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------------------, 1999, Some Relationships
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APPENDICES
Figure 1. Appendices: From Supply and Use tables to
Input-Output Tables
Supply Table
Use Table
Production Matrix
Use table for Imports
Use table for Domestic output
Transformation of Supply and Use Tables to Symmetric
Input-Output Table
Technology Assumption
Assumption of fixed sales structure
Model A Production Technology
Assumption
Model B Industry Technology
Assumption
Model C Fixed Industry Sales
Assumption
Model D Fixed Product sales
Structure Assumption
Product by Product Input-Output Tables
Industry by Industry Input-Output Tables
Source: José M. Rueda-Cantuche, Jörg Beutel, Frederik
Neuwahl, Andreas Löschel, Ignazio Mongelli, 2005, A Symmetric
Input-Output Table for EU27: Latest Progress: 20.
Table 1. Appendices: Transformation of make and use
matrices into symmetric input-output tables
|
MODEL A
Product by Product
Product technology based
|
MODEL B
Product by Product
Industry technology based
|
MODEL C
Industry by Industry
Fixed Industry sales structure
|
MDEL D
Industry by Industry
Fixed Product sales structure
|
|
Input Coefficients
|
AA(U,V) = UV-T
|
AB(U,V)=
U(diag(Ve))-1V(diag(VTe))-1
|
AC(U,V) =
diag(Ve)V-TU(diag(Ve))-1
|
AD(U,V) =
V(diag(VTe))-1U(diag(Ve))-1
|
|
Intermediates
|
ZA = AA(U,V)diag(VTe)
|
ZB = AB(U,V)diag(VTe)
|
Zc = AC(U,V)diag(Ve)
|
ZD = AD(U,V)diag(Ve)
|
|
Final Demand
|
FA = Y
|
FB = Y
|
FC = diag(Ve)V-TY
|
FD = V(diag(VTe))-1Y
|
|
Value Added
|
VAA =
WV-Tdiag(VTe)
|
VAB = W(diag(Ve))-1V
|
VAC = W
|
VAD = W
|
|
Output
|
qA =
(I-AA(U,V))-1FAe
|
qB = (I -
AB(U,V))-1FBe
|
gC =
(I-AC(U,V))-1FCe
|
gD = (I-AD(U,V))-1FDe
|
|
Negatives
|
YES
|
NO
|
YES
|
NO
|
Legend for the transformation of make and use tables into
input-output tables at basic prices
A=
Technical Coefficients Matrix Y = Matrix for
Final demand by Product and Category VT =
Supply Matrix
W = Matrix of Value added by component and by Industry
U = Use Matrix
e = Column Vector of Ones
Note: T will
denote transposition and -1 inverse of matrix. Since the two operations
commute, their composition may be denoted -T. Also, diag will denote
diagonalization whether by suppression of the off-diagonal elements of a square
matrix or by placement of the elements of a vector
Source: José M. Rueda-Cantuche, Jörg
Beutel, Frederik Neuwahl, Andreas Löschel, Ignazio Mongelli, 2005,
A Symmetric Input-Output Table for EU27: Latest
Progress: 21
Table 2. Appendices: Input-Output Table Set in the Form of a Social
Accounting Matrix
(i) (ii) (iii)
(iv) (v)
Domestic Production
Institutions
Products
Activities Factor Services Domestic RoW
TOTALS
Domestic Production Use of
Raw Dom. Final Export of goods Demand
(i) Products Materials
Demand (market & non Factors for
Products
.
Prices)
Services (f.o.b) market prices
(ii) Activities Gross Out-
Gross output
. .
Puts
of products
.
(Producer
(producer
.
Price )
price)
(iii)Factor Services Payments for
Demand for
. Factor services
fact. services
. . .
(including VAT)
market prices
Institutions I. Taxes on I.
Taxes on Factor services Factor income
Total income
(iv)Domestic Products +
activities + supplied plus received from
generated by
. . . import operating
surplus VAT receipt abroad
contributions
. . . duties
of Government
or production
(v)Rest of the World Import of
Factor income Total
domestic . . .
goods and paid abroad
expenditure on
. . . . non-factor
and imports of
foreign goods .
services factor
services and
services . . .
(c.i.f)
TOTALS Supply of Gross
outputs total supply of Total expenditure Total foreign
. products at of products
factor services on production expenditure
. market valued at pro- at
market prices at market prices on domestic
. . prices ducer prices
goods
&services
Source: Grahan Pyatt, 1988, A SAM Approach to
modeling, Journal of Policy Modeling, University of Warwick.
| 
