Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

The Asian Economy: Trade Structure Interpreted by
Feedback Loop Analysis1
By
Michael Sonis*, Joaquim J.M. Guilhoto** and Geoffrey J.D. Hewings***

Abstract

In this paper, some new perspectives are advanced that provide a more comprehensive
view of the interactions between the economies of Asia. This analysis focuses on the potential for uncovering alternative perspectives about the role of linkages and multipliers in
input-output systems.

The analysis draws on some pioneering work by Miyazawa in theidentification of internal and external multiplier effects. Paths of direct and indirect depen

dency are revealed as well as the nature and strength of feedback loops. In addition, somepotential exists for contributions to the debate raised by Krugman (1991, 1993) on the roleof regionalism versus multilateralism.

Using these methods, it is possible to provide insights into the way in which these
economies are integrated, the strength of the integration and the potential consequences ofaction in one economy on the rest of the system. The analysis parallels some earlier workon the European economies and will provide the basis for future comparative analysis as
updated tables are produced.

1.

Introduction

Recent discussions that focused on the problems of the Uruguay Round of the General Agreement
on Tariffs and Trade [GATT] together with the emergence of strengthened and expanded free
trade areas [such as NAFTA; European Union and MERCOSUL/MERCOSUR] have createdthe need for careful analysis of the nature of internal and external dependence among nations
and, within any nation, among the constituent regions. The picture obtained from inspectionof import and export flows is only one (and often the smaller) part of the nature of dependence;

there is a need to consider the indirect effects and, in addition, the possible feedbacks that may

accrue from expansion of links between any two countries rippling through a broader set of
economies and returning to expand activity in the originating economy. However, until recently,
a dearth of data precluded the type of analysis conducted here; the development of consistentintercountry input-output tables for Europe enabled the first attempt at an understanding ofintercountry dependencies (see Sonis, Oosterhaven and Hewings, 1993). This paper will explore
similar perspectives with a set of Asian intercountry input-output tables for 1985. In a sense,

it may be considered to complement the recent contributions of Ota (1994) and Adams et al(1993) with the caveat that it is restricted to the Japan-Asia-US trade relationships.
There seems to be general agreement that the processes of economic change are often stim
ulated by a relatively small number of sectors initially even if the whole economy ends up
experiencing change. While this perspective is advanced for an individual economy, can a sim

ilar perspective be applied to a set of interacting economies, either nations or regions?

In a

Manuscript received March 13, 1995. Revised June 7, 1995.

* University of Illinois, USA and Bar Ilan University, Israel** Universidade de Sao Paulo, Brazil*** University of Illinois, USA

1The support provided by FAPESP and by REAL (University of Illinois) to Guilhoto is gratefully acknowl
edged. The comments of an anonymous referee on an earlier version helped to clarify some important points.

Trade Structure and Feedback Loop Analysis 25

companion paper (Sonis et al 1994), some alternative perspectives to this debate are offered;these perspectives are drawn from papers by Sonis et al. (1994b) and Guilhoto et al (1994)
that attempted to intervene in the debate on linkages that have continued between Cella (1984),
Guccione (1986), and Clements and Rossi (1991, 1992) on Cella's decomposition technique.
However, the major contribution of this present paper is to place these debates into a broader

context through an examination of the macro-level feedback loops that can be identified from thecountry-to-country trading patterns. This paper only draws on a small set of these perspectives(see Sonis et a/., 1994a for a more comprehensive evaluation) that adopt an hierarchy of micro-,meso- and macro-levels of economic analysis. The feedback loop analysis offers the potential for

insights into some of the issues that have been raised by Krugman (1991, 1993) in the debate
on regionalism versus multilateralism. It is felt that this perspective will help to inform us on
the nature of economic structure and, most critically, on the ways in which the transmission of

structural change penetrates the complex web of interactions that characterize an economy.
The paper is organized as follows; in the next section, a brief review of feedback loop analysis
will be provided.

The major empirical evaluation will occur in section 4; the analysis will

be presented at a very high level of aggregation essentially, one-sector analysis, to enable anappreciation of the major loops in trade interactions. The paper will conclude with an evaluationand interpretation of the findings.

2.

Closed Feedback Loops

Consider a system of n region and m sectors; assume that the transactions between the regions
can be presented by an nmxnm block matrix X, of transactions flows:

X\2

xln \

^21

^22

X2n

\ Xn\

Xn2

Xnn /

X =

(1)

where each block

represents the transaction flows from sectors in region r to those in region 5. Define:(3)
namely, the sum of flows between all sectors within each submatrix, Xrs. Hence, an aggre
gated nxn matrix may be defined as:

t = \\U\(4)

The major focus of this paper will be the identification of multi-regional feedback loops thatreveal the economic self-influence of each region.

This self-influence can be represented by achain of transactions in which the flows leave a region and "journey" through the rest of theregions before returning to the origin.

A series of aggregate transactions are specified suchthat each region is allowed precisely one transaction flow entering it and one flow leaving it.

Economically, a series of transactions, of course, represents a chain of bilateral influences which

are based on either backward or forward linkages depending on the point of view one takes.
Such a series of transactions, in which each region appears only once with one incoming flow

and one outgoing flow, may indeed be called a feedback loop because each and every region in26 Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

such a loop influences itself at the end of the loop (assuming one starts the loop with the regionat hand). A feedback loop is complete if it includes all regions.

The economic interpretation of a feedback loop is straightforward. It indicates how strongly(at each hierarchical level) each region is tied to all other regions included in that loop. By
focusing on complete loops, one can evaluate the place and position of each and every region
vis a vis all other regions. Considering only complete feedback loops is technically possible aseach non-complete feedback loop can be extended to a complete one through the addition ofloops that include the regions outside the non-complete loop. Moreover, a hierarchical analysisof the set of all complete loops is simpler than a hierarchical analysis of the set of all possible
loops. For a set of n regions the amount of all complete feedback loops is already equal to n!
A complete feedback loop is either closed or can be decomposed into a set of closed sub-loops.
If the entering flow and the leaving flow for the same region are identical, the smallest closed
sub-loop possible has been identified, i.e. the influence that a region directly exerts on itself,
the domestic self-influence.

In the case of two regions, with the transactions matrix:
X =

X li

(5)

X 22

the aggregated transactions matrix:
T =

(6)

hi

includes only two feedback loops:
in

0

0

<22

To =

0

<12

til

0

(7)

This provides the basis for the following decompositions of X and T into a sum of its feedback
loops:

in

ti2

T =

0

0

(8)

— -Li + J-2

and

X =

X li

X 12

■^21

-^22

X 12

= x1 + x2(9)With a three-region system:/ *11

x=[ x21
\ x31

X\2

^13

Xi2
X32

^23
-^33

T =

(10)

^22
^33

there are six feedback loops:

T, =

T4 =

T, =

0
0

t12

0

0

<23

0

0

tu

0

0

0

t22

0

*31

0

0

(11)

Trade Structure and Feedback Loop Analysis

27

These feedback loops generate two diiferent decompositions:andA similar structure would characterize the decompositions of X. A more complete interpre

tation of the notion of self-influence may be provided by considering the matrix, T2, presented

in stylized form with unit entries replacing the non-zero components. Thus, the following per
mutation matrix may be developed:

/ 0

0

1 \
(12)

This matrix implies the following chain, with the first region sending to the third, the third
to the second and the second back to the first.
7*1

—►

T3

r2

<—

T

I

<—

(13)

This scheme provides a translation or permutation of the series (1, 2, 3) into (3, 1, 2) andso on until the original series is replaced. This is shown in (14) below:
12

I

3

1

3

1

1

2

1

I

1

2

3

1

I

I

1

1

2

3

/ 1
0

0
1

(14)

This also implies that:

Pi =

\0 0

0 \
0

(15)

1 /

and

T| = I

\

0

0

0

0

0

t32*21*13*2l*i3*32

0

)

(16)

are diagonal matrices, where the products ^13^32^21,^21^13^32 and ^32^21^13 are the indices fromthe first, second and third columns of (14).

For the case of n regions, the situation is more complicated. It is possible to prove that forn regions, the number of decompositions is equal to:

One natural method for dealing with such a large amount of complete feedback loops is of course
the derivation of some hierarchical structure. Essentially, the proposed Hierarchical Feedback28 Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

Loop Approach attempts to extract complete feedback loops that successively account for themost "explanation" in each stage of the selection process.

The procedure continues until all transaction flows have been included. It is important tonote that the matrix form of a complete feedback loop can be presented with the help of asubmatrix Tx of flows extracted from the matrix T = \\tij\\ of all aggregated transaction flows.
Such a submatrix Tx represents a complete feedback loop if it includes in each row and in eachcolumn only one non-zero entry from the matrix T and zeros elsewhere. One can define the flow

intensity of a complete feedback loop as the sum of all transaction flows of the corresponding
submatrix Tx.

Further, if all non-zero entries of Tx are replaced by units, a so-called permutation matrix Px

is obtained. This zero-one matrix corresponds to some permutation of the sequence of numbers

l,2,...,n. Such a permutation (of regions) represents the structure of the corresponding complete
feedback loop. The submatrices Tx are referred to as quasi-permutation matrices.
It is important to note that for each permutation matrix Px there is an integer k such that

Pk is the unit matrix I. For that k, the corresponding quasi-permutation matrix Tx has theproperty that T% is a diagonal matrix, implying that the corresponding feedback loop indeed
represents the notion of self-influence.

The hierarchy of all complete feedback loops is defined as the sequence of quasi-permutation
submatrices Tx chosen according to the rank-size of their flow intensities. This means that on
the top of the hierarchy one finds the complete feedback loop with the maximal flow intensity.

The problem of the determination of the quasi-permutation submatrix with the maximal flow
intensity is mathematically equivalent to the solution of the optimal personnel assignment ofn persons (here rows) between n jobs (here columns) in such a way that one person will have
one job while profit is maximized (see Danzig, 1963). Here profit is defined by the size of thetransaction flows in matrix T.

Drawing on Sonis et al. (1993b), the procedure may be summarized in the following steps:

Step 1: For the matrix T = \\iij\\ of all the aggregate flows, find an optimal solution of
the linear programming personal assignment problem, the solution of which is equivalent to thestandard transportation problem of linear programming.

The solution determines the quasi-

permutation submatrix, Tx and the corresponding permutation matrix P\ associated with thecomplete feedback loop with maximal flow intensity.

This loops will be placed first in thehierarchy. Obviously, it would be possible to make the selection based on other criteria.

For

example, instead of the maximization of total flow, one could require that the choice of T\ bemade on the basis of max min tij, implying that the selection focuses on the feedback loops
whose weakest chain is as strong as possible.

Step 2: Replace in T the flows from T\ by arbitrary large (in absolute terms) negative
numbers, -M, and find for this new matrix T

an optimal solution of corresponding Person

nel Assignment problem. This solution gives the next complete feedback loop, represented by
the corresponding quasi-permutation sub-matrix T2, the permutation matrix P2, and the corre
sponding permutation sequence of regions.

Step 3 through n-1. Repeat Step 2 for the matrix T .

After n-1 steps, one obtains a sequence of n complete feedback loops, ordered according to
the decreasing size of their flow intensities. Moreover, this hierarchical sequence corresponds tothe sequence of quasi-permutation submatrices with the property:

(18)

30

Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

Therefore, the following nested hierarchical decomposition satisfies the rules of the Matrioshka principle:

A =Trade Structure and Feedback Loop Analysis 31

Table 1: The Asian Input-Output Table, 1985
INDON

MALAY

PHIL

SING

THAIL

1

2

3

4

5

6

1

52721.32

101.81113.46961.3547.27

291.77242.6120620.17

232.441766.99470.93144.54

3

17.76

90.13

21661.10

88.14

31.00

73.21

4

568.631457.1242.17

13935.74

480.93116.185

38.64

254.9429.56

158.4230105.53

198.726

172.60171.85225.611639.63

155.56319404.30

7205.41

187.5996.52

370.53172.71492.428160.08178.85113.52

175.75128.900.00

91813.39

1756.96286.401582.111106.246028.28CHINA

101138.35

821.02690.081323.42459.372266.39T

56878.79

25640.44

23490.86

22002.0833158.44

329015.81

TAIWAN

KOREA

JAPAN

USA
10

Total

1

361.81745.749369.144095.4068809.072

377.571045.643678.82

1571.58

29951.29

3

81.50

90.77

836.661102.05

24072.32

4

210.70195.751332.69

1632.97

19972.88

5

83.38

130.43834.10705.5832539.30
328675.11

7

9

6

0.00

0.00

5316.121589.44767603.18

304.791980.485521.5676935.19

8

106.9294001.03

2646.293612.79

101124.13

93546.145116.59

1313103.41

22540.20

1356879.72

103159.664551.1018404.88

3196351.30

3229165.57

T75530.86

106181.84

1357502.59

3238722.87

5268124.58

Source: Institute of Developing Economies (1992).

4.

The Asian International Input-output Tables, 1985 and Feedback
Loop Analysis

The data used in this analysis were derived from a set of international input-output tables
prepared by the Institute of Developing Economies (1992). The tables provide information not
only on intra-country flows but flows between ten countries. These flows are sector specific, inthat the flow is shown from a sector in one country to a sector in another country. All data arereported in the producers' prices of the producing country; these prices were then converted to
US dollars (for details on the construction of the tables, refer to Ota, 1994). Since the tables
were constructed as key tools in the analysis of interdependency, the use to which they are being

put in this paper is appropriate. In the next section, some of the major findings at the one-sector

and three-sector levels of aggregation will be reported. For the three-sector level of aggregation,

the individual sectors were grouped into Primary (P), Manufacturing (M) and Services (S).
At the first level of analysis, all transactions were aggregated into one sector to reveal themacro-level structure of the feedback loops.

Table 1 shows the structure of the flows; thedominance of the intra-country flows is readily apparent. However, without a detailed inspectionof the table, it would be difficult to understand the dominant inter-country linkages. This is donein Table 2. Note that the inter-country transactions account for only 2.6% of total transactions,although for some countries, the percentages are often much higher.

32

Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

Table 2: Decomposition of One-Sector Transaction Flows into Feedback Loops% of Inter-

Domestic

Inter-country

Transactions

Transactions

country

Cumulative

97.30%

2.60%

Transactions%

I (JAP USA) (CHI SIN MAL KOR IND TAI) (PHI THA)

33.3

33.3

II (JAP CHI PHI TAI USA KOR THA MAL SIN IND)

20.6

53.9

III (JAP KOR MAL PHI IND USA TAI SIN THA CHI)

13.8

67.7

IV (JAP TAI PHI MAL) (USA CHI THA IND SIN KOR)

10.5

78.2

V (JAP MAL THA TAI KOR) (USA SIN) (CHI IND PHI)

6.2

84.4

VI (JAP IND THA SIN CHI USA MAL TAI) (KOR PHI)

5.1

89.5

VII (JAP SIN PHI) (USA IND CHI MAL) (KOR TAI THA)

4.3

93.8

VIII (JAP THA USA PHI SIN) (CHI TAI MAL IND KOR)

3.5

97.3

IX (JAP PHI USA THA) (CHI KOR SIN TAI IND MAL)

2.7

100

Nine feedback loops are presented in Table 2; these are arranged hierarchically to enable

an appreciation of their dominance in the trading system.

Not surprisingly, the Japan-USA

sub-loop dominates accounting for over 88% of the first feedback loop.

This total feedback

loop accounts for one-third of the inter-country transactions. The second most important loop

involves Japan and China (53.9%) and Taiwan and the USA (35.3%) together with the remaining
countries. Taken together, the first two feedback loops account for over 53% of the inter-country
transactions. Thereafter, a slow decline in the importance of the transactions may be observedwith the dominant position of Japan revealed very clearly. In the fourth feedback loop, there

are two interesting sub-loops, one centered on Japan and one centered on the USA.
However, an inspection of the loops in Table 3 does not lead to a straightforward appreciationof the nature of the feedback loops that have been identified. Attention is now drawn to a set offive figures that present these feedback loops graphically. Figure 1 shows the decomposition of
the aggregate-level feedback loops; the spatial nature of the loop is readily apparent. Note alsothat the sub-loops are rather simple. Figure 2 presents the second and third loops; the patternof interaction is now decidedly more complex with the loops involving a larger number of theindividual countries.

Trade Structure and Feedback Loop Analysis 33

Table 3: Hierarchical Decomposition of the First Aggregate Feedback Loopfrom Table 2 into 3 Sectoral/lnter-country Feedback Loops(JAP USA):I-(MjapSusaSjapPusa){PjapMusa)(54.8%)

2.(PjapPusaSjapSUSa )(MjapMusa)(36.9%)(99.2%)(0.8%)

HPjapSusaMjapPusa)(SjapMusa)(65.9%)(34.1%)(99.1%)(0.9%)(8.3%)(CHI SIN MAL KOR IND TAI):(MchiMsinMmalMkorMindMtai)•■< SS^L._^....

^.._«

^..,)

(7.7%);<^%){{PchiSsinPmalPkorPindPtaiSchiMsinSmalMkorSindMtai)(95.6%)(MchiPsinMmalSkorMindStai)(5.4%)
3.

(5.5%)(PHI THA):

1.

(MphiPtha)(PphiSthaSphiMTha)(85.2%)

2.

{PphiMthaMphiStha){SphiPtha)(63.6%)

3.

(36.0%)(36.4%)(MphiMThaSphiStha)(PphiPtha)(99.9%)(44.3%)(36.4%)( 19.7%)(0.1%)

Note: The percentages should be interpreted as follows. For the first entry (JAP USA), the first loop is com
prised of three sets of sub-loops whose percentages account for 54.8%, 36.9% and 8.3% of the total (JAP USA)

interaction. This loop can be broken down into two further sub-loops comprising 99.1% and 0.9% of the total forthis loop. The third loop (PHI THA) has three sub-loops; the first accounts for 44.3% of the total interaction
between these two countries and can be broken down into two further sub-loops accounting for 85.2% and 36.4%
respectively.

Trade Structure and Feedback Loop Analysis

II

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Figure 4: Second Inter/lntrasectoral Transactions Loop within the First Aggregate Feedback Loop

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38 Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

An examination of the sectoral interactions reveals different patterns for each sub-loop. In thecase of the Japan-USA exchange, all sectors are involved with the exception of manufacturingin the USA for the first of the transaction sets.

When this sector does become involved, it

accounts for a very small percentage of the flows. In contracts, over 92% of the second sub-loop
flows between the remaining countries involves linkages between the manufacturing sectors; theother smaller sub-loop charts a more complex pattern of sectoral and country interdependency

but it encompasses a relatively small set of flows. The exchanges between the Philippines andThailand provides a pattern that is not dissimilar to the one exhibited for Japan-USA.

The second of the major sub-loops is shown in Figure 4. The complexity of the transactions
begins to assert itself with rather extensive loops embracing in types of sectors in the ChinaSingapore-Malaysia-Korea-Indonesia-Taiwan loop. This pattern is reinforced in Figure 5 where
the third of the major sub-loops is portrayed. In this case, the loop involves all sectors in all of
the six countries. However, it accounts for only 5.5% of this whole loop which itself only 11%of the interregional flows.

5.

Conclusions

One of the major problems with an evaluation of international trade has been the ability toprobe into the nature and strength of the interdependencies so revealed. Feedback loop analysis
is offered as one technique that may be able to highlight these complex patterns of flows by
focusing on the nature of the path of dependencies. How can this analysis be linked with someof the recent debates that have centered on some findings, admittedly promulgated under rather
severe assumptions, by Krugman? In making some preliminary evaluation, attention will also

be drawn to some earlier findings reported for Europe by Sonis et al (1993b). In the Europeancase, over 90% of the flows were accounted for by intra-country transactions in 1980; in contrast,
the case presented here revealed that this category accounted for close to 97% of the flows. In theEuropean case, it was noted that domestic transactions had, in fact, decreased over time, whileinter-country flows had increased. What was not clear was the degree to which this represented
trade creation rather than trade diversion (see Krugman, 1991). In the Asian case, the necessary
time series comparative analysis has not been completed, thus an answer to the question of trade
diversion will have to await further study.

In the European application, the first major sub-loop accounted for 40% of the overall inter country flows; in Asia, the first sub-loop accounted for 33%. However, with the emergenceof the expanded European Union, the dominance of a core (German, France, the Netherlands

and Belgium) began to dissolve over the period 1970 through 1980. The dominant position ofJapan-USA trade in the first sub-loop (88% of the flows) raises the question as to whether thishegemonic position will be eroded over time. Here is where Krugman's ideas become important;in his analysis, it is assumed, initially, that each country operates in a noncollusive manner in or

der to maximize welfare. Given his findings that overall welfare decreases to a 'pessimum'2 when

the number of world trading blocs is three, thereafter to rise again, how can the results of the

feedback loop analysis be incorporated in further consideration of this finding? While Japan's

trade with the USA has captured a great deal of attention, Japan also plays an important rolein the other feedback loops (see Table 2).
Given the findings of the Asian analysis, the progress towards greater integration in Europe

and Krugman's theoretical findings, can one draw any conclusions from the feedback loop anal
ysis? It is ironic that the world is moving towards the three great trading blocs (Europe, North
America and Asia), the number that coincides with Krugman's (1991) finding of a 'pessimum' inworld welfare. However, the strength of the Japan-USA trade suggests that there may be strong
2'Pessimum' is Krugman's term and generally accepted now.

Trade Structure and Feedback Loop Analysis 39

interbloc trading relationships that may undermine the apparent appearance of tendencies towards greater internal-to-the bloc-trading relationships. Furthermore, within countries, little
analysis has been conducted to see whether there are any pronounced tendencies in the natureand strength of interregional trading patterns. In addition, questions need to be raised about
the trade diversion argument in the context of a spatial trading hierarchy that encompasses

region, nation and multinational blocs.

A more extensive analysis of the trading relationships conducted by Lee and Roland-Hoist(1994) in a computable general equilibrium framework suggested some strong asymmetries inregional demand and supply linkages under more liberal trading relationships, but with overall

gains to each country and the region. However, they note that:

Whether these results suggest the existence of more complex self-interested strategies,
including patterns of optimal tariff discrimination, is an open question. While they dosuggest the existence of a large space of co-operative and non-co-operative bargaining
solutions, it should be emphasized that considerable gains can be realized for most of
the region's population by applying the simple rule of more liberal, undistorted trade.

Looking ahead to the publication of tables for 1995, what might be the expectations for the
trading feedback loops? Are the patterns evident in 1985 likely to evolve and, if so, in whatfashion? Or are the relationships likely to strengthen but not change in terms of dyadic interaction? Will the adoption of GATT/WTO agreements significantly change these relationships?
One of the pieces missing in Krugman's analysis is the notion of trading power; not all nations
are price-takers and many exhibit evidence of monopolistic or oligopolistic tendencies in certain
commodities. Using some notions from optimal portfolio diversification theory, one might ask
also whether nations with more diversified trading relationships are likely to be better off (inwelfare terms) than those with more limited and dominating trading relationships? Lee andRoland-Hoist (1994) suggest that even the smaller trading nations would benefit from liberalized trade but the sector by sector results suggest that the imposition of non tariff barriers (suchas quotas) on imported textile products into the US or Japan could seriously undermine thegains from trade for textile exporters such as the Philippines or Korea.
However, the evidence provided by the feedback loop analysis and the Lee and Roland-

Hoist analysis does not offer an alternative path between the status quo and complete tradeliberalization. With the addition of further time series data, these questions can be explored. In
particular, Sonis and Hewings (1993) have provided a new interpretation of Miyazawa's (1966)
notion of internal and external multiplier that may have value for trade analysis. There remain
many issues related to the notions of key sectors within an international context and the potential
for an application of the field of influence and decomposition techniques (see Sonis et al 1993c,
Sonis and Hewings, 1994) to explore the nature of change. The underlying premise would seemto reinforce the nation that trade has to be viewed both spatially and hierarchically.

40 Journal of Applied Input-Output Analysis, Vol.2, No.2, 1995

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