Do consumers make rational choices for their Part D Plan?

To answer this question, one can examine how individuals choose health plans based on premiums, expected out of pocket cost, plan quality, and other factors. A paper by Abaluck and Gruber (2011) use data from 2006 and find that up to 70% of seniors appear to choose plans that are not optimal. Do these conclusions hold with more recent data? And are there improved methods for answering this question.

One question is how does one treat the error term in these regressions. In a standard random utility model, the error term captures heterogeneous tastes for unobserved product attributes. People are not perfectly rational, however, and thus the error term could also capture optimization error, genuine randomness in decision making, or other types of confusion.

To answer this question and examine whether PDP plan choice has improved in more recent data, a working paper by Keane et al. (2019) use a finite mixture of mixed logit model or MM-MNL model. Their basic approach uses the following model: 

U_ij = (Pj)α+[E(oop)ij]β1 + (σ^2_ij)β2 + (cj)β3 + (Qj)β4 + e_ij

In this equation, P is the premiums for plan j, E(oop) is the expected out of pocket costs,  σ^2_ij is the variance in out of pocket costs, cj, is a vector of financial characteristics of plan j that affect OOP, and Qij is a vector of plan quality measures, which in this study includes both star ratings and indicator variables for plan “brand”.

The authors initially conceive of 2 latent classes of individuals.  The rational, risk neutral individual would be indifferent to premiums and out of pocket costs (assuming the impact from discounting is small given the 1 year time horizon covered by Part D Plans) and thus α = β1. Also rational individuals should be indifferent among different financial characteristics (cj) that lead to the same E(oop) and σ^2_ij and thus β3=0. In short, we can divide the world into rational individuals where utility is defined as:

U_ij = [Pj + E(oop)ij]β1 + (σ^2_ij)β2 + (Qj)β4 + e_ij

with probability p and with probability 1-p individuals are not rational and have utility as described in the first equation.  In short, conditional on a person’s latent type (i.e., rational vs. not) and his/her preference parameters, we have a simple multinomial logit model.

The authors also extend this model by: (i) considering more than two types where the “rational” type is defined as above, and the data is used to determine the other types and (ii) the authors let individual characteristics (e.g., age, presence of Alzheimers’ disease, depression) affect individual decision-making ability.

The authors highlight the benefit of their model, saying:

Given estimates of the decision utilities of the confused type, as well as the distribution of their parameter vector ), we can learn how their behavior is sub-optimal. Do many consumers…place excessive weight on premiums vs. OOP costs? Or are these excesses statistically significant but quantitatively small?  Are there particular “irrelevant” financial attributes of insurance plans that consumers tend to overweigh in making decisions? 

The authors then use PDP administrative data from non-low income subsidy individuals as well as data from the Medicare Current Beneficiary Survey to test this approach.

The authors have a number of interesting findings. First, individuals place more weight on premium reduction than reducing future out-of-pocket cost. Second, a plan’s brand plans an important part in plan choice for some consumers. In general, fewer than one-in-ten consumers are perfectly rational from an economist’s defminition..

…we find that 9.8% of consumers are classified as the “rational” type, while 11.4% place excess weight on low premiums, and 78% place value on plan characteristics that are irrelevant once one conditions on the distribution of plan costs…As expected, people with dementia and depression are more likely to be “irrational.” And the bulk of the econometric error term is attributed to optimization error

A more important question may be, does this matter? If people are choosing incorrectly, are these error costing them $5 per year or thousands of dollars? The authors perform a welfare analysis to see how welfare would improve if people picked a more optimal plan.

…we find welfare losses to be modest except in a small subset of cases (e.g., people with dementia and depression face a high variance of OOP costs, suggesting they are not well insured). In contrast to traditional choice models, in our framework consumer welfare can be enhanced by eliminating “bad” options from the choice set. But as in Ketcham et al. (2019) we find that such policies lead at best to trivial welfare improvements. This occurs for two reasons: (i) Part D premiums are heavily subsidized, so even a “bad” plan is better than no plan, and (ii) given consumer heterogeneity, very few plans are “bad” for everyone. 

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