Adverse selection

1
Adverse selection

• Lecture 3 - Economics of insurance
• EOCN6053 Selected topic in financial economics
• Raymond Yeung, PhD
• Honorary Assistant Professor
• 15 February 2007

2
Rate making (price setting) in practice

• In the real world, insurance companies compete by
  offering competitive premium rates
• An insurer needs to consider on one hand whether
  their premium rate, adjusted by its quality of
  services, is at least as lower than its
  competitors an understanding of elasticity is
  needed
• Another major consideration is regulatory
  requirement. In many countries, premium rate is
  highly regulated, also called tariffication (e.g.
  India). Rate regulation is often applied to what
  we called statutory insurance e.g. compulsory
  third party motor liability

3
Methods of rating in non-life insurance

• Judgement rating each risk exposure is
  evaluated based on the underwriters judgement,
  e.g. natural catastrophes
• Class rating exposure of similar
  characteristics are placed in the same
  underwriting class and each is charged the same
  rate, e.g. group medical insurance
• Merit rating a rating plan by which class rates
  are adjusted upward or downward according to the
  loss experience of the insured, e.g. motor
  insurance

4
Methods of rating in life insurance

• Life insurance is rated according to mortality
  table, often published by insurance regulator or
  the countrys actuary society
• For example, premium for a term life insurance
  with X of sum assured can be computed as
• If the life policy is paid by installment, net
  annual level premium can be computed as

5
Challenges and issues

• In the end, how insurance companies face two
  constrasting goals commercial consideration
  (economic efficiency) and social / regulatory
  obligation (equity)
• Similar to banks, insurance companies are
  conventionally, morally, not supposed to make
  huge profit, or extract consumer surplus too much
• Furthermore, the community always longs for
  universal coverage in order to protect all
  population from risk exposure e.g. medical care

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Theory of adverse selection

• Theory of demand for insurance states that when
  an insurance contract is actuarially fair, the
  optimum from consumer point of view is to buy
  full coverage.
• Consumer has been assumed homogeneous in terms of
  their risk profile. Insurance company will not
  incur loss by offering a single contract one
  single premium rate per dollar of compensation.
• In reality, consumers are heterogeneous. One
  important consequence is that when an offer is
  acceptable to one type, it may not be acceptable
  to another.

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Theory of advese selection

• If insurance company can accurately observe the
  risk profile of every individual, they can
  discriminate the consumers by offering insurance
  policies with different premium rates.
• In reality it is not practical because there is a
  cost associated with risk rating. Furthermore,
  some risk types are almost unidentifiable.
• A single item menu often attracts those who are
  high risk and deters those who are less risk,
  resulting in self-selection of adverse groups
  into the insurance pooling, further driving up
  the premium rates. The process can go on until
  the whole pool vanishes, i.e. death spiral

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1. Adverse selection model

• Consider a simple two-state model where a
  consumer faces a good or a bad state. The
  expected utility can be written as
• For simplicity, assume the insurance contract is
  offered without deductible so that the insured
  received a fixed amount of payment in the bad
  state. Also assume zero loading factor.
• Assume insurance companies are risk neutral and
  operate in a competitive insurance market,
  insurance contracts are actuarially fair.

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1. Adverse selection model

• Lets relax the model and assume there are two
  types of individuals high risk and low risk
• and there are ß of high risk type. The average
  risk profile in the market can be weighted as
• Suppose insurance firm cannot observe there are
  two risk types and offer a single contract and
  set pp. The insurance company expects the
  following FOC holds

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1. Adverse selection model

• High risk type will buy this contract with full
  coverage because they would have expected
• which is currently cheaper than in the case when
  the insurance companies charge them pH
• Low risk type will demand for less than full
  coverage because recall our full coverage result
  CL

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1. Adverse selection model

• implies
• In order for FOC to hold, given u()lt0
• There is no surprise due to Mossins model

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1. Adverse selection model

• The expected profit to the insurance companies is
  
• The first term is now negative because of
  additional risks from the high-risk individuals
• In a competitive equilibrium, expected profit to
  the insurer must be zero, implying

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1. Adverse selection model

• Solve the zero profit condition, one can find
  that the only situation for the insurer to
  balance the book is to have
• This result contradicts our earlier finding that
  low risk type will not demand for full coverage
  if premium is set as
• This in turn implies that in this case the
  insurer will run a loss which will not be a
  competitive equilibrium

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1. Adverse selection model

• In Rothschild Stiglizs paper, the contract is
  offered as a single pair (P,L)
  take-it-or-leave-it. In that setting, low risk do
  not buy insurance at all
• This average contract leaves the insurer to serve
  the high-risk community. If, instead of just two
  discrete risk type, pi increases continuously,
  the whole insurance market will collapse as the
  process of screening out goes on, resulting in
  what we called death sprial

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1. Adverse selection model death sprial
drop out the 3rd round
drop out in the first round
drop out the second round
High risk
Low risk
P1
P2
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1. Adverse selection model - exceptional

• A pooling contract is not entirely impossible but
  depending on the proportion of risk types in the
  population
• It may be the case where the low risk is just
  willing to participate but insurer can extract
  their consumer surplus to subsidize the loss
  making group
• Rothschild Stigliz suggests that in general
  setting the only possible equilibrium, if it
  exists, must be a separating equilibrium.
  Otherwise, there is no equilibrium at all.

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1. Adverse selection model

• The high-risk will always find it beneficial and
  buy this contract, similar to all other contract
  where Plt PH
• We need to search for a separating equilibrium
  by offering two contracts high-risk (PH, CH) and
  (PL, CL) so that they satisfy the participation
  constraints

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1. Adverse selection model

• The schemes should also need to prevent high-risk
  type from choosing the product targeting the
  low-risk
• Likewise, the incentive compatibility constraint
  for the low-risk would be

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1. Adverse selection model

• To be a competitive equilibrium, the final
  constraint requires zero profit to the insurer
• The last condition reflects that whether there is
  an equilibrium pair depend critically on the
  proportion of risk types in the pool
• These constraints define the set of possible
  equilibria where it is the interest for different
  risk groups to reveal their truth. The existence
  of these sets of revelation mechansim is called
  revelation principle

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2. Rating and screening

• Insurer can design a mechanism to allocate
  different contracts to appropriate type of the
  insured
• Subject to one participation constraint and one
  incentive constraint

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2. Rating and screening example

• For the same benefit level, the rate offered to
  low risk is always attractive to the high risk.
  Insurer can only adjust the benefit level
  downward to be consistent with the incentive
  constraint
• The participation constraint requires that given
  the original premium the low risk still finds it
  is their interest to participate
• The optimal contract would be an actuarially
  unfair contract as surplus is transfer to the
  insurer