Hidden Overconfidence and Advantageous Selection

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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

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Agenda

1. Introduction
2. Model
3. Market Equilibrium
4. Conclusion

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1. Introduction
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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

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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

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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.

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The Purpose

• An alternative reason for advantageous selection
  
• hidden heterogeneity in degrees of overconfidence

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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)

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Intuition

• overconfidence
• might imply less insurance
• might also imply less self-protection, i.e. high
  risk type
• gt negative correlation between risk type and
  insurance coverage

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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

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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

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Main findings

• Separating, and partial pooling equilibria can
  exist.
• Separating equilibria can predict adverse
  selection or advantageous selection.

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2. Model
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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 ?
• They have the same objective probability of loss
• p(F)p or p(f)ltp depending on investment in
  self-protection F?0,f
• Subjective belief of loss probability
• r type p or p(f)
• o type g(p ) or g(p(f) )
• ggt0, g(p(F) ) lt g(p )
• g(p )lt p(f)
• Hidden information about types of customers and
  hidden action

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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

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Investment in Self-protection

• r type will invest in self-protection iff
• o type will invest in self-protection iff
• Assume ?o lt0

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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.

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3. Market Equilibrium
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Proposition 1 No pooling
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Proposition 2 first best separating equilibrium
(advantageous selection)
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Proposition 3 second best separating
equilibrium (advantageous selection)
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Proposition 4 partial pooling equilibrium
(advantageous selection)
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Proposition 5 separating equilibrium with
linear premium
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Proposition 6 no equilibrium
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Adverse selection if
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4. Conclusion
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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.

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Thank you for your attention!