Measuring Electricity Generation Efficiency

Data Envelopment Analysis

versus

Fixed Proportion Technology Indicators

• John Gleason, Creighton Universityo Information Systems & Technology, College of Business

• Darold Barnum, University of Illinois at Chicagoo Managerial Studies, College of Businesso Information & Decision Sciences, College of Business o Pharmacy Administration, College of Pharmacy

DEA theory requires input substitutability

Relationship between substitute inputs, holding output constant

Negative Slope

Output: 10 motorbus-miles (speed = 10 mph)

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But, some inputs are not substitutable

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Point frontier envelops the data

Point frontier

Relationship among fixed proportion inputs, holding output constant

Rectilinear distances between target DMU and production frontier

Models for measuring rectilinear distance

• DEA Additive Model (ADD)• Fixed Proportion Additive Model (FPA)• Only difference is the location of the

benchmark point on the production frontier

Fixed Proportion Additive (FPA)

1 11

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k km k jm jm

FPA I x y x yMin

How about Electricity Generation?

• Capital – MW capacity• Labor – FTE employees• Energy – BTUs• Holding MWh output constant– Cannot substitute capacity for employees– Cannot substitute employees for BTUs– Cannot substitute BTUs for capacity

Relationships among electricity generation inputs, holding MWh output constant, 70 Coal-fired plants

P(z>4.1) = .000P(z>9.1) = .000

P(z>.23) = .821

Comparison of FPA and ADD estimates

• 2007 data for 70 U.S. generation plants• Both models use the same metric, but

measure efficiency from different points• ADD efficiencies averaged 42% greater than

FPA efficiencies• ADD efficiencies of the DMUs ranged from

3.6% greater to 100% greater than FPA• ADD estimates were extremely biased and

had strikingly low precision

But . . .

• None of the exigent published studies have used the ADD model

• Most use the CCR or BCC radial models, which measure a DMU’s percentage of full efficiency when inputs are substitutable

• We compare the CCR model with the Fixed Proportion Ratio (FPR), which measures a DMU’s percentage of full efficiency when inputs are not substitutable

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Fixed Proportion Ratio (FPR) Measure

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 10 20 30 40 50 60 70

DMUs in FPR Order

FPR

ERM

CCR

•For all 70 DMUs , R2(FPR, CCR) = 0.83

• For 24 DMUs with efficiency above 70%, R2(FPR,CCR) = 0.33

•Of more concern is the fact that the rank orders vary a lot

•CCR ranks ranged from 29 higher to 24 lower than FPR ranks

•Radial measures (like CCR or BCC) are unacceptable•Very large upward bias•Very low precision

Results

•Unfortunately, almost all published DEA efficiency studies of electricity generating plants have used radial measures

•Thus, it is likely that most publications to date report electricity generating plant efficiency estimates that are significantly biased, imprecise, and report very inaccurate efficiency rankings.

•Given the energy and environmental crises we are facing, this problem is of even greater concern if such studies are used for policy or operating decisions.

CONCLUSIONS . . .

Thank you!