i) Our model of the selection of Health plan explicitly values options provided to enrollees that can be exercised under different contingencies. This is the fundamental innovation of this work, where we separately value the embedded option of receiving (partial) coverage for care from out-of-network providers under a PPO. The values of these options (the price one pays for flexibility as the future unfolds) are based on the current health status, income, out-of-pocket premium cost, etc., as well as the likelihood of developing a serious and or chronic health condition that typically increases with age.
ii) The evolution of health status over time is explicitly modeled as a stochastic process which describes the following: An individual’s health fluctuates continuously over time and tends to deteriorates with age. In addition to these small fluctuations over time (and the general downward trend), there exists a small probability every period that an individual will develop a serious illness or that his health will experience a large and discontinuous drop. Our model represents this evolution as the combination of a continuous random walk with a downward drift and a Poisson jump process. The individual makes the decision based on current situation (health, income, etc.) whether they should stay with the HMO or switch to a PPO.
iii) Most existing models focus on different willingness-to-pay for coverage by individuals with different risk profiles. Our model addresses different willingness-to-pay for provider quality (represented as value received from enrolling in a plan) as a function of both health risk profile and income. The model is informed by empirical findings in the literature that higher income enrollees sort to PPOs, even after controlling for differences in premium. Survey results indicating that employers view PPOs as appealing to higher income employees also motivate this modeling choice.
The model is solved computationally and its implications are tested empirically through a Logistic model of binary choice using data from the National Health Interview Survey (NHIS). Preliminary results indicate that higher income, a lower health status, the severity of a chronic condition and a lower out-of-pocket premium (over that of HMOs) increase the likelihood of enrolling in a PPO.