1. Why People Value Health Insurance
When people get sick, their utility decrease for many reasons such as:
- Feeling bad from sickness
- Lose leisure time
- Lose income from days of work off
- Costs of health care
Insurance is a pooling of wealth to allow monetary compensation for losses arising from an adverse event, and therefore insures you against "costs of health care". Risk aversion is the key concept which generates:
- consumption smoothing
- demand for insurance
If people knew their probability (p) of getting ill, and if the consumption of people when they were healthy was CH=y and unhealthy was CS=y-e, the expected consumption and utility of an individual will be
E(C)=pCS+(1-p)CH
E(U(C))=pU(CS)+(1-p)U(CH)
However, if the individual was risk averse and therefore the demand curve was concave, the individual will gain more utility from constantly consuming the expected level of consumption than the expected utility above. This means that U(E(C))>E(U(C)), where U(E(C))=U(pCS+(1-p)CH).
Now, what happens if there was an option for insurance. Imagine an agent can now buy an insurance paying £b in the case of adverse event at a price of £m per unit. The total cost of insurance will be £mb, and now the consumption level will be
CH=y -mb
CS=y-e-mb+b
The agent's work is to decide the level of b to maximise the expected utility E(U(C))=pU(CS)+(1-p)U(CH). The optimal solution will be b=e, which means that full insurance maximises the utility of the individual. Full insurance also implies that the individual will keep the same consumption level CH=CS=y -me over time, which means full consumption smoothing.
Additionally, if the insurance was actuarially fair, that is if:
- The insurance had no administrative costs
- Insurer makes expected profits of zero (assumes a perfectly competitive insurance market)
the premium m would equal the probability p of getting ill: E(Profit)=Revenue - Expected Pay-out=mb-pb <=> m=p.
This means that actuarially fair full insurance gives consumer the expected value of consumption in every state of the world.
2. Health Insurance Market Failure
To assess the market failure of the insurance market, the first fundamental theorem of welfare economics can be applied as previously have been.
- Perfect competition
- No externalities or public goods
- Complete markets
- Probabilities must be independent across insurees
- Probabilities must be less than one
- Complete and symmetric information
- Probabilities must be known or estimable
- No adverse selection
- No moral hazard
The most important violations of these assumptions in health insurance would be adverse selection and moral hazrd. Other sources of violations might be:
- As scale increases, risk pooling improves and transaction costs decrease --> insurance has a quasi-natural monopoly characteristic
- Immunisations and communicable diseases might cause externalities
- Communicable diseases might violate independency of probability
- Chronic illnesses and pre-existing conditions might bring probability up to one
Health Insurance Market Failures due to Adverse Selection
Adverse selection occurs when there are hidden characteristics. When a buyer or seller's characteristic is unobservable to the other side of the market, the less desirable types of buyer/seller may disproportionately participate in the market causing adverse selection.
A seminal analysis on this issues was produced by Akerlof (1070) using the car market.
- The quality of a used car is known by the seller but not completely observable to the buyer.
- Buyers formulate their willingness to pay based on the average quality of the cars.
- At this price, only low quality sellers will sell their car.
- Buyers anticipate this and revise their willingness to pay downwards.
- Sellers anticipate this and the highest quality sellers previously in the market now withdraw.
- ………..until finally the market can collapse altogether.
Rothschild & Stiglitz (1976) analysed adverse selection in insurance markets. Suppose that the insurers know the distribution of risks in the population, but does not know the individual buyer's risk of adverse events. If the insurer offered a full insurance at an average actuarially fair rate for the whole population, those who would buy the insurance will be:
- Agents who know their expected medical costs will be higher than the average
- Agents who know their expected medical costs will be lower than the average, but value the insurance due to their risk averse preference (they are willing to sacrifice some expected consumption to eliminate risk).
The consequence of these market may differ whether you assume a pooling equilibrium or a separating equilibrium. In the case of pooling equilibrium, the two possible outcomes are:
- No insurance: lowest risk type may drop out of the market because the premium is too high. If insurer responds by adjusting premium upwards to reflect average expected loss for remaining participants, lowest risks that purchased insurance last time will now drop out. The insurer makes a loss again, and …..so on. Once the process starts, it keeps going until the market collapses. The outcome ends up socially inefficient, as socially efficient outcome is full insurance for everyone.
- Full insurance: may occur if the lowest risk type in the population is so risk averse that they buy the insurance at the average actuarially fair rate for the whole population. Outcome will be socially efficient, as everyone receives full insurance. However, some argue that it is not equitable, since the healthy subsidises the sick.
Two of the broad classes of response to adverse selection are:
- Compulsion: force low risks to purchase insurance, thus subsidising high risks and preventing health insurance death spiral.
- Screening: offer partial insurance contracts designed to appeal to low risk types. This is better than dropping them out of the insurance market altogether, but is still socially inefficient.
Health Insurance Market Failures due to Moral Hazard
Moral hazard occurs when there are hidden actions. When an agent can take actions that are not observed by a principal, the agent might make an undesirable change in behaviour resulting from protection from the consequences of that behaviour. It is an agency problem that arises in the market. In the case of health insurance market, the principal is the insurer, and the agent is the doctor and the patient. The insurer agrees to cover cost of illness, and wants doctors and patients to take actions to ensure that costs do not become excessive. Therefore, unlike physician-induced demand in which doctor exploits advantage over the patient, with moral hazard the risk is that the doctor and/or the patient will exploit information advantage over the insurer.
There are potentially three types of moral hazards, each of which can be undertaken by suppliers and consumers of care.
Most of the moral hazard in health insurance market is considered to come from the supplier side, as consumer moral hazard in health insurance is likely to be limited given that:
- Being sick is inherently unpleasurable, reducing utility in many ways that aren't insured against.
- The value of benefits from health insurance is low or zero to a person who isn't sick.
The extent of moral hazard may be determined by:
- How easy/costly it is to observe if adverse state has occurred
- How costly it is to change behaviour in order to enter adverse states
- Generosity of insurance coverage
Feldstein (1973) analysed the deadweight-loss from moral hazard caused by health insurance. It models health insurance as a subsidy to patients for each unit of health care bought. In presence of taxes and subsidies, societal benefit from a market is:
Welfare=Consumer Surplus+Producer Surplus+Tax-Subsidy
The idea is that taxes generate revenue that can be put to other users, and subsidies must be financed by taking money from elsewhere.
Assuming that:
- The marginal cost of producing an office visit (physicians time, supply etc.) is constant
- The patient has a downward-sloping demand curve for health care
- The patient is in a large group, so that his medical spending is irrelevant for the insurance premium he pays
The marginal price for the patient will be fully covered by the insurance, and therefore the level of consumption Q1 will depart from the socially efficient consumption level Q0, causing a deadweight loss in the market.
Considerations in regards to the Feldstein Model
The description above assumes that the entire change in demand due to decreased price is caused by moral hazard. However, health insurance may have both income effects and substitution effects, and moral hazard is only related to substitutional effects. The increase in demand due to income effect is not coming from moral hazard. Income effects are less important for small purchases as doctor visits, but may be more important for larger ones such as chemotherapy. In relation to health insurance, income effects matter because of:
- Risk pooling: key feature of health insurance is not just consumption smoothing within individual's lifetime, but also risk pooling across individuals. Most people with health insurance will not break even over lifetime, but small minority are subsidised by the rest, which indicates that health insurance can have large income effects.
- Cross-subsidisation: many health insurance programs, especially those run by governments, have a redistributive components: rich people pay in more than they get back. Health insurance can have large income effects due to this progressive financing structure.