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

2. Assumptions 1. 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 2.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 3.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? 1. 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? 3. 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)  EV  charitable)

19. Questions? Thank you.