This document summarizes key concepts from a presentation on linear similarity between input-output matrices. It discusses how direct purchase and direct sales matrices have the same structure, with matching traces, determinants, and characteristic values, despite different appearances. It also shows that traditional multipliers and linkage indices are linearly related. The document questions some traditional assumptions around multipliers and proposes alternative approaches like considering final demand distributions and avoiding "procrustean" actions when analyzing linkages between sectors.

1. Linkages,
Impact & Feedback
in Light of
Linear Similarity
Nikolaos Adamou, Ph.D.
Business Management
BMCC / CUNY
16th International Input – Output Conference
Istanbul, Turkey, 2 – 6 July 2007
www.io2007.itu.edu.tr

2. The basis of Linear Similarity
Same data
Same assumption
sectoral gross output
Proportional
to purchases & sales
X Yx
~ := X ij
Xij
H aij := aij
xj xi
x
Row distributions
Column distributions ~ Yx 1
A
1
Hm
xm 1
Ym xm
A
11
Hx
1

3. Similarity:
matrices have different appearances
Direct purchase Direct sales
A ~
coefficients coefficients
A
[ ]
[I−A] ~
Production Allocation
I−A
[I−A]
~
[I−A] Total interrelations Total interrelations
.
−1
−1
in production in allocation
3

4. St. Mark
St. Apostles
Venice
Similarity:
Constantinople
matrices have the same structure
( )
tr (I − A ) = tr I − A
~
same trace
net purchases and sales of an industry to itself
matching each other
( )
det (I − A ) = det I − A
~
same determinant
purchases & sales provide the same ratio of
net to gross output
same characteristic values
purchases & sales provide the same signals
4

5. Augusztinovics ’
Fundamental Identity
Lets not ignore it
~
H x ZY = HZ Yx but take it as a starting point of our analysis
value
added
final demand
Sum of row elements total value added
Sum of column elements total final demand
Sum of all elements net production
5

6. questioning traditional theory
► Multipliers ???
column & row summation of Leontief inverse
► linkage indices ???
Rasmussen’s Power & Sensitivity of Dispersion
6

7. Row & Column Multipliers
Power & Sensitivity of Dispersion
4.5 2.5
4.0
2.0
3.5
3.0
1.5
2.5
2.0
1.0
1.5
1.0 0.5
0.5
0.0
0.0
01 02 03 04 05 06 07 08 09 10 11 12 13
01 02 03 04 05 06 07 08 09 10 11 12 13
Power of Dispersion
Total Column Total Row
Sensibility of Dispersion
Same image, different scale 7

8. Traditional multipliers & Rasmussen’s linkage indices
are linearly related
Relationship between
Relationship between
Total Row Sum & Sensitivity of Dispersion
Total Column Sum & Power of Dispersion
2.5
2.5
y = 0.5858x + 3E-07
Sensitivity of Dispersion
Power of Dispersion
y = 0.5858x + 2E-07
2.0
2.0 2
R =1 R2 = 1
1.5
1.5
1.0
1.0 0.5
0.0
0.5
1.0 1.5 2.0 2.5 3.0 3.5 4.0
1.0 1.5 2.0 2.5
Total of Row Coefficients
Total of Column Coefficients
of the Leontief Inverse
of the Leontief Inverse
8

9. Linkage is a connection
given by two (or more) matrices
Linkages are either
multipliers connection
from a sectoral demand or
or sectoral value added
to sector’s output
from a sectoral demand to
distributions sectoral value added
& vice versa
connection from
one dimensional (Markov)
value added (final demand)
two dimensional
to sectors or
final demand & value added
9

10. Multipliers are linkages that:
transmit
action to an activity &
generate
Result
Multipliers refer to industrial sectors
10
NOTE: a multiplier is not just any algebraic or matrix multiplication

11. Smashing the Leontief inverse into pieces
& act “procrustean” to exogenous factors
Unitary Multiplier Structure Uniform Multiplier Structure
columns
rows
eliminate the impact
stretch
of (n–1) sectors to zero &
the impact of all
then stress the remaining to
sectors to a unit
a unit
11
Procrustean actions

12. contrary to traditional assumptions
actual final demand requires attention
to its distributions
1995 1 2 3 4 5 6 7
Total Demand -
Consumption.
Gross Output
Consumption
Consumption
Intermediate
Government
Households
Increase in
Total Final
Formation
In Trillions of Yen
(Private)
Demand
Imports
Exports
Output
Capital
Stocks
Out
13.3 0.1 4.1 0.0 0.2 0.5 0.0 -2.4 2.5 15.8
1 Agriculture, forestry and fishery
7.4 0.0 0.0 0.0 0.0 0.0 0.0 -5.8 -5.8 1.7
2 Mining
195.8 2.8 63.8 0.7 39.1 1.2 37.9 -26.7 118.8 314.6
3 Manufacturing
8.1 0.0 0.0 0.0 80.0 0.0 0.0 0.0 80.0 88.1
4 Construction
17.3 0.0 7.5 1.6 0.0 0.0 0.0 0.0 9.1 26.5
5 Electric Power, Gas and Water Supply
36.1 2.2 50.5 0.0 10.4 0.2 3.1 -0.2 66.2 102.3
6 Commerce
29.0 0.0 7.8 0.0 0.0 0.0 0.6 -1.0 7.4 36.3
7 Finance and insurance
10.6 0.0 53.5 0.0 0.0 0.0 0.0 0.0 53.5 64.2
8 Real estate
32.6 0.7 14.7 -0.1 0.8 0.2 3.7 -2.5 17.5 50.1
9 Transport
9.5 0.1 5.2 0.0 0.0 0.0 0.0 -0.1 5.3 14.8
10 Communication and Broadcasting
0.5 0.0 0.8 25.0 0.0 0.0 0.0 0.0 25.8 26.2
11 Public Administration
65.6 13.5 64.0 41.9 9.2 0.0 1.3 -4.4 125.4 191.0
12 Services
6.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.6 -0.5 5.5
13 Activities not elsewhere classified
431.9 19.4 271.8 69.2 139.7 2.1 46.8 -43.7 505.2 937.1
Intermediate Input
12

13. Unit distributions that matter
Other Activities
Distributions of Final Dem and & Value Added
Services
Public administ.
100%
Communication
75%
Transport
Real estate
50%
Finance
25%
Commerce
0% Electric power
Construction
-25%
1995 2000 1995 2000 Manufacturing
Mining
Total Final Demand Total Value Added
Agriculture
13

14. Leontief Inverse
1 2 3 4 5 6 7 8 9 10 11 12 13
1995 Leontief
1 Agriculture 1.15 0.01 0.06 0.02 0.01 0 0.01 0 0.01 0.01 0.01 0.02 0.01
2 Mining 0.01 1.01 0.03 0.02 0.06 0 0 0 0.01 0 0.01 0.01 0.01
3 Manufacturing 0.35 0.20 1.75 0.57 0.19 0.11 0.12 0.04 0.28 0.11 0.23 0.30 0.23
4 Construction 0.01 0.01 0.01 1.01 0.05 0.01 0.01 0.04 0.02 0.02 0.02 0.01 0.01
5 Electric power 0.02 0.05 0.05 0.03 1.12 0.02 0.01 0.01 0.04 0.02 0.05 0.04 0.03
6 Commerce 0.08 0.05 0.11 0.12 0.04 1.03 0.02 0.01 0.07 0.02 0.04 0.07 0.04
7 Finance 0.07 0.09 0.05 0.05 0.06 0.08 1.12 0.06 0.10 0.03 0.02 0.05 0.20
8 Real estate 0.01 0.02 0.02 0.02 0.02 0.04 0.03 1.01 0.03 0.02 0.01 0.02 0.02
9 Transport 0.08 0.29 0.08 0.10 0.07 0.07 0.04 0.01 1.14 0.05 0.06 0.05 0.05
10 Communication 0.01 0.01 0.01 0.02 0.01 0.02 0.03 0 0.02 1.07 0.02 0.03 0.01
11 Public Adm. 0 0 0 0 0 0 0 0 0 0 1 0 0.08
12 Services 0.07 0.12 0.16 0.16 0.15 0.09 0.15 0.03 0.21 0.18 0.12 1.13 0.13
13 Other Activities 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01 1.01
14

15. Similar Leontief Inverse
1995 Similar Leontier 1 2 3 4 5 6 7 8 9 10 11 12 13
1 Agriculture 1.15 0.07 0.02 0 0.01 0.01 0.03 0 0.03 0.01 0 0.01 0.04
2 Mining 0 1.01 0 0 0 0 0 0 0.01 0 0 0 0.01
3 Manufacturing 1.75 0.05 0.55 0.34 0.47 0.08 0.53 0.28 0.02 0.26 0.96
1.28 6.08
4 Construction 0.13 0.16 1.01 0.10 0.10 0.11 0.02 0.17 0.09 0 0.07 0.15
1.09
5 Electric power 0.01 0.95 0.02 0.02 1.12 0.01 0.04 0.01 0.03 0.02 0 0.02 0.06
6 Commerce 0.03 0.19 0.04 0.01 0.08 1.03 0.23 0.07 0.15 0.17 0 0.05 0.16
7 Finance 0.01 0.06 0.01 0 0.02 0.01 1.12 0.01 0.03 0.07 0 0.03 0.05
8 Real estate 0.01 0.05 0.01 0.03 0.02 0.01 0.11 1.01 0.01 0.01 0 0.01 0.11
9 Transport 0.04 0.20 0.04 0.01 0.07 0.03 0.14 0.02 1.14 0.06 0 0.05 0.09
10 Communication 0.01 0.03 0.01 0 0.01 0 0.01 0.01 0.01 1.07 0 0.01 0.03
11 Public adm 0.02 0.10 0.02 0.01 0.05 0.01 0.02 0 0.03 0.04 1 0.02 0.10
12 Services 0.23 0.82 0.18 0.03 0.28 0.13 0.28 0.07 0.18 0.35 0.01 1.13 0.37
13 Other Activities 0 0.02 0 0 0.01 0 0.03 0 0.01 0 0.02 0 1.01
15

16. Z
Leontief & its similar inverses
yield a unique output multiplier
( )
~T
Zy = h Z = x
T from a model
~ y
Z
Z
T
h
( )
~ T
Zy m = h Z T to a multiplier
m
16

17. A Unique Multiplier takes into account:
y1 y2 yn h1 ~ h2 ~ hn ~
z11 n + z12 n + L + z1n n = n z11 + n z 21 + L + n z n1
∑y ∑y ∑y ∑h ∑h ∑h
1 1 1
1 1 1
distributed final demand
affecting the
rows of the Leontief inverse
&
distributed value added
affecting the
columns of the similar Leontief inverse
17

18. Unique Gross Output Multiplier
0.7 Agriculture
Mining
0.6
Manufacturing
Construction
0.5
Electric power
0.4 Commerce
Finance
0.3
Real estate
T ransport
0.2
Communication
0.1 Public administ.
Services
0.0
Other Activities
1995 2000
A unit of final demand and value added increases sectoral gross output
18

19. Disaggregate gross output multiplier
Leontief inverse post–multiplied to ZYd
Z Yd a final demand distribution matrix
Impact of each type of final demand
on the industrial gross output result
linkage
~
Value added distribution matrix
~ Hd Z
Hd
Z pre–multiplied to the similar Leontief inverse
Impact of each type of value added on the
industrial gross output
19

20. Decomposed disaggregate multiplier
(I+A+A2+A3+A4 …) Yd
Final demand
affecting direct purchases
affecting second round purchases
affecting third round purchases …
~ ~2 ~3 ~4
Value added Hd (I+ A + A + A + A +…)
affecting direct sales
affecting second round sales
affecting third round sales …
20

21. Distributions (Markov & two dimensional)
are special linkages
Direct distributions of a sectoral unit of
i.
output as: ⎡A⎤
[ ]
~
sales A Yx or purchases ⎢H ⎥
⎣ x⎦
Total distributed unit of output:
ii.
~
allocated ZYx
produced H xZ
Hx (I+A+A2+A3+A4 …)
iii. Decomposed ~ ~2 ~3 ~4
(I+ A + A + A + A +…)Yx
21

22. The Linkage structure
of Leontief & its similar Inverses
Rows of the Leontief inverse connect to
final demand distribution
Columns of the Leontief inverse connect to
value added relationship to output
Columns of the similar Leontief inverse connect to
value added distribution
Rows of the similar Leontief inverse connect to
final demand relationship to output
22

23. Augusztinovics
Linkages from both sides ~
H m ZYx
H x Z Ym
Final Structure Matrices Adamou
~
H x Z Yd = H d ZYx
Sectoral unit of output distributed to:
columns of production rows of allocation
~
ZYx
H xZ
Multiplier Matrices
Demand driven Production Value added driven Allocation
~
HmZ
ZYm
~
ZYd Hd Z
23

24. Production - Markov Final Structure Matrix
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
1995
Cons.
OH
2000
1995
Private
Cons.
2000
1995
Imports Exports Formation Cons.
Gov.
2000
1995
Capital
2000
1995
2000
1995
2000
Consumption out HH Compensation of employees Operating surplus
Depreciation of fixed capital Indirect taxes * (less) Current subsidies
Government Consumption increases employee compensation, operating surplus &
24
decreases depreciation

25. Allo c a tio n - M a rko vF ina l S truc ture M a trix
-20% 0% 20% 40% 60% 80% 100%
1995
2000
1995
2000
1995
2000
1995
2000
1995
2000
1995
2000
C o ns um ptio n o ut HH C o ns um ptio n (P riva te ) C o ns um ptio n Go ve rnm e nt C a pita l F o rm a tio n
Inc re a s e in S to c ks Expo rts Im po rts
Depreciation affects private & government consumption & capital formation
25

26. Production & Allocation Final Structure Matrices
are identical
in their two dimensional distribution
1995 2000
Consumption Out_HH
Consumption Out_HH
Private Consumption
Private Consumption
Capital Formation
Capital Formation
Increase in Stocks
Increase in Stocks
Consumption
Consumption
Government
Government
Exports
Imports
Exports
Imports
Total
Total
Consumption out
HH 0.00 0.02 0.01 0.01 0.00 0.01 -0.01 0.04 0.00 0.02 0.01 0.01 0.00 0.00 0.00 0.04
Compensation of
employees 0.02 0.26 0.10 0.15 0.00 0.06 -0.05 0.53 0.02 0.26 0.09 0.16 0.00 0.05 -0.04 0.54
Operating surplus 0.01 0.13 0.02 0.03 0.00 0.02 -0.02 0.19 0.01 0.13 0.02 0.04 0.00 0.02 -0.02 0.20
Depreciation of
0.01 0.10 0.04 0.04 0.00 0.02 -0.02 0.01 0.10 0.02 0.04 0.00 0.01 -0.01
fixed capital 0.18 0.16
Indirect taxes * 0.00 0.04 0.01 0.02 0.00 0.01 -0.01 0.08 0.00 0.04 0.01 0.02 0.00 0.01 -0.01 0.07
(less) Current
subsidies 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 -0.01
1.00 1.00
Total 0.04 0.54 0.16 0.25 0.00 0.11 -0.10 0.04 0.54 0.14 0.28 0.00 0.09 -0.09
26

27. Feedback Matrices
Connecting two final structure matrices
Yd
Z
~ Ym
Yd Z
Hx Z
Hd
~ Yx Hd Hx
Z
From the distributed final demand & value added
to their relationship with the gross output
27

28. Final Demand Feedback Matrices
~ ~
T T T T T T
Y Z H HmZYx Y Z H H d ZYx
m x d x
Decision Process Process
Summing
Junction Terminator
Final demand
28

29. Value Added Feedback Matrices
~
~ TT T
H m ZYx Ym Z T H T
T
H d ZYx Yd Z H x
x
Decision Process Process
Summing
Junction Terminator
Value added
29

30. Feedback two dimensional matrices
~ ~
H d ZYx Yd ZT H T
T
T T T
Y Z H H d ZYx x
d x
Symmetric matrices
Same eigenvalues
Feedback Markov matrices
Same eigenvalues
Dominant value is a unit
~ ~
T T T
H m ZYx Ym Z T H T
T
Y Z H HmZYx
m x x
30

31. Feedback Feedback - Final Demand
0.6
Matrices
C o ns um ptio n. Out HH
0.5
C o ns um ptio n
0.4
Go ve rnm e nt C o n.
0.3
0.2 C a pita l F o rm .
0.1
Inc re a s e in S to c ks
0.0
-0.1 Expo rts
1995 2000 Im po rts
Feedback - Value Added
0.6
C o ns um ptio n o ut HH
0.5
C o m pe ns a tio n
0.4
Final demand’s
0.3
Ope ra ting s urplus
0.2
feedback changes
De pre c ia tio n o f fixe d
0.1
c a pita l
0.0
Indire c t ta xe s *
while value added
-0.1
1995 2000 (le s s ) C urre nt s ubs idie s
feedback does not
31

32. Multiplier Matrix
Value Added (cause)
Final Demand (result)
[I − A ]
i= ~T
Y T
Hi
Z
sectors
Transposed
Types types of
Production
similar
of final value added
matrix
Leontief
demand
inverse
32

33. Multiplier Matrix
Final Demand (cause)
Value added (result)
[ ]
~
i = I − AT
T
Y
sectors H i
Z
types of value added
Transposed Leontief Types
allocation inverse of final
matrix demand
33

34. Final Demand - Value Added Multiplier
0.3
Ag riculture
M ining
M anufacturing
0.2
Co ns tructio n
Electric p o wer
Co mmerce
0.1
Finance
Real es tate
Trans p o rt
0.0
Co mmunicatio n
1995 2000 1995 2000 Pub lic ad minis t.
Services
-0.1 Hd Cause of impact Yd Other Activities
34

35. complete view
WISDOM
35

36. Japanese Economic structure 1995
1995 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7
Intermediate Output
Total Final Demand
Consumption. Out
Capital Formation
Increase in Stocks
Communication
Total Demand -
Manufacturing
Electric power
Public Admin.
Consumption
Consumption
Gross Output
Construction
Act. not else
Government
Households
Agriculture
In Trillions of Yen
Commerce
Real estate
Transport
classified
(Private)
Services
Finance
Exports
Imports
Mining
1 Agriculture, Forestry & Fishery 1.9 0.0 9.9 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.2 0.0 13.3 0.1 4.1 0.0 0.2 0.5 0.0 -2.4 2.5 15.8
2 Mining 0.0 0.0 5.3 0.8 1.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.4 0.0 0.0 0.0 0.0 0.0 0.0 -5.8 -5.8 1.7
3 Manufacturing 2.5 0.1 124.7 25.9 1.4 3.8 1.3 0.2 5.4 0.4 2.7 26.8 0.5 195.8 2.8 63.8 0.7 39.1 1.2 37.9 -26.7 118.8 314.6
4 Construction 0.1 0.0 1.4 0.2 1.2 0.6 0.1 2.3 0.5 0.2 0.5 1.2 0.0 8.1 0.0 0.0 0.0 80.0 0.0 0.0 0.0 80.0 88.1
5 Electric Power, Gas & Water Supply 0.1 0.0 5.9 0.6 2.5 1.2 0.2 0.2 0.9 0.2 0.9 4.6 0.1 17.3 0.0 7.5 1.6 0.0 0.0 0.0 0.0 9.1 26.5
6 Commerce 0.7 0.0 17.2 6.2 0.3 1.1 0.2 0.1 1.8 0.1 0.5 7.8 0.1 36.1 2.2 50.5 0.0 10.4 0.2 3.1 -0.2 66.2 102.3
Finance & Insurance
7 0.5 0.1 4.3 1.0 0.7 5.9 3.5 3.3 3.1 0.2 0.1 5.4 0.9 29.0 0.0 7.8 0.0 0.0 0.0 0.6 -1.0 7.4 36.3
8 Real Estate 0.0 0.0 1.1 0.3 0.3 3.8 0.7 0.5 0.8 0.2 0.0 2.8 0.1 10.6 0.0 53.5 0.0 0.0 0.0 0.0 0.0 53.5 64.2
9 Transport 0.7 0.4 9.3 4.7 0.7 5.3 0.7 0.2 5.3 0.4 0.8 3.9 0.1 32.6 0.7 14.7 -0.1 0.8 0.2 3.7 -2.5 17.5 50.1
10 Communication & Broadcasting 0.0 0.0 0.9 0.5 0.1 1.9 0.7 0.0 0.3 0.9 0.4 3.7 0.0 9.5 0.1 5.2 0.0 0.0 0.0 0.0 -0.1 5.3 14.8
11 Public Administration 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.0 0.8 25.0 0.0 0.0 0.0 0.0 25.8 26.2
12 Services 0.2 0.1 20.7 7.0 2.4 5.3 3.8 1.0 6.6 2.0 1.9 14.3 0.3 65.6 13.5 64.0 41.9 9.2 0.0 1.3 -4.4 125.4 191.0
13 Activities not elsewhere classified 0.2 0.0 2.3 0.2 0.2 0.6 0.1 0.5 0.2 0.1 0.4 1.2 0.0 6.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.6 -0.5 5.5
Intermediate Input 6.8 0.8 203.2 47.5 11.1 29.6 11.4 8.3 24.9 4.7 8.1 72.8 2.6 431.9 19.4 271.8 69.2 139.7 2.1 46.8 -43.7 505.2 937.1
Consumption expenditure outside
1
households (row) 0.1 0.1 6.4 1.7 0.6 2.7 1.3 0.3 1.1 0.2 0.5 4.4 0.0 19.4
2 Compensation of employees 1.5 0.3 54.3 29.3 4.6 49.9 14.0 2.5 16.7 4.9 16.8 78.3 0.2 273.2
Operating surplus
3 5.2 0.2 20.1 3.1 3.6 11.3 6.0 28.4 2.8 1.5 0.0 15.2 2.3 99.7
Depreciation of fixed capital
4 1.8 0.2 16.8 4.5 5.4 5.0 3.7 20.8 3.3 2.8 0.8 15.5 0.3 80.8
Indirect taxes *
5 0.6 0.1 14.3 2.2 1.5 4.0 1.6 4.1 1.6 0.6 0.1 5.8 0.0 36.5
(less) Current subsidies
6 -0.2 0.0 -0.4 -0.2 -0.2 -0.2 -1.5 -0.2 -0.3 0.0 0.0 -1.1 0.0 -4.3
Value Added 9.0 0.9 111.4 40.6 15.3 72.7 24.9 55.9 25.2 10.1 18.1 118.2 2.9 505.2
Domestic production (gross inputs) 15.8 1.7 314.6 88.1 26.5 102.3 36.3 64.2 50.1 14.8 26.2 191.0 5.5 937.1
36

37. Japanese Economic structure 2000
2000 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7
Capital Formation
Increase in Stocks
Communication
Total Demand -
Manufacturing
Electric power
Public Admin.
Consumption
Consumption
Gross Output
Construction
Intermediate
Act. not else
Government
Households
Agriculture
Total Final
Commerce
Real estate
In Trillions of Yen
Transport
classified
(Private)
Services
Demand
Finance
Exports
Imports
Mining
Output
C. Out
1 Agriculture, Forestry & Fishery 1.6 0.0 8.4 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.3 0.0 11.5 0.1 3.9 0.0 0.2 0.8 0.1 -2.1 2.9 14.4
2 Mining 0.0 0.0 7.4 0.7 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.1 0.0 0.0 0.0 0.0 0.0 0.0 -8.7 -8.7 1.4
3 Manufacturing 2.5 0.1 122.9 21.6 1.7 3.2 1.3 0.2 6.1 0.5 2.9 28.2 0.4 191.4 3.3 61.6 0.5 39.7 -0.6 46.6 -34.3 116.8 308.2
4 Construction 0.1 0.0 1.3 0.2 1.3 0.5 0.2 2.8 0.5 0.2 0.6 1.4 0.0 9.0 0.0 0.0 0.0 68.3 0.0 0.0 0.0 68.3 77.3
5 Electric Power, Gas & Water Supply 0.1 0.0 6.3 0.5 1.6 1.2 0.2 0.2 0.9 0.3 1.0 5.5 0.1 18.1 0.0 8.1 0.8 0.0 0.0 0.0 0.0 8.9 27.0
6 Commerce 0.7 0.0 16.3 4.9 0.4 1.4 0.2 0.1 1.6 0.1 0.5 8.3 0.1 34.6 1.9 45.9 0.0 10.7 0.1 4.5 -0.7 62.4 96.9
Finance & Insurance
7 0.5 0.1 4.0 0.9 0.8 4.9 2.9 3.3 2.9 0.5 0.1 5.8 1.0 27.6 0.0 10.5 0.0 0.0 0.0 0.4 -0.4 10.5 38.1
8 Real Estate 0.0 0.0 0.9 0.3 0.2 2.9 0.6 0.4 0.7 0.4 0.0 2.7 0.0 9.1 0.0 56.7 0.0 0.0 0.0 0.0 0.0 56.7 65.9
9 Transport 0.6 0.4 8.2 4.0 0.7 4.6 0.7 0.1 5.0 0.5 1.1 4.2 0.2 30.5 0.5 14.7 0.0 0.7 0.0 4.3 -2.9 17.4 47.9
0.8
10 Communication & Broadcasting 0.0 0.0 1.1 0.9 0.1 2.5 0.1 0.4 2.7 0.5 4.9 0.1 14.2 0.2 7.8 0.0 0.0 0.0 0.1 -0.1 7.9 22.1
11 Public Administration 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 0.7 0.0 0.7 34.8 0.0 0.0 0.0 0.0 35.5 36.2
12 Services 0.2 0.1 23.1 6.4 2.8 6.3 5.0 1.7 6.7 3.6 2.8 19.3 0.3 78.2 13.1 71.1 49.7 10.4 0.0 1.6 -4.8 141.0 219.2
13 Activities not elsewhere classified 0.1 0.0 1.7 0.3 0.1 0.6 0.3 0.3 0.2 0.1 0.0 0.7 0.0 4.4 0.0 0.0 0.0 0.0 0.0 0.0 -0.2 -0.2 4.2
Intermediate Input 6.3 0.7 201.5 40.9 11.7 28.3 12.1 9.2 25.0 8.8 9.5 82.3 2.9 439.4 19.2 281.0 85.7 130.0 0.3 57.5 -54.2 519.5 958.9
Consumption expenditure outside
1
households (row) 0.1 0.1 5.6 1.3 0.5 2.3 1.3 0.2 1.0 1.4 0.6 4.7 0.1 19.2
2 Compensation of employees 1.3 0.2 53.1 26.8 4.7 47.3 12.5 2.4 14.8 5.9 16.6 89.8 0.3 275.6
Operating surplus
3 4.7 0.2 16.9 1.4 3.5 10.0 9.0 29.6 2.6 1.5 0.0 16.7 0.4 96.5
Depreciation of fixed capital
4 1.5 0.1 16.7 4.1 5.0 4.8 3.4 20.7 3.0 3.8 9.5 20.3 0.4 93.4
Indirect taxes *
5 0.7 0.1 15.0 3.3 1.7 4.5 1.5 4.0 1.6 0.7 0.1 6.9 0.1 40.0
(less) Current subsidies
6 -0.2 0.0 -0.6 -0.3 -0.3 -0.2 -1.6 -0.2 -0.2 0.0 0.0 -1.5 0.0 -5.2
Total Value Added 8.1 0.7 106.6 36.5 15.3 68.6 26.0 56.6 22.9 13.3 26.7 136.9 1.3 519.5
Domestic production (gross inputs) 14.4 1.4 308.2 77.3 27.0 96.9 38.1 65.9 47.9 22.1 36.2 219.2 4.2 958.9
* (except custom duties and commodity taxes on imported goods)
37