Quality Disclosure and Regulation

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.title[
# Quality Disclosure and Regulation
]
.subtitle[
## Scoring Design in Medicare Advantage
]
.author[
### <strong>Author:</strong> Benjamin Vatter, Stanford University (MIT upcoming)
]
.author[
### <strong>Discussant:</strong> Ian McCarthy, Emory University and NBER
]
.date[
### AHEW, October 1, 2022
]

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# What's the point?

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# 1. Endogenous quality (Spence, 1975)

- **Setting:** Monopoly (or oligopoly) when firms set both price and quality
- **Intuition:** Firm invests to the point where marginal quality valuation meets marginal costs of quality, but socially optimal quality depends on average valuation
- **Takeaway:** Profit-maximizing quality will differ from socially optimal quality when the marginal customer is not representative of the average

Natural in the presence of adverse selection, where the marginal patient is almost always different from the average patient

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# 2. Types of quality disclosure

- Self-disclosed quality via advertising
- Word-of-mouth and aggregated reviews form users (Google, Rotten Tomatoes, etc.)
- Third-party rating agencies
- **Government regulation via mandated disclosure or licensing**

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# The main idea

- Need some form of quality disclosure to aid decision making
- Full-disclosure likely yields under-investment in quality

--
- Regulator can improve quality via coarse rating scores
- but...firms will respond to the scoring design accordingly

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# Context

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# Medicare Advantage

.pull-left[
  ![](images/mma-kff-2020.png)
]

.pull-right[
  ![](images/mma-kff-plantype.png)
]

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# Selecting an MA plan

When someone nears 65, they'll receive:

- Medicare & You Booklet (128 pages in 2022)
- Points beneficiary to Medicare's online plan finder tool
- **Lots** of other marketing materials touting different types of plans
    - Standalone Part D plans
    - Medicare supplemental plans
    - Medicare Advantage plans
- Assume someone has decided to search for an MA plan online

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.center[
 ![:scale 80%](images/PlanSearch_Step1.png)
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.center[
 ![](images/PlanSearch_Step2.png)
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.center[
 ![](images/PlanSearch_Step3.png)
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.center[
 ![](images/PlanSearch_Step4.png)
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.center[
 ![](images/PlanSearch_Step5.png)
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.center[
 ![:scale 75%](images/PlanSearch_Step6.png)
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.center[
 ![:scale 65%](images/MedicarePlanFinder_37920_Knox.png)
]

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.center[
 ![](images/StarRatings.png)
]

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# Preview of findings

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1. Estimate structural model of price **and quality investments**
2. Identify optimal scoring design

.pull-left[
  ![](images/best_linear_substitute_aggregator_paper-1.png)
]

.pull-right[
  ![](images/best_substitute_eqm_unpacking_custom_levels_4-1.png)
]

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# Some points of applause

- Substantial contribution, both theoretical and empirical
- Highly policy relevant

"To address this, I completed the data by reviewing a decade of public communications by CMS aimed at insurers. I recover year-to-year changes to the scoring design, **replicating the public scoring assignment perfectly.**"

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# Setup and estimation

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**What's new here?**
- Endogenous quality investments with imperfect mapping into quality scores
- Endogenous scoring design

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`$$u_{ij} = \underbrace{\alpha_i P_{j}}_{\text{premium}} + \underbrace{\beta_i b_{j}}_{\text{coverage}} + \underbrace{\mathcal{E}_{\psi}[\boldsymbol{\gamma}'\boldsymbol{q}|\psi(q_{j})]}_{\text{quality}}  + \underbrace{\lambda'z_{ij}}_{\substack{\text{Obs.}\\\text{attributes}}} + \underbrace{\xi_{j}}_{\substack{\text{unobs.}\\\text{preferences}}} + \underbrace{\varepsilon_{ij}}_{\sim \text{T1EV}}$$`

Note: when you see `$j$`, think `$jmt$`

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# Demand estimation

Two(three)-step process:
1. Estimate mean preferences, `$\hat{\delta}_{j}$`, from `$u_{ij} = \color{red}{\delta_{j}} + \color{blue}{\kappa_{ij}} + \varepsilon_{ij}$`

2. TSLS regression of `$\hat{\delta}_{j}$` on observable characteristics and fixed effects.

3. (if needed) Estimate preference for quality by minimizing the square difference between a contract fixed effect and expected quality, `$\eta_{j} - \boldsymbol{\gamma} \mathcal{E}[\boldsymbol{q} | r, \psi]$`, across time periods (pairwise time period differences).

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# Question/concern

Estimating preferences for quality...
- within an estimated fixed effect, `$\hat{\eta}$`
- within an estimated mean preference, `$\hat{\delta}$`

--
- What does the distribution of these fixed effects look like?
- How much variation exists in **within-contract** quality (or expected quality) over time?

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`$$\pi_{f}(\boldsymbol{q}, \psi) = \max_{\{p_j\}_{j \in J_{f}}} \sum_{j \in J_{f}}\underbrace{D_{j}(\boldsymbol{p}, \psi(\boldsymbol{q}))}_{\text{demand}} (\underbrace{R_j(p_j)}_{\text{mg. revenue}} - \underbrace{C(\boldsymbol{q}_j, \boldsymbol{z}_{j}, \boldsymbol{\theta}_j)}_{\text{mg. cost}})$$`

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# Pricing (insurance costs) estimation

- Profit maximization yields standard `$MR=MC$` expression
- Recover marginal costs
- Decompose marginal costs into part due to quality, other observable components, and residual, `$$MC=\boldsymbol{\theta}^{c}_{q}\boldsymbol{q} + \boldsymbol{\theta}_{a}^{c}\boldsymbol{a} + c$$`

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`$$\max_{\boldsymbol{x}_f \in \mathbb{R}^{|\mathcal{Q}| \times |J_f|}}  \underbrace{\int  E\left[\pi_{f}(\boldsymbol{q}_f, \boldsymbol{q}_{-f}, \psi)\right] dF(\boldsymbol{q}_f|\boldsymbol{x}_f)}_{\text{expected insurance profit}} - \underbrace{I(\boldsymbol{x}_f, \boldsymbol{\mu}_{\boldsymbol{f}})}_{\text{investment cost}}$$`

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# Quality (investment costs) estimation

- Equate marginal revenue from quality investment with marginal investment cost
- Assume investment costs are quadratic and **separable across products and categories**

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# Question/concern

- Costs almost surely are **not** separable across categories
- Investment in network changes access, outcomes, patient surveys
- Investment for one contract likely spills over into other contracts for same insurer
- How much does this matter?

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`$$\max_{\psi \in \Psi} E_{\boldsymbol{q}}[\underbrace{CS(\psi, \boldsymbol{q})}_{\substack{\text{Consumer}\\\text{surplus}}} + \rho^{F}\underbrace{\sum_{f}V_f(\psi, \boldsymbol{q}) -  I(\boldsymbol{x}_f^*(\psi), \mu_f)}_{\substack{\text{Insurer}\\\text{profit}}} - \rho^{G}\underbrace{Gov(\psi, \boldsymbol{q})}_{\substack{\text{Government}\\\text{spending}}} \vert \boldsymbol{x}^*(\psi)]$$`

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# Scoring design estimation

- Designer chooses scoring rule, `$\psi$`, from class of rules, `$\boldsymbol{\Psi}$`
- Trades off information for efficiency
- Paper shows that any monotone partitional score reduces to two elements: an aggregator and a cutoff function
- Considers optimal design among the set of designs with no more than 15 partitions and quadratic aggregators, setting `$\rho^{F}=1$` and `$\rho^{G}=0$`, for year 2015

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# Question/concern

- Do optimal cutoffs and aggregator change in different years?
- With different `$\rho^{F}$` and `$\rho^{G}$`?
- No firm response to quality bonuses, but costs to CMS could be in `$\rho^{G}$`

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# Main results

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# Demand

.center[
  ![:scale 75%](images/quality_value_coeffs-1.png)
  ]

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# Supply

| Category      | Insurance Costs, `$\theta_{q}$`     | Investment Costs, `$\mu_{k}$` |
| ------------- | ---------------------------------:| ---------------------------:|
| Access        | 31.16                             | 15.620***                   |
| Intermediate  | 108.40***                         | 19.530***                   |
| Outcome       | 16.810***                         | 15.000***                   |
| Patient       | -244.30***                        | 14.730***                   |
| Process       | -175.60***                        | 1.106                       |

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# Scoring design

.pull-left[
  ![:scale 80%](images/best_linear_substitute_aggregator_paper-1.png)
]

.pull-right[
  ![:scale 80%](images/best_linear_replacement_cutoff_placement_paper-1.png)
]

- Optimal design involves linear aggregator among 5 partitions
- Pooling at the bottom, with very little demand for low-quality plans
- Closely matches consumer WTP (except for Intermediate category?)
- **Question:** How much is 3.5 vs 3.6 just noise?

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# Scoring design with uninformed beneficiaries

.pull-left[
  ![:scale 80%](images/best_linear_substitute_aggregator_paper-1.png)
]

.pull-right[
  ![:scale 80%](images/robust_linear_reduction_compare_paper-1.png)
]

- Is CMS pretty close already?
- Current design seems consistent with some feasible set of preferences
- Would be very interesting to know under what preferences the current design is actually optimal

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# Welfare

.center[
  ![:scale 57%](images/best_substitute_eqm_unpacking_custom_levels_0-1.png)
]

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# Welfare

.center[
  ![:scale 57%](images/best_substitute_eqm_unpacking_custom_levels_1-1.png)
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# Welfare

.center[
  ![:scale 57%](images/best_substitute_eqm_unpacking_custom_levels_2-1.png)
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# Welfare

.center[
  ![:scale 57%](images/best_substitute_eqm_unpacking_custom_levels_3-1.png)
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# Welfare

.center[
  ![:scale 57%](images/best_substitute_eqm_unpacking_custom_levels_4-1.png)
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# Considerations for this paper

(not necessarily actionable)

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# The bid process

.pull-left[
  ![:scale 75%](images/mma-bids.png)
]

.pull-right[
- Not just setting price
- Separate Part D bid process
- Ability to use Part C rebate to go toward Part D premium
]

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# Contracts vs plans

- Beneficiaries choose plans, defined by specific premium and benefits
- Quality is measured by contract

--
- Paper argues that there is really only one plan per contract
    - Makes sense in recent years but maybe not in early years
- Can't have it both ways
    - Price variation within contract good
    - but product differentiation within given quality score irrelevant?

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# Scoring design

Does (should) the setup incorporate...

- Bonuses for high scores? **No**
- Contract consolidation of plans? **No**
- Part D quality? **No**
- Penalty for high-variance contracts (i-factor)? **Maybe**
- Alert for ratings below 3 stars or at 5 stars? **Maybe**

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# Scoring design