Abstract— As a way of risk management, insurance plays an important role in people’s daily life. Health insurance becomes one of the most concerned insurance types owing to its closely relationship with health, which is paid a lot of attention by people. Because of the information asymmetry and the participation of physicians, health insurance market has developed a unique principal-agent relationship among three participants, which creates a barrier to its normal operation. This paper defined the special characteristics of medical insurance market in the first part. Then the problems of insured’s moral hazard and physician’s supplier-induced demand were analyzed in the main part. Relevant conclusions were summarized in the last part.
Key words— Health Insurance; Principal-agent; Moral Hazard; Supplier-induced Demand
I. PREAMBLE
As a method of risk management, insurance originated from uncertainty and it is often reached in the insurance contract. In the contract, the insured paid a fixed amount (premium) to the insurer to set up an insurance fund, which will be used to compensate for the future damages caused by disasters or accidents covered by the contract. Insurance fund can make the losses of a few members being shared by all the insured. From an economic perspective, insurance achieved a loss-sharing.
Health insurance is established to compensate for the losses caused by disease. Like other types of insurances, insurer received medical insurance premium from those who are under disease threat to set up health insurance fund in the form of contract. When the insured go to medical institution for illness treatments and medical expenses generate, the insurance agency will give them a certain degree of compensation. Since health is the most basic and important issue in people’s daily life, health insurance has become one of the most concerned insurances.
II. ELABORATION OF HEALTH INSURANCE
There are two types of health insurances. One is social health insurance with a nature of welfare, forcibly supplied by the state. The other is commercial medical insurance, and it has a private nature--participated voluntarily. The operation purpose of the first type is to ensure the features of nonprofit and welfare, while the latter one is to get profit. Nevertheless, both of them are faced with insured with same characteristics and can help insured reduce economic burden caused by illness treatment and avoid medical risks. So suppliers of the two kinds of insurances are called insurer.
A. Principal-agent Relationship in Health Insurance Market
On the basis of the above description, we can attempt to clarify the health insurance entities and the relationships between them. The insured are individuals and the insurer is governments (social insurance) or insurance companies (commercial insurance). As the supplier of medical service, physician will be involved in the process of insurance inevitably, which is different from other insurances. The process of health insurance can be described in the following figure, in which solid lines represent the cash flow and dotted lines indicate the service flow. [1]
In this way, there appears a principal-agent relationship of three participants in the health insurance market. [2]
1) Insurer and insured
There is a principal-agent relationship of economic sense between insurer and insured. In order to disperse risk, the insured need to find individuals with a similar risk level to share burden and ward off risk together. Otherwise this task will cost a lot if the individual does it alone. As an economic entity engaged in risk spreading business, insurance company has advantages in the aspects of information and technology, and it can supply insurance services to every insured with a low cost. In this way, insurance company becomes the insured’s agent.
2) Insured and physician
Owing to the trust to professionals and lack of related knowledge, the insured would like to entrust physicians as his health agent. This kind of principal-agent relationship is different from its normal sense in economics. First, the two players don’t have the right of free choice. Insured usually can’t choose physician across medical institutions freely because the physician is a representative of medical institution and is in a monopoly position. It is more difficult for physician to choose among patients. Second, the output of the principal-agent relationship is health, which is fully belonged to the insured and can’t be divided between insured and physician. Physician can’t get inspiration from the output.
B. Health insurance’s features
The above three-player principal-agent process determines the health insurance has its own specificities besides the features of general insurances, which can be summarized as follows.
1) Insured’s behavior is difficult to monitor
When people have health insurance, they will not cautious about their health as much as before. However, the insurer can only see the results of the disease and it is hard to determine whether the results are due to the insured’s negligence or not.
3) The course of treatment is hard to control
Medical expense is another difficult item for insurer to monitor. Insurer and insured have the same interest before disease occurs. Both of them want to have a relatively low disease incidence. However, once the disease happened, the insured’s interests will deviate from the insurer’s, and they want to use the best drugs and equipments.
4) Induced demand caused by physician
The insured cannot fully aware of the degree of their illness, possible treatment options, as well as the benefits and costs of each program. In most cases, insured have to rely on his or her physician to make right decisions for them. There is a difference between interests of insured and insurer, and both of them want physician consider issues standing on their side. But when physician’s economic interests is proportional to the medical resource consumption, the motivation of inducing the patient to increase consumption will arise.
The above first and second points constitute the moral hazard problem in health insurance, and the third point is the problem of supplier-induced demand. Both of the two problems will cause an excessive use of medical resource and bring obstacles to the normal operation of health insurance.
III. MODEL BUILDING AND ANALYZING
A. Analysis of the Demand Side’s Moral Hazard
From the establishment of principal-agent relationship, occurrence of disease to the compensation of loss, the insured and insurer will go through a game process of several rounds. Insured’s moral hazard in health insurance will be discussed in this part on the basis of game theory.
1) Assumptions
l The two players of the game are insurer and insured. Both of them take the maximization of their own economic interests as the fundamental purpose.
l Insured’s initial wealth is, and has to pay a premium to get health insurance. If the loss is, he can receive a compensation from insurer, .
l When there is health insurance, the insured can choose to be honest or dishonest. The disease incidence under honest circumstance is, and under dishonest circumstance is. Because insured will use more high quality medical services when he is dishonest, the loss will raise to from. Obviously,,, .
l Insurer’s initial wealth is, and will supply a compensation for insured’s loss after receiving a premium.
l Facing with the insured who has been ill, insurer can’t distinguish whether the illness and medical expense are caused by moral hazard. The cost of investigation on insured’s integrity is.
5) Model Building
When illness happened, there will be an obvious game process, the phases are as follows:
When, insured propose for participation of insurance; when, insurer choose to supply or not supply insurance; when, insured choose to be honest or dishonest; when , insurer choose to check insured’s integrity or not.
Specifically, we can get the following dynamic game process.
6) Analysis
Use backward induction to analyze the above dynamic game model.
In the forth phase, the outcome of not check is better than check for insurer whether the insured is honest or not. That is,
(1)
(2)
This is because the cost of supervision and check in health insurance is very high. The examination cost of a particular insured is always much higher than compensation. Furthermore, insurer can’t find out the exact information in most cases. If cannot find the evidence of insured’s dishonest, insurer will get even lesser earnings, (2) will turn to (3).
(3)
When the loss of inspection outweighs the gain, the insurer hope the equilibrium can be arrived [Honest, Not Check], because:
(4)
When the insured are sure that the insurer will not implement an inspection, they will choose honest or dishonest entirely base on their own interests. Among the elements of the insured’s earning, the only thing the insurer can influence is. In order to make insured choose to be honest, the following inequality should be satisfied.
(5)
After sorting, we can get the following inequality.
(6)
Let,be the personal payment rate of loss and, inequality (6) turns to (7).
(7)
It can clearly be seen that personal payment rate is not in a rigorous incremental process relative to the increasing loss. The establishment of personal payment rate of different loss levels has a direct relationship with the probability of disease and the size of loss, which are usually quite different to the same insured because of moral hazard. The greater the gap between honest and dishonest, the larger the space for a high personal payment rate when the loss is small. And a high rate can promote insured to be cautious about his health even when there is insurance. In this way, moral hazard of the demand side can be controlled in a certain extent.
B. Analysis of Supplier-induced Demand
Physician’s income of curing each patient can be expressed by the following equation. [5]
in which (8)
represents physician’s income from the service he supplies. is the payment for medicine and medical equipment, and it depends on daily medical resource costand treatment days. When, the increase ofis beneficial for physician. For his own interest, physician will use a variety of ways to makelarger, such as a lot of prescription, expensive drugs, extending the length of hospitalization, etc. Such motivation becomes stronger with the increasing of.
Because physician has the power of making decisions on medical care, he will try his best to induce patients to increase the medicine demand in order to avoid a falling price caused by excessive supply. The process can be shown by the following figure. The initial demand and supply are indicated byandrespectively, and the equilibrium point is. When supply increases, the equilibrium point will decrease to. In order to avoid profit loss due to falling price, physician will induce patients to increase demand and make demand curve shift rightward to. Then the equilibrium can be reached at the point, at which the price and consumption amount of medical resource are higher than the actual level. In this way, the medical price continues to uplift and a waste of medical resources becomes unavoidable.
To limit the physician’s induction motivation, approaches from the aspect of and can be considered. In order to make as small as possible, physician’s income should only has a relationship with the service he supplies. In order to make out of physician’s control, the treatment approach of every illness should be programmed and transparency.
IV. CONCLUSIONS
From the above analysis of demand side’s moral hazard and supplier-induced demand, advices on controlling the cost of medical insurance and reducing the waste of medical resources can be proposed.
A. The personal payment rate should be different under different losses. A relatively higher personal payment rate should be carried out at low losses when insured’s moral hazard is difficult to observe. That including two situations: diseases which are hard to make sure if it was caused by negligence and diseases which are easier to use unnecessary costly treatment plan. A high initial personal payment rate can establish a relatively high entry cost and prevent the occurrence of moral hazard.
B. For common diseases, standardized treatment procedures should be developed. Then payment can be set according to the disease’s type. This can control the insured’s possibility of using medical resources excessively and prevent the induced demand caused by physician.
C. For outpatient, the way of capitation can be taken as a reference. When each patient gets a consumption quota, physician’s income will has an inverse relationship with the amount of medical resources the insured use. Then physician will have the motivation to help the insured to prevent disease from happening. In this way, the insured can save expenditure and the excessively use of medical resources can be controlled.
Three shortcomings of the above analysis should be noted. First, using insured’s income instead of utility function simplifies the analysis process, but brings about some bias. Second, use discrete variables to measure the insured’s losses. In fact, the loss level is a very complex continuous function. This also brings an impact on the result. Third, the influences of adverse selection problems were not analyzed. These three points need to be concerned in the future studies.
REFERENCES
[1] David M. Cutler, Richard J. Zeckhauser, “The Anatomy of Health Insurance”, Handbook of Health Economics, A.J. Culyer and J.P.Newhouse,pp.563-643.
[2] Juan Feng, Xiao Shen, Qing Xiang, “Analysis on the three parties principal-agent relationship in health insurance”, China Health Management, Vol. 3, pp.171-173, 2009.
[3] Shiyu Xie, “Economic Game Theory”, Fudan University Press, 2002.
[4] Weiying Zhang, “Game Theory and Information Economics”, Shanghai People’s Publishing House, 2003.
[5] Artur Raviv, “The Design of an Optimal Insurance Policy”, The American Economic Review, Vol. 69, No. 1, pp.84-96, 1979.
Baihui Liu