Cost and Efficiency Analysis of
En-route Traffic Control
C. Edward Huang
Adib Kanafani
University of California, Berkeley
NEXTOR Workshop, Asilomar, CA
Sep 4-7, 2007
1
Draining AATF
(in 2003$,
billions)
FAA Cost
AATF Receipt
$14
$12
$10
$8
1998
1999
2000
2001
2002
2003
2
2004
2005
2006
2007
Cost Up, Revenue Down
Dep/Arr Counts
Total Center Cost
AATF Receipt
130
120
110
100
90
80
1999
2000
2001
2002
20 US En-route Centers
3
2003
2004
Motivation
• Cost is one important aspect of ATC financing
• Very few cost studies (FAA 1995, FAA 2005)
• Limitations of previous studies:
• no multi-year comparison
• linear assumption between output and cost
• no efficiency evaluation of ATC
• Strategies to promote efficiency
4
Outline of Presentation
• Data
• Cost Analysis
• Stochastic Frontier Analysis
• Conclusions
5
20 Mainland Centers
• All operated by FAA
• Account for 25% of FAA cost in 2004
6
picture source: wikipedia
Data
Cost
FAA Cost Accounting System
Cost allocated to centers in 30+ accounts
Only direct costs (labor, capital) are used
Product
ATADS (Air Traffic Activity Data System)
Departure/arrival and overflight counts
Price
Average controller salary
Average capital price (capital exp./stock)
1999~2004, 6 yr x 20 centers=120 obs
•
•
•
•
•
•
•
7
r characteristics of en-route control centers are also considered: relative siz
of sectors within each center.
Descriptive
Statistics
Table 1: Descriptive Statistics
Variable
TC
Qda
Qo
wl
wk
Size
Sectors
Mean
18.14
14.23
13.06
11.83
3.95
3.70
3.83
Min
17.61
13.53
11.41
11.68
3.77
2.10
3.30
Max
18.57
14.66
14.17
11.93
4.09
4.61
4.16
Std Dev
0.21
0.27
0.74
0.09
0.11
0.58
0.22
(Between)
0.19
0.27
0.75
0.00
0.00
0.58
0.22
(Within)
0.09
0.05
0.07
0.09
0.11
0.00
0.00
• Everything logged
Total Cost=Labor+Capital
•
the descriptive statistics
of all the variables
in natural logarithms.
Qo=overflights
• Qda=2*departures,
It is
of total cost (TC) and traffic outputs (Qda , Qo ) is mostly cross-sectional
Most variation of outputs is between centers
yearly fluctuation is relatively small. On the other hand, since there is only
8
bor (wl ) or capital price (wk ), their variance
comes entirely from time-serie
ts in Figure 1 suggest a log-linear relation between traffic and cost.
•
Cost Functions
• Easier to deal with multiple products
• Cobb-Douglas setting is used
• Pooled vs. Panel
• Y=Labor+investment
• X=dep/arr, overflights (Q),
salary, capital price (w)
9
Pooled
• Center ID’s are ignored
Y=total cost
dep/arr
overflight
salary
capital price
constant
R-squared
F
coeff.
std. err.
0.51
0.13
1.28
-0.37
-4.52
0.76
89.99
0.035
0.013
0.551
0.412
4.940
t
14.7
10.2
2.3
-0.9
-0.9
• Dep/arr flights are more costly
(about 4X overflight)
• Economy of density exists
• Can be viewed as long-run cost function
10
LN(Total Cost)
18.6
18.2
1999
2004
17.8
17.4
13.4
13.6
13.8
14.0
14.2
14.4
14.6
14.8
LN(Dep/Arr)
• Cost relation is similar between 99 and 04
11
Labor force is inline with traffic
Labor Cost
Dep/Arr Counts
Labor Year
130
120
110
100
90
1999
2000
2001
2002
12
2003
2004
Panel (Fixed-effect)
Y=total cost
dep/arr
overflight
salary
capital price
constant
R-squared
F
coeff.
std. err.
0.09
0.88
1.21
-0.37
-2.61
0.49
33.60
0.118
0.109
0.329
0.253
3.230
t
0.8
0.8
3.7
-1.5
-0.8
• Total cost is not sensitive to traffic level
• May be due to inflexibility in inputs and
lack of control on outputs
• Short-run cost: salary is determinant
13
LN(Total Cost)
18.6
ZDC
18.2
1999
2004
ZME
17.8
ZLC
17.4
13.4
13.6
13.8
14.0
14.2
LN(Dep/Arr)
14.4
14.6
14.8
• Different trends within centers make output
coefficients insignificant
14
All Efficient Assumption
LN(Total Cost)
18.6
Stochastic Error(vi)
Stochastic Error(vi)
18.2
17.8
17.4
13.4
13.6
13.8
14.0
14.2
LN(Dep/Arr)
15
14.4
14.6
14.8
Stochastic Frontier Analysis
LN(Total Cost)
18.6
Inefficiency(ui)
18.2
Stochastic Error(vi)
r
e
i
t
n
o
r
F
t
s
Co
17.8
17.4
13.4
Stochastic Error(vi)
13.6
13.8
14.0
14.2
LN(Dep/Arr)
16
14.4
14.6
14.8
ward Huang and Adib Kanafani
viation from the estimated model is considered random noise and can be accounte
implied from
that every
observation
the same efficient
level.and can be accounted for
eviation
the estimated
modelisisatconsidered
random noise
posed
in 1977[9][10],
Stochastic
Analysis
s implied
that every observation
is atFrontier
the same
efficient (SFA)
level. relaxes this all-efficient a
An
additional
technical
inefficiency
term
u
doposed
adds an
additional error
term (uFrontier
to capture
cost
ind
in 1977[9][10],
Stochastic
Analysis5(SFA)
relaxes
thisinefficiency
all-efficient of
assum
i ) to Equation
nd
adds an additional error term (ui ) to Equation 5 to capture cost inefficiency of individ
tions:
m
n
Stochastic Frontier Analysis
•
vations:
lnCi!
!
! y
m
!
n
= β0 +! βk lnYki +!
βjw lnwji + vi + ui
lnCi = β0 +
y
β
k=1 k lnYki +
w
βj
j=1
lnwji + vi + ui
j=1
k=1
inefficiency error term (ui ) can take several forms of distributions, but most comm
he
inefficiency
error term (ui ) can
take several
forms of distributions, but most commonl
rmal,
truncated-normal[11],
or
gamma
distribution[12].
Distribution
of u can
be half-N, truncated-N,
ormal, truncated-normal[11],
or gamma
distribution[12].
facilitate the comparison
of
efficiency among observations, an inefficiency score
gamma,
etc
facilitate the comparison of efficiency among observations, an inefficiency score is of
ed. In the case of a Cobb-Douglas cost function, cost inefficiency score is define
ated. In the case of a Cobb-Douglas cost function, cost inefficiency score is defined as
Inefficiency
Score
(log-linear):
costwithout
without
inefficiency
ofmodeled
modeledcost
cost with
with inefficiency
inefficiency totocost
inefficiency
or or
•
•
! i!
C
Ci = exp(u )
IE
=
i
IEi = C = exp(ui ) i
Ci i
res can
betweenone
oneand
andinfinity.
infinity.The
The
lower
score,
closer
the o
cores
canbe
beanywhere
anywhere between
lower
thethe
score,
the the
closer
the obser
thecost
costfrontier
frontier and hence
otothe
hencemore
morecost-efficient.
cost-efficient.
17
dom effects panel models (Table 2). Nonetheless, cost inefficiency is detected to be
The associated inefficiency scores for each center are then calculated and regressed a
sizes and numbers of sectors (Figure 4 and Table 3).
Inefficiency Scores
Inefficiency Score vs. Size of Controlled Airspace
Center
Efficiency
ZLC
ZNY
ZAU
ZFW
ZKC
ZJX
0.3
ZDC
ZLA
ZAB
ZID
ZOB
ZME
ZTL
0.2
ZHU
ZOA
ZBW
ZOA
ZMP
ZMA
ZDV
ZNY
0.0
Efficiency
1.049
ZDV
1.276
1.055
ZOB
1.286
ZID
1.293
1.137
ZMA
1.304
1.208
ZLA
1.308
ZDC
1.316 ZSE
1.105
1.209
ZSE
ZMP
ZSE
0.1
Center
0.4
1.213
ZBWZAB
1.218
ZTL
ZJX
1.232
ZME
1.241
ZLC
0.3
Ln(Score)
0.4
Inefficiency Score vs. Number of Sectors
0.2
ZOA
ZKC
1.343
ZFW
1.352
0.1
ZHU
ZAU
ZAU
ZFW
ZKC
ZDC
ZLA
ZMA
ZID
ZOB ZDV
ZME
ZTL
ZBW
ZMP
ZAB
ZJX
1.356
ZNY
ZHU
1.436 ZLC
• random-effect time-invariant model
• half-normal distribution of inefficiency
0.0
2.0
2.5
3.0
3.5
4.0
4.5
5.0
3.2
3.4
3.6
Ln(Size)
ID
ZAB
ZAU
ZBW
Center
Albuquerque
Chicago
Boston
ID
ZDC
ZDV
ZFW
Center
ID
Washington
ZHU
Denver
ZID
Dallas Fort Worth ZJX
3.8
4.0
Ln(Sectors)
Center
Houston
Indianapolis
Jacksonville
ID
ZKC
ZLA
ZLC
Center
Kansas City
Los Angeles
Salt Lake City
ID
ZMA
ZME
ZMP
Center
Miami
Memphis
Minneapolis
ID
ZNY
ZOA
ZOB
Center
New York
Oakland
Cleveland
ID
ZSE
ZTL
Center
Seattle
Atlanta
4.2
Explaining inefficiency
Y=score
size
coeff.
std. err.
t
-0.00025
0.00077
-0.3
sectors
0.0065
0.0020
3.3
constant
0.95
0.11
8.9
R-squared
0.41
F
6.00
19
center sizes and numbers of sectors (Figure 4 and Table 3).
Inefficiency Score vs. Size of Controlled Airspace
Inefficiency S
0.4
0.4
ZAU
ZFW
ZKC
0.3
ZDC
ZLA
0.3
ZMA
ZDV
ZME
ZTL
ZBW
ZOA
ZSE
Ln(Score)
Ln(Score)
ZID
ZOB
0.2
ZHU
ZMP
0.2
ZOA
ZAB
0.1
0.1
ZJX
ZNY
ZNY
ZLC
0.0
0.0
2.0
2.5
3.0
3.5
4.0
4.5
5.0
3.2
3.4
Ln(Size)
• Size is not related to inefficiency
ID
ZAB
ZAU
ZBW
Center
Albuquerque
Chicago
Boston
ID
ZDC
ZDV
ZFW
Center
ID
Washington
ZHU
Denver
ZID
Dallas Fort Worth ZJX
Center
Houston
Indianapolis
Jacksonville
ID
ZKC
ZLA
ZLC
Center
Kansas City
Los Angeles
Salt Lake City
ID
ZMA
ZME
ZMP
Center
Miami
Memphis
Minneapolis
Z
Z
Z
20
Figure 4: Inefficiency Scores and Center Cha
tors (Figure 4 and Table 3).
ontrolled Airspace
Inefficiency Score vs. Number of Sectors
0.4
ZAU
W
KC
ZHU
C
ZLA
ZFW
ZKC
0.3
ZMA
Ln(Score)
ZSE
ZMP
ZDC
ZLA
ZMA
ZID
ZOB ZDV
ZDV
W
OA
ZHU
ZME
0.2
ZSE
ZOA
ZTL
ZBW
ZMP
ZAB
ZAB
0.1
ZJX
ZJX
ZNY
ZLC
ZLC
0.0
4.0
nter
ID
hington
ZHU
nver
ZID
ort Worth ZJX
4.5
5.0
3.2
3.4
3.6
3.8
4.0
4.2
Ln(Sectors)
Center
Houston
Indianapolis
Jacksonville
ID
ZKC
ZLA
ZLC
• More sectors is related to inefficiency
Center
Kansas City
Los Angeles
Salt Lake City
ID
ZMA
ZME
ZMP
Center
Miami
Memphis
Minneapolis
ID
ZNY
ZOA
ZOB
Center
New York
Oakland
Cleveland
ID
ZSE
ZTL
21
nefficiency Scores and Center Characteristics
Center
Seattle
Atlanta
Conclusion
• Departure/arrival flights are costlier than
•
•
•
overflights
Economy of density exists in en-route ATC
In the short run, the cost structure is more
related to price than output.
To plan for the long run, technology upgrade
may be necessary to remain cost-efficient
22
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23