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# Parallel_Session_1_Talk_2_Widmer

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Talks of the Swiss Health Economics Workshop 2013

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### Parallel_Session_1_Talk_2_Widmer

1. 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. 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. 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. 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. 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. 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. 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. 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 SHEW 2013, Lucerne 8
9. 9. Output Variability Between Hospital Types SHEW 2013, Lucerne 9
10. 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. 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. 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. 13. Econometric Results for the Risk-adjusted Cost Frontier SHEW 2013, Lucerne 13 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. 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. 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 SHEW 2013, Lucerne 15
16. 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 SHEW 2013, Lucerne 16
17. 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 SHEW 2013, Lucerne 17
18. 18. SHEW 2013, Lucerne 18