As table 4 shows, the calculations for shadow prices are sensitive to how much information individuals have in making their predictions. In Figure 3 we graph the profit-maximizing q’s for two services, mental health/substance abuse and musculoskeletal care as individuals know more and more of the information contained in prior use in the absence of risk adjustment. Distortions go up exponentially as information improves.
In the case of the q for mental health and substance abuse, the damage from selection incentives accelerates rapidly around the 30% range. For the muskuloskeletal category the graph is smoother than in the mental health and substance abuse care. When individuals know as much as 50% of prior use, profit-maximizing q’s go off the charts, signaling that incentives to over and underprovide are very strong.
These results highlight the importance of what individuals can forecast for the implications of selection incentives and risk adjustment. Individuals of course do “know” what they have used in the past; the issue is how well can they use this information to predict. Individuals cannot reasonably be expected to forecast based on population information, but on the other hand they are likely to have more private information than we give them credit in the models here. Unfortunately, there is no good way to know if the informational assumptions explored here bound what we can really expect individuals to be able to anticipate.
A Welfare Index
Results in Table 4 can be summarized in a single measure of the selection-related distortion. The welfare loss can be approximated by:
where Aqs is the discrepancy between the q for service s and the second best q, and Ams is the change in spending induced by the discrepancy in q. For purposes of this analysis we define Aqs as the difference between qs and the weighted average q for all service types contained in Table 4. Thus, for each service s, we take the expenditure-weighted average q for each information/risk adjustment combination, and compute Aqs based on that. Since Aqs is in percentage terms, Ams is simply Aqs multiplied by demand elasticity, which we assume for simplicity is 0.25 for all services. When individuals know age-sex and 25 percent of the information in prior use, the welfare loss without risk adjustment is only 1.9% of spending, and this is reduced to 1.3% by both risk adjusters.
The next step in this analysis would be to find the “optimal risk adjustment.” Given a set of variables available for risk adjusting, equation (14) could be minimized with respect to the weights on the risk adjusters. Conventional risk adjusters are derived from coefficients from a regression of adjuster variables on total expenditures in a population. These weights are in general not optimal from an economic standpoint. (Glazer and McGuire, 1998).