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A Short Guide to DEA Regulation Per AGRELL Peter BOGETOFT 2001

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© SUMICSID2 OUTLINE 1. Who Are We ? 2. The DEA Popularity 3. Widespread Concerns About DEA 4. The Consultant’s Answer 5. The Theorist’s Answer 6. Lessons from Theory 7. Conclusions 8. Literature 9. Appendix

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© SUMICSID3 WHO ARE WE ? Per Agrell, ph.d, docent, KVL, CORE/UCL Peter Bogetoft, dr.merc, professor, KVL Decision Theory (MCDM), Efficiency Evaluation (DEA) and Incentive Theory (Agency, Contracts)

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© SUMICSID4 WIDE USE OF DEA Regulators of electricity distribution often use DEA CountryReg.App.Eval.Meth. Development / In use AustraliaEx anteCPI-DEA/SFA/StatU DenmarkEx anteCPI-COLSD/U EnglandEx anteCPI-DEA/COLSU FinlandEx postDEA?D NetherlandsEx anteCPI-DEAU New ZealandEx anteCPI-DEAU NorwayEx anteCPI-DEAU SpainEx anteIdeal-NetD SwedenEx postDEA/Ideal-netD Use of DEA to estimate industry-wide or individual productivity improvement potentials.

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© SUMICSID5 WHY IS DEA SO POPULAR ? Easy to use minimize regulator’s effort Easy to defend Yes: 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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© SUMICSID6 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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© SUMICSID7 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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© SUMICSID8 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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© SUMICSID9 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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© SUMICSID10 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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© SUMICSID11 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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© SUMICSID12 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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© SUMICSID13 Linkage of two literatures: Production theory DEA etc. Performance Eval. Incentives theories Agency etc. See appendix 1 for more on this. RESEARCH APPROACH (I) Org. model DEA

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© SUMICSID14 RESEARCH APPROACH (II) The Basic Problem: Given cross section, time series or panel information: (input, output) for DMUs i=1,…,n what should we ask an agent to do and how should we reimburse him/her ?

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© SUMICSID15 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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© SUMICSID16 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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© SUMICSID17 STATIC INCENTIVES (II) Situation –Technological uncertainty, –Risk neutrality –DMU maximizes { P rofit + slack} where 0< <1 is the relative value of slack Result: –Optimal revenue cap under non-verifiable costs is k + C DEA (y) Constant + DEA-Estimated Cost Norm

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© SUMICSID18 STATIC INCENTIVES (III) Result: –Optimal revenue cap with verifiable costs: k + c+ ( C DEA (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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© SUMICSID19 DYNAMIC INCENTIVES (I) Additional dynamic issues –Accumulate and use new information –Avoid ratchet effect Result: –Optimal revenue cap under verifiable costs k + c t + ( C 1-t DEA (y) –c ) Constant + Actual Costs+ of DEA-Est. Cost Savings

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© SUMICSID20 DYNAMIC INCENTIVES (II) Situation: –Limited catch-up capability Result: –Optimal revenue cap with limited cath-up capability: k + c t + ( (1- (1-E 0 )) t C 1-t DEA (y)/E 0 –c t ) Constant + Actual Costs+ of adjusted DEA-est. cost savings

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© SUMICSID21 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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© SUMICSID22 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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© SUMICSID23 DYNAMIC INCENTIVES (V) Situation: –Support innovation (frontier movements), –Support info dissemination (sharing) Result: –An operational scheme with innovation and dissemination is: k + c t + ( C 1-t DEA (y) –c t ) + b t I +b t D Incentive = Cost+Profitshare+Innovation+Dissemination b t I = innovation premium b t D = dissemination premium (C t-1 –C t )

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© SUMICSID24 STRUCTURAL DEVELOPMENTS Final concerns: Scale adaptation Scope adaptation through 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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© SUMICSID25 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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© SUMICSID26 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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© SUMICSID27 SOME CURRENT EVENTS Sixth European Workshop on Efficiency and Productivity Analysis, Copenhagen, Denmark, October 29-31, 1999 –www.flec.kvl.dk/6ewepawww.flec.kvl.dk/6ewepa Seventh European Workshop on Efficiency and Productivity Analysis, Oviedo, Spain, September 25-27, –www19.uniovi.es/7ewepawww19.uniovi.es/7ewepa INFORMS Conference, Dynamic DEA Regulation session, Hawaii, June 17-20, –www.wpi.edu/~jzhu/deainforms.html

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© SUMICSID28 LITERATURE (1) Some are downloadable at Agrell, P., P. Bogetoft and J.Tind, Multi-period DEA Incentive Regulation in Electricity Distribution, Working Paper, Agrell, P., P. Bogetoft and J.Tind, Incentive Plans for Productive Efficiency, Innovation and Learning, Int.Journal of Production Economics, to appear, Bogetoft, P., Strategic Responses to DEA Control, Working Paper, Bogetoft, P. Non-Cooperative Planning Theory, Springer-Verlag, Bogetoft, P, Incentive Efficient Production Frontiers: An Agency Perspective on DEA, Management Science, 40, pp , 1994.

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© SUMICSID29 LITERATURE (2) Bogetoft, P, Incentives and Productivity Measurements, International Journal of Production Economics, 39, pp , Bogetoft, P, DEA-Based Yardstick Competition: The Optimality of Best Practice Regulation, Annals of Operations Research, 73, pp , Bogetoft, P., DEA and Activity Planning under Asymmetric Information, 13, pp. 7-48, Journal of Productivity Analysis, Bogetoft, P. and D. Wang, Estimating the Potential Gains from Mergers, Working Paper, 1999.

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© SUMICSID30 Appendix 1: APPROACH (1) Context Multiple, 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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© SUMICSID31 Appendix:1 APPROACH (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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© SUMICSID32 ECO- general insight, description/ understanding OR- specific proposal, prescription/ normative Bad match? Overkill? Applied Theoretical foresee regulated firm behaviour provide appropriate motivation/ prescription Performance measurement (OR-) - discipline Provides rich description of production for economic theory Appendix:1 APPROACH (III)

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© SUMICSID33 Appendix:1 APPROACH (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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© SUMICSID34 Appendix 2 THE 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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© SUMICSID35 Appendix 2 THE NORWEGIAN SCHEME (II) Core of the regulatory scheme: R t =PI t,t-1 QI t,t-1 (1- - G t ) R t-1 c t + min X t R t c t + max X t where Rrevenue ccosts PIprice index QIquantity index Gtruncated DEA efficiency min{(1-E 0 )/(1-E low ),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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