Overconfidence

1. (Lichtenstein, Fischhoff & Phillips, 1982) (true accuracy) Calibration line Answers in which people report 80% confidence. Only 65% are correct. Answers in which people report 80% confidence; only 65% are correct. (confidence) Introduction Example Model Results Evolution Variants Overconfidence • Participants answer “trivia” questions • Report confidence (subjective probability) of being correct • Instructed to be calibrated (sometimes with incentives)

2. (Lichtenstein, Fischhoff & Phillips, 1982) (true accuracy) Calibration line Answers in which people report 80% confidence. Only 65% are correct. Answers in which people report 80% confidence; only 65% are correct. (confidence) Introduction Example Model Results Evolution Variants Overconfidence • Interpretation: overestimating accuracy of private information • Studied in many papers (Oskamp, 1965; …) • Recent surveys: Griffin & Brenner (2004), Skala (2008) Rational Explanations (confidence)

3. Introduction Example Model Results Evolution Variants Motivation (1) • Existing economic models assume overconfidence • Directly (Odean, 98, Gervais & Odean, 01), Sandroni & Squintani, 07) • Positive utility from good self esteem (Compte & Postlewaite, 04; Köszegi, 06; Weinberg, 09) • Strategic interaction  overconfidence • Risk-averse principals prefer overconfident agents 3

4. Motivation (2) Existing Evolutionary foundations for overconfidence: Group selection (Bernardo & Welch, 01): improve aggregation of information  a few overconfident agents survive Second-best outcome; compensates another bias (e.g., excess risk aversion): Wang (91), Blume & Easly (92), Waldman (94) Introduction Example Model Results Evolution Variants • Gene’s interest in diversification  overconfidence • First-best outcome, individual selection, everyone is overconfident 4 4

5. Contents Introduction Motivating example Model Results Evolutionary stability Variants and Extensions Introduction Example Model Results Evolution Variants 5 5 5

6. Introduction Example Model Results Evolution Variants Related Phenomena • Better than average • Over-optimism about the future • Underestimating confidence intervals • Literature:Lichtenstein et al. (1982), Soll & Klayman (2004), Teigen & Jorgensen (2005), Svenson (1981), Alicke & Govorun (2005), Taylor & Brown (1988) Experts 6

7. Motivating Example Introduction Example Model Results Evolution Variants 7 7

8. pi(independentof others) 1-pi q (positively correlated with others) 1-q failure success failure success Introduction Example Model Results Evolution Variants Risk-averse venture capital CEO Analyst 1 Analyst n manages investments in his area (chooses a startup company) Own judgment/intuition Accepted guidelines 8

9. Introduction Example Model Results Evolution Variants Model 9

10. Private:0<pi<1~f(p)(evaluated as gi(pi) Public: 0<q<1~f(q) (evaluated correctly) Stage 2:agentsreceive signals Own judgment (ap) Accepted guidelines (aq) Stage 3:agentschoose actions pi(independentof others) 1-pi q (positively correlated with others) 1-q failure success failure success Introduction Example Model Results Evolution Variants Payoffs: Agent: 1 (success) / 0 (failure) Principal: h(#successful agents)(h’>0, h’’<0) Risk-averse Principal Stage 1:principal chooses bias profile g1 gi:[0,1][0,1] gn 10

11. Intuition Agent – only cares if he succeeds: Dominating strategy: Choose apiff gi(pi)>q Bias profile uniquelydetermines actions Risk-averse principal – cares for total number of successes: Tradeoff: higher expectation  lower variance Agents with q-d<pi should choose ap Chooses overconfident agents: g(p)=p+d >p Introduction Example Model Results Evolution Variants

12. Comments Why not using monetary incentives? Risk-neutral stock owners  informal mechanisms Introduction Example Model Results Evolution Variants • r - correlation between agents that choose aq • Benchmark: r =1 (all agents that follow aqsucceed or fail together) Correlation • Technical assumption: decreasing absolute risk aversion

13. Results Introduction Example Model Results Evolution Variants 13

14. Introduction Example Model Results Evolution Variants Main Result • Unique optimal bias profile exists: • Homogenous profile: i gi=g • Represents overconfidence(g (p)>p,0<p<1) • Induces the first-best payoff • Strictly better than any other profile • Depends only on h & fp • Asymptotic result (sufficiently many agents) Intuition Existence Uniqueness Details Contrary 14

15. Introduction Example Model Results Evolution Variants Comparative Statics (1) • principal I is more risk-averse than principal II ( , Y’>0, Y’’<0)  hires more overconfident agents: p , g*I(p)>g*II(p) • Intuition: • More risk-aversion  • Principal cares more for variance (less for expectation)  • More agents should follow ap (their judgment)  • Agents should be more overconfident 15

16. Comparative Statics (2) If r (correlation) becomes larger  the principal hires more overconfident agents Intuition: Higher correlation  More aggregate risk from aq (following guidelines)  More agents should follow ap  Agents should be more overconfident Introduction Example Model Results Evolution Variants Correlation 16 16

17. Introduction Example Model Results Evolution Variants Comparative Statics (3) • Harder tasks (accurate signals are less likely) induce more overconfidence • Hard-easy effect (Lichtenstein, et al., 1982; Moore & Healy, 2008) • Intuition: • Principal wants agents with the most accurate private signals to choose ap • In an harder environment, each pi is more likely to be among the most accurate 17

18. Introduction Example Model Results Evolution Variants Overconfidence & Evolutionary Stability

19. Private:0<pi<1~f(pi)(evaluated as gi(pi) Public: 0<q<1~f(p) (evaluated correctly) Agentsreceive signals Introduction Example Model Results Evolution Variants Evolutionary Model (Only Agents) g1 gi:[0,1][0,1] gn Each type induces a (possibly random) bias function Own judgment (ap) Conformity (aq) Each agentmakes an important decision pi(independentof others) 1-pi q (positively correlated with others) 1-q failure success failure success Which type will survivein the long run? Payoff (fitness): Agent: H (success) / L (failure) 19

20. Intuition #offspring : product of the average fitness in each generation The type that maximizes the geometric mean of the average fitness prevails the population (large population, long run) Evolutionary dynamics behaves as it were a risk-averse principal with logarithmic utility: h(#successful agents)=ln(average fitness) Lewontin & Cohen (1969), Mcnamara (1995), Robson (1996) Introduction Example Model Results Evolution Variants 20 20 20

21. Results (1) In the long run all agents are overconfident Overconfidence level depend on the potential gain D=(H-L)/L, r & fp Explains finding such as Yates et al. (2002): Different societies present different levels of overconfidence Introduction Example Model Results Evolution Variants 21 21 21 21

22. Results (2) Larger D (more important decisions) induces more overconfidence (Sieber, 1974) Intuition: larger D  more aggregate risk in aq more overconfidence When g(p)~ 1, p is much smaller (for large D-s) False certainty effect (Fischhoff et al., 1977) : people are often wrong when certain in their private information Results hold for any CRRA utility Introduction Example Model Results Evolution Variants 22 22 22 22

23. Introduction Example Model Results Evolution Variants Variants & Extensions • Social welfare • Risk averse agents • Agents as experts • Costly private signals • Bias w.r.t. the public signal • Choosing the number of agents • Underestimating variance • Underusing base rates g* interpretation Example k alternatives 23

24. Summary Explaining overconfidence as the result of diversification Novel evolutionary foundation of overconfidence and its observed properties (1st best, no other bias, no group selection) Demonstrate why principals prefer overconfident agents in some strategic interactions E.g., CEO and analysts in a venture capital Introduction Example Model Results Evolution Variants Future Research 36 36 36

25. Future Research Applying the model to voting / career-motivated experts Noisy signals about the quality of the candidates Each voter (also) wishes to vote correctly Social planner wishes that most voters vote correctly Requires relaxing a few technical assumptions: Non-risk-averse principal (e.g., step functions in voting) (Ex-ante) asymmetric agents Small number of agents More general signaling systems (p1,…,pk; q1,…,qk) Introduction Example Model Results Evolution Variants 37 37 37 37

26. Introduction Example Model Results Evolution Variants Optimal g in the CRRA Case(with perfect correlation)

27. Hard-Easy Effect (true accuracy) Easy tasks (Lichtenstein, Fischhoff & Phillips, 1982) Calibration line Hard tasks (confidence)

28. Related Literature (Models of Overconfidence) Conflict with future selves (Bénabou & Tirole ,QJE 2002) Positive emotions improve performance / utility: Compte & Postlewaite (AER 2004), Köszegi (2006), Weinberg (2009) Taking credit for lucky successes (Gervais & Odean, 2001) Apparent overconfidence due to unbiased random errors Van Den Steen (AER 2004), Moore (2007), Benoit & Dubra (2008) Influence of overconfident agents Odean (JoF 1998), Sandroni & Squintani (AER 2007) Evolutionary foundations: Bernardo & Welch (2001), Blume & Easly (1992), Wang (1991), Waldman (AER 1994) Introduction Example Model Results Evolution Variants 56 56 56 56

29. Private: pi~f(pi)(evaluated as gi(pi) Public: q~f(p) (evaluated correctly) Stage 2:agentsreceive signals Introduction Example Model Results Evolution Variants Stage 1:principal chooses bias profile g1 gi:[0,1][0,1] gn Stage 3: agentschoose actions Own judgment (ap) Accepted guidelines (aq) pi(independentof others) 1-pi Common lottery 1-q q Independent lotteries failure success Total successprobability: q 57 failure success failure success