Foul' forms of risk sharing

This section first summarizes the choices that have been made with respect to the essential elements of risk sharing. Then four forms of risk sharing are presented more formally by introducing some parameters. An important aspect of risk sharing is the proportion shared expenditures. This is the proportion of all expenditures that is retrospectively paid for by the regulator. The higher this proportion, the lower an insurer's incentives for efficiency. Based on an assumption with respect to the distribution of individual health care expendi-tures, an indication of the relation between the parameter(s} of the forms of risk sharing and the resnlting proportion shared expenditures is presented. Finally some implementation issues of the four forms of risk sharing are discussed.

3.3.1 Summary of choices

For the empirical analyses in the second part of the study, the following choices have been made:

(I) Each insurer is allowed to select itself agiven percentage of its members; if the members have to be designated before the start of the year, it is called risk sharing for high-risks. If the members can be designated at the end of the year, it is called risk sharing for high-costs. The fraction of members is set by the regulator. A special case is risk sharing for all members.

(2) The risk sharing applies to all types of care within the specified benefits package.

(3) Insurers are entitled to a certain percentage of the costs of a designated member as far as these costs are above a certain threshold.

(4) The risk sharing is budget-neutral from the regulator's point of view and it is mandatory for each insurer to contribute to the financing of the risk sharing.

The risk sharing is financed via a proportional reduction of the normative costs.

3. Forms of risk sharing

For a brief description of the forms of risk sharing, the next subsection intro-duces four parameters.

3.3.2 Risk sharing parameters

Given the choices of the previous subsection, the forms of risk sharing studied here can be described by four parameters (Van Vliet, 1997):

p: The fraction of members that an insurer is allowed to designate for risk sharing. Of course, this fraction varies between zero and one. A special case is a fraction of one, when the risk sharing applies to all members.

D: Dummy variable that indicates whether the designation of members whose expenditures are (partly) paid by the regulator, can be done at the start of a year (D =0) or at the end of the year (D = 1).

T: The threshold above which the costs of designated members are (partially) reimbursed. Of course, the threshold is greater than or equal to zero. A special case is a threshold of zero, when the risk sharing applies to all costs of the designated members.

a: The fraction of the costs of designated members - possibly above a threshold - that is reimbursed. Of course this fraction varies between zero and one. A special case is a fraction of one, when all costs of designated members -possibly above a threshold - are shared.

The following values of three parameters imply no risk sharing at all: p equals zero; and/or T is infinite; andlor a equals zero. The influence of the three parameters is roughly as follows: the higher p or a and the lower T, the more extensive the risk sharing. If p equals one, T equals zero and a equals one, the most extensive form of risk sharing arises, i.e. the situation of full cost reim-bursement. Further limiting the possibilities such that each form of risk sharing has essentially one parameter only, yields four main forms of risk sharing.

Table 3.2 presents these four forms. By choosing different parameter values for a certain form of risk sharing, one may get different variants of this form.

60

3.3 FOllr forms of risk sharing

Table 3.2. Description of four forms of risk sharing

Name p D T a

Risk sharing for high-risks (RSHR) p 0 0 1

Risk sharing for high-costs (RSHC) p 0 1

Outlier risk sharing (ORS) 1 1 T

Proportional risk sharing (PRS) I 0 a

Slight modifications would be: risk sharing for high-risks 6r high-costs with proportional cost based payments (0< a < 1); outlier-cost based payments (O<T< (0); or with proportional outlier-cost based payments (O<T< 00; O<a< I), Outlier risk sharing 6r proportional risk sharing may be combined to get proportional outlier-cost based payments (O<T< 00; O<a< 1).

Of course, other combinations of the four main forms are possible as well,

Because risk sharing for high-risks is a prospective form of risk sharing, for this form it is clear that the usefulness of risk sharing strongly depends on the capitation formula employed. The question is whether insurers are able to identify members for whom they expect to be underpaid given the capitation formula. Given a demographic capitation formula, insurers can easily do this by using the claims history of their members. The proportion shared expenditures then provides a clear indication to the regulator of how bad its capitation formula really is. If in the future, the regulator is able to improve its capitation formula, it will become more difficult for the insurers to select members for whom they expect to be underpaid and their costs will decrease. Therefore, given the fraction of members for whom some risk is shared, an improvement of the capitation formula will lead to a reduction of the proportion shared expenditures under risk sharing for high risks. Under the three retrospective forms of risk sharing, an improvement of the capitation formula will not lead to a reduction of the proportion shared expenditures.

3.3.3 Proportion shared expenditures

An important aspect of risk sharing is the proportion shared expenditures. In the case of proportional risk sharing, the proportion shared expenditures equals the weight on the actual costs. Under risk sharing for high-risks or high-costs, the

3. Forllls of risk sharing

proportion shared expenditures equals the costs incurred by the designated members expressed as a fraction of the costs of all members. In the case of outlier risk sharing, the proportion shared expenditures equals the costs incurred above the threshold expressed as a fraction of the total costs.

Under the assumption that the probability density function of individual health care expenditures consists of a combination of an alternative distribution (yes/no costs) and a lognormal distribution (with parameters I" and a) for those mem-bers with positive costs, Van Vliet (1997) derived the following formulae for the proportion shared expenditures (PSE)14:

(3.1) RSHR: PSE = 1-<I>(<I>-l(1-p)-p*a).

(3.2) RSHC: PSE = 1-<I>(<I>-l(1-pi1r)-a).

(3.3) ORS: PSE ⁼ (I-<I>(c-a» - T*7f*(I-<I>(c» with c=(iog(T)-I')/a.

The parameters I' and a of the lognormal distribution can be calculated with equation (3.4) and (3.5) given the mean costs (E(AC», the probability of positive costs (7f) and the coefficient of variation (cv).

(3.4) E(AC)

=

7f*exp(,t+0.5*a') and (3.5) a' = 10g[7f*(cv'+ I)].

Under the assumption that the average costs are Dfl 2,000, the coetficient of variation is 4 and the probability of positive costs is 0.8 and the correlation between the costs in two consecutive years is 0.3, Figure 3.1 gives an indica-tion of the proporindica-tion shared expenditures under risk sharing for high-risks and for high-costs till' various fractions of designated members. The higher the fraction of designated members, the higher the proportion shared expenditures.

The Figure shows that, given a certain fraction of designated members, risk sharing for high-risks yields a smaller proportion shared expenditures than risk sharing for high-costs. For instance, with 2% designated members, risk sharing for high-risks yields a proportion shared expenditures of about 5 % whereas risk

14 Under risk sharing for high risks it is assumed that an insurer designates those members with the highest costs in the previous year and p is the first-order autocorrelation of the costs, 62

3.3 FOllr forms of risk sharing

Proportion shared expenditures 0.7

0.6 0.5

0.4

0.3

::(

. . _____

.c.---• . . . .c.---• ~~

RSHe

o

0.01 0.02 0.03 0,04 0.05 0.06 0.07 0.08 0.09 0.1 Fraction designated members

Figure 3.1 The proportion shared expenditures under RSHR and RSHC given the fraction of designated members (E(AC)=DI1. 2,000; cv=4; 1T=O.8 and p=0.3)

sharing for high-costs yields a proportion shared expenditures of about 35 %.

The reason is that under risk sharing for high-risks, members are designated in advance of the year whereas under risk sharing for high-costs this is done at the end of the year.

Figure 3.2 gives an indication of the proportion shared expenditures under outlier risk sharing given various threshold amounts. The higher the threshold, the lower the proportion shared expenditures.

For instance, a threshold of Dfl. 10,000 yields a proportion shared expenditures of about 0.3, a threshold of Dfl. 35,000 yields a proportion of about 0.1.

Figure 3.3 gives an indication of the fraction of members whose costs exceed a certain threshold in a year. Under outlier risk sharing, these persons are the designated members. The higher the threshold, the lower is the fraction of

Proportion shared expenditures 0.7

0.6

0.5 0.4 0.3

0.2 0.1

o o

5 10 15

3. Forms of risk sharing

20 25 30 35 40

Threshold ('DII1,OOO)

~~~--~~~~--~

Figure 3.2 The proportion shared expenditures nnder outlier risk sharing given the threshold (E(AC)=DI1. 2,000; cv=4; 1T=0.8)

designated members. About 5 % of the members have health care expenditures above Dfl. 10,000. About 2% of the members exceed the threshold of Dfl.

20,000 and about 1 % exceed Dfl. 30,000.

The proportion shared expenditures provides a rough measure of the reduction of an insurer's incentives for efficiency caused by the addition of risk sharing.

The higher the proportion shared expenditures, the lower an insurer's incentives for efficiency in general. However, given a certain proportion shared expendi-tures, the different forms of risk sharing may have different effects on an insurer's incentives for efficiency. Therefore the measurement of an insurer's incentives for efficiency under risk sharing will be further investigated in the next chapter.

64

3.3 FOllr forms of risk silaring

Fraction designated members 0.25

0.2

0.15

0.1

0.05

\

" ... .

~

~ _{. ~}

o~----~----============ o

5 10 15 20 25 30 35 40 Threshold ('DlI1,OOO)

Figure 3.3 The fraction of designated members under outlier risk sharing given the threshold (E(AC)=Dfl. 2,000; cv=4; 11=0.8)

3.3.4 Implementation issnes

This subsection describes some implementation issues of the four forms of risk sharing.

With respect to the money flows between insured members, insurers and the regulator, risk sharing can be implemented as follows:

- All members that choose the same insurance modality pay the same additional premium directly to the insurer of choice.

- The regulator calculates the capitation payments as in the situation without risk sharing. The insurers receive these capitation payments as in the situation without risk sharing.

- At the end of the year each insurer informs the regulator about the costs of its members designated for risk sharing. The regulator calculates for each insurer

3. Forllls of risk sharing

its gross risk sharing reimbursement. Furthermore the regulator calculates for each insurer the price that it has to pay to finance the risk pool. The net risk sharing reimbursement for an insurer is calculated as gross risk sharing reim-bursement minus this price. An insurer with positive net risk sharing reimburse-ment receives this amount from the regulator and vice versa.

In comparison with the situation without risk sharing, each insurer has to make a list of its designated members. Furthermore each insurer must provide, depending on the exact form of the risk sharing reimbursements and the price of risk sharing: the costs of individual designated members 6r the total costs of the group of designated members.

Implementing risk sharing for high-risks requires rules of how to deal with enrolment and disemolment during the year whereas with the other forms of risk sharing this is not necessary. Several options are possible.

(I) The most simple option would be that at the start of the year each insurer designates the percentage of its members for whom it is allowed to share the risk. Members who switch to another insurer during the year keep their status of designated or non-designated member. The same holds for those members who die during the year.

In the second and third option insurers will be able to designate (a fraction of) members who enrol during the year and who form a predictable loss.

(2) A second option would be that designated members who switch to another insurer or die during the year can be replaced by new members only. Because only newly emoling members can still be designated for risk sharing, it is not possible that insurers designate those members with (almost certain) high costs in the year, without being able to predict this at the start of the year.

(3) A third option would be to allow designation for risk sharing on the contract renewal date which can be any day of the year. Members that are designated for risk sharing are designated for one year. This option requires that the regulator registers the starting date of the risk sharing per designated member.

In comparison with the other two options, it will be more difficult to keep track of the percentage of designated members per insurer and their costs.

If an insurer has designated more members than it is allowed to - this is only 66

3.3 Four forms of risk sharing

possible in the second and third option - this can be corrected for by lowering the costs of its designated members pro rata.

With respect to (dis)enrolment during the year, it should be noted that if the contract renewal date is the same for each member, the potential implementation problems of risk sharing for high-risks are greatly reduced.

Risk sharing requires that each insurer registers the costs of individual mem-bers. In some circumstances this may pose difficulties because such cost data are not readily available for all types of care within the specified benefits package. Beebe (1992) suggested to base risk sharing on those types of care for which cost data are already available, but the present study assumes that risk sharing does not make a distinction between several types of care within the specified benefits package. Implementation problems caused by the omission of necessary cost data may be alleviated by the use of standard prices in conjunc-tion with utilizaconjunc-tion data.

In document Risk sharing as a supplement to imperfect capitation (pagina 65-73)