed money may raise public-good provision from zero to a positive equilibrium at or above the threshold.

“He predicts that seed money may increase the amount of public-good provision in a charitable fund-raiser from zero to some positive equilibrium level * G (greater than or equal to the threshold level).”

Andreoni's theory predicts a move from zero participation to a positive equilibrium participation level, but it does not predict that contributors would increase their gift sizes.

“A third puzzle is that while Andreoni's theory predicts an increase from zero participation to some positive equilibrium amount of participation, it does not predict an increase in gift size by those contributing.”

At that critical seed level, the theory predicts a discrete increase from zero to at least the $3,000 threshold.

“at the critical level of seed money t, there should be a discrete increase in public-good provision from zero to some amount greater than or equal to the $3,000 threshold level.”