Transcript Data Envelopment Analysis

Data Envelopment Analysis
MSc in Regulation and
Competition
Quantitative techniques in
Practice
John Cubbin, City University©
DEA
• What it is - recap
• Farrell measures of Efficiency
– technical
– allocative
– scale
• Dangers of DEA
• Later today: productivity over time
What it is
Mathematical programming approach to measuring
distance from a frontier.
Uses Inputs , outputs, (and noncontrollables)
Can be expressed as a ratio of weighted outputs to
weighted inputs
Ek = vjk Yj k /ui k Xi k
Xi k = input i Yj k = output j for kth unit
uik ,vjk are weights chosen to maximise score of unit
k,
uik ,vjk are constrained. Must not cause Em > 1 for
any other unit m
An Economic Interpretation
Due to Michael Farrell (1957)
Technical efficiency = OB/OA
Capital
A
Other things
equal = output
B
Min combinations
required (isoquant)
O
Labour
An Economic Interpretation
(Output maximisation orientation)
Technical efficiency = OB/OA
Output 2
(e.g. lines)
D
Other things
equal = inputs
C
Max combinations
achieveable
(production frontier)
O
Output 1
(e.g. calls)
Economic Interpretation (3)
• The isoquant and production frontier are not known
directly, but might be estimated from known data,
using piecewise interpolation
Capital
K
E
B is an artificial
observation - a
combination of
F and G
O
F
A
L
B
G
Min combinations
H
J
required (isoquant)
Labour
Allocative efficiency
• Depends on knowing prices
• AE = min cost/actual cost = OD/ OB
Capital
A
B
D
Efficient
Isocost
line
C
O
Min combinations
required (isoquant)
Labour
Scale efficiency
Output
M
T.E. = PR/PA
S.E. = PQ/PR
T.& S.E = PQ/PA
P
Q
R
A
O
This is input orientation. What about output orientation?
Input
Running DEA
•
•
•
•
Purpose - built software
Excel/Solver macros
Organise data for input
Identify inputs, outputs and
noncontrollables
• Run
• Interpret
How reliable is DEA?
• Depends on whether frontier can be
populated by efficient firms:
– number of observations
– number of dimensions
– closeness to frontier of enough firms
– distribution of variables
Dangers of DEA(1)
Outliers appear efficient
Capital
K
F
B is an artificial
observation - a
combination of
F and G
O
L
B
G
A
H
E
J
Min combinations
required (isoquant)
Labour
Dangers of DEA(2)
• Technical efficiency is not economic efficiency
Output 2
(e.g. meter
reading)
B is technically
efficient but
economically
inefficient
Iso value lines
B
D
C
O
Max combinations
achieveable
(production frontier)
Output 1 (e.g. energy)
Dangers of DEA (3)
Dilemma: to include or not to include
variables
•Include => spuriously efficient
•Exclude => spuriously inefficient
No well-established statistical test for
inclusion/ exclusion