To use a specific hypothetical example, suppose the eHealthinsurance.com premium for a HDHP is $100 per month, but people who choose such plans are exceptionally healthy with actual medical expenses of only $50 per month. Even after adding $15 (for example) per month for administrative costs, the premium for people who actually choose the HDHP is $65 per month. In our original work, we would have used the $100 monthly premium. Now, with the use of claims data and some actuarial modeling, we are able to calculate an estimate closer to the true risk profile of an individual and model a $65 monthly premium. Without this correction, the probability of choosing a HDHP at a premium of $100 would be less than with a more accurate premium estimate of $65.

To capture the relationship between costs and health risk, we estimated a health care cost model for the individuals who chose each plan. We used that model to develop premium estimates that fed back into the choice model. We "iterated" - i.e. went back and forth - between the choice model and the cost model until the market converged to a stable set of choices and premiums. Our method is illustrated in Figure 2. Starting from a premium that is too high for equilibrium (i.e., point A), the premium falls and enrollment increases until the two lines converge to a single premium and enrollment (i.e., Point B). There is no guarantee that the model will be stable as shown here. We know that the "choice depends on premium" line (i.e. the demand curve) slopes downward, but the "premium depends on choice" line might slope up or down. The model will be stable if the demand curve is the steeper of the two lines.

**Figure 2: Model of Health Insurance Choices and Costs**

**Figure 2** illustrates our method of capturing the relationship between costs and health risk. Starting from a premium that is too high for equilibrium (i.e., point A), the premium falls and enrollment increases until the two lines converge to a single premium and enrollment (i.e., Point B). There is no guarantee that the model will be stable as shown here. We know that the "choice depends on premium" line (i.e. the demand curve) slopes downward, but the "premium depends on choice" line might slope up or down. The model will be stable if the demand curve is the steeper of the two lines.

To implement this new iterative approach we had to construct premiums from expected health care costs in the individual and ESI markets. Premiums obviously depend on expected costs, but they also depend on how costs are aggregated across individuals. How many individuals are in the insurance pool? Does the premium for a particular person depend on his or her experience, or on the experience of the group? In other words, how are premiums "rated" in the individual and ESI markets?

The two rating methods we used were individual experience rating (IER) for the individual health insurance market and group experience rating (GER) for the ESI market.^{10} The premium for each rating method was generated as follows:

*Individual Market:*Given that the premium for each person in the individual market is based on his or her own health care costs, we estimated how much each person would spend under each type of insurance plan (PPO, HSA, etc.). We added a loading fee of 30% to arrive at the premium for each choice in the individual market.^{11}*Employer-sponsored Market:*The first step in GER is to define the “pool” that determines the premium rates. We used 3 pools based on establishment size – small establishments, medium-size establishments, and large establishments.^{12}

We predicted the costs of each person in each plan. Then we calculated the average cost across all people who work for employers in each of the 3 pools. For example, the average cost of the HMO for employees of small establishments may be $3,000 for a single policy and $7,000 for a family policy. The average cost of the HMO was different in medium-size and large groups. Then, we added loading fees to get predicted premiums for each pool in the ESI market.

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