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A Short Guide to DEA Regulation
Per AGRELLPeter BOGETOFT
2001
© SUMICSID 2
OUTLINE
1. Who Are We ?2. The DEA Popularity3. Widespread Concerns About DEA4. The Consultant’s Answer5. The Theorist’s Answer6. Lessons from Theory7. Conclusions8. Literature9. Appendix
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WHO ARE WE ?
• Per Agrell, ph.d, docent, KVL, CORE/UCL– [email protected], [email protected]
• Peter Bogetoft, dr.merc, professor, KVL– [email protected], [email protected], [email protected]
• Decision Theory (MCDM), Efficiency Evaluation (DEA) and Incentive Theory (Agency, Contracts)
Eco Plan
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WIDE USE OF DEA
• Regulators of electricity distribution often use DEA
Country 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/Ideal-net D
• Use of DEA to estimate industry-wide or individual productivity improvement potentials.
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WHY IS DEA SO POPULAR ?
Easy to use• minimize regulator’s effort
Easy to defendYes:
• easy to explain • mild regularity assumptions• handles multiple inputs and outputs
No:• explicit peers can be challenged• slack and noise possibly entangled
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WIDESPREAD CONCERNS
Regulators, firms and researchers:
• 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”“DEA bends itself backwards to make
everyone look as good as possible.”Correct ?
Yes:• Minimal Extrapolation Principle and weak a priori
regularity on technology
No:• Noise and Best Practice not distinguished.
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THE THEORIST’S ANSWER
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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HOW DEA IS PERFORMED
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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WHAT DEA IS USED FOR
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 are more unstable than others
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WHEN/WHERE DEA IS APPLIED
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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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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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
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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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DYNAMIC INCENTIVES (I)
Additional dynamic issues– Accumulate and use new information– Avoid ratchet effect
Result:– Optimal revenue cap under verifiable costs
k + ct+ •( C1-tDEA(y) –c )
Constant + Actual Costs+ of DEA-Est. Cost Savings
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DYNAMIC INCENTIVES (II)
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
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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 Norwegian CPI-DEA scheme (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+Dissemination
btI = innovation premium
btD = dissemination premium •(Ct-1–Ct )
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STRUCTURAL DEVELOPMENTS
Final concerns:Scale adaptation
Scope 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 regulation – supports– Concession granting– Monitoring and incentive regulation– Information dissemination
DEA may be popular in regulation for the wrong reasons – but there are good reasons as well
There is a theoretical foundation based on a combination of DEA and agency theory
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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. – www.wpi.edu/~jzhu/deainforms.html
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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/ understandingOR - 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 ModelDEA cost model to estimate individual inefficiencies and general productivity development
• Payment SchemeRevenue cap with rate-of-return restrictions and an efficiency incentive.2 year review period5 year regulation periodDeviations (+/-) accounted for in next regulation period
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Appendix 2 THE 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%)
