Main results
Complexities of Health Insurance Choice
Ian McCarthy, Emory University and NBER
Emory University, 2024
Overview
- Health insurance is a complex product, and selecting a plan is a difficult task for enrollees
- Do people make ‘good’ health insurance choices?
Abaluck and Gruber (2011), “Choice Inconsistencies Among the Elderly…”
Background and Motivation
Background and Motivation
Research Question
- Significant cost differentials across many plan choices in Medicare Part D
- ‘Quality’ of choice has potentially large welfare implications for enrollees
Research question: What factors to Part D enrollees consider when choosing a plan?
Model
- CARA utility: \[U(C) = -exp( -\gamma (W-C)),\] with \(C \sim N(\mu, \sigma^2)\)
- Indirect utility: \[u(\mu, \sigma^{2}) = E[U(C)] = -\alpha exp (\gamma \mu + \frac{1}{2} \gamma^2 \sigma^2),\] where \(\alpha = -exp (\gamma W)\)
- First-order taylor approximation around \((\mu', \sigma^{2'})\) yields: \[u(\mu, \sigma^{2}) \approx u(\mu', \sigma^{2'}) -\alpha \gamma (\mu - \mu') - \frac{1}{2} \alpha \gamma^2 u(\mu', \sigma^{2'})(\sigma^2 - \sigma^{2'})\]
Model
- Total costs, \(C\), composed of a fixed premium, \(\pi\), and variable out of pocket cost, \(OOP\)
- Implies \(\sigma^{2} = var(C) = var( \pi + OOP) = var(OOP)\) and \(\mu = E[C] = E[\pi + OOP] = \pi + \mu^{*}\)
- Dropping constant terms and adding an error term: \[u = -\alpha \gamma u(\mu', \sigma^{2'})(\pi + \mu^{*}) - \frac{1}{2} \alpha \gamma^2 u(\mu', \sigma^{2'}) \sigma^2 + \varepsilon\]
Estimating equation
\[\begin{align*} u &=& -\alpha \gamma u(\mu', \sigma^{2'})(\pi + \mu^{*}) & - \frac{1}{2} \alpha \gamma^2 u(\mu', \sigma^{2'}) \sigma^2 & + \varepsilon \\ &=& \beta_{0} \pi_{j} + \beta_{1} \mu_{ij}^{*} & + \beta_{2} \sigma^{2} & + \lambda x_{j} + \delta q_{b(j)} + \varepsilon_{ij} \end{align*}\]
- CARA risk aversion coefficient, \(\gamma = 2 \times \frac{\beta_{2}}{\beta_{1}}\)
- \(x\) captures other financial plan characteristics (e.g., deductible)
- \(q\) captures plan ratings and other non-financial attributes (constant across plans within an insurer, or ‘brand’ in the paper)
Data and estimation
- Data from 2006 Medicare Part D enrollment and drug utilization (private data)
- Plan characteristics (public)
- Multinomial logit discrete choice model, estimated via MLE
- Estimate \(\mu\) from observed drug expenditures
- Estimate \(\sigma^{2}\) from observed drug expenditures among ‘similar’ individuals
Key findings
\[\beta_{0} \pi_{j} + \beta_{1} \mu_{ij}^{*} + \beta_{2} \sigma^{2} + \lambda x_{j} + \delta q_{b(j)} + \varepsilon_{ij}\]
- \(\beta_{0}=\beta_{1}\). Should trade-off one dollar in premium and one dollar in out of pocket costs, but results suggest \(\beta_{0} > \beta_{1}\)
- \(\lambda=0\). Shouldn’t care about other financial aspects conditional on OOP costs and premiums, but \(\lambda \neq 0\) in general
- \(\beta_{2} < 0\). Should prefer plans with lower variance in OOP costs, but \(\beta_{2}\) often very small
Main takeaway: Enrollees far overweight premiums
- 27% increase in consumer welfare if enrollees picked the cost-minimizing plan (partial equilibrium)
Ketcham et al. (2012), “Sinking, Swiming, or Learning to Swim in Medicare Part D”
Motivation
While enrollees may make bad Part D decisions, they may learn over time
Model, data, and estimation
\[\Delta o_{i} = \alpha + \gamma \Delta h_{i} + \Delta \varepsilon_{i}\]
- \(\Delta\) denotes changes from 2006 to 2007
- \(o_{i}\) is overspending, measured as difference between observed costs and those under the lowest cost plan
- \(h_{i}\) is health status
- Data from CMS and CVS Caremark
- Estimate via OLS
Main results
Key findings
- Large reductions in overspending from 2006 to 2007, unexplained by changes in health
- Reductions appear to be driven by switching plans
- Switchers were more likely to experience more overspending in 2006
- Good evidence that individuals are learning in this market and evolving their plan choices accordingly
The Debate
Ketcham et al. (2016), “Choice Inconsistencies among the Elderly…: Comment”
Key point of contention
- Are choices consistent with maximization of some utility function?
- Or, are choices consistent with maximization of a specific utility function?
Jonathan D. Ketcham, Kuminoff, and Powers (2016) argue that the former is sufficient and that deviations from the latter are not necessarily evidence of poor decision making
Specific concerns raised
- Imperfect assignment of individuals to plans in Abaluck and Gruber (2011)
- Failure to consider quality in notions of ‘good’ choice (e.g., formulary restrictions, prior authorization, customer service, mail order options, etc.)
Abaluck and Gruber (2016), “Choice Inconsistencies among the Elderly…: Reply”
Main response
- Searching for plans dominated in all dimensions, with increasing number of quality measures, is unreasonable and has little power
- Jonathan D. Ketcham, Kuminoff, and Powers (2016) allow flexible brand preferences, which implies that dominated choices can only be made among plans from the same brand
- Speaks to the definition of the ‘efficient frontier’ of choices
Summary of the debate
- Extent of choice inconsistencies differs based on normative assumptions
- Can we find other dimensions of plans that may rationalize observed choices? Not fully, but yes
- Should we engage in such an exercise?
Significant survey evidence that Medicare enrollees are confused:
- 73% of seniors (91% of pharmacists and 90% of doctors) say prescription drug plans are too complicated
- 60% of seniors say “Medicare should select a handful of plans that meet certain standards so seniors have an easier time choosing”
References
Abaluck, Jason, and Jonathan Gruber. 2011. “Choice Inconsistencies Among the Elderly: Evidence from Plan Choice in the Medicare Part D Program.” American Economic Review 101 (4): 1180–210. https://doi.org/10.1257/aer.101.4.1180.
———. 2016. “Choice Inconsistencies Among the Elderly: Evidence from Plan Choice in the Medicare Part D Program: Reply.” American Economic Review 106 (12): 3962–87. https://doi.org/10.1257/aer.20151318.
Ketcham, Jonathan D., Nicolai V. Kuminoff, and Christopher A. Powers. 2016. “Choice Inconsistencies Among the Elderly: Evidence from Plan Choice in the Medicare Part D Program: Comment.” American Economic Review 106 (12): 3932–61. https://doi.org/10.1257/aer.20131048.
Ketcham, Jonathan D, Claudio Lucarelli, Eugenio J Miravete, and M Christopher Roebuck. 2012. “Sinking, Swimming, or Learning to Swim in Medicare Part D.” American Economic Review 102 (6): 2639–73.
Complexities of Health Insurance Choice Ian McCarthy, Emory University and NBER Emory University, 2024