1

FORMULATION OF TECHNICAL, ECONOMIC

AND ENVIRONMENTAL EFFICIENCY

MEASURES THAT ARE CONSISTENT WITH

THE MATERIALS BALANCE CONDITION

byTim COELLI

Centre for Efficiency and Productivity Analysis, University of Queensland, Brisbane, Australia

Ludwig LAUWERSCentre for Agricultural Economics, Brussels, Belgium

Guido VAN HUYLENBROECKDepartment of Agricultural Economics, Ghent University, Belgium

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Outline

• Introduction

• Literature review and critique

• Proposed environmental efficiency measures

• Implementation using DEA

• Application to Belgian pig farms

• Conclusions

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Introduction• Traditional efficiency measurement methods do

not include pollution• Some authors proposed methods that include a

pollution variable as an extra variable in the production model – as a “bad output” or an input

• We argue that many of these latter methods are inconsistent with the materials balance condition – which essentially states that “what goes in must come out”

• Plus these methods tend to assume that all pollution reduction must be costly

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Introduction (continued)

• We propose a new method that is consistent with the materials balance condition

• The method looks at pollution minimisation in an analogous way to the standard cost minimising model

• The method explicitly allows for both cost increasing and cost decreasing pollution reduction

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Traditional efficiency analysis• Does not account for environmental damage• Only traditional inputs and outputs are included

in the model• E.g., in electric power generation

– Inputs = labour, capital, fuel, other– Output = electricity– Air pollution not considered

• E.g., on a pig fattening farm– Inputs = labour, capital, feed, piglets, other– Output = pig meat– Nutrient pollution in soils and water not considered

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Traditional efficiency measures

• Normally we estimate the production technology set ( ) by fitting a production frontier over the data (using DEA or SFA methods)

• We then measure the efficiency of each firm as either:– The amount by which it can expand output ( )

using its current inputs ( ) and remain feasible

– or, the amount by which it can reduce inputs while still producing the same output

T),(|max xyx

T)/,(|max xy

y

T

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Efficiency measures

input

outputfrontier

●A

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Efficiency measures including pollution

• Färe et al (1989)– Air pollution in paper mills– Included a pollution variable ( ) as a “bad output” in

the production model– Weak disposability was imposed on the pollution

variable to reflect that its disposal was costly– A hyperbolic efficiency measure was used which

sought to simultaneously expand outputs and reduce inputs and bad outputs

z

Tz )/,/,(|max xy

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Efficiency measures including pollution (2)

• Färe et al (1996)– Air pollution in electricity generation– Included a pollution variable as a “bad output” in the

production model– Weak disposability was imposed on the pollution

variable to reflect that its disposal was costly– Productive efficiency measure sought to reduce

inputs

– Environmental efficiency measure sought to reduce pollution

Tz ),/,(|max xy

Tz )/,,(|max xy

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Efficiency measures including pollution (3)

• Reinhard et al (2000)– Nitrogen pollution on intensive dairy farms– Included a pollution variable as an input in the

production model– Productive efficiency measures sought to reduce all

inputs

or expand outputs

– Environmental efficiency measure sought to reduce pollution

Tz )/,/,(|max xy

Tz )/,,(|max xy

Tz ),,(|max xy

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Are these past methods consistent with the materials balance condition?

• Materials balance condition:

a and b are (K1 and M1) vectors of known non-

negative constants • Consider first the Reinhard et al (2000) environmental

efficiency measure

• Can we reduce pollution without changing inputs or outputs? - the answer is no – it will violate the materials balance condition

• The only solution to is =1

ybxa z KM RxRy ,

ybxa /z

Tz )/,,(|max xy

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Consistency?

• In addition – if we apply the Färe et al (1989) efficiency measure

to the MB condition we obtain

or

so the only solution is =1 again• This applies to the other models as well…

ybxa //z

2ybxa z

Tz )/,/,(|max xy

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Proposed efficiency measures

• Do not include the pollution variable into the model

• Treat it in an analogous manner to the cost efficiency model

• We first review the cost efficiency case

• Then we introduce the environmental efficiency case

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Cost efficiency

• Cost minimisation

• Cost efficiency

• Technical efficiency

• Allocative efficiency

• Note

TC yx,xwwy,x

|min)( K Rw

CE = wxc / wx.

TTE yx,xy

|min),(

= wxt / wx = w(x) / wx =

AE = wxc / wxt

CE = TE AE

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Cost minimisation

x1

x2 0

isoquant

iso-cost line wx

iso-cost line wxt

iso-cost line wxc

(x1t, x2t)

(x1, x2)

(x1c, x2c)

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Environmental efficiency• For a fixed output level, minimisation of the surplus

means minimisation of the nutrient content of the inputs

• Surplus minimisation

• Environmental efficiency

• Technical efficiency is the same as before

• Environmental allocative efficiency

• Note

TTE yx,xy

|min),(

ybxa S

xaN

TN yx,xaay,x

|min)(

EE = axe / ax

EAE = axe / axt

EE = TE EAE

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Surplus minimisation

x1

x2

isoquant

0

iso-nutrient line ax

iso-nutrient line axt

iso-nutrient line axe

(x1t, x2t)

(x1, x2)

(x1e, x2e)

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Costs and benefits

x1

x2

isoquant

0

iso-nutrient line axc

iso-nutrient line axe

(x1t, x2t)

(x1, x2)

(x1e, x2e)

iso-cost line wxe

iso-cost line wxc

(x1c, x2c)

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Summary figure

x1

x2

unit isoquant

iso-cost line

iso-nutrient line

0

nutrient minimising point

cost minimising point

I

II

III

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Generalisations• More than one pollutant

– Identify optimal point for each, or– Specify weights and identify a single

“environmental” optimal point

• An “overall” optimal point – Include measures of the social costs of

pollution

• Pollution abatement activities– Involves the explicit use of extra inputs– Include a “pollution abatement” (good) output

variable

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Data envelopment analysis implementation

min, ,

st -yi + Y 0,

xi - X 0,

0

min ,xi* (aixi*),

st -yi + Y 0,

xi* - X 0,

0

Technical efficiency

Environmental efficiency

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Application to Belgian intensive pig-fattening farms

• Nutrient pollution (mostly phosphorous) from manure causes eutrophication and acidification of soils and water in Flanders

• Output = pig meat• Inputs = feed, piglets, labour, capital and other• Preliminary regression analysis:

– Latter 3 inputs are statistically insignificant (and minor in terms of costs)

– Constant returns to scale (CRS)

• Hence simple DEA model with two inputs and CRS

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DEA results

Efficiency measure Mean Stdev. Min Max

Technical efficiency (TE) 0.897 0.055 0.727 1.000

Environmental allocative efficiency (EAE) 0.940 0.046 0.763 1.000

Environmental efficiency (EE) 0.843 0.065 0.670 1.000

Allocative efficiency (AE) 0.985 0.021 0.877 1.000

Cost efficiency (CE) 0.883 0.057 0.722 1.000

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Reduction in pollution?

• Total phosphorous in inputs on Flanders pig fattening farms is 38.1 million kg P2O5 per year

• In pig meat output it is 13.6 million kg P2O5

• Thus the surplus is 24.5 million kg P2O5

• Potential reduction is 15.7% of 38.1 = 6.0 million kg P2O5

• This is approximately ¼ of current surplus

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DEA for pig farms

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

feed/output

pig

let/

ou

tpu

t

isoquant

iso-cost line

iso-nutrient line

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Implied shadow cost?

• The two optimal points differ– in costs by 4.6% and – in nutrient surplus by 5.3%

• Implied cost of phosphorous reduction is 27 Euros per kg P2O5

• Current manure treatment cost is 6 Euros per kg

• So aim for cost min point (in this case)

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Conclusions

• New environmental efficiency measure– Consistent with materials balance condition– Can be decomposed into technical and

allocative components– Emphasizes that pollution reduction need not

be always costly

• Application to Belgian pig farms– One quarter of phosphorous surplus can be

reduced before abatement activities considered