Journal ofApplied Input-Output Analysis, Vol. 13 & 14, 2008

DETECTION OF KEY SECTORSBY USING SOCIAL ACCOUNTING MATRICES:AN ALTERNATIVE APPROACH1by

M. Alejandro Cardenete2, Caspar J. Llanes3
M. Carmen Lima4, Carmen R. Morilla5
Abstract

This paper provides a new methodology for the detection of productive key sectors within anational (or regional) economy. In contrast with other methods applied so far, this one presents two innovations. Firstly, the so-called traditional models, which are based on building
normalised backward and forward linkage indicators, are combined with more modern ex
traction models. Secondly, Social Accounting Matrices (SAM) are the databases used instead of Input-Output Tables (IOT), in order to determine those indicators. This paper at
tempts to show the advantages of this system by empirically applying it to the SAM for
Spain in the year 2000, in order to detect the key sectors in Spanish economy.

Keywords: Input-Output Tables, Social Accounting Matrix, national accounting, key
sectors.

1

INTRODUCTION

The systems to determine productive key sectors are usually classified into two methodological categories: the so-called traditional models, and the hypothetical extraction

Contact author: M. Carmen Lima: Department of Economics, Universidad Pablo de Olavide Ctra.
Utrera, km.l. 41013 Seville, SPAIN, mlimdia@upo.es

1 Acknowledgements
The first author would like to thank the funding provided by the Centre for Andalusian Studies

Foundation and is also very grateful to the SEC2003-05112/ECO research project from the Spanish
Ministry of Science and Technology. The first and second authors would like to thank the General
Secretariat for Economic Affairs of the Andalusian Regional Government. The first and third authors

are grateful to the "Excellence Research Project" SEJ-01252 and to the SEJ-246 research project,both from the Andalusian Regional Government, as well as to the XT0039-2004 research project,from the Catalonian Regional Government. The fourth author would like to thank the National Institute for Statistics. The authors take responsibility for any error in this paper.
2 Department of Economics, Universidad Pablo de Olavide.
3 General Secretariat for Economic Affairs, Andalusian Regional Government.

4 Department of Economics, Universidad Pablo de Olavide.
5 Department of Applied Economics II, Universidad de Sevilla.

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

models. Briefly, both traditional and hypothetical models are based on the combinationof two indicators: a backward linkage (BL) indicator and aforward linkage (FL) indicator, which are traditionally obtained from a symmetrical input-output table (SIOT).
The backward linkage indicator (BL) analyses the effect of a change in the final

demand of a specific sector on the economy total production, whereas the forward link
age indicator (FL) values the effect that a global change in the final demand of all sec
tors has on the production of a specific sector.

Through these indicators it is possible to determine the key activity sectors in an
economy. Those sectors, supported by their generating a high multiplier and fostering
effect on production, can be used to design strategies for development as part of theeconomic policy.

In this paper, following Cardenete and Sancho (2006), we suggest the use of a So
cial Accounting Matrix (SAM), which is a more complex database than the traditional
SIOT, to detect the key sectors. It is well known that Social Accounting Matrices bringabout an enlargement of the traditional input-output frame, since they reflect the com
plete circular flow of income. From this perspective, the measurement of the economictransactions incorporated in a SAM allows the extraction of more precise information
about the different economic agents, such as producers, consumers, public administration and the foreign sector, as well as about the behaviour of the productive factors6.
The methodological proposal in this paper rests on a simple approach that seeks
to extend the input-output approach to account for all the backward and forward link
ages between sectors, factors and demand. This method combines the so-called tradi

tional models, based on building normalised backward and forward linkage indicators,
with more modern extraction models and it uses Social Accounting Matrices (SAM) as
databases instead of Input-Output Tables (IOT). This is a simple way to enlarge the setof interdependencies to effectively include the missing links between production andthe income and expenditure side. Lost output will also translate now into lost factor income and reduced expenditure, hence furthering the economic impact of the extracted
sector.

The present paper is divided into several sections. First of all, we will briefly goover the main models used to detect key sectors, paying particular attention to thosethat will be useful for our empirical application. In the next section we will present theresults of the simulations already done and we will then finish with a summary of themain conclusions.

2 MODELS FOR THE DETECTION OF KEY SECTORS.

The analysis of the so-called linkages, which are used to examine the interdependence
between productive structures, has had a long history since the pioneering works ofChenery and Watanabe (1958), Rasmussen (1956) or Hirschman (1958).

6 For furtner advantages in the use of multipliers based on SAM instead of on IOT, see Roland-Hoist,
D.W. (1990).

DETECTION OFKEY SECTORS BY USING SOCIAL ACCOUNTING MATRICES: AN ALTERNATIVE APPROACH

85

In this paper we suggest the use of the methodology developed by Rasmussen (1956)
to obtain the BL, and that of Augustinovics (1970) designed to obtain the FL, both ofthem considered as traditional models. Concerning the BL, we particularly propose thedatabase to be a SAM and not a SIOT. This SAM should have a high degree of endogenisation in the institutional sectors, which would allow an adequate close of the circular flow of income. At the least, not only productive factors' (labour and capital) rent
should be endogenised, but also that of households. In this way, if we analyse the BL
we find out that the change in the final demand of a certain sector will not only reflect
how the rest of the sectors may change in order to 'supply' that alteration in the final
demand, but also, since the productive activity will increase, the factors' remunerationand the consumers' expenditure will increase as well, thus influencing the productive
sectors again in a "second round".
Starting with the model proposed by Rasmussen (1956), we calculate the associated inverse matrix Bt = (/-A,)"1, being / an identity matrix of size n and A, the aver
age tendency matrix of expenditure between the different endogenous accounts in the
SAM.

Furthermore, we derive a vector B} in which each element corresponds with thesum of a column in the matrix (we can develop an analogous analysis for rows). The
elements of the associated inverse matrix B, are denoted by by.

Bj=ibij

7=1.../i(1)/=i

The next step is to obtain the expression of the BL. Following Rasmussen (1956)
and Hirschman (1958) we can normalise the previous equation as:
BLj

JL

j = l...n(2)

ij = 1.../I(3)nwhere V is:
n

V =

n

Once this indicator is normalised, if the backward linkage is above one, a one unitchange in the final demand of sector j will generate a growth above the average on the
global activity of the economy.

In 1976, Jones stated that the detection of FL as defined by Rasmussen (summa
tion of rows in Leontief inverse matrix) did not have the property of being a symmetri
cal measurement as far as BL (summation of rows in Leontief inverse matrix) are con

cerned. From a similar perspective, Augustinovics (1970) had already brought up thedetection of FL by means of the rows summation of the Ghoshian inverse matrix, in
which the distribution coefficients (6\) - obtained from the SIOT by dividing each cellby the row total and not by the column total - replace the technical coefficients. Ghoshmodel calculates changes in gross sectoral outputs for exogenously specified changes
in the sectoral inputs of primary factors. Ghosh's 'supply-driven' input-output model isa well-known alternative to Leontiefs traditional 'demand-driven' input-output model,
as Dietzenbacher (1997) observed.

This way, FL is calculated as 0,-.:

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Oi = T>Sij

i = l...n

(4)

;'=i

From where we may obtain a valuation of the global effect that altering the supply of primary inputs in a particular sector has on all sectors. As it is shown in equation (2), the normalisation process of 0, is as follows:

FLj = yLi = l.../i

(5)

lV
n

Again, after its normalization, if the indicator is above one, a one unit change inall sectors will generate a growth above the average in sector i. In this case, we will
use the SIOT for the simple reason that, if primary inputs, which are the thread of thecircular flow of income, are kept as exogenous, the economic interpretation lying in FL
will lose its meaning once the institutional sectors are endogenized through the use of
the SAM.

Those sectors in which both forward linkages and backward linkages values areabove one will be considered to be key sectors.

As opposed to the already commented traditional models, hypothetical extraction
models value the importance of a sector by analysing the consequences derived fromits elimination. Depending on whether a sector is included or not, the output may present differences, which will measure the importance of such sector. The first approach
to applying this methodology was that of Paelinck et al. (1965), which was further developed and refined by Strassert (1968), Schultz (1977), Cella (1984), Clements (1990)
and Heimler (1991). In this paper we follow Dietzenbacher et al. (1993) approach,which is a reviewed version of previous extraction models.7
The importance of a sector is presented in terms of backward and forward link

ages within a system with and without the extracted element. Following this last ap
proach, we will briefly explain the first of those linkages8, BL, as it is presented in thefollowing equation. In this case, the importance of a key sector is calculated as the dif
ference in the total output of the complete economic system once that sector has been
extracted:
x-x

xr-r

U

l:

(/-A!)"1 0
0(I-ArnV J(6)Where x is the total output in a complete economic system, x is the total output
once the sector has been taken out, L is Leontief inverse matrix, A is the technical coefficients matrix, / is the final demand vector, and the superscripts i and r represent
the extracted sector and the rest of the system respectively. If we work with an 10 table, the n order of the matrices will coincide with that of productive sectors. However,
if we work with a SAM, it will turn out to be a higher number equivalent to the num
ber of sectors considered as endogenous. According to Dietzenbacher et al. (1993), total effects of the left part of the equation reflect the backward linkages of sector i on

7 A review of the extraction models can be found in Miller and Lahr (2001).
8 For details on the obtaining of BL and FL, see Dietzenbacher (1993).

DETECTION OF KEY SECTORS BY USING SOCIAL ACCOUNTING MATRICES: AN ALTERNATIVE APPROACH

87

the rest of the economy and those of the rest of the economy on sector i. In our em
pirical application we calculate vector x-x by taking out one sector at a time; so that it
will be done n times.

Any element (/, j) in this matrix will represent that case in which sector j has
been extracted. This (j, j) diagonal matrix will measure the rest of the sectors' backward linkage on sector;. This is what we call intrasectorial backward feedback effect.
Therefore, those elements that do not belong to the matrix's main diagonal will
actually represent the backward linkages. If we add up the elements of each column inthe extraction matrix, we will obtain the total effects (or total linkages).
In terms of the forward linkage, the difference is as follows:(xl-x),(xr- xr)' = (vV")

Gi

a:

G"

Gn

o

(i-b:yx(7)

Where v denotes the primary input vector, G is the Ghosian inverse, B is the out
put allocation matrix and the rest of the elements have already been described above.
See Dietzenbacher et al. (1993) for a further development of the extraction model.
In this second methodology, we can see the same arguments repeated when interpreting the outcomes if we use the SAM and the SIOT. Consequently, we will use theSAM to calculate BL, and the SIOT to calculate FL.

3

DATABASE AND EMPIRICAL APPLICATIONThis work has been developed by taking a domestic Social Accounting Matrix for
Spain, which was elaborated by Morilla and Llanes (2004). This matrix was created ac

cording to SEC959's criteria and was disaggregated in 30 activity sectors. For its updat
ing the "Cross Entropy Method" (CEM), which was developed by Robinson et al.
(2001), has been applied.

We have proceeded to calculate the BL and FL that correspond to each activity
sector, which can be consulted upon in the appendix in detail.
In order to simplify, we will now present the detected productive key sectors,
which are shown in Table 1. The first simulation presents the key sectors that havebeen exclusively detected from the SIOT by following a combination of Rasmussen's
BL and Augustinovics' FL traditional models. In the other two columns, key sectors
detected through the use of a traditional model again and through a hypothetical ex
traction model are shown respectively. However, in this case, a SAM has been used for
the BL, whereas the FL have resulted from using an IO table.
When a SAM is used to calculate the backward linkage, one may see that we can detect a number of key sectors (11) higher than the number resulting from using an IO
table (7) exclusively. The new detected sectors are services such as Trade and Repair(21), Transport and Communications (23), Real Estate and Business Services (25). Thisis due to the fact that multiplier effects of the Services activity are minimised if only

See Carrasco (1999).

Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Table 1: Comparison of key sectors by using different methodologies and databases.

Traditional Models•8

I

Extraction Models

BL Rasrmussen IOT

BL Rasmussen SAM .

BL Dietzenbacher SAM

FL Augustinovics IOT

FL Augustinovics IOT

FL Dietzenbacher IOT

7

6

7

14

7

20

15

14

21

17

15

22

20

17

23

22

20

25

24

21
22
23

24
25

Notes: IOT refers to Input Output Table; SAM refers to Social Accounting Matrix; the calculation of
FL and BL has already been explained above.
Source: Own elaboration.

intermediate relations of an exclusively productive character are taken into account.

Since Services are more intensive in labour force, their effects are therefore potentiatedby the circular flow of income.

The simulation corresponding to the hypothetical extraction model is still more

restrictive as far as the number of detected key sectors is concerned (just 6). This isdue to the fact that apart from being influenced by inner productive interrelations, thismodel also takes into account the actual quantitative importance of a sector in theeconomy as a whole. In this case, the key sectors are also branches of services, except

for Food, Beverage and Tobacco Industries (7) as well as for Building Industry (20).

4 CONCLUSIONS

Although the detection ofkey sectors has had a long history, it is worth mentioning thecontributions of Rasmussen (1956), Augustinovics (1970) and, most recently, Dietzen
bacher et al. (1993). These methodologies share their capacity to select those sectors

within an economy which are capable of vigorously boosting and transmitting a proc
ess of growth in production, employment or GDP in the short term.

The contribution of this paper consists of extending key sector analysis from an
Input-Output approach to a SAM framework. This allows us to explore and measure
the effects that added endogeneity has for the detection and output evaluation of key
sectors. The use of one or other of the models and the choice of a database to whichthose models are applied can lead to complementary analyses to determine the key sec
tors within an economy, as proved in this paper. In particular, our method uses the So-APPENDIX: Table A-1: BL and FL from SAM-2000 and IOST-2000 for Spain ender different simulations.
—

'••'-

—-:

-•

'

•

~

-

Traditional Models

-• •

1

BL Rasmussen IOST

Sectors'-1Ameulture, stockhreeding,^hiwang^nd^ilViciiltuie
2 Fishing ~ ." """"*;*•* ••"*; ' ""'"- -.--<•.•••

0,95

3 Energy products extraction

0,87:4 Extraction of.intends other than energy products
5 petroleum refine and nuclear fuel processing
6 Electric power, gas and water production and distribution
a tad; beverageandHobaccoindustry

1,02

1,02

0,70

0,88

1,38
0,98

8 Ifextile and clothing industry

2

BL Rasmussen SAM
1,18

D

I

Extraction Models,
3

4

n

5

FL Augustinovics IOST BL Dietzerabacher SAM

FL Dietzembacher IOST

0,91

0,67

1,16
1,20

0,57

0,04

0,57

0,04

1,14
0,52

0,59

0,07

0,63

0,17

1,07
1,35
0,97

1,15

0,50

2,01
0,81
0,88

1,27
0,26

1,65
3,45
2,62

0,10

0,49

0,73

0,15

0,56

1,08
1,05
0,99

0,86

0,36

12 Chemical industry

0,89

0,89

0,45

1,26
1,83

13 Rubber processing and plastic materials industry

0,85

0,83

0,68

0,19

1,48

14 Non-metallic mineral products industry

1,09
1,07

1,17

1,08

0,44

1,03

1,20

0,72

1,58
2,85

U Paper industry; publishing* graphic arts and reproduction

15 Metallurgy and metallic products manufacture

o

1,55
1,63
0,22
0,34
0,68

1,29
1,06
1,03
0,97

9 Leather and footwear industry
10 Tiniiber and cork industry

O
OO

a

*<

c

o
oo

O
n

n

(cont.)
Traditional Models

Sectors

1

2

BL Rasmussen IOSTBL Rasmussen SAM

4

5

1,01

1,03

0,77

0,36

2,41

1,21

1,20

1,07

0,45

1,31

18 Transport material manufacture

0,93

1,04

0,61

1,52

19 Various irianufacturing industries
20 Building industry

1,09
1,14

0,78
1,07

0,84

0,26

1,17

1,18

2,44

1,94

2,96

21 Motor vehicle trade and repair

0,89

2,07

5,23

1,03
0,86
2,07
0,84

1,17
1,20
1,12

1,21

22 Hotel industry

1,44
1,00
1,95

1,67

3,96
4,40
4,13
4,70
3,93
0,50
0,53
0,70
0,36

25 Real estate and renting activities; business services
26 Public Administration, defense and social security
27 Education

28 fiealth and veterinary activities; social services
29 Other social and community service activities^3<N^useholdsHhitTO&~do^--*—^^™.^«™^.

Source: Morilla, C.R. and Llanes, G. (2004) and own elaboration.

1,54
1,15

a

FL Augustinovics IOST BL Dietzerabacher SAM FL Dietzembacher IOST

17 Electric, electronic and optical materials and equipment industry

24 FinanciaLtecokerageoaExtraction Models
3

16 Machinery and mechanical equipment building industry

23 Transport* warehousing and communications

o
'Z

1,51
0,49

1,21

2,43

1,16

0,76

0,90

1,17

0,64

0,75

0,79
0,70
0,76
0,90

1,17

0,71

0,82

1,18

0,78

0,56

. 0,60L_.

1,18

0,55

Note: Identificat on of key sectors: Acti vity sectors with both BL

0,17

and FL values above 1.

2
n
m

>

H
Cfl

25
<
Cfl

>

I
I ^O

90

Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

cial Accounting Matrix since it reflects the effects derived from the circular flow of income. Therefore, it allows reaching more precise conclusions, especially in relation to

the strategic importance of certain activities of the Services sector, which could be
eclipsed by those key sectors detected exclusively from a SIOT perspective. The differ
ential effects can be important enough to provide valuable information to help policy
makers in accomplishing a more insightful design of industrial and development policies that may affect the economy as a whole.

REFERENCES

Augustinovics, M. (1970) "Methods of International and Intertemporal Comparison of Structure", in A. P. Carter and A. Brody (Ed.) Contributions to Input-Output Analysis, pp.
249-269, Amsterdam, North-Holland.

Carrasco, F. (1999) Fundamentos del Sistema Europeo de Cuentas Nacionales y Regionales(SEC 1995). Ediciones Piramide. Madrid.

Cardenete, M. A. and Sancho, F. (2006) "Missing Links in Key Sector Analysis", Economic
Systems Research, 18 (3), pp. 319-327.

Cella, G. (1984) "The Input-Output Measurement of Interindustry Linkages", Oxford Bulletinof Economics and Statistics, 46, pp. 73~84.

Chenery, H. B. and Watanabe, T. (1958) "International Comparisons of the Structure of Pro
duction", Econometrica, 26, pp. 487-521.

Clements, B. J. (1990) "On the Decomposition and Normalization of Interindustry Linkages",
Economics Letters, 33, pp. 337-340.

Dietzenbacher, E. (1992) "The Measurement of Interindustry Linkages: Key sectors in The
Netherlands", Economic Modelling, 9, pp. 419-437.

Dietzenbacher, E.. van der Linden, J. A. and Steenge, A. E. (1993) "The Regional Extraction
Method: EC Input-Output Comparisons", Economic Systems Research, 5, pp. 180-206.

Dietzenbacher, E, (1997) "In vindication of the Ghosh model a reinterpretation as a pricemodel", Journal of regional Science, 37 (4), 1997, pp. 629-651.

Heimler, A. (1991) "Linkages and Vertical Integration in the Chinese Economy", Review of
Economics and Statistics, 73, pp. 261-267.

Hirschman, A. (1958) The strategy of economic development, New Haven: Yale University
Press.

Jones, L. P. (1976) "The Measurement of Hirschman Linkages", Quarterly Journal of Eco
nomics, 90, pp. 323-333.

Miller, R. E. and Lahr, M. L. (2001) "A taxonomy of extractions", in: M. L. Lahr and R. E.

Miller (Eds.) Regional Science Perspectives in Economic Analysis: A Festschrift in
Memory ofBenjamin H. Stevens, pp. 407-411 (Amsterdam Elsevier Science).
Morilla, C. R. and Llanes, G. (2004) "Multiplicadores domesticos SAMEA en un modelo
multisectorial ecoambiental de la economia espaiiola", mimeo.

Paelinck, J., Caevel, J de and Degueldre, J. (1965) "Analyse Quantitative de Certains

Phenomenes du Developpement Regional Polarise: Essai de Simulation Statique dTtineraires de Propagation", In: Problemes de Conversion Economique: Analyses Theoriques etEtudes Appliquees (Ed. Genin M. T. ) pp. 341-387, Bibliotheque de lTnstitut deScience Economique, Paris.

Rasmussen, P. (1956) Studies in Inter-Sectorial relations, Einar Harks, Copenhagen.
Robinson, S., Cattaneo, A. y El-Said, M. (2001) "Updating and Estimating a Social Accounting Matrix Using Cross Entropy Method", Economic Systems Research, 13 (1), pp. 47-

DETECTION OF KEY SECTORS BY USING SOCIALACCOUNTING MATRICES: AN ALTERNATIVE APPROACH

91

64.

Roland-Hoist, D. W. (1990) "Interindustry analysis with social accounting methods", Economic Systems Research, 2 (2), pp. 125-145.

Schultz, S. (1977) "Approaches to Identifying Key Sectors Empirically by Means of InputOutput Analysis", Journal of Development Studies, 14, pp. 77~96.
Strassert, G. (1968) "Zur Bestimmung Strategischer Sektoren mit Hilfe von Input-Output
Modelen", Jahrbucher fur Nationalokonomie und Statistik, 182, pp. 211-215.