Module 3: Hospital Pricing and Competition

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# Module 3: Hospital Pricing and Competition
## Part 3: Understanding Competition
### Ian McCarthy | Emory University
### Econ 372

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# Central Empirical Issues
At least 2 related issues in studying hospital competitiveness:
1. How do we measure "competitiveness"?
2. What is the effect of competition?

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# Measuring competitiveness
- Common measure is Herfindahl-Hirschman Index (HHI), `$\sum_{i=1}^{N} s_{i}^{2}$`.
  - 2,500 is considered **highly concentrated**
  - 1,800 is considered **unconcentrated**
- "Willingness to pay" is more recent measure (theoretically supported)
- Both require a measure of the geographic market

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# Defining the market
Lots of subjectivity...
- Radius around a hospital?
- Concentric circles to define "catchment" areas?
- Patient/physician referrals?
- At what product-level do hospitals compete?

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# Trends in competitiveness
Almost any way you define it, hospital markets are more and more concentrated (less competitive) in recent decades.
- 1990: 65% of MSAs highlgy concentrated, 23% unconcentrated
- 2006: 77% highly concentrated, 11% unconcentrated

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# Hospital concentration over time

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  ![](pics/GHT1.png)
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  ![](pics/GHT2.png)
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<div class="smalltext">Source: <a href="https://www.aeaweb.org/articles?id=10.1257/jel.53.2.235">Gaynor, Ho, and Town (2015). The Industrial Organization of Health Care Markets. Journal of Economic Literature.</a></div>

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# Hospital concentration over time
- More data and [interactive report](https://healthcostinstitute.org/hcci-originals/healthy-marketplace-index/hmi) from the Health Care Cost Institute.
- [Presentation](https://nihcm.org/publications/hospital-consolidation-trends-impacts-outlook) from the National Institute for Health Care Management

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# Why?
Historical perception of hospital competition as "wasteful" and assumption that more capacity means more (unnecessary) care:
- Limit public spending by limiting competition
- Prevalence of certificate of need (CON) laws

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# Effects of reduced competition
1. Higher prices
2. Lower quality, [2020 NEJM Paper](https://www.nejm.org/doi/full/10.1056/NEJMsa1901383)
3. Maybe lower costs (but not passed on to lower prices)<br>

Effects for both "in-market" and "out-of-market" mergers

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# Modeling competition and prices

Health care providers compete on both quality and price (possibly other dimensions such as access or wait times). This complicates our theoretical analysis of competition.

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# Competition with fixed prices

- Demand: `$q_{j}=s_{j}(z_{j}) \times D(\bar{p})$`
- Costs: `$c_{j}=c(q_{j},z_{j}) + F$`
- Profits: `$\pi_{j} = \bar{p}q_{j} - c_{j}$`

Hospitals choose quality such that:

`$$\frac{d \pi_{j}}{d z_{j}} = \left(\bar{p} - \frac{d c_{j}}{d q_{j}} \right)\left(\frac{d s_{j}}{d z_{j}}D + s_{j}\frac{d D}{d z_{j}} \right) - \frac{d c_{j}}{d z_{j}}=0$$`

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# Competition with fixed prices

- Increase in competition will tend to increase quality
- Negative welfare effects if `$\frac{d D}{d z_{j}}$` is sufficiently small and fixed costs are large

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# Competition with market prices

Profit given by `$\pi = q(p,z) \times (p-c-d\times z) - F,$` which yields
`$$\begin{align*}
p &= \frac{\epsilon_{p}}{\epsilon_{p}-1} (c+dz) \\
z &= \frac{\epsilon_{z}}{\epsilon_{z}+1} \frac{p-c}{d}
\end{align*}$$`

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# Competition with market prices

Rewrite in terms of elasticities:
`$$\begin{align*}
\epsilon_{p} &= \frac{p}{p-c-dz} \\
\epsilon_{z} &= \frac{dz}{p - c - dz}
\end{align*}$$`

Taking the ratio and solving for `$z$` yields, `$$z = \frac{p}{d}\times \frac{\epsilon_{z}}{\epsilon_{p}},$$`

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# Competition with market prices

Dorfman-Steiner condition:

- Quality increases if the quality elasticity increases or if price increases
- Quality increases if the price elasticity decreases or the marginal cost of quality decreases
- **Prediction for competition:** If competition has a large effect in terms of price elasticity (i.e., consumers are heavily responsive to the price effects from increased competition), then quality may decrease. If instead competition has a large effect in terms of quality elasticity (i.e., consumers are more responsive to quality changes), then quality will increase.