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Extensive lectures of How Health Systems Work
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How health systems workLecture 1 – 8-11-2022
Healthcare is complicated → for example when a new policy is coming in, then more calculations
need to be done to calculate all the different actions that may occur.
As Trump said, it is really complex → the policymakers cannot really predict how a new policy will be,
a lot of actors are involved in this.
Enter Chaos → with the covid pandemic, no one really knew how new policies will help and what the
effect would be.
How to analyse complex systems?
- Start ‘simple’: health economics
o A toolbox for rational analysis of complicated issues
- Introduce complexity: health policy
o How to design, implement and evaluate policies in an irrational environment
- As an innovator, policy maker, manager, you will need to ‘navigate through the system’
- This course aims to provide the necessary tools to do so
- The Netherlands is regularly used as a case study
Why health insurance? → lot of people have a health insurance just to insure yourself when there
are unexpected costs. Also, in the Netherlands it is mandatory to have health insurance. This is
because we all have to contribute with the costs for the patients who are ill.
There are lot of difference insurances; health, dental, car, funeral, etc.. These insurances are really a
free market, it is unregulated.
Why insurance? → it has to do with the risks and probabilities. So insure yourself for unexpected
costs.
- Suppose your risk of getting into a skiing accident is 5%. Health costs are €3000. Insurance
costs €175. Would you take insurance?
- Suppose your risk of getting ill is 0.5%. health costs are €120.000. insurance costs €700.
Would you take insurance?
, - Suppose your risk of getting a common cold is 10%. Health costs are €30. Insurance costs
€3.50. Would you take insurance?
Expected costs = health costs x probability
Often it is → the higher the potential costs, the more likely people will get insurance. So in case 2 you
would really want an insurance.
Case Health costs Probability Expected costs
1 €3000 0.05 €150
2 €120.000 0.005 €600
3 €30 0.1 €3
Choice of health insurance:
- Apply CBA (cost benefit analysis): express utility of insurance and no insurance, and compare
- The main trade-off is: do I pay a little upfront, or risk paying much more later in case
something happen?
- Depends on:
o Time preference: do I like to have more wealth now or in the future?
▪ More wealth now → you are less likely to take up insurance, because the
incomes – premium has a higher weight
o Loss aversion: how much disutility does it costs to lose a small amount versus a large
amount (i versus ph)
o Risk aversion: play on safe or roll the dice? (ph versus E(h))
Loss aversion: losing a euro makes you more sad than gaining a euro makes you happy.
Valuation of money:
- In case of linear utility function: each euro makes you equally happy
- 1 euro = 1 util
- Risk neutral → indifferent between fair insurance or paying for care
- Diminishing marginal utility: the first euro makes you ecstatic, after €1000 euro you are like
mweh
- Risk averse → willing to pay a small amount to reduce chance of losing a large amount
o Most people are risk averse
- For example:
o 10% chance of getting ill: costs are $8000
o 90% chance of staying healthy and pay $0
o 10% chance of getting ill and pay $8000
o → expected costs are 0.1 * $8000 + 0.9 * 0 = $800
o If you would be offered a premium of $800 to insure against the risk, would you take
it?
▪ Yes if risk averse
▪ Indifferent if risk neutral
▪ No if risk loving
, Here you see the risk aversion. If your income increases
then your utility will also increase, however this
increase does not go really fast.
- Suppose U = ln(w) → income of €10.000, then the
utility is 9.21
- p=0.1, H=8000
- E(c) = p * h = 800
- W= 10.000
- U (w)= 9.21
- Suppose you have to pay the healthcare costs of
8000, then the wealth decreases to 2000 → utility declines to U(W-H) = 7.6
- Suppose you pay the insurance of 800, then the wealth decrease to 9200. The utility
decrease to 9.13 ; U(W-i)= 9.13
- E (U(H)) = 0.1 * 7.6 + 9 * 9.21 = 9.05 → this is the expected utility
- The U(W-i) > E(U(H)) → so therefore it would be beneficial to take up insurance
Time preference:
- Opportunity costs of spending now versus spending in the future
- Suppose you have to purchase health insurance for €5800 at the beginning of a year. What
else could you do with that money?
- If you save the money, you receive interest
- You can buy more next year
- Supply and demand equalize
until the time preference for
consuming now is about equal to
the interest rate.
- This implies that insurance is more prevalent in wealthy countries with low interest rates
o Positive interest rates → you save money now, so you have more consumption in the
future.
o Low interest rate → insurance would be more preferable, because it will be least
costly
The maximum willingness to pay is actually the willingness to pay for extra amount for have
insurance or not. When the utility of insurance and the utility of not having an insurance are equal
Becoming a health insurer:
- Suppose chances of having a skiing accident are 5%, and costs are €3000. What premium
would you ask for skiing accident insurance?
o € = €150 premium → this is the minimum they have to ask to cover their
costs, so mostly the insurance ask more.
o The €150 premium is called the Actuarially Fair Premium (AFP)
- Suppose all people have wealth of €10000 and utility function U=ln(w). What is the
maximum premium you could ask?
o €176.76
o Extra costs to cover insurer expenses are called Loading Factor (Lf)
- Suppose chances of having a skiing accident for males are 10% and for females are 1% (or
vice versa). What premium would you ask?
o If you are able to differentiate between sexes: then €300 for males and €30 for
females → this is called premium differentiation
➔ In the Netherlands insurance companies are not allowed to make profit, however in other
countries they are.
, The law of large numbers:
- Suppose 10 persons (r=0.05) buy insurance (i=170) against a skiing accident (H=3000). What
are your expected profits?
o €200 on average expected
- What is your chance of making a loss?
o 1-(0.95^10)= 40% → 40% chance of having a loss, because more people get accidents
and then you are not able to cover all the costs with the premium.
o Total premium income =1700. If already one person files a claim (this costs 3000)
then the profits are already <0. This is one minus the probability that none of the 10
persons files a claim; which is: 1-(0.95^10)= 40%
- Suppose 100 persons (r=0.05) buy insurance (i=170) against a skiing accident (H=3000). What
is your chance of making a loss?
o P(R(1)>57)= ~17%
o Premium income = 170000. Net profit is <0 if the insurance company has to pay out
more than 56 accidents (= 170000/3000). Chance of 56 accidents in a population of
1000: P[x>56] is a cumulative binominal distribution function with [r=0.05; N=1000).
Then the probability calculation shows ~17%
- For 10000 persons the chance of loss is 0.14%
o For 10000 persons then after 566 accidents pay outs there is not profit anymore.
Again the r=0.05 and the N=10000, and then you get the probability of 0.14%
➔ This is the law of large numbers (LOLN)
➔ Risk pooling
➔ This does not work well with systemic risks
A health insurance glossary:
- Consumers choose a healthy plan
- Consumers pay a premium
- Price differentiation or community rated premiums
- Insures are entitled to a benefit package
- Choice of provider may be limited in restricted choice plans/closed network plans
- Upon use, insurance companies generally restitute the claim amount after payment of the
patient
- High costs may be paid directly by the insurance company in natura/cashless claims
- Patients may have to pay part of the costs themselves: cost sharing. For example deductibles,
coinsurance, copayments
Market failure in insurance markets (free uncontrolled insurance markets):
- Insurance may attract bad risks: adverse selection → this means that people with high risks
take insurance and people with low risk do not take insurance.
- Suppose chances of having a car accident are 10% for Tim and 1% for Tom. Health costs
associated are €10000. What is the actuarially fair premium if you cannot differentiate
between Tim and Tom?
o €550 → 5.5% x 10000
- What would Tim be willing to pay for insurance (disregard DMU), how about Tom?
- Who would purchase insurance? What is the expected loss for the insurance company? Does
the premium cover this loss? What is the new AFP for the insurance company?
o Because the expected costs for Tim are €1000 and for Tom are €100, Tim will
purchase insurance because the expected costs are higher then he have to pay for
premium of the insurance. Tom will not take insurance since his costs are lower then
the premium.
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