Flavors of Actuarial Equivalence

For health care actuaries the next few years are likely to be taken up with various actuarial equivalences. Actuarial value is at its core an idea for expanding actuarial equivalence.  HHS has indicated that modifications to essential benefits will need to be actuarially equivalent.  Health plans will be developing new products in response to reform and need to provide some comparison to existing products describing their actuarial equivalence.

Actuarial equivalence is attempt to make describe how two separate policies are the same.  Since all insurance products are fundamentally transformations of a random variable, the claim distribution, it makes sense to incorporate two important concepts from probability: equivalence in distribution and equivalence in mean.

Two policies are equivalent in distribution if they would pay out the same amount of benefits for any claim history.  This is a strong condition basically requiring the policy to be the same. Actuaries are unlikely to see this type of equivalence when working on a subset of benefits in a health plan but may see it when developing completely new products.  Actuaries may start with a completely new policy design but as the policy continues to evolve with input from stakeholders, the policy may end up with a complicated benefit formula that in practice pays like a standard deductible and coinsurance or deductible and copay plan.  As a final check in product development in may be helpful to compare new products to a very simple existing product.  If it takes some time to understand the scenarios in which the new policy would pay differently if may be time to rethink whether the value add in product complexity is useful. Alternatively, it may make communicating with outside stakeholders easier as there is an easy reference plan.

Equivalence in mean is more common and is typically used to evaluate changes in a smaller subset of benefits.  Two alternate configurations are equivalent in mean if for a given claim distribution, the benefit payment will be the same.  Actuarial value is the application of this idea to an entire policy but equivalence in mean is typically applied to portions of the benefit package. For example, if two physical therapy and occupational therapy1  each have a 20 visit cap, what would be the equivalent cap on both service types combined? The combined cap will be less than total because some members in the reference population will use more than 20 visits of one service but none of the other so combining the caps will pay for services that were not covered in the separate caps.

Equivalence in mean also produces winners and losers.  The distribution used is typically a standard or representative population but this distribution may be composed of subdistributions that are affected differently. Some members will be better off under one of the benefit plans. In the physical vs occupational therapy example, policy holders who use both services extensively, for example major stroke victims, may benefit from the separate caps but policy holders who only use one type of service, some who has orthopedic work on knees, may benefit from the combined caps. Actuaries may increasingly need to work to determine who are the winners and losers in an actuarial equivalence to show that plans are using actuarial equivalence in a non-discriminatory manner.

Health actuaries will be called on to return to one of the core skills, determining when future payments are the same under uncertainty.  Actuaries will need to understand when two policies are effectively same but provide an analysis of when two policies are similar but different how are they different.

1 Occupational therapy is therapy designed to restore the basic daily skills. An example would be helping some relearn how to hold silverware after a stroke.

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