per j. agrell peter bogetoft 2001-06-06 dea - a fresh cure for health care reimbursement? plenar...
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Per J. AGRELLPeter BOGETOFT
2001-06-06
DEA - A Fresh Cure for Health Care Reimbursement?
Plenar talk at XXI Spanish Congress of Health Economics, Oviedo, June 6-8, 2001
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Outline
1. Who Are We ?2. DEA3. Widespread Concerns About DEA4. The Consultant’s Answer5. The Theorist’s Answer6. Lessons from Theory7. Conclusions8. Literature9. Appendix
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The SUMICSID Team ?
Dr. Per J. Agrell, CORE/UCL– pja@sumicsid.com
Prof. dr. merc. Peter Bogetoft, KVL– pb@sumicsid.com
Decision Theory (MCDM), Efficiency Evaluation (DEA) and Incentive Theory (Agency, Contracts)
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Wide Use of Dea
• CCR(1978); 1000 papers 2000
• Regulators use DEA to estimate industry-wide or individual productivity improvement potentials.
• E.g. electricity distribution often use DEACountry Reg.App. Eval.Meth. Development / In useAustralia Ex ante CPI-DEA/SFA/Stat UDenmark Ex ante CPI-COLS D/UEngland Ex ante CPI-DEA/COLS U Finland Ex post DEA? DNetherlands Ex ante CPI-DEA UNew Zealand Ex ante CPI-DEA UNorway Ex ante CPI-DEA USpain Ex ante Ideal-Net DSweden Ex post DEA D
• Is DEA useful in health regulation ?
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Performance Evaluation
PROCESSPROCESS
Exogenous factors(Non-discretionary resources or products)
Resources(Inputs)
Products(Outputs)
Management(Effort / Ability)
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Rational Ideal Evaluation
TEACHING
RESEACH
E
B
C
A
T
Ideal
Pref.U(.)
Effectiveness
=
=
Actual Performance
Ideal Performance
U (D)
U (Ideal)D
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Practical Problems
IN NON-IDEAL REALITY:
LACK OF INFORMATION:Neither preferences nor possibilities are known.Information is at best decentralized and not immediately available.We need full investigation, communication, choice procedures (DEA, MCDM etc)
STRATEGIC BEHAVIOR:Agents may not choose desired output unless given proper incentivesAgents may misrepresent information.We need full mechanism design procedures (Game, Agency, Auction etc theory)
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Basic Ideas
U n kn ow n p e f. U
U n kn ow n p oss . T
R e la tive E ffic ien cy
E ffic ien cy
E ffec tiven ess i, iU x y
max U (x,y) s.t. (x,y) T
Produce more with less
Estimate empirical reference technology T*
i i, iE min E Ex y T
i i iE min E Ex ,y T *
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Basic Efficiency Measures
Farrell (1957)
INPUT BASED : E = find largest proportional contractions of all inputs E
= minimal input/actual inputsE= 0.7 means that all inputs could be reduced by 30%
OUTPUT BASED: F = find largest proportional expansions of all outputs F
= maximal feasible output / actual outputF=1.4 means that all outputs could be expanded by 40%
ALTERNATIVE MEAURES:non-radial, directional, additive,… but Farrell’s easiest to interpret.
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(Relative) Technical Efficiency 1
INPUT,fte
OUTPUT, DRG x
A
B
C
D
120
75
1 200
2 000
TE-OUT
TE-IN
TE-IN = 75/120 = 62,5%
TE-OUT = 2000/1200 = 167 %
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(Relative) Technical Efficiency 2
TEACHING
RESEARCH
E
B
C
A
D
Fixed input
O
D’
| ' |1.3
| |
ODF
OD
ASS PROF
FULL PROF
F
I
J
H
G
Fixed output
I’
| ' |0.6
| |
OIE
OI
O
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Other Efficiency Concepts
TECHNICAL EFFICIENCY (TE)Right methods, procedures etc given input and output mix
ALLOCATIVE EFFICIENCY (AE)Right input mix given prices
COST EFFICIENCY (CE)Technical and allocative efficiency: CE=TE•AECorresponds to TE in a cost model
SCALE EFFICIENCY (SE)Right scale of operation (max output per input, min average cost)TE(crs)=TE(vrs) • SE
PROFIT EFFICIENCY (PE)Right input-output mix given prices
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Alternative Estimation Principles
FRONTIER ANALYSIS
Resource, M$, Staff budget
Performance, DRG x, Health care
AnotherHospital Co
100
1 000
2 000
Smalll HMO
50
THEORETICAL NORMS
STATISTICAL METHODSCathCH
GIANT CH
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DEA Estimation
• Weak regularity assumptions– Free disposability– Convexity– Return to Scale
• Minimal Extrapolation Principle • Very flexible, best practice frontier
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Basic DEA Models
INPUT
OUTPUT
A
B
C
ED
OUTPUT
A
B
C
E
D
INPUT
OUTPUT
A
BC
E
D
INPUT
FDH VRS
CRS
OUTPUT
A
B
C
E
D
INPUT
DRS
FDH
DRS CRS
VRS
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DEA Pros and Cons
PROS– Requires no or little preference, price or priority information– Requires no or little technological information– Makes weak a priori assumptions– Handles multiple inputs and multiple outputs– Provides reel peers– Identifies best practice– Cautious or conservative evaluations (minimal
extrapolation)– Supports learning and planning and motivation
CONS– Relatively weak theory of significance testing (sensitivity,
resampling, bootstrapping, asymptotic theory)– Lack of focus of goals
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Why evaluate?
Applications of Evaluations
Plan, reallocate,...MotivateLearn, explore, stat,...
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Why Is DEA So Popular ?
• EASY TO USEminimize regulator’s effort
• EASY TO DEFENDYes:
easy to explain mild regularity assumptionshandles multiple inputs and outputsNo:explicit peers can be challengedslack and noise possibly entangled
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Widespread Concerns
Regulators, firms and researchers:
THE MEASUREMENT PROBLEM– Is it possible to capture complex output like in health ?– Would it not be better to trust parties and use
retrospective (cost-plus) payment ?
THE NOISE PROBLEM– Is DEA the appropriate procedure given its sensitivity to
noise ?– Would it not be better to use econometric methods, SFA
etc ?
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The Consultant’s Answer
“DEA puts everyone in their best light”
Correct ?Yes:
Minimal Extrapolation Principle and weak a priori regularity on technology
In TE multiplicity of goals allowedNo:
Noise and Best Practice not distinguished.
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The Theorist’s Answer (I)
The measurement problem:
– Not unique to health – e.g. university evalution extremely complex!
– DEA work well with multiple inputs and outputs– Is the problem many outputs – or a complex
functional form ?– Conflicts of interest/ Asymmetric information makes
cost-pus / pure retrospective payment problematic
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The Theorist’s Answer (II)
The appropriateness of DEA depends on:
How it is performed– METHODOLOGY
What it is used for– OBJECTIVES
When/where it is used– CONTEXT
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Methodology
To be well-executed, it might involve:
• Careful data collection• Sensitivity analysis
• Monte Carlo, peeling techniques, alt. technology assumptions
• Stochastic programming• Hypothesis test
– Boot strapping, re-sampling, asymp. theory
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Objectives
• DEA can– improve efficiency, distribution, social welfare– support concession granting, monitoring and information
dissemination– reduce administrative workload
• Noise may not matter– large impact on few units and small impact on many units– counteracted by regulator’s discretion (40% red.over 3
years) – some DEA estimates (e.g. MPSS) are more unstable than
others
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Context
• Important aspects:– Technology (general assumptions plus impact of effort)– Information (noise, uncertainty, asymmetry)– Preferences (firms, customers, regulator, society)
• DEA is most appropriate when – Uncertainty about the structure of the technology (rates of
substitution etc) is as significant as individual noise
• Hence:– Noisy data, simple technology -> use SFA, Econometrics– Better data, complex technology -> use DEA
• See more details below
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Lessons from Theory
Some models and results connecting incentive and productivity analysis techniques:
– Research Approach– Super- Efficiency– Static Incentives– Dynamic Incentives– Structural Developments
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•Linkage of two literatures:
Production theoryDEA etc.
•Performance Eval.
Incentives theoriesAgency etc.
•See appendix 1 for more on this.
Research Approach (I)
Org. model
DEA
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Research Approach (II)
THE BASIC PROBLEM:
Given cross section, time series or panel information:
(input, output) for DMUs i=1,…,nwhat should we ask an agent to do and
how should we reimburse him/her ?
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Research Approach (III)
Reject
Accept
Technology perhapslearned by agents
Effort and Slackselected
(Inputs, Outputs)observed
Compensationpaid
Possiblereporting
Historicaldata
Incentive schemesproposed
..... .....
Private Costs and Slack
Production, costs etc
Incentives
DMU DMU DMU
REGULATOR
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Super Efficiency
• Efficiency– can provide incentives to match others, but not
to surpass norm– multiple dim. model further facilitates shirking– Nash Equilibria involve minimal effort
• Super Efficiency– exclude the evaluated unit from the technology
definition– can support the implementation of most plans
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Efficiency and Shirking
D
C B
A
OUTPUT 2
OUTPUT 1
Max Effort Output
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Static Incentives (I)
• Situation:– Technological uncertainty,– Risk aversion– Individual noise
• Result:– DEA frontiers are incentive efficient (supports optimal
contracts) when noise is exponential or truncated
• Result:– DEA frontiers asymptotically incentive efficient when noise
is monotonic
• Payment:– B = B(x,y,CDEA)
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Static Incentives (II)
• Situation– Technological uncertainty,– Risk neutrality– DMU maximizes {Profit + •slack}
where 0< <1 is the relative value of slack
• Result:– Optimal revenue cap under non-verifiable costs is
k + CDEA(y)
Constant + DEA-Estimated Cost Norm
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Static Incentives (III)
• Result:– Optimal revenue cap with verifiable costs:
k + c+ •( CDEA(y) –c )
Constant + Actual Costs+ of DEA-est. cost savings
• Extensions:– Similar schemes work under varying demand assumptions,
genuine social benefit function, etc.
• Hence: DEA provides an optimal revenue cap !
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Static Incentives (IV)
Cost
Production y
DEA Estimated Cost Norm CDEA(y)
Actual Cost
Yardstick Cost
Savings
Payment = Lump Sum + Actual Cost + Savings
DEA-based Yardstick Competition
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Dynamic Incentives (I)
• Additional dynamic issues– Accumulate and use new information– Avoid ratchet effect
• Result:
k + ct+ •( C1-tDEA(y) –c )
Constant + Actual Costs+ of DEA-Est. Cost Savings
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• Situation:– Limited catch-up capability
• Result:– Optimal revenue cap with limited cath-up capability:
k + ct+ •( (1-(1-E0))tC1-tDEA(y)/E0 –ct )
Constant + Actual Costs+ of adjusted DEA-est. cost savings
Dynamic Incentives (II)
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Dynamic Incentives (III)
Dynamic, DEA based yardstick schemes solve many of the usual CPI-x problems:
• Risk of bankruptcy with too high x• Risk of excessive rents with to low x• Ratchet effect when updating x• Arbitrariness of the CPI measure• Arbitrariness of the x parameter• Inability to include changing output profiles
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Dynamic Incentives (IV)• Situation:
– Single dimensional output– Constant return to scale– Fixed relative factor prices– Exogenous constant frontier shift of – No difference between profit and slack value =1
• Result:– The CPI-DEA scheme used in electricity distribution in
Norway (see appendix 2) is optimal
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Dynamic Incentives (V)
• Situation:– Support innovation (frontier movements),– Support info dissemination (sharing)
• Result:– An operational scheme with innovation and dissemination is:
k + ct+ •( C1-tDEA(y) –ct) + bt
I+btD
Incentive = Cost+Profitshare+Innovation+Disseminationbt
I = innovation premium
btD = dissemination premium •(Ct-1–Ct )
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Structural Developments
• Final concerns:Scale adaptationScope adaptationthrough incentives and concession granting
• Mergers:Adjust DEA based yardstick to share scale and scope gains
• Auctions:DEA based yardstick to aggregate multi-dimensional bids
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Conclusions (I)
DEA frontiers – sufficient for exponential noise, truncated noise and– asymptotically sufficient for monotone noise
DEA based revenue cap optimal under considerable technological uncertainty
SFA, Econometric revenue cap useful under considerable individual uncertainty
Dynamic re-estimation, ex ante commitment to ex post regulation, solves many CPI-x problems
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Conclusions (II)
DEA useful technique in yardstick regimes – supports– Complex technology– Partially undefined objectives– Conflicts of interest among agents– Asymmetric information– Organizational learning and innovation
DEA makes minimal assumptions and its results are hard to refute, even under varying objectives.
Theory combines DEA and agency theory.
Health care regimes complemented with DEA may be beneficial.
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Some Current Events
Sixth European Workshop on Efficiency and Productivity Analysis,
Copenhagen, Denmark, October 29-31, 1999
– www.flec.kvl.dk/6ewepa
Seventh European Workshop on Efficiency and Productivity Analysis, Oviedo, Spain, September 25-27, 2001.– www19.uniovi.es/7ewepa
INFORMS Conference, Dynamic DEA Regulation session,
Hawaii, June 17-20, 2001.
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Literature (1)
Some are downloadable at www.sumicsid.com
Agrell, P., P. Bogetoft and J.Tind, Multi-period DEA Incentive Regulation in Electricity Distribution, Working Paper, 2000.Agrell, P., P. Bogetoft and J.Tind, Incentive Plans for Productive Efficiency, Innovation and Learning, Int.Journal of Production Economics, to appear, 2000.Bogetoft, P., Strategic Responses to DEA Control, Working Paper, 1990.Bogetoft, P. Non-Cooperative Planning Theory, Springer-Verlag, 1994.Bogetoft, P , Incentive Efficient Production Frontiers: An Agency Perspective on DEA, Management Science, 40, pp.959-968, 1994.
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Literature (2)
Bogetoft, P, Incentives and Productivity Measurements, International Journal of Production Economics, 39, pp. 67-81, 1995.Bogetoft, P, DEA-Based Yardstick Competition: The Optimality of Best Practice Regulation, Annals of Operations Research, 73, pp. 277-298, 1997.Bogetoft, P., DEA and Activity Planning under Asymmetric Information, 13, pp. 7-48, Journal of Productivity Analysis, 2000.Bogetoft, P. and D. Wang, Estimating the Potential Gains from Mergers, Working Paper, 1999.
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Appendix 1:Approach (1)
ContextMultiple, rational, intelligent agents with private info and action
DEA
1) Set up an explicit contextual model using agency theory
2) Assume planner uses DEA 3) Find agents’ response 4) Viability: Prevails incentive
compatibility, will players be obedient and honest ?
5) Performance: Does proposal lead to efficient outcome ?
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Appendix:1Approach (2)
Pick a model with a view towards:
– Conservatism - put DEA in best possible light
– Realism - use relevant context
– Faithfulness- use DEA modification and motivation that are fair to original purposes.
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ECO - general insight, description/ understanding OR - specific proposal, prescription/ normative
•Bad match? Overkill?
• Applied
• Theoretical
foresee regulated firm behaviourprovide appropriate motivation/ prescription
Performance measurement (OR-) - disciplineProvides rich description of production for economic theory
Appendix:1Approach (III)
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Appendix:1Approach (IV)
A Naive Solution:– Estimate cost function: C(output)– Find Benefit Function: B(output),– Choose to maximize {Benefit - Costs}– Pay estimated costs, actual costs, yardstick costs or similar
New questions:– How estimate C(.) ? Use DEA ? Econometrics ?– What is the optimal payment ?– How should additional information feed into the process ?– etc
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Appendix 2The Norwegian Scheme (I)
Cost Model:– DEA cost model to estimate individual inefficiencies
and general productivity development
Payment Scheme:– Revenue cap with rate-of-return restrictions and an
efficiency incentive.– 2 year review period– 5 year regulation period– Deviations (+/-) accounted for in next regulation
period
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Appendix 2The Norwegian Scheme (II)
Core of the regulatory scheme:Rt=PIt,t-1•QIt,t-1 •(1--•Gt) •Rt-1
ct+min •Xt Rt ct+max •Xt whereR revenuec costsPI price indexQI quantity indexG truncated DEA efficiency min{(1-E0)/(1-Elow),1} general productivity improvement (1,5%, Malmquist based) catch up coefficient (max 38.24% eliminated in 4 years) rate-of-return bounds (2%-15%)
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