Economics of Insurance

1
Economics of Insurance

• Lecture 5

Insurance Crime and Moral Hazard
2
Crime and moral hazard
Lets start with full fair insurance
X2 19100 - 19X1
U X½
U ins 30.9031
19100
955
100
1000
955
Contract Gross Premium Rate 0.05
Prob bad event 0.05
3
Crime and moral hazard
Over insurance
X2 19100 - 19X1
Suppose the client thinks about over insuring,
say by paying 100
U X½
U FULL ins 30.9031
19100
E(U OVER ins) 30.736
So the client wont over insure
2000
(as to be expected from Arrows first law)
955
NOTE This means the client receives gross
compensation of 1900 100 2000
Over insurance NC 1900
MORE THAN THE VALUE OF ASSETS UNDAMAGED!
100
1000
955
900
Over insurance premium 100
Contract Gross Premium Rate 0.05
Probability of bad event 0.05
But would they choose to do so?
No! Check their UTILITY.
4
Crime and moral hazard
Now consider MORAL HAZARD
This occurs when a decision or the existence of a
market
CHANGES PARAMETERS UNDERLYING THE CHOICES A BUYER
OR SELLER CHOICES MAKES
The current well discussed example of moral
hazard concerns the roles of the Bank of England
as lender of last resort to Northern Rock bank.
It is argued that this makes poor decision on
business strategy or risky lending MORE LIKELY as
banks believe that the BoE will always ensure
they are not bankrupted
In the case of insurance it might be said that
moral hazard arises through the changing of the
behaviour or choices of any or all parties in a
risky situation by the belief that the financial
damage of a bad event will be compensated for by
the insurance company.
So since there will be no, or lesser, financial
damage, more underlying risks will be taken
5
Crime and moral hazard
Now consider MORAL HAZARD
The EXISTENCE of an insurance contract might
change
The PROBABILITY of the bad event
For example, a firm might consider that since
being covered by insurance against accident to
their employees or clients reduces the effect on
the firm of such an event,
it will spend less money on safety equipment!
The financial consequence (VALUE OF OUTCOME) of
the bad event
For example, doctors in a private hospital might
spend more money, though using more expensive
techniques, on someone who is known to have high
insurance compensation value rather than on
someone with little or no insurance.
There is more to be said on both these examples,
but today we will concentrate on the fairly
straightforward example of CRIME
6
Crime and moral hazard
Lets return to our earlier example
7
Crime and moral hazard
Lets return to our earlier example
X2 19100 - 19X1
The client over insures by paying 100.
BUT DECIDES to deliberately cause the bad event
U X½
U FULL ins 30.9031
19100
E(U OVER ins) 30.736
SO E (U) is now
1 x 2000½
44.7214
So the client wont over insure
So the client WILL over insure
2000
(as to be expected from Arrows first law)
NOTE This means the client receives gross
compensation of 1900 100 2000
Over insurance NC 1900
MORE THAN THE VALUE OF ASSETS UNDAMAGED!
100
1000
900
Over insurance premium 100
Contract Gross Premium Rate 0.05
Prob bad event 0.05
The probability of the bad event is now ONE
But would they choose to do so?
No! Check their UTILITY.
8
Crime and moral hazard
This is of course fraudulent
So a client may not follow this course of action
They may have moral scruples
But this raises the interesting case that such
behaviour is not covered by (at least simple)
utility maximising models
So there is a paradox
Utility maximising behaviour provides a strong
case for market based insurance
BUT COULD LEAD TO MORAL HAZARD THAT BADLY DAMAGES
THE MARKET
Moral beliefs might mitigate moral hazard and so
improve the markets performance
BUT GIVE NO GENERAL REASON AS TO WHY THE MARKET
IS EFFICIENT OR DESIRABLE IN THE FIRST PLACE
9
Crime and moral hazard
How much moral hazard is rational?
There is no general answer to this question
because
PROBABILITY and value of OUTCOMES become
ENDOGENOUS
That is they are determined within the process
being modelled
Our model of insurance therefore cannot always
specify in advance what the probabilities of
events will be, nor necessarily what the
financial outcomes will be.
They cannot be treated as EXOGENOUS parameters
In our example, the probability of the bad event
changed from 0.05 to 1 through the existence of
the insurance contract.
10
Crime and moral hazard
How much moral hazard is rational?
There are numerous considerations that can
however be modelled or considered ad hoc
11
Crime and moral hazard
How much moral hazard is rational?
There are numerous considerations that can
however be modelled or considered ad hoc
The putative criminal might well consider
maximising their utility by using the WHOLE value
of the asset to raise the premium
19100
2000
This would give a net compensation of
Over insurance NC 19000
19000
Over insurance NC 1900
100
1000
900
Over insurance premium 100
Over insurance premium 1000
12
Crime and moral hazard
What can insurance companies do?
Make sure insurance contracts specify that
morally hazardous behaviour nullifies the
contract no compensation will be paid and
penalties imposed
Make sure clients have no record of insurance
fraud before a contract is agreed
Investigate claims ex post
Investigation and data may held centrally, as
these are public goods
We will expand on this topic in class
Lobby for greater police effectiveness in
prosecuting fraud
Lobby for higher penalties for those convicted of
fraud
Reduce over-insurance possibilities contractually
or with co-insurance