Hidden Overconfidence and Advantageous Selection

1. Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei, Taiwan Yu-Jane Liu Professor, Department of Finance National Cheng Chi University, Taipei, Taiwan Larry Y. Tzeng Professor, Department of Finance National Taiwan University, Taipei, Taiwan ARIA

2. Agenda • Introduction • Model • Market Equilibrium • Conclusion ARIA

3. 1. Introduction ARIA

4. Motivation (1/3) • Relation between RISK TYPE and INSURANCE COVERAGE • ADVERSE selection: • Theoretical prediction: positive • Empirical evidence is mixed: • positive: health insurance, annuities • negative: life insurance, long-term care insurance, reverse mortgages, medigap insurance ARIA

5. Motivation (2/3) • ADVANTAGEOUS selection (de Meza and Webb, 2001) • explained by heterogeneous (hidden) degree of risk aversion • more risk-averse implies more insurance • more risk-averse might imply more self-protection, i.e. lower risk type ARIA

6. Motivation (3/3) • Empirical evidence on the sign of the negative relationship between degree of risk aversion and risk type is mixed • negative: long-term care insurance • positive: automobile and Medigap insurance • There should exist other factors which induce advantageous selection. ARIA

7. The Purpose • An alternative reason for advantageous selection: • hidden heterogeneity in degrees of overconfidence ARIA

8. Overconfidence • Why? • Svenson (1981): Half the drivers in Taxes judged themselves to be among the safest 20%, and 88% believed themselves to be safer than the median driver. • What? • Optimistic on risk probability • Langer (1975), Weinstein (1980) and Larwood and Whittaker (1977) show that CEOs tend to underestimate the failure of investment projects. • “Bad things cannot happen to me.” • Optimistic on information quality • Daniel, Hirshleifer and Subrahmanyam (1998), Gervais and Odean (2001), and Gervais, Heaton, and Odean (2005) ARIA

9. Intuition • overconfidence • might imply less insurance • might also imply less self-protection, i.e. high risk type => negative correlation between risk type and insurance coverage ARIA

10. Most Related Literature (1/2) • Model setting: de Meza and Webb (2001, Rand) • Hidden information cause different types of individuals. • De Meza and Webb: degree of risk aversion • Our: degree of overconfidence • The ex ante objective loss probabilities of different type of individuals are the same. • Different type of individuals would make different decisions on the investment for self-protection to reduce the loss probability. • One dimension approach ARIA

11. Most Related Literature (2/2) • Heterogeneous risk perception • One dimension: Koufopoulos (2002, working) • Oligopoly market • Main findings: two types of separating equilibrium • advantageous selection • One risk type in equilibrium but the less optimistic individuals will purchase more coverage than the more optimistic individuals • Two dimension: Jeleva and Villeneuve (2004, ET) • Monopoly ARIA

12. Main findings • Separating, and partial pooling equilibria can exist. • Separating equilibria can predict adverse selection or advantageous selection. ARIA

13. 2. Model ARIA

14. Assumptions and Notations (1/2) • Competitive insurance market • Two types of customers: those who is overconfident (type o) and those who don't (type r) with proportion θ • They have the same objective probability of loss: • π(F)=π or π(f)<π depending on investment in self-protection F∈{0,f} • Subjective belief of loss probability • r type: π or π(f) • o type: g(π ) or g(π(f) ) • g’>0, g(π(F) ) < g(π ) • g(π )< π(f) • Hidden information about types of customers and hidden action ARIA

15. Assumptions and Notations (2/2) • The expected utility of the type i insured is where • W: initial wealth • L: loss size • p: premium rate • Q: coverage ARIA

16. Investment in Self-protection • r type will invest in self-protection iff • o type will invest in self-protection iff • Assume Δo <0 ARIA

17. Game structure • Stage 1 • Insurers make binding offers of insurance contracts specifying coverage Q and premium rate p. • Stage 2 • Individuals choose either a contract from the set of contracts offered or no contract. If the same contract is offered by two insurers, individuals toss a fair coin. • Stage 3 • Individuals choose whether or not to invest in self-protection. ARIA

18. 3. Market Equilibrium ARIA

19. Proposition 1: No pooling ARIA

20. Proposition 2 : first best separating equilibrium (advantageous selection) ARIA

21. Proposition 3 : second best separating equilibrium (advantageous selection) ARIA

22. Proposition 4 : partial pooling equilibrium (advantageous selection) ARIA

23. Proposition 5 : separating equilibrium with linear premium ARIA

24. Proposition 6 : no equilibrium ARIA

25. Adverse selection: if ARIA

26. 4. Conclusion ARIA

27. Contribution and findings • Our paper provides a theoretical model of hidden overconfidence to explain advantageous selection in the insurance market. • We demonstrate that: • Separating (partial pooling) contracts in a form of advantageous selection is equilibrium when the deviation in belief of the loss probability between the rational type of insured and the overconfident type of insured is relatively large. • neither the rational type of insured nor the overconfident type of insured expend any effort to reduce the loss probability, and both purchase insurance at the same premium rate, when the deviation in belief of the loss probability between the rational type of insured and the overconfident type of insured is relatively small. • Separating contracts in a form of adverse selection is equilibrium when the degree of overconfidence of the overconfident type insured is less severe. ARIA

28. Thank you for your attention! ARIA