Talks of the Swiss Health Economics Workshop 2013

1. Lucerne, 13. Sept. 2013
Swiss Health Economics Workshop 2013
Choice of Reserve
Capacity by Hospitals:
A Problem for Prospective
Payment?
Philippe Widmer, philippe.widmer@polynomics.ch
Article: Widmer, P., M. Trottmann, P. Zweifel (2013): Choice of Reserve Capacity by
Hospitals: A Problem for Prospective Payment?, work in progress

2. The stochastic production function is described by
‫ݕ‬ ൌ ‫ܧ‬ ‫ݕ‬ ൅ ݃ ‫,ݔ‬ ‫ݖ‬ ߠ ‫ܧ ݄ݐ݅ݓ‬ ‫ݕ‬ |݂ ‫ݔ‬ : ൌ ‫ݕ‬ത, ߪ௬
ଶ
ൌ ݃ ‫,ݔ‬ ‫ݖ‬ ଶ
∗ ‫ݎܽݒ‬ ߠ
Hospitals need to plan their resources based on expected future production
They minimize an ex-ante rather than an ex-post cost function
If inputs are too low, patients are turned away or have to wait for treatment
If inputs are too high, the hospital has to cover cost of reserve capacity
which appears inefficiently high
Production Planning with Output Uncertainty
y
f(y)
‫ݕ‬ത ‫ݕ‬ఈ
ߙ
‫ݕ‬ത = expected output
‫ݕ‬ఈ = targeted output
ߙ = probability of having to
turn away patients

3. Hospital management sets a probability ߙ which defines an output
level ‫ݕ‬௔ reflecting desired production possibilities
‫ݕ‬௔ ൌ ܲ‫ݎ‬ሾ1 െ ߙ|‫ݕ‬ത, ߪ௬
ଶ
ሿ
The cost minimizing problem of the hospital is
min
௫
‫ݓ‬ ∗ ‫|ݔ‬ሺ‫ݕ‬ത ൅ ‫ݕ‬෤ሻ ൑ ݂ ‫ݔ‬ ൌ ‫ܥ‬ ‫ݕ‬ത, ‫ݕ‬෤, ‫ݓ‬ ‫݁ݎ݄݁ݓ‬
‫ݕ‬෤ ൌ ‫ݕ‬௔ െ ‫ݕ‬ത ൌ ‫݌‬ିଵ 1 െ ߙ ‫ݕ‬ത, ߪ௬
ଶ െ ‫ݕ‬ത
‫ݓ‬ = vector of input prices
‫ܥ‬ ‫ݕ‬ത, ‫ݕ‬෤, ‫ݓ‬ = ex-ante cost function
The optimal input demand function ‫ݔ‬∗ሺ‫,ݓ‬ ‫ݕ‬ത, ‫ݕ‬෤ሻ also depends on
expected output ‫ݕ‬ത and targeted output ‫ݕ‬෤
Cost Minimization with Production Uncertainty
SHEW 2013, Lucerne 3

4. The influence of production uncertainty on hospital costs depends
on the management’s risk aversion and regulation governing
reserve capacity
For a risk-neutral hospital management, production uncertainty has
no influence on input decisions
This type of hospital management minimizes the quasi-fixed costs
associated with the expected value of output
Cost Minimization with Production Uncertainty
SHEW 2013, Lucerne 4

5. Incentive Problems with Prospective
Payment Systems
SHEW 2013, Lucerne
In 2012, Switzerland introduced prospective payment system
This exposes to the risk of excessive variable cost
Reimbursement is determined according to case severity and
expected amount of resources needed
It fails to account for uncertainty
This not only creates incentives to increase cost efficiency but also
to optimize reserve capacity
5

6. Incentive Problems with Prospective
Payment Systems
SHEW 2013, Lucerne
Hospital management faces a trade-off between the risk of unmet
patient demand and the risk of excess capacity
Differences in risk exposure could easily cause some hospitals to
appear inefficient although they operate in a cost-efficient way
Prospective payment faces the challenge of creating incentives for
sufficient reserve capacity
6

7. H1: Randomness in output combined with risk aversion on the part of
management affect hospitals’ input choices and hence cost
confirmed
H2: Public hospitals and especially university hospitals have higher
marginal cost of targeted production than private ones due to a higher
degree of risk aversion of their management
confirmed
H3: Prospective payment causes lower marginal cost of targeted
production than retrospective payment because hospitals must bear
the cost of targeted capacity
partly confirmed
This findings are derived from a multilevel Stochastic Frontier Model based on
a Cobb-Douglas variable cost function of about 100 Swiss hospitals between
2004 and 2009
Hypotheses
SHEW 2013, Lucerne 7

8. Expected output is estimated by an autoregressive process of order
one [AR(1)]:
‫ݕ‬ത௜௧ ൌ ‫ܧ‬ ‫ݕ‬௜௧ ൌ ‫ݕ‬ො௜௧ , ‫݄ݐ݅ݓ‬
‫ݕ‬௜௧ ൌ ߜଵ‫ܨܦ‬௜ ൅ ߜଶ‫ݕ‬௜,௧ିଵ ൅ ߝ௜௧ , ܽ݊݀
‫ݕ‬ො௜௧ ൌ ߜመଵ‫ܨܦ‬௜ ൅ ߜመଶ‫ݕ‬௜,௧ିଵ
DF = Hospital-specific dummy variable
Targeted output ‫ݕ‬෤ is derived from:
‫ݕ‬෤ ൌ ‫݌‬ିଵ
1 െ ߙ௜ 0, ܸܽ‫ݎ‬ሺߝ̂௧ ௜ , with ܸܽ‫ݎ‬ ߝ̂௧ ௜ ൌ
1
ܶ െ 1
෍ ‫ݕ‬௧ െ ‫ݕ‬ො௧ ௜
ଶ
்
௧ୀଵ
Risk aversion of management is still latent
Estimating Expected Ouptut and Production
Uncertainty
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9. Output Variability Between Hospital Types
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10. Output Variability Between Hospital Types
SHEW 2013, Lucerne
Tested groups w-valueof output
variability
p-value
Hospital (private/public) 13,386 5.351e-12
Public hospitals (university/nouniversity) 2,956 1.608e-04
Privatehospitals, degreeof specialization(high/low) 77 1.317e-01
Hospital (DRGpayment/noDRGpayment) 36,728 3.102 e-01
Output variability differs between hospital types
Public hospitals have systematically higher output variability than private
hospitals
University hospitals have highest output variability
No significant difference found between hospitals under DRG payment and
those under conventional (per-diem) payment
10

11. Cobb-Douglas variable cost function (first level):
ln
௏஼
௉೘
ൌ ߚଵ,௜ ൅ ߚଶ,௜݈݊ ‫ݕ‬ത ൅ ߚଷ,௜݈݊ ‫ݕ‬෤ ൅ ߚସ,௜݈݊
௉೗
௉೘
൅ ߚହ݈݊ ‫ܭ‬ ൅ ߚ଺ܼ ൅ ߚ଻‫ܦ‬௧ ൅ ߩ௜,௧,
with ߚ஺,௜~ܰ 0, ߪఉ
ଶ
∀ ‫ܣ‬ ∈ ሼ1, 2, 4,5ሽ
Note: ߚଷ,௜ is a random parameter indicating the marginal cost of reserve
capacity
Econometric Specification of the Risk-adjusted
Cost Function
SHEW 2013, Lucerne 11
ܸ‫,ܥ‬ ܻത, ܻ෨ Variable operational expense (VC), No. of expected inpatient cases,
CMI-adj. (E(CASES)), Production uncertainty (Risk)
݈ܲ , ܲ݉ Labor input price, average wage per employee (PL), Price of other
production inputs (PM),
‫ܭ‬ No. of beds (BEDS)
ܼଵ, … , ܼସ No. of specialties (SPEC), Dummy=1 for emergency room (EMER),
Share of inpatients with supplementary insurance (INSUR), Share of
acute care cases (ACUT)

12. The marginal cost of reserve capacity is related to hospital types
(second level):
ߚଷ,௜ ൌ ߛ଴ ൅ ෍ ߛ௖‫ܫ‬௖,௜ ൅ ߬௜, ‫߬ ݄ݐ݅ݓ‬௜~ܰ 0, ߪఉయ
ଶ
஼
௖ୀଵ
Econometric Specification of the Risk-adjusted
Cost Function
SHEW 2013, Lucerne 12
‫ܫ‬ଵ ൌ 1 for subsidized public hospitals (PUBL)
‫ܫ‬ଶ ൌ 1 for prospective payment with DRG (DRG )
‫ܫ‬ଷ ൌ 1 for prospective payment with DRG in year=t-1 (DRG 1)
‫ܫ‬ସ ൌ 1 for university hospitals (TEACH)

13. Econometric Results for the Risk-adjusted
Cost Frontier
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Variables1
Model 1 Model 2 Model 3
Coefficient t-value Coefficient t-value Coefficient t-value
‫ݐ݊ܽݐݏ݊݋ܥ‬ 0.669 5.1 0.801 6.3 0.756 5.4
‫ܧ‬ሺ‫ܵܧܵܣܥ‬ሻ 0.635 18.0 0.625 18.2 0.645 21.1
ܲ‫ܮ‬ 0.449 20.0 0.445 20.1 0.447 18.1
‫ܵܦܧܤ‬ 0.398 9.6 0.386 9.8 0.359 11.1
ܵܲ‫ܥܧ‬ 0.001 1.7 0.001 2.0 0.001 2.1
‫ܴܧܯܧ‬ 0.043 2.0 0.046 2.2 0.070 3.2
‫ܴܷܵܰܫ‬ 0.002 4.7 0.001 3.4 0.002 3.8
‫ܷܶܥܣ‬ 0.002 3.1 0.002 3.2 0.002 3.1
ܴ‫ܭܵܫ‬ 0.004 3.2
No. of firms 538 538 538
BIC -932.5 -888.2 -892.1
1) Parameters for technical changearenot shown

14. Econometric Results for the Risk-adjusted
Cost Frontier
SHEW 2013, Lucerne 14
Variables Model 1 Model 2 Model 3
Coefficient t-value Coefficient t-value Coefficient t-value
ܴܲ‫ܸܫ‬ -0.006 -2.6 -0.006 -2.1
ܷܲ‫ܮܤ‬ 0.011 4.3 0.011 3.7
ܶ‫ܪܥܣܧ‬ 0.008 3.0 0.011 6.0
‫ܩܴܦ‬‫ݐ‬ 0.001 0.9 0.001 0.6
‫ܩܴܦ‬‫ݐ‬െ1 -0.002 -1.7 -0.002 -1.5
No. of firms 538 538 538
BIC -932.5 -888.2 -892.1

15. Large public hospitals and especially university hospitals face much
higher output uncertainty than small specialized (often private)
clinics
Higher degree of uncertainty leads to a significant increase in
hospital cost ceteris paribus
At a given level of output uncertainty, public hospitals opt for more
reserve capacity in order to meet patient needs
The finding of a positive relationship between output uncertainty
and hospital cost poses a challenge to regulators designing
payment systems
Conclusions
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16. Hospital payment needs to take operating risk into account
Hospitals with high exposure to risk and especially university
hospitals struggle to stay profitable in the current system
In the longer run, current payment creates incentives for hospitals to
specialize in the services with minimum uncertainty of demand and
to reduce their reserve capacity
Conclusions
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17. Because unmet patient need is not measured in the data base, the
effects of output variability cannot be separated from latent risk
aversion on the part of hospital management
Yearly data fail to reflect the need for hospital to deal with demand
variation in much shorter time periods
The data are at the hospital level, while departments presumably
differ in their exposure to risk
Limitations
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