Global Journal of HUMAN SOCIAL SCIENCE
Sociology, Economics & Political Science

Volume 12 Issue 14 Version 1.0 Year 2012
Type: Double Blind Peer Reviewed International Research Journal
Publisher: Global Journals Inc. (USA)
Online ISSN: 2249-460x & Print ISSN: 0975-587X

The Expansion Input – Output Tables
By Bui Trinh, Kiyoshi Kobayashi & Pham Le Hoa
Kyoto University, Katsura, Japan.

Abstract - This paper is an attempt in order to present some variance of input-output expansion.
The System of National Accounts with version 1968 and 1993 recommended on social
accounting matrix, but until now some countries compiled SAM from supply and use tables andsome other countries compiled SAM from input-output system. SAM seems to apply for CGE
model but it is not meaning in SAM multipliers analysis. The parallel with ideas of social
accounting system developed by Stone (1961), Pyatt and Roe (1977) is demographic-economic
modeling was knew by Miyazawa’s concept. These ideas developed in order to describe theinterrelation between income from production, income from redistribution, consumption,
accumulation, it like as “no start and no the end” in Buddha theory.

Keywords : input-output, social accounting matrix, demographic-economic modeling, System of
National Accounts.
GJHSS-C Classification : 349999

The Expansion Input Output Tables

Strictly as per the compliance and regulations of:© 2012. Bui Trinh, Kiyoshi Kobayashi & Pham Le Hoa. This is a research/review paper, distributed under the terms of the Creative
Commons Attribution-Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

The Expansion Input – Output Tables
variance of input-output expansion. The System of National
Accounts with version 1968 and 1993 recommended on social
accounting matrix, but until now some countries compiled
SAM from supply and use tables and some other countries
compiled SAM from input-output system. SAM seems to apply
for CGE model but it is not meaning in SAM multipliers
analysis. The parallel with ideas of social accounting systemdeveloped by Stone (1961), Pyatt and Roe (1977) isdemographic-economic modeling was knew by Miyazawa’s
concept. These ideas developed in order to describe theinterrelation between income from production, income fromredistribution, consumption, accumulation, it like as “no startand no the end” in Buddha theory.

Keywords : input-output, social accounting matrix,
demographic-economic modeling, System of National
Accounts.
I.

IntroductionT

he Input – output extension are one of the usefultools of economic research. The matrixes can beused for policy analysis and economic planning,and offers an efficient means of summarizing complex
economic relationships and identifying gaps in statisticalinformation.
In the past decades, there hhas been a
noticeable shift of interest from the basic input-output
table to the social account matrix (SAM) as evident fromtr
the increased momentum in thee design, construction
and use of social accounting mamatricess inn many countries(Piatt and Roe, 1997; Cohen et al., 1984; Pyatt andRound, 1985). The argument in favor of working with
SAM or extended input-output models is the increasingly
prevalent requirement by policyy – makers and the larger
public alike appraise.
es are compiled
Social accounting matrices
according to the same accounting principles used for
input-output table; each transaction is recorded twice sothat any inflow to one account must be balanced by an
outflow of another account. The extension of inputoutput table based on linking the location of production
account and the location income and consumption of
institutional as household, Government and enterprise.
Another way, the Miyazawa’s concept of theinterrelation income multiplier was designed to analyze
the structure of income distribution by endogenous
consumption demand in the standard Leontief model;
Author Į : System of National accounts department – GSO, MPI.
E-mail : buitrinhcan@gmail.com
Author ı : Department of Urban Management, Kyoto University,
Katsura, Kyoto, Japan. E-mail : kobayashi.kiyoshi.6n@kyoto-u.ac.jp
Author ȡ : The Director of consultant Company on Accounting.

these ideas were also incorporated in the familiar social
account systems developed by Stone (1961), Pyatt andRoe (1997), and in the parallel developments ofdemographic-economic modeling associated with Batey
and Madden (1983); In order to linkage the concept oninterregional input output modeling and demographic –economic modeling may be considered the function
system.

Social Accounting Matrix

II.

Being an ext
extension of the existing national
economic accounts,
nts, a SAM is a consistent andcomplete representation
esentation
atio of the socio-economic systemthat capturesinterdependencies
of institutionales the interdep
rde egroups. Itt is bothoth a conceptual framework and a datam thatat can support ana
systemanalyses of socio-economic
ev
policythe socio-economic
cy issues,es, used to evaluatechaimpactor serve as a databasempact
pa of exogenous changes,
for general equilib
m modeling.
equilibriu
equilibriumIII.

pdatinga
Updat
Input-Output Table

An input-output
table describes the flowsiamong the various sectors of the economy. It represents
the value of economic transactions in a given period oftime.. Transactions of goods and services are broken
down by intermediate and final use. An input-output
table also shows the cost structure of production
activities: intermediate inputs, compensation to laborand capital, taxes on production.
The SAM can be extended by input-output
framework or supply and use tables. The first of all wehave to compile or update a input-output table (orsupply and use tables). The Leontief system wasdescribed by equations as follows:
A.X+Y=X
X= (I-A)-1.Y
Y=C+G+I+E–M
Mi/TDDi<1
TDDi = ICi + Ci + Gi + Ii

'X1

I  A .'Y

1
2
3
4
5
6

Where A is the direct input coefficient matrix
X is vector of supply or sectoral output
Y is vector of final demand(I - A)-1 is the Leontief Inverse, or matrix of multipliers
C is final consumption of household
G is final consumption of government
I is gross fixed capital or capital formation
E is export
M is import© 2012 Global Journals Inc. (US)Global Journal of Human Social Science ( CD ) Volume XII Issue XIV Version I

Abstract - This paper is an attempt in order to present someYear 2012

Bui Trinh Į, Kiyoshi Kobayashi ı & Pham Le Hoa ȡ

The Expansion Input – Output Tables

Year 2012

Mi is import of commodity i
TDDi is total domestic demand of commodity i
From these basic relations of the I/O table, thefollowing formulas were derived with formula (7) take
into account the three changes in X, namely pricechanges, technical changes and changes in Y (final
demand) through the years. Given the structure of the
National’s economy and the relatively short time breakfrom the last updating of input-output table which wasfor the year t1, formula (8) was used to calculate thetechnical coefficient matrix A for the updated year t2 I/O
table, which assumes that there was no or small change
in prices and technical change

Global Journal of Human Social Science ( CD ) Volume XII Issue XIV Version Ixijt 2

xijt 2
vakjt 2§ xijt1 · t1¨
¸  II j¨ II 2003 ¸© j ¹§ xijt1 ·¨¸  GI tj1¨ GI 2003 ¸© j ¹§ vakjt1 ·¨¸  VAJt1¨ VA 2003 ¸© j ¹

Therefore this must be recalculated to get a(1x Commodity) vector. This could be done with thedata from the last input-output table or S.U.T as follows:
From last I/O or S.U.T, the supply matrix S is
taken out. This is an industry-by-commodity matrix Witha simple formula presented below, the commodity-bycommodity GI vector can be calculated

GI tc2s'.GI ta2

Where

GI tc2 is vector of gross input by commodity of the year
(7)t2

GI ta2 is column vector of gross input by industry of the(8)year t2
s is coefficient matrix of S with dimension (industry x
product)

(9)

Where

dimensms ’ is transpose of s with dimension(product x industry)
The use matrix of the S.U.T can be used to get
se m
the usematrix of the year t2:

ed –x ijt 2 is the amount of the product of sector i absorbed

Ut2

as its input – by sector j in year t2

U t1 .GGI ta2orb –x ijt 2 is the amount of the product of sector i absorbedWith

as its input – by sector j in year t2

U 22003 is coeff
coefficient matrix of use table in year t1

II tj1 is an element of the vector II in 2003 or the totalintermediate input in year t1
to II in year t2
II tj 2 is an element of the vector

vakjt 2 is an element of the value added matrix in year t2,
d at factor costwhere k is factor of value added

vakjt1 is an element of the value added matrix in year t1,
where k is factor of value added at factor cost

VA tj1 is an element of the vector value added in year t1
VAJt 2 is an element of the vector value added in year t2
These formulas were used to compute thetechnical coefficient matrix A and therefore theintermediate demand matrix of the input-output table
and the value added matrix, which is broken-down into
payments to labor and capital, depreciation, and indirect
taxes.
As stated above, equation (8) was used with anassumption that technological change and the change
in prices have not occurred during the last years. One
issue with the vector GI is of course the property of thisvector since it is an(1x industry) vector.
© 2012 Global Journals Inc. (US)

(10)

(11)

U 22005 is ccoefficient matrix of use table in year t2
From the above formulas, now the A matrix of I/O in year
t2 c
can be computed using the following formula:

A U t 2 .s 1(12)With s-1 is an inverse of matrix s (commodity
technology assumption)
But while coming at matrix A, one problem
arose. Some elements of this matrix is negative and thus
should be corrected by changing it to 0. Further, tobalance the I/O table, we use RAS method.
The value added matrix and the final demandmatrix is left to be computed. The value added matrix
can be calculated from the formula:

B

A.GI tc2(13)

where B is the matrix containing both the A
matrix and the value added matrix
The final demand or the Y was computed using
equation (3).

The Expansion Input – Output Tables

and (5) to compute the ratio of imported goods in Total
domestic demand. From this structure of imported
goods in domestic demand, the intermediate input
matrix can easily be achieved. The value added matrix
of non-competitive table remains the same as in thecompetitive table. In the final demand matrix, all theelements are different except for the export vector.

a) Competitive I/O table:
In the competitive I/O table the intermediate
inputs include both commodities produced domesticallyand imported.

V.

b) Non-competitive I/O table:

Sam Building

In this section, the construction of the SAM will
be discussed greatly in detail. Constructing a SAM table
is a rather complicated issue and requires deep
knowledge of the SNA, the input-output table, supply
and use tables as well as different updating andbalancing methods namely the RAS method, not least
the knowledge on the performance of the National’s
economyThe Social
track the monetary flowsc Accountsubetween industries and institutions. The relation between
a SAM andd an I/O table
ble is the fact that the input-output
accounts are a subset of the entire social accounts
recorded in a country. The social accounts track allmonetary flows, both market and non-market. The
markett flows are those between producers of goods
and services and consumers, both industrial, and nonindustrial (i.e households, government, investment, andtrade). The non-market flows are those between
households
lds and government, government andhouseholds,
ld capital and households and so on. Theseflows are often called inter-institutional transfers.
A classical and very simple aggregate versiono SAM is introduced in the table below:ofIn this kind of I/O tables, the intermediate inputs
arebroken-down into
commodities produced
domestically and commodities imported from the rest of
the world.
For the purpose of analyzing the economy
based on the I/O table, the competitive table is not ofmuch use for the reasons stated above; the competitive
table does not separate the intermediate inputs which
are produced by domestic industries from the imported
intermediate inputs. Thus the precision and theusefulness of the analysis based on the competitive
table is a matter for arguing.
Meanwhile a non-competitive table with import
clearly separated from intermediate inputs produced
domestically and thus with two intermediate input
coefficient matrix Ad (domestic A) and Am (importrt A) willl
give the users a much better picture of the economy.
on
Following is the indirect method of how to comeomefrom the competitive I/O table at a non-competitive I/O
table.
Coming from the basic relations
ations of the I/O tabletabwith equations from (1) to (6), we take the equations (4)Table 1 : SAM Framework expansion from S.U.T (Supply and Use tables).

1-Industry
2-Commodity
3-Factors
4-Institutions
5-ROW

(1)

(2 )

(3)

(4 )

(5 )

ry
Industry

Commodity

Factors

Institutions

ROW

Make matrix

1x5

Use matrix
xxxxxxx

xxxxxxx
4x2

4x3
5x3

5x1

Each cell represents a sub-matrix. Rows
represent an institutional or industry receipt of income.
Columns represent an institutional or industry payment
or expenditure. In a SAM table, rows and columns
balance exactly so all flows are counted.
Following is the explanation of the datacontained in each cell of the above example of anaggregated SAM.
1. Industry is the industry sectors from the I/O table
2. Commodity is the commodities also from the I/O
table

3.

4x5
5x5

Factors include the value-added elements:
x
x

4.

4x4
5x4

Types of Labor incomes (L)Type of capital incomes (K)Institutions include
Households
Government
Enterprises (basicallyprofits)x Capital
x Inventoryxxx

consistsofcorporate© 2012 Global Journals Inc. (US)Year 2012

Competitive and Non-Competitive
i/o TablesGlobal Journal of Human Social Science ( CD ) Volume XII Issue XIV Version I

IV.

The Expansion Input – Output Tables

5.

ROW
imports
exports
Again, the building of SAM extended by inputoutput system requires a certain source of data, namely:
1. Data of Intermediate Inputs and Gross Inputs
2. S.U.T in year t1xx

Export and Import of goods and services
Balance of Payment
State budget
Updated non-competitive I/O in year t2
The detailed elements of the SAM extended by
input-output system are in the following table.

3.
4.
5.
6.

Year 2012

Table 2 : SAM expansion from I/O table.
(2 )

(3)

(4 )

(5 )

Commodity

Factors

Institutions

I-S

ROW

1x1
2x1
3x1

1x2

1-Commodity
2-Factors
3- Institutions
4-Saving
5-ROW




Global Journal of Human Social Science ( CD ) Volume XII Issue XIV Version I

(1)

4x2
5x1

From table 2 can convert to table 3 can apply apaper of Bui Trinh, Kiyoshi Kobayashi and Kwang Moon
Kim (2012).
VI.

Demographic – Economic
Modeling

Miyazawa expanded I/O model into a
demographic model - economic modeling and thismodel has been completed by Batey and Maddenen(1983). The model introduces the concept of Leontief
inverse matrix and expand Leontief extended system for
Keynes multipliers, which can analyze the rerelationshipbetween income groups and consumer groups,
respectively. The model is also used to analyze thestructure of income in order to describe
quantitativelyithe relationship between income from production andincome not from production. In which case, it isclassified according to the system of national accounts
published by the United Nations (UN "System of
National Accounts - SNA", 1993), non-production-princome includes income from pr
property and income fromtransfer.
Demographic - Economic model is created byMiyazawa (1966), it’s a similar form to the Social
Accounting Matrix, in order to describe the distribution
and redistribution of the economy. Essentially, theDemographic – Economic model and the Social
Accounting Matrix are similar and it could easily bechanged from one model to another depending on otherstudy purposes. In this study, Demographic – Economic
model is developed in institutional regions (households,
other type of enterprise, State region is divided by typeª A c1«h 0«« g c2«¬ e c3Or,© 2012 Global Journals Inc. (US)

g1
g2
0
g3

1x5
2x4

0º
e1 »»
.
e2 »
»
e3 ¼

4x3
5x3

4x4
5x4

4x5
5x5

nstitutiona regions are considered asof tax). These institutional
les: saving and relations with foreign
endogenous variables:
re consideredons
countries are
as exogenous
variables. Thisex
model is a combination between the notion of intern I/O
O model and demographic - economic model,
regional
as presented in matrix form below:-1F+ =P=AP+F=(I-A)(14)

The SAM can be used similarly, note that thematrix, A is not only descries production account but
also
descries re-distribution from property and transfer;athe vector of row total, x, represents the endogenous
variables, whereas the vector f represents theexogenous variables. The vector of endogenous
variables,
x, can be solved in equation (15):vax = Af + x = (I-A)-1x = Mx

(15)

Where,
M is the aggregate multiplier matrix.
Another way, the Miyazawa’s concept of theinterrelation income multiplier was designed to analyze
the structure of income distribution by endogenous
consumption demand in the standard Leontief model;
these ideas were also incorporated in the familiar social
account systems developed by Stone (1961), Pyatt andRoe (1997), and in the parallel developments ofdemographic-economic modeling associated with Batey
and Madden (1983); In order to linkage the concept oninterregional input output modeling and demographic –economic modeling may be considered the following
system:ª x1 ºª f1 º«x »« »« 2 » + « f2 » =« x3 »« f3 »« »« »¬ x4 ¼¬ f4 ¼ª x1 º«x »« 2»« x3 »« »¬ x4 ¼(16)

The Expansion Input – Output Tables

g2
0
g3

0º
e1 »»
ªA c º= «»e2 »¬ v B¼»e3 ¼

Where: A – direct input coefficients matrix; x1 is
a vector of output; x2 is total income for fold division ofhousehold groups; x3 is total income of Government
institutional; x4 is total income of enterprises institutional;
h is an matrix (vector) of households income groups
from production; g is a vector of Government income
form production (indirect taxes minus subsidies); e is anmatrix of income of enterprises groups from production(operating surplus and consumption of fixed capital); c1
is a corresponding matrix of household consumption
coefficients; g1 is a vector of Government consumption
coefficients; c2 is a vector on redistributing between thehousehold groups and Government institutional; c3 is amatrix on redistributing of household institutional toenterprise groups; g2, g3 are expenditure of Government
to households and enterprises institutional; e1, e2, e3 are
matrixes on redistribute from enterprise institutional tohousehold, government and other groups of enterprises.
Regarding equation (18) the vector v, c and can identify
as below:

ªhº
« »
v= g
« »
«¬ e »¼
c=

>c1

g1

(18)

0@

(19)
(

'1
ª x1º ª« x' » = «1¬ ¼ ¬' 2 ..vv.(( I  A)
Where: ¨ 1 is interpreted ass enlarged Leontief
inverse, the elementary of ¨ 1 includes direct impact,
indirect impact and induce effects by household andgovernment consumptions, they contain elements which
are larger than those of the (I-A)-1 matrix, because they

(17)

ª0
«c
« 2
«¬c 3

e1 º
e 2 »»
e3 »¼

B=

(20)

ª x2 º« »x’ = x 3« »«¬ x 4 »¼(21)ª f2 º« »f’ = f 3« »«¬ f 4 »¼

(22)



ite equationequ
We canc re--write(1ª A c º ª x1 ºª x1 ºª f1 º« v B » . « x ' » + « f '» = « x ' »
¬
¬ ¼
¼ ¬ ¼
¬ ¼

(23)

Miyazawaysuggested an innovative way ofpartitioning the system of regions and the developmentsof demographic – economic modeling associated withtey and Madden (1983); the other innovative way for
Batey
lin
linking of sectoral and institutional, it is also referred asinternal and external multipliers and relation (24) may beobtained:' 1 .c.( I  B ) 1 º ª f 1º». « »'2¼ ¬ f '¼

(24)

include extra output required to meet the consumption
groups output effects. ¨ 2 is interpreted as enlarged
Miyazawa matrix multipliers, the matrix ¨ 2 can be
decomposed as follow:¨2 = (I – (I-B)-1.v.(I-A)-1.c)-1.(I – B)-1
(I – B)-1 is referred as internal multipliers of re distribution income and (I – (I-B)-1.v.(I-A)-1.c)-1 is referred
as external multipliers that induced effects by income
from production, these mean income from re-distributiondose not dependent direct income from re-distributionof each institutional, but also dependent re-distribution
income of other institutional and induced byconsumption expenditure.

g2
0
g3

Year 2012

g1

(25)

¨1.c is a matrix of production induced byendogenous consumption.
v.(I-A)-1 is a matrix of endogenous income
earned from production.
Note that equation (24) ca n be re write as bellow:© 2012 Global Journals Inc. (US)Global Journal of Human Social Scie nce ( CD ) Volume XII Issue XIV Version Iª A c1«h 0«« g c2«¬ e c3

The Expansion Input – Output Tablesª x1º ª' 11« x' » = « 0
¬ ¼ ¬

0 º ª
I
( I  A) 1 .c º ª( I  A) 1.
«».«' 22 »¼ ¬( I  B) 1 .v
I
0
¼ ¬

º
0
1 »
( I  B) ¼

Where:

Year 2012¨1 = ¨11.(I-A)-1 and ¨2 = ¨22.(I-B)-1¨11 = (I – A – c.(I-B)-1.v)-1 and ¨22 = (I – (I-B)-1.v.(I-A)-1.c)-1

Global Journal of Human Social Science ( CD ) Volume XII Issue XIV Version IThe equation (26) introduce the hierarchicalsequence of modeling which multiplicatively separates
the enlarged Leontief inverse matrix and enlarged
Keynesian multipliers matrix, interrelationship multipliers
from the interrelationship effects
We shall explain how to define and measureinterrelationship feedback effects in interrelationshipsettings. Solving the equation (23), (24) and (26) for X 1
and X’ yields:
X’ = (I-B)-1.v. X1
X1 = (I-A)-1.c.X’

(27)
(28)

These are the interrelationship feedback effects.
The equation (27) and (28) present the relationshipbetween production and total income.
The
DemographicEconomic
modeling
described in table 4 below:© 2012 Global Journals Inc. (US)(26)

The Expansion Input – Output Tables

Table 3 : Demographic- Economic modeling 2005..
(1)

(2)

Comm House
odity

hold

(3)

(4)

(5)

(6)

Government

Enterprises

Inves

ROW

tment

VAT Special Other Import Direct Transfers State
consu

taxes

duties

taxes

Non-

(7)

FDI

Total

state

mption
taxes
1x2

1x8

1x13
1x14

odity
2HouseholdCompen

2x1

2x8

2x13

sations

2x14

of
employees
VAT

3x1

Special

4x1

3x14
4x14

consumption
3Govertaxes
Other taxes

nment Import

5x1
6x1

5x14
6x2

6x12

6x14

duties4EnterDirect taxes

7x2

Transfers

8x2

7x9

7x10

7x11

7x13

7x14

8x13

8x14

State

9x1

9x8

9x9

9x10

9x11

9x14

Non-State

10x1

10x8

10x9

10x10 10x11

10x14

11x9

11x10 11x11

11x14

12x9

12x10 12x11

prises FDI

11x1

5-

12x2

12x3

12x13

Saving
6-

13x1

13x2

14x1

14x2

13x8

13x11 13x12

ROW
7Total

14x3

14x8

14x9

14x10 14x11 14x12 14x13

12x14
13x14
14x14

© 2012 Global Journals Inc. (US)Year 2012

1x1

Comm



Global Journal of Human Social Scie nce ( CD ) Volume XII Issue XIV Version I

1-

The Expansion Input – Output Tables

Year 2012

Below in table is the explanation of each cell in the SAM 2005 table

Global Journal of Human Social Science ( CD ) Volume XII Issue XIV Version ICell 1x1

represents the updated non-competitive I/O 2005, including the intermediate input matrix

Cell 2x1

Total payments by industries to household (compensations of employees)

Cells 3x1, 4x1,
5x1, 6x1
Cells 9x1, 10x1,
11x1

Payments by industries to government namely indirect taxes and import duties
Operating surpluses and depreciations of the enterprises

Cell 13x1

Total foreign imports to industry use or payments to imports

Cell 1x2

Payments made by household to commodities or total final consumption of household

Cell 6x2, 7x2, 8x2

Taxes paid by household to government

Cell 12x2

Household saving

Cell 13x2

Imports to household final demand

Cell 12x3

Government saving

Cell 1x8

Transfers made by government to state commodities

Cell 2x8

Transfers made by government to household

Cell 9x8, 10x8

Transfers made by government to state and non-state enterprises

Cell 7x9, 7x10,
7x11
Cell 9x9, 10x9,
11x9,0x10, 10x10,
11x10,
9x11,
10x11, 11x11

Payments in terms of Direct taxes made by enterprises to government
Inter-institutional transfers by enterprises to enterprises and property incomes

Cell 13x11

Transfers made by the FDI enterprises to the rest of the world

Cell 6x12

Import duties paid to the government

Cell 13x12

Import of investment goods

Cell 1x13

ExportCell 2x13

Payments from the rest of the world to household

Cell 7x13, 8x13

Tax payments and transfers from the rest of the world to the government

Cell 12x13

Foreign transfers
VII.

Conclusion

This paper is an attempt in order to present
some variance of input-output expansion. The System of
National Accounts with version 1968 and 1993
recommended on social accounting matrix, but until
now some countries compiled SAM from supply anduse tables and some other countries compiled SAM
from input-output system. SAM seems to apply for CGE
model but it is not meaning in SAM multipliers analysis.
The parallel with ideas of social accounting systemdeveloped by Stone (1961), Pyatt and Roe (1977) isdemographic - economic modeling was knew by
Miyazawa’s concept. These ideas developed in order to© 2012 Global Journals Inc. (US)describe the interrelation between income fromproduction, income from redistribution, consumption,
accumulation, it like as “no start and no the end” inBuddha theory.
Especially, The analysis of I/O models anddemographic - economic model showed the changes ofthe economy cause of different impacts to sectors andinstitutional regions. So, calculation on this element isnecessary to plan the tax policy and other policies. Suchas, analyze the index of power of dispersion shows that
this index of the sector is very large, then, if you
stimulate development of this sector, it highly impacts
other sectors in the economy

The Expansion Input – Output Tables

Bacharach, M. (1970), ‘Biproportional matrices andinput-output change”, Cambridge University press,
London.
2. Batey P. W. J. & Madden M. 1983, “ The Modelingof Demographic-economic Change Within theContext of Regional Decline: Analytical Proceduresand Empirical Results”, Socio-Economic Plan,
Vol.17, No. 5, pp.315-328.
3. Bui Trinh, Kiyoshi Kobayashi, Kwang Moon Kim(2012) “The Supply and Use tables: The approachfor conversion to input-output table” Journal ofAdvances in Management and Applied Economics,
Volume 2, Issue 2
4. Bui Trinh, Nguyen Ngoc Anh (2009) “Updating aVietnam SAM 2005 A hybrid approach”, DEPOCEN
working paper series No. 16
5. Bui Trinh, Kiyoshi Kobayashi, Nguyen Quang Thai,
Nguyen Viet Phong, Pham Le Hoa (2012) “Analyzingsome economic relations based on expansion
input-output model” International journal of businessand management, Vol. 7, No. 19- Published by
Canada center of Science and education.
6. CIEM/NIAS “New SAM of Vietnam, 2000”, National
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The Expansion Input – Output Tables

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