Measuring Efficiency

1
Measuring Efficiency in Public Sector
Organisations with Data Envelopment and Stochastic
Frontier Analysis
2
Contents
1. Definitions
2. Non-Parametric Models Data Envelopment
Analysis
3. Parametric Models Stochastic Frontier
Analysis
4. Examples
5.Conclusions
3
1. Definitions
4
1.1. Efficiency
output
Productivity / Efficiency

Relative Efficiency/ Inefficiency
0
Input
5
Output 2 / Input
Efficiency
where
weight given to output i
0
Output 1 / Input
6
In general,
Efficiency
where
weight given to the mth input
7
1.2. Technical, Allocative and Economic Efficiency
Output 2 / Input
Organisations 1 and 2 are both Technically
Efficient whereas Organisations 3, 4 and 5 are
not
but
Isocost
Organisation 1, compared to Organisation 2 is
also Allocatively (i.e. Input-Price) Efficient
Organisation 4 exhibits Technical (or X- or
Managerial) Inefficiency
Organisations 5 and 3 exhibit both Allocative and
Technical Inefficiency
0
Output 1 / Input
8
1.3. Output and Cost Orientation
Output 2 / Input
Input 2 / Output
0
0
Output 1 / Input
Input 1 / Output
Input Orientation Example Two Inputs One Output
Output Orientation Example Two Outputs One
Input
9
1.4. Constant and Variable Returns to Scale
output
CRS
VRS
0
Input
10
1.5. Parametric and Non-Parametric Approaches
Parametric We assume that Inefficiency is
distributed in a certain
way. (Stochastic Frontier
Analysis)
Non-Parametric We let the data estimate an
Efficiency Frontier.
(Data Envelopment Analysis)
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2. Non-Parametric Models Data Envelopment
Analysis
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2. Non-Parametric Models Data Envelopment
Analysis
Example One Input (Lecturers) and Two Outputs
(Research and Teaching)
7 6 5 4
Y2/X
B
E
F
A
C
3 2 1
D
G
Y1/X
0 1 2 3 4
5 6 7
13
2. Non-Parametric Models Data Envelopment
Analysis
7 6 5 4
Y2/X
B
E
F
A
Efficient Frontier
C
3 2 1
D
G
Y1/X
0 1 2 3 4
5 6 7
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2. Non-Parametric Models Data Envelopment
Analysis
7 6 5 4
Y2/X
B
Lecturer D is Technically Inefficient
E
F
A
P
Lecturer C is both technically and
allocative inefficient
C
3 2 1
D
G
Y1/X
0 1 2 3 4
5 6 7
15
2. Non-Parametric Models Data Envelopment
Analysis
Efficiency
but
weights V and U are unknown
And this is the main benefit of DEA it
estimates the optimal weights for us
16
2. Non-Parametric Models Data Envelopment
Analysis
7 6 5 4
Y2/X

• DEA assigns the best possible weight to each
  unit

B
E
F

• DEA constructs a piecewise linear frontier
  which envelops
• any inefficient units

A
P
C
3 2 1
D

• DEA measures inefficiency as the radial
  distance from an
• inefficient unit to the frontier

G

• DEA is fully driven by the data (with its pros
  and cons)

Y1/X
0 1 2 3 4
5 6 7
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2. Non-Parametric Models Data Envelopment
Analysis
Advantages

• Easy to use

• Allows multiple inputs and outputs

• No specified functional form

• No prior weights specification

Disadvantages

• No account for random noise / error

• No goodness of fit measures

• Sensitive to outliers

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3. Parametric Models Stochastic Frontier Analysis
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3. Parametric Models Stochastic Frontier
Analysis
DEA
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3. Parametric Models Stochastic Frontier
Analysis
OLS Linear Regression
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3. Parametric Models Stochastic Frontier
Analysis
OLS Non-Linear Regression
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3. Parametric Models Stochastic Frontier
Analysis
Corrected OLS Non-Linear Regression
Most efficient country
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3. Parametric Models Stochastic Frontier
Analysis
Stochastic Frontier
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3. Parametric Models Stochastic Frontier
Analysis
Corrected OLS Non-Linear Regression
Inefficiency
Corrected OLS does not allow for any errors
25
3. Parametric Models Stochastic Frontier
Analysis
Stochastic Frontier
Stochastic Error
Stochastic Error
Inefficiency
SFA does allow for errors
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3. Parametric Models Stochastic Frontier
Analysis
SFA

• Not completely moulded by data appeals to
  economic theory

• Uses full sample information

• Allows for errors

• We are not so interested in the bs but in the
  error term

Because inefficiency is embedded into this term!
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3. Parametric Models Stochastic Frontier
Analysis
SFA separates the residual into two parts
where
Inefficiency (we need to assume how it is
distributed)
and
stochastic error
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3. Parametric Models Stochastic Frontier
Analysis
Advantages

• Accounts for random noise / error

• Goodness of fit measures

• Deals with outliers

• Closer to economic theory

• Uses full sample information

Disadvantages

• Problems with multiple inputs/outputs

• No preferred specified functional form

• Large sample is needed

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4. Examples
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4. Example 1 DEA
The efficiency of Australian universities a data
envelopment analysis M. Abbott and C.
Doucouliagosa Economics of Education Review 22
(2003) 8997

• 36 universities, 1995

• Input orientation

• Variable Returns to Scale

• Ouputs
• Number of Full-Time Equivalent Students
• Research Quantum Allocation (i.e. Government
  funding) received by the university

• Inputs
• Number of Full-Time Equivalent Academic Staff
• Number of Full-Time Equivalent Non-Academic
  Staff
• Expenditure on all Inputs other than Labour
• Value of non-current assets (proxy for capital
  stock)

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4. Example 1 (cont.) DEA
The efficiency of Australian universities a data
envelopment analysis M. Abbott and C.
Doucouliagosa Economics of Education Review 22
(2003) 8997
32
4. Example 2 DEA over time
Assessment of Technical and Scale Efficiency of
the National Transplant System (in
Brazil) (Avaliação da Eficiência Têcnica e da
Eficiência de Escala do Sistema Nacional de
Transplantes) A. Marinho and S. de Souza
Cardoso Boletim IPEA Institute of Applied
Economic Research (Brazil) - February 2007

• All organ transplants carried out in Brazil
  during 1995 and 2003
• (Total numbers and by organ)

• Output orientation

• Both CRS and VRS models

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4. Example 2 (cont.) DEA over time
Assessment of Technical and Scale Efficiency of
the National Transplant System (in
Brazil) (Avaliação da Eficiência Têcnica e da
Eficiência de Escala do Sistema Nacional de
Transplantes) A. Marinho and S. de Souza
Cardoso Boletim IPEA Institute of Applied
Economic Research (Brazil) - February 2007
(All transplants Constant Returns to Scale)
(All transplants Variable Returns to Scale)
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4. Example 3 Two-Stage DEA
THE MEASUREMENT OF POLICE FORCE EFFICIENCY AN
ASSESSMENT OF U.K. HOME OFFICE POLICY Leigh M
Drake Richard Simper Contemporary Economic
Policy Oct 2005, pp. 465-482

• 51 Police Force Areas in England and Wales,
  2001-2002

• Two-stage DEA (the second stage, a
  Tobit-regression on Fear of Crime data)

• Both Output and Input Orientation

35
4. Example 3 (cont.) Two-Stage DEA
THE MEASUREMENT OF POLICE FORCE EFFICIENCY AN
ASSESSMENT OF U.K. HOME OFFICE POLICY Leigh M
Drake Richard Simper Contemporary Economic
Policy Oct 2005, pp. 465-482
36
4. Example 3 (cont.) Two-Stage DEA
THE MEASUREMENT OF POLICE FORCE EFFICIENCY AN
ASSESSMENT OF U.K. HOME OFFICE POLICY Leigh M
Drake Richard Simper Contemporary Economic
Policy Oct 2005, pp. 465-482

37
4. Example 3 (cont.) Two-Stage DEA
THE MEASUREMENT OF POLICE FORCE EFFICIENCY AN
ASSESSMENT OF U.K. HOME OFFICE POLICY Leigh M
Drake Richard Simper Contemporary Economic
Policy Oct 2005, pp. 465-482
Technical Efficiency
Technical Efficiency
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4. Example 4 - SFA
The Provision of Library Services by English
Local Authorities Philip Stevens National
Institute of Economic and Social Research,
Discussion Paper No. 259, 2005

• 139 Local Authorities in England 2000/1

• Cost (i.e. Input) Orientation

• Three alternative distributional assumptions of
  inefficiency

Environmental Variables

Inefficiency
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4. Example 4 (cont.) - SFA
The Provision of Library Services by English
Local Authorities Philip Stevens National
Institute of Economic and Social Research,
Discussion Paper No. 259, 2005
40
4. Example 4 (cont.) - SFA
The Provision of Library Services by English
Local Authorities Philip Stevens National
Institute of Economic and Social Research,
Discussion Paper No. 259, 2005
41
4. Example 4 (cont.) - SFA
The Provision of Library Services by English
Local Authorities Philip Stevens National
Institute of Economic and Social Research,
Discussion Paper No. 259, 2005
42
4. Example 5 DEA SFA
The technical efficiency of container ports
Comparing data envelopment analysis and
stochastic frontier analysis Kevin Cullinane,
Teng-Fei Wang, Dong-Wook Song, and Ping
Ji Transportation Research Part A 40 (2006)
354374

• 57 Terminals in biggest 30 container ports in
  the world, 2001

• Output orientation

• DEA both with CRS and VRS

• 4 alternative distributional assumptions used -
  SFA model

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4. Example 5 (cont.) DEA SFA
The technical efficiency of container ports
Comparing data envelopment analysis and
stochastic frontier analysis Kevin Cullinane,
Teng-Fei Wang, Dong-Wook Song, and Ping
Ji Transportation Research Part A 40 (2006)
354374
44
4. Example 5 (cont.) DEA SFA
The technical efficiency of container ports
Comparing data envelopment analysis and
stochastic frontier analysis Kevin Cullinane,
Teng-Fei Wang, Dong-Wook Song, and Ping
Ji Transportation Research Part A 40 (2006)
354374
45
4. Example 5 (cont.) DEA SFA
The technical efficiency of container ports
Comparing data envelopment analysis and
stochastic frontier analysis Kevin Cullinane,
Teng-Fei Wang, Dong-Wook Song, and Ping
Ji Transportation Research Part A 40 (2006)
354374
Robustness Analysis
46
4. Example 6 Preliminary Analysis of Waste
Management Efficiency in Northern Ireland

• Data for 20 District Councils
• April 2005-May 2006
• Cost (input) orientation
• Total Cost
• Total Income per Household, Tons sent for
  composting and recycling
• Total Area (as environmental factor)
• DEA Variable Returns

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4. Example 6 (cont.) Preliminary Analysis of
Waste Management Efficiency in Northern Ireland
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4. Example 6 (cont.) Preliminary Analysis of
Waste Management Efficiency in Northern Ireland
Source WasteDataFlow
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4. Example 6 (cont.) Preliminary Analysis of
Waste Management Efficiency in Northern Ireland
If we remember, D is technically inefficient but
C is both technically and allocative inefficient.
7 6 5 4
Y2/X
Councils with efficiency scores below 1 exhibit
technical inefficiency, but only Castlereagh does
not present allocative inefficiency as well
P
C
3 2 1
D
Belfast, for example, should increase the tonnage
of materials sent for recycling by 78 per
cent and total income from waste disposal by 14
per cent
Y1/X
0 1 2 3 4
5 6 7
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5. Conclusions
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5. Conclusions

• DEA and SFA are two different approaches to
  measuring efficiency

• Both can be applied to Panel and Cross Sectional
  Data

• Sometimes results not fully compatible

• Sensitivity analysis (and caution!) required

• Both techniques may provide useful insight and
  can inform policy

52
Measuring Efficiency in Public Sector
Organisations with Data Envelopment and Stochastic
Frontier Analysis