Self-interest in Charity

1. Self-interest in Charity ECON488a post-experiment presentation By Andy & Joyce

2. Assumptions • Everybody has an inherent level of “charitability” that is constant. • The actual level of charitability displayed varies around this, depending on the conditions • E.g. IQ • Since the experiment conditions remain the same, the level of charity is assumed to be the same for each ID # throughout all the rounds.

3. Assumptions • Expected Value is a constant function of endowment, holding donation constant • May not be true: do poor people expect (or “want”) to get more out of a lottery than rich people who donate the same amount? • (try non-linear regression)

4. Assumptions • Every donation is composed only of charity and self-interest. • Mutually exclusive, by definition • To find “% of donation in self-interest”, we use self-interest/donation*100%.

5. Other considerations • Just as everybody differs according to “inherent charitability”, we also differ by risk aversion. • In a charitable lottery experiment, you can’t really tell if donations differ because of charitability or risk preference. • Assume that the probability estimates (prob_est) that people submit already incorporate their personal risk aversion.

6. Results • N = 151 • All take fixed effects into account (xtreg) • All are statistically significant (P>|t|=0)

7. Results • Donation = 0.618 initial_endowment – 2.78 • 95% CI for coefficient = (0.500, 0.735) • People donate about 60% of their endowment. (50-75%)

8. Results • Donation = 2.51 round + 22.3 • Individual donations increase as the game progresses. • People get more optimistic? • People get more risk-loving? • People feel more magnanimous after seeing others benefit?

9. Results • Donation = 0.261 EV_est + 16.8 • EV_est = prob_est*500 • I.e. expected value of donation = estimated probability of winning * size of prize • Makes sense: donation increases with EV_est

10. Results • Donation = 0.920 max_lott + 11.6 • Max_lott should be same as EV_est • I.e. expected value of donation = maximum you’d pay for a lottery ticket • (meant to dump the charity part and elicit self-interest only) • Also makes sense: increasing function

11. charitable selfish

12. charitable selfish

13. Regressions differ: • Regression lines: • Donation = 0.261 EV_est + 16.8 • 0.270 EV_est if nocons (uncharitable) • Donation = 0.920 max_lott + 11.6 • 1.04 max_lott if nocons (charitable) • In terms of % of people who are charitable instead: • Higher % of charitable people using max_lott than EV_est.

14. Why the difference? • Probability of winning is difficult to estimate. • Donating more gives you greater chance of winning • Though you do know your initial endowment relative to others, not sure how much they’ll donate • “Noisy” statistic: easier to think in “nice” numbers, do rounding e.g. 5/100 or 20/100 v.s. 12/37 • Since EV_est = prob_est*500, EV_est is affected.

15. Why the difference? • Prob_est = 1.99 prob_real • Tend to overestimate your probability of winning by double • (but then, why does a lower % of people appear charitable in the donation v.s. EV_est graph as compared to v.s. max_lott?)

16. Why the difference? • Max_lott is more intuitive. • Note how many more points lie along 45 degree line of indifference between charity and self-interest • (a.k.a. “coldhearted-economics-major syndrome”) • If this is so, then we can say that the majority of people appear to be charitable (from the graph).

17. Using regression lines (nocons), • EV_est: • % in self-interest = 27% ( 2%) • max_lott: • % in self-interest = 104% ( 5%) • (bursting with goodness???)

18. Testing hypotheses (?) • If donation =  EV + u, • Where EV = expected value and u = residual = “charity” • And we assume that u~(0,), • I.e. charity has a mean of 0 and some variance • We can test the null hypotheses that: •  = 1 (i.e. donation = EV  indifferent) •  > 1 (i.e. donation < EV  selfish) •  < 1 (i.e. donation > EV  charitable)

19. Questions? Thank you.