Two different models are presented in this section. First, results from a nested logit model that includes only plan characteristics are presented. Second, results are presented that include both plan characteristics and interactions between individual and plan characteristics.
Premium elasticities are estimated both from the beneficiary's perspective (representing a change in out-of-pocket premium) and the insurer perspective (representing a change in out-of-pocket premium plus the plan payment). The premium elasticity is given by:
The first half of the bracketed term
represents the within-sector price elasticity (the effect of a premium change on the probability that M+C enrollees choose a particular plan) while the second half
represents the intersector price elasticity (the effect of a premium change on the probability of joining the M+C sector).
presents the results of the nested logit model with plan characteristics only. Premium has a negative sign and is statistically significant (p<.001). The total out-of-pocket premium elasticity of demand is equal to −0.13. This indicates that a 10 percent increase in a M+C plan's premium is associated with a 1.3 percent decrease in the plan's enrollment. The estimated within sector out-of-pocket premium elasticity is −0.12, while the cross sector out-of-pocket premium elasticity is equal to −0.01. This indicates that most of the 1.3 percent who disenroll from the M+C plan as a result of the premium increase will choose another M+C plan, if available, other than FFS Medicare.
The insurer-perspective within-sector premium elasticity is equal to −3.87, while the cross-sector elasticity is −0.69. These larger elasticities reflect the larger value of the base premium used to calculate the elasticity. If a plan increased its out-of-pocket premium by 10 percent of the total premium, its enrollment would decline by 45.6 percent.
The second way to show the effect of a premium change is to estimate the expected change in market share for a particular plan j for a given dollar change in premium:
While this market-share equation is analogous to the elasticity equation given above, it has a decided advantage over the elasticity because it is not dependent on a particular premium value. The first half of (1) represents the within sector change in market share
, multiplied by the proportion of the sample in the M+C sector (MSk
). The second half
represents the intersector change in market share. The probability that an individual picks the M+C sector (MSk
) is 0.308. The conditional probability of picking a particular plan within the M+C sector
is equal to 0.252.6
The change in the jth plan's unconditional market share (including the FFS sector) for a $1 change in the jth plan's premium is −0.00062. This suggests that a $10 premium increase leads to a 0.62 percentage point decrease in the plan's market share. The typical M+C plan in this model has an unconditional market share (i.e., including FFS) of 7.76 percent, which suggests that if the typical plan raised its premium $10, its market share would drop from 7.76 percent to 7.14 percent. That loss represents the bulk of the lost market share would be to other M+C plans if they are available, with very few beneficiaries switching to FFS as a result of the premium increase.
The presence a drug benefit is associated with an increased probability of joining a particular M+C plan (β=0.589, p <.001). Similarly, the probability of joining is negatively correlated with higher copayments for generic prescription drugs (β=−.080, p <.001).
Individuals are more likely to join a staff model plan, relative to the reference group (IPA model), while individuals were not more likely to join group model plans. For-profit status of the M+C plan is strongly (t =14.75) and negatively (β=−.917) associated with enrollment. Overall, beneficiaries prefer nonprofit staff model plans, although the large coefficient on the nonprofit variable suggests that it may be correlated with omitted variables, such as the brand name advantage enjoyed by plans such as Blue Cross Blue Shield or Kaiser.
Among other plan characteristics, vision coverage, multiple benefit options, and having copayments for primary care, emergency room services, mental health coverage, and ambulance services are all significantly associated with membership, while charging a copayment for hearing benefits and dental coverage are not. Although the coefficients for vision coverage, emergency room copayments, ambulance services, and mental health coverage have the expected signs, the coefficient for primary care copayment does not. This may be due to omitted plan characteristics associated with higher primary care copayments, or plans with superior provider networks that may have higher primary care copayments. The positive coefficient for multiple benefit packages indicates that more popular plans offer multiple benefit packages more often.
In the model predicting sector choice, M+C enrollees are younger (β=−.039, p <.001), and healthier as measured by self-rated health. Interestingly, M+C joiners were more likely to have a chronic illness. Demographically, M+C members were more likely to be married (β=.279, p <.001) and less likely to have income over $20,000 (β=−.562, p <.001). County average Medigap premiums are positively correlated with the probability of joining a M+C plan, reflecting the substitution between M+C plans and Medigap, with a Medigap premium elasticity of 0.209.
To better understand the magnitude of the effects reported in , the coefficients for key significant variables were transformed to marginal probabilities (). The most important plan characteristic is the drug benefit. Offering a drug benefit increases the probability of selecting a particular M+C plan by 43.7 percent and the probability of selecting the M+C sector by 3.5 percent. In contrast, the total effects of vision coverage (1.8 percent) and mental health copayment (2.2 percent) are much less important.
Marginal Probabilities and Elasticities
presents the results of the nested logit model including both plan characteristics and interactions of individual and plan characteristics. The interaction of high income and premium was significant and positive, indicating that the premium elasticity for M+C plans decreases as income increases. College education, interacted with the plan offering a drug benefit, was significant (p =.025) and positive, indicating that the attractiveness of drug coverage increases with education.
Nested Logit Coefficients Including Individual Interactions
Our two interactive markers of selection indicated that drug and vision benefits were attractive to high-cost beneficiaries. First, the coefficient on the interaction between chronic illness and drug benefits is positive, indicating that beneficiaries with these chronic illnesses are more likely to choose plans with drug benefits (β=0.102, p =0.03). Second, we found that diabetics were more likely to join plans that offer vision benefits (β=0.021, p =0.08).
also includes plan characteristics, for which the results are generally similar to , and individual characteristics. The coefficient of self-rated health is negative, indicating favorable M+C sector selection. However, the coefficient of chronic illness is not a significant predictor of M+C sector choice in the interactive model.