Typhoon Over

Trade Typhoon Over Japan: ^Turbulence Metaphor and Spatial Production Cycles Feedback Loops ^{of the} Japanese Economy,

1980-85-90

M. SONIS

a’b’*,

G.J.D.HEWINGS andY. OKUYAMA

aRegionalEconomicsApplications Laboratory, UniversityofIllinois, Urbana-Champaign, USA;bDepartmentof^Geography,Bar-Ilan University, Ramat-GanT2100, Israel;CDepartmentofPlanning, State Universityof^NewYork,Buffalo, NY, USA

(Revised 14 April2001)

Thispaperdeals with the turbulence similitude betweenwhirlpoolstructure ofatmospheredisturbances and the spatial production cycles. Such an analogy leads to the production cycles feedback loops superposition analysisof trade feedbacksreflectingthe economicphenomenaof horizontalandvertical tradespecifications.Moreover,the visualization of thisprocessis achieved withthehelpofcoloringthe differentpermutationmatricespresentingthehierarchy of productioncyclesfeedbackloops. Inthis mannerthequalitative presentationofJapaninter-regional andinter-industry trade, 1980-85-90,is visualized andinterpreted.

Keywords: Spatial production cycles; Feedbackloops;"Matrioshka"imbedding principle;Turbulence analogy;Multi-regionaleconmicanalysis

INTRODUCTION

The use of similarity between physical and economic phenomena has a long tradition in economic analysis.

Such use started from application in economics of differential and integral ^calculus and methods of linear algebraandvectoranalysis,which came into existencefor thedescriptionofphysical phenomena.Thereasonforuse ofphysical analogies is the possibility of utilization of strong well-established technique of mathematical anal- ysis. Thejustificationofthis use can be achievedonlyif the meaningof results ofanalysisiseconomically sound without any reference to physical analogy. Thus, such justification^canbe achieved if thereis atransferofideas from the deepnessofunderstanding^ofphysical phenom- enon to the deepness of understanding of economic phenomenon. The purpose ^ofthis paper is to carry ^out such a transfer of ideas from the deepness of under- standing ^of physical phenomenon of turbulence to the deepness of understanding of economic phenomenon of spatialproductioncycles.

Inthehydrodynamicturbulence aflow ofenergyfrom largeto small scales isone of the main characteristics of fully developed homogeneous isotropic turbulence in three spatial dimensions.

Energy

is pumping into the

system at large scales, transferred to smaller scales through ^a hierarchy of eddies of decreasing sizes, and dissipates ^at the smallest scale. This cascade of kinetic energy generatesthescalingbehavior ofeddies(Richard- son, 1922).

The turbulence analogy means that the big inter- regional production cycles^feedbackloopsof intermediate input ^{flows are} decomposed into feedback loops of intermediateinput^flowsbetween economic activities and furtherdecomposedintotheloopsof flowsonthe scale of individual industries.

Moreover,

the scaling of eddies is analogoustothe hierarchy of economicsubsystemswhich is presented with the help of so-called "Matrioshka"

(Russian doll within doll, within doll...) embedding principle

(cf

^{Sonis and}Hewings, 1990).

Thejustificationof consideration ofa setofproduction cycles feedback loops of inter-regional trade flows is basedon an important phenomenon^ofverticalspecializ- ation which describes the use of imported inputs for producing goods ^{that are} exported (Bruelhart and Hine,

1999).

Balassa (1967, p. 97), coined the term of vertical specialization.

In

the paperby Hummels etal. (1998, p.

81),thefollowingdefinition of verticalspecializationwas introducedand discussed:"(1)^agoodmustbeproducedin

*Corresponding author. Address:DepartmentofGeography,Bar-IlanUniversity, Ramat-Gan52100, Israel; E-mail: [email protected].

ISSN 1026-0226 ^(C)2002Taylor &FrancisLtd

multiplesequential stages,(2)twoor more countriesmust specialize inproducingsome, butnotall, stages,and(3)at least one stage must cross an international border more than once Thus,countrieslinksequentiallytoproduce a finalgood."

The analysis of the hierarchy of spatial production cycles feedback loops ^of inter-industry flows has been elaborated in the series ofpapers by SonisandHewings (Sonisetal. 1993, 1995a,b,

1997).

There are two other main economic reasons for choosing to analyze trade structure using ^feedbackloop analysis.^First,mostanalyticalwork on trade has focused onexplanation offlows,with littleattentionbeing^devoted to the spatial geographic structure of these flows.

For

example,issuesof concentration of flows and the role of localization ofparticularindustries have been shownby

Krugman

(1991,

1993)

tobe of considerable importance.

Krugman (1993)

notes that:

"...

international specializ- ationand tradecannotbeexplained simply byanappealto comparative advantage, that is, loosely speaking, by countries trading in order to take advantage of their differences."

While

Krugman’s

ideashavebeendeveloped explicitly inthe contextoftrading relationshipsbetween economies at one spatial level, there isnot areasonto suggestthat manyof the sameforces that condition international trade relationships will also influence those between regions within a country. What has yet to be explored is the identification of aspatial hierarchyoftrade flows anditis herethat feedbackloop analysisprovides thepotentialfor uncovering the nature, strength and spatial linkages of trade flows.

We

willexplore thehierarchy of trade flows not at only one spatial ^level (between regions within a country),but also withinhierarchyof economic activities and their sub-divisions.

The secondreasonisthatempiricalmodels of trade tend to be either very macro in nature

(such

as computable general equilibrium

models)

^or they operate at a very micro, sector-by-sector level. Feedback loop analysis is offered as a more meso-level approach; in essence, it shares some of the goals of structural path analysis (Defourny and Thorbecke,

1984)

in that both methods attempttorevealthe multitude ofpathsorlinkageswithin aneconomy.Whereas structuralpath analysisoperatesata very micro-level (individual paths ^between sectors), it does offer theopportunitytoprovidesome formofranking orhierarchyfor thesepaths.

In

addition, themethodologies share thepropertythat eachpathin astructuralpathis part of aglobal production cyclesfeedbackloopthat includes the transactionsbetween allsectors.Thefeedback loop analysis identifiesthemostprominent productioncycle loops, first for flows foranaggregationofactivityinto just oneregion andthen for a three-sectoractivity aggregation. Further,the analysis will continue with moredetailed (and thus more complex)feedbackloopsfor anumber of sub-activities

(cf

Sonisetal.,

1993).

Theturbulence similitude leadstotheapplication^{of the} mathematical tool of the block-permutation matrices,

naturally presenting the spatial economictrade feedback loops.

The application of the perturbation matrices for the analysisofflow matrices is well known(see,forexample, Gower, 1977; Sonis, 1980; Slater,

1981).

Part of them based on the transfer from flow matrix to double- stochastic matrix (Jurcat and

Ryser,

1967; Feinberg, 1970), which allows the use of the well-known classical Birkhof-vonNeumanntheorem about thedecomposition ofadouble-stochastic matrix intothe convex combination of the permutation matrices (Christofides, 1975, p.

386)

and, conceptually treats the flow as the stream of homogeneous unpressable liquid with the continuity property, which means the preservation ^{of the} flow volume. Furthermore, the transfer to double-stochastic matrixhas aquestionableeconomicmeaning.

The method ofspatial productioncyclesfeedbackloop analysisused in thispaper givesthepossibilitytoavoid the numerical manipulations with flows and allows the consideration ofthe non-homogeneous flows of different streams(goods)and theuseof turbulenceanalogy.

In

this papertheeconomicflows of intermediategoodsdevoidall mechanical properties ofphysical^{flows: the}velocityand continuity of flows has no economic meaning; only the originand destination of flow and theirintensity^aretaken into consideration. Nevertheless, such "week" assump- tions allows to consider the analog of the Birkhof-von

Neumann

theorem: each economic flow matrix can be presentedas a sumof permutation matrices,presentingthe spatial production cycles feedbackloops.

THE MULTI-REGIONAL SPATIAL PRODUCTION CYCLES FEEDBACK LOOPS AND BLOCK- PERMUTATION MATRICES

Consider a multi-regional multi-countries inter-industry system described with thehelpof^asquareblock-matrix, F, ofinter-regional inputsof thefollowingform:

F F2 Fn

Fz F22

^F2,

F

(1)

Fnl Fn2 Fnn

It is assumed that there are n regions in which there exist rndivisionsoftheeconomy, organizedintoactivities and there isthe subdivision of activities in the different sub-categories.The central point of thespatial production cyclesfeedbackloops decomposition analysisistheuseof spatial/functional feedback loops represented by the block-permutation matrices.

By

definition, a block- permutation matrix includes in each block-row and block-columnonly one non-zeroblock.

Within athree-region system:

F F12 F13 F21 F22 F23 F31 F32 F33

thereare sixblock-permutationsub-matrices"

F()(2)(3)

F

^{0 0}

0

F22

⁰

0 0

F33

F(132)

0 0

F13

F21

^{0 0}

0

F32

⁰

F(123)

0

F12

⁰

0 0

F23

F31

^{0 0}

F()(23)

Fll

^{0 0}

0 0

F13

0

F32

⁰

0

F12

⁰

F(12)(3) F21

^{0 0}

0 0

F33

F(13)(2)

0 0

F13

0

F22

⁰

F31

^{0 0}

and

(2)

(3)

(4)

through the adoption of a hierarchical stepwise approach; the procedure operates at successive levels in the system, but the approach ateach stage is similar.

This top-down decomposition may be considered analogously to an exfoliationprocess in the removal of the layers of an onion or, using the turbulence analogy to the construction of hierarchy of feedback loops (whirlpools) ^ordered with the help of aggregated cumulative flows within the blocks belonging ^{to the} loop. The productioncycles feedbackloops onthe inner hierarchical level of economic activities should be placesinto the loops of the higher levels in the form of the Matrioshka doll in which successively smaller dolls ofexactly the sameshapeandstylearenested within the larger dolls.

Hence,

the Matrioshka approach examines the intra- and inter-regional transactions interms of the hierarchical structure of feedback effects drawing upon the superposition principle conceptual ^framework (see Sonis,

1982).

The superposition principle considers the economic system ^{as a} decentralized system ^{that is} comprised of a set of subsystems acting according to different and often conflicting and non-commensurable objectives. These objectives may be presented in the form of extreme tendencies or trends; the hierarchical viewpoint enables the analyst to extract the tendencies from themost tothe leastimportant.

In

this fashion, the procedureisnotunlikethatused inprincipal component analysis.

In

thenextsection, themethodologyforextracting^the system^ofspatial productioncyclesfeedbackloopswillbe presented togetherwith the additivedecompositionof the matrix of directinputs. Inthis fashion, it will bepossible toproduce^asuperpositionofspatial productioncyclesfor themulti-regionaleconomy.

SUPERPOSITION OF SPATIAL PRODUCTION CYCLES FEEDBACK LOOPS

F F(1)(2)(3)

--1-

F(132)

^q-

F(123)

F(1)(23) q--F(12)(3) q-F(13)(2). (5) Here

the

block-permutation

^matrices

F(132),F(123

represent the different three-lateral spatial production cycles, the block-diagonal matrix

F(1(2O)

represent the

"circulation"of intermediate flows within thesameregion and the block-permutations

F(1)(23),F(13)(2),F(12)(3)

^rep-

resent the bilateral trade between two regions and the

"circulation" within the remainedregion.

In

thecaseofnregions,there existsn! differentblock- permutationmatrices and it ispossible toprove that the number ofpossible additive decompositions ^{of the}type

(5)

isequalto(n

1)!(n 2)!...

2!.

Thus, theproblem erases tochoose from this verybig set ofpossible decompositions ^the decompositions with thesound economicmeaning.Thisproblemcanbesolved

The major element ofthe feedbackloop approachisthe identification of series of (aggregate) block-permutation matrices such that eachregion is allowed precisely ^one aggregated block-flow entering ^it and one block-flow leavingit.

A

series ofblock-flowseconomicallyof course represents achainof bilateral influences which are based on eitherbackward of forwardlinkages depending^onthe pointof view one takes.

Such a series of block flows, in which each region appearsonly^oncewithoneincomingblock-flow and one outgoing block-flow, may indeed be called a feedback loop ^because each and every region in such loop influences itself at the end of the loop (assuming one startstheloopwiththeregionat

hand). A

feedbackloopis completeif it includes allregions.

The economicinterpretationofafeedbackloopisthat eachfeedbackloop representsthespatial productioncycle that indicates how strongly (at each hierarchical level) each region is tied economically to all other regions

included intothatloop.

In

the analysis,wewillonlylook atcomplete loops.

By

focusing^oncomplete loops,one can evaluate theplace andposition ofeach andevery region vis-t-vis all other regions.

Considering only complete feedback loops is techni- cally possibleas eachnon-completefeedbackloopcanbe extendedtoacompleteonethroughthe additionofloops including^the regions^outside thenon-complete loop.

A

productioncycle, represented byacompletefeedback loop is eitherclosed orcanbe decomposedinto a setof closedsub-loops. Iftheenteringflow and theleavingflow for the same region are identical, we have the smallest production cycle possible, i.e. the influence thata region directlyexerts onitself; this is the domestic self-influence.

One natural method for dealing with such a large amount of complete feedback loops is of course the derivation ofsome hierarchical structure. Essentially,^the hierarchical feedback loop approach attempts to extract completefeedbackloopsthatsuccessivelyaccountfor the most"explanation"in each stage of the selectionprocess.

The procedure continues until all transaction flows have been included. It is important to note that each block matrixFof thetype

(1)

canbereplaced bythe numerical matrix

TF

^{whosecomponentsarethesum}of all economic flows in thecorrespondingblock--theaggregatedblock- flows. Such a sub-matrix

TF

represents ^a complete feedback loop if it includes in each row and in each column only one non-zero entry from the matrix

F

and zeros elsewhere. One can define the flow intensity ^{of a} complete feedback loop as the sum of all flows of the correspondingsub-matrix

TF.

If all non-zeroentries of

TF

^arereplaced byunits, the result isaso-called permutationmatrixP_v.Thiszero-one matrixcorrespondsto somepermutationof the sequence of numbers 1, 2,...,n. Such a permutation (of regions) represents ^the structure of the corresponding production cycle complete feedback loop. The corresponding ^sub- matrices

TF

^{arereferredtoas}quasi-permutationmatrices.

Itisimportant^tonote that for eachpermutation^matrix P_Fthere is anintegerk such that

PF

^isthe unit matrixI.

For

thatk,thecorresponding quasi-permutation^matrix

Tv

has thepropertythat

TF

^{isadiagonalmatrix,implyingthat}

the corresponding feedback loop indeed represents the notionof

self-influence.

Thehierarchyof allcompletefeedbackloopsis defined as the sequence of quasi-permutation sub-matrices

Tv

chosenaccordingtothe rank-size of theirflow intensities.

Thismeans that on thetop^ofthehierarchy,^onefindsthe production cycle complete feedback loop with the maximalflow intensity.

The problem of the determination of the quasi- permutation sub-matrix with the maximal flow intensity ismathematically equivalenttothe solutionof the optimal personnelassignment ofnpersons(here rows)betweenn jobs (here columns) in such a way that one person will have one job while profit is maximized (Dantzig, 1963;

Sonisetal.,

1993).

Here profitis definedbythe sizeof the flows inmatrix

TF.

THE APPROXIMATIVE PROCEDURE FOR THE DERIVATION OF PRODUCTION CYCLES FEEDBACK LOOPS

The following ^crude approximative procedure for the derivationofproduction cycles^canbeproposed:first ofall inthe matrix

TF

^ofall intermediate flowswewillchose the biggestflow. This flow will define the firstcomponentof productioncycle. Second,we willexclude from matrix

TF

the row and column including this component. In the remaining matrix we will chose the ^next biggest component of the production cycle, etc. After n- 1 suchstepsthefeedbackloop usuallywill be identified.

Unfortunately,thissimpleprocedurenotalways giving the closed loop, because there are cases when on some stepitwillbe impossibletofind thecomponentfor choice.

In

this case it is necessary to apply the Beckmann-

Koopmans

algorithm, which usually helps to find the second best component.Itispossibletoguessthissecond bestcomponentinmanycases.

Aftern 1 steps,^oneobtainsasequenceofncomplete feedbackloops, orderedaccording to thedecreasing size of their flow intensities.

Moreover,

this hierarchical sequence corresponds to the sequence ^of quasi-permu- tation sub-matrices with the property:

T TF ⁺ TF2

^{at- at-}

TFn ⁽⁶⁾

This decomposition, ^{in turn,} generates ^the decompo- sitionof the matrixFofintermediateflows intoasumof block-permutationmatricesF1,

F2 ^Fn,

corresponding totheorderedsetof allfeedbackloops:

F=FI+F2+ +Fn

⁽⁷⁾

Forthepurposesof visualizationitispossibleto convert the matrix

F

of intermediate flows into colored map by coloring ^eachblock-permutation matrix

F

into different color in such a way that the rank-size hierarchy of productioncycle feedbackloops, corresponding to rank- size sequence of their flow intensities, will be colored accordingtothe sequenceof colors in a rainbow.

THE MATRIOSHKA

IMBEDDING

PRINCIPLE FOR THE NESTED HIERARCHY OF FEEDBACK LOOPS

Itisnecessaryandpossible tocombinetheinter-regional and inter-activity interdependencies. To this aim, the aggregatedtableneedstobereplaced bythe detailedtable describing the interplay between the inter-activity and internationalinterdependencies. Further,it is importantto stress that the flexible form of the production feedback loop analysis employed in this analysis allows an easy extension to the spatio-sectional level.

In

^{such an} extension, the analysiswill relateto activitiesper region.

Thus, thehierarchyof the feedbackloops will reflect the

TABLE The hierarchy ofJapanproductioncyclesfeedbackloops,1990

Hokkaido Tohoku Kanto Chubu Kinki Chugoku Shikoku Kyushu Okinawa

Total intra-regional flow

FeedbackDoop: (Kanto,Chubu, Kinki) (Hokkaido.Tohoku) Chugoku,Kyushu) (Shikoku, Okinawa) FeedbackLoop;(Kanto,Khaki,Chubu) Hokkaido. Okinawa) (Chugoku, Shikoku) Tohoku,Kshu) FeedbackLoop:(Kanto,Tohoku) (Kinki, Chugoku) (Chubu. Kyushu, Okinawa) (Hokkaido, Shikoku) FeedbackLoop; (Kanto,Kyushu)(Khaki, Shikoku) (Chubu.Chugoku,Hokkaido) Tohoku,Okinawa) FeedbackLoop; (Kanto.Chugoku) (Kinki,Okinawa,Kyushu,Hokkaido)(Chubu,Tohoku,Shikoku) FeedbackLoop:(Kanto,Hokkaido) (Kinki, Kyushu) (Chubu,Shikoku,Tohoku) (Chugoku,Okinawa) FeedbackLoop:(Kanto,Okinawa, Kinki,Tohoku,Chugoku<Chubu, Hokkaido,Kyushu, Shikoku) FeedbackLoop: (Kanto,Shikoku,Kyushu,Chubu,Okhaawa) Kinki, Hokkaido,Chugoku, Tohoku)

Totalinter-regionalflow Tradeflows

!304,003,099

27’849’9211 ^24133%

24,767,206 21.63%

18,721,586 16.35%

12,496,993; 10.92%

9,924,655 8.67%

9,453,439 8.26%

5,956,426 5.20%

5,315,626 4.64%

114,485,852 !.00.00^% 418,488,95.!.

inter-activity interdependencies intertwined spatially, enabling ^{one to} distinguish ^the spatial extent of multi- regionalindustrialcomplexes.

Astructureof nested feedbackloophierarchiescould be extracted for the general case of ann-region/m-activities input-outputsystem. Of course, the Matrioshkaprincipleis applicabletothedisaggregationof regionsintosub-regions and further successive spatial and activitiesdisaggregation.

DATA

The data used in this analysis ^were derived from publications of Ministry of International Trade and Industry ^of

Japan,

^1980-1995.

First of all these data were aggregated on the geographical level of nine big economic regions:

Hokkaido, Tohoku,

Kanto,

Chubu, Kinki, Chugoku, Shikoku, Kyushu and Okinawa. Further, the level of three main economic activities was considered: Primary (P) (agriculture), Manufacturing (M)and Services (S). In turn, the Primary, Manufacturing and Services activities were sub-divided into following groups: Primary: P (agriculturalactivities),p (non-agricultural); Manufactur- ing: M(non-durable goods),m(durable goods); Services:

S (Business services)ands(personal services).

VERTICAL

SPECIALIZATION

OF

THE JAPANESE TRADE,

1980-85-90

The analysis ^ofthe vertical specialization of the trade is naturally placedonthree hierarchical levels of the spatial

economy: ^Firstlevelisthegeographical^levelof different economic regions (countries); ^Secondlevelisthe spatial macro-economic level of inter-regional Primary (Agri- culture), Secondary (Manufacturing) and Tertiary (Ser- vices)economic activities; andthirdlevel of inter-regional intra-activities, presenting the overall trade between industries belonging ^to different economic activities. In thispaper, ^weconsiderthe following sub-division of the Primary, Manufacturing and Services activities in the following groups: Primary: P (agricultural activities), p (non-agricultural); Manufacturing: M (non-durable goods),m(durable goods);Services: S (Business services) ands(personal services).These threehierarchicallevel of loopsareconnected with thehelpof Matrioshkaprinciple:

thespatialfeedbackloops decomposedintointer-regional activities loops, which, in turn are decomposed into the inter-regional sub-inter-activities feedbackloops. Oneach hierarchical level within this hierarchicalMatrioshka the hierarchy of feedback loops introduced on the base of overall intensity (sum) of the trade flowing through the loops. Thishierarchical structure oftrade feedbackloops represent the turbulence similitude described and explainedinintroduction.

Hierarchy of Spatial ProductionCyclesInter-regional Feedback

Loops

The application of linear programming personnel assignment algorithm ^to the tables of inter-regional tradein

Japan,

1990ispresentedwiththehelpof colored TableI.

Thehierarchy^{of the}spatial^feedbackloopsispresented bythe sequenceof colors of thelight spectruminsucha

TABLE II Qualitative description oftwobiggestspatial production cyclesfeedbackloops, 1980-85-90

8o

Kani

N

Chu

N

Shi Kyu

0^u

85

HokTohKanChuKin ChuShi KyuOki

Toh

Kin

Shi N

Oki

9O

HokTohKanChu KinChu Shi Kyu^Oki

Chu

N

Chu

N

Shi Kyu

Oki

N

way ^thattrade flows in each identified feedback loop is colored in the same color. Comparing the results of analysis of1990-yeardatawiththedata for 1980-1985it is possibleto seethat thehierarchy of spatial production cyclesfor all 3 yearsisverysimilarand the intensities of feedbackloopsare diminishedin thesamerate.Especially important the similarity of two first biggest feedback loops: each of them in each time period, 1980-85-90,

includetheveryintensivetriadof three central economic regions,

Kanto,

Chubu and Kinki, supplemented by bilateral dyads of feedback between other regions.

Moreover, the first and second inter-regional loops are almost symmetrical, andthissymmetry^iscompleteinthe period 1990. (see^Table II).

The meaning of thisgrowingspatialsymmetryisin that there is a tendency towards the intensive bilateral trade TABLEIII Qualitative characterization of the vertical specialization feedbackloopsforthe triad(Kanto,Chubu, Kinki) from thefirstinter-regional, inter-activitiesfeedbackloop,1990

Kanto Chubu Kinki

First inter-activities feedback loop

Second inter-activities feedback loop

Third inter-activities feedback loop

TABLEIV Total inter-regional,inter-activitiesand sub-activities feedbackloopsstructurefor the triad(Kanto,Chubu, Kinki), 1990

Firstinter-activities feedback

loop

sub-activitiesfeedback

loop

.2sub-activitiesfeedback loop

Second inter-activities feedback

loop

sub-activities

feedback

loop 2

sub-activitiesfeedback loop

[!i

^Third inter-activitiesfeedback

loop

1

sub-activitiesfeedback loop sub-activitiesfeedbackloop

P P P P

M M w M

m ^m

S S iS

relationships ^between regions. In the midst of this bilaterally ^connected production cycles the triads (Kanto, Chubu, Kinki) and (Kanto, Kinki, Chubu) are emerging. Theprominence of thesetwo triads is already recently stressed in the literature. Ihara (1999, p. 104), concludes "about 66.1% of the total

Japanese

population arefound in the

Kanto,

Kinki and Chubu regions, and the samethreeregions’ product^{amount to} 72.9% of thetotal value of nationalproducts.

In

other words, these regions have alreadyformedamegalopolisin

Japan."

Moreover,

Ihara noted the essential difference between the economic intensity of flows in the triads (Kanto, Chubu, Kinki)and(Kanto,Kinki,Chubu):"...the indirect input-inducing effect derived from Chubu to Kinki via

Kanto,

turnedouttoberelativelysmaller than thatderived fromKantotoKinki via Chubu..."

Further, in the special research devoted^toevaluationof the role of the Kanto region in the growth of

Japanese

Regional economies Akita (1999) provided ^an extended growth-factor decomposition method based on a three- region inter-regionalsystem.

Table III represents the qualitative characterization of vertical specialization of these three regions included in

the first spatial production cycle ^feedback loop. The functional economic content of this feedback loop is presentedin Table IV.

Wehaveahierarchyof three inter-activitiesproduction cycle feedback loops each of it including two sub- activities loops. Within the first inter-activities feedback loop the most prominent is: (1) sub-activities feedback loop which include the trade flows not abandoning the sub-activity; (2) sub-activityloopwhich flowing between sub-activities within the activity. The second and third inter-activities loops present the more complicated flow structurebetween the sub-activities.

The fine structure of production cycles of the inter- regional economic activities and sub-activities feedback loopscanbe extracted from the TableV presenting these loopsinmyriadof details.

THE USEFULNESS

OF

TURBULENCE ANALOGY

IN THE ANALYSIS OF INTER-REGIoNAL TRADE

It is important to note that the consideration of the production cycle ^feedbackloops inthe trade theory is a

TABLE V Hierarchy of inter-regional, activities,inter-activitiesspatial productioncycles,1990

;nogoKn

ILLKOKU.

Kyusnu

relatively new substantialeventconnectedto the detailed analysis of vertical specialization of trade flows. Thus, the turbulence analogy ^is connected with an essential phenomenonintradetheory.

Further,thisanalogyleadstothe decomposition of the globaltrade into spatial productioncycle feedbackloops whose structural role is similar to the role of individual whirlpools inthe turbulencetheory. Thus, the analytical technique of the permutation matrices and of the decomposition of flow into feedbackloopscanbe utilized in trade. Moreover, the economic intensity ofdifferent feedbackloops^is analogous^tothe distribution of energy between different whirlpools. Such a similarity leads to thehierarchicalordering of theproductioncyclefeedback loops with respect to intensity of flows within the productioncycle loop.

Furthermore, the scaling of feedback loops, which is connected to spatial and functional production cycle economicdisaggregation^oftrade, leadstotheMatrioshka imbedding principle of hierarchicalinclusionofeconomic activities flowsinto the spatialloops.

The essential consequence of the decomposition of the overall matrix trade flow into the sum. of block- permutation matrices of production cycles feedback

loops is the possibility to visualize the trade feedback loopswiththehelpof coloring of different feedbackloops in different colors. This visualization represents in fine detail the rich information about spatial and economic interdependencies within inter-regional trade ^on the spatial macro-economic level of inter-regional Primary Secondaryand Tertiaryeconomicactivities, sub-activities and individualindustries.Insuchamannerthetrade tables canbe convertedintocoloredspatialandfunctionalmaps of the hierarchy of production cyclesfeedbackloops.

References

Akita,T. (1999)"Therole of theKantoregioninthegrowth ofJapanese regional economies 1965-1985: an extended growth-factor decomposition analysis",In: Hewings,G.J.D., Sonis,M., Madden, M.and Kimura,Y.,eds, Understanding and InterpretingEconomic Structure (Springer, Berlin), pp 155-166.

Balassa, B. (1967) Trade Liberalization among Industrial Countries (McGrawHill,New York).

Bruelhart,M.and Hine, R.C.(1999)lntra-industry Trade and Adjustment (St.MartinsPress, New York).

Christofides, W. (1975) Graph Theory. An Algorithmic Approach (AcademicPress,NewYork).

Dantzig,G.B. (1963) Linear ProgrammingandExtensions (Princeton UniversityPress,Princeton,NJ).

Defourny, J. and Thorbecke, E. (1984) "Structuralpath analysis and multiplierdecomposition withina social accounting matrix frame- work",EconomicJournal94, 111-136.

Feinberg, S.(1970) "An^iterativeprocessfor estimationof contingency tables", AnnalsofMathematicalStatistics41, 907-917.

Gower, J.C. (1977) "The analysis ofsymmetryand ortogonality", In:

Barra, J.R.,ed,RecentDevelopments in Statistics (NorthHolland, Amsterdam), pp^109-123.

Hummels, D., Rappoport, D. and Kei-Mu Yi (1998) "Vertical specialization and the changing nature of world trade", Federal ReserveBankof^{NewYork,EconomicPolicyReview,June.}

Ihara, T. (1999) "Diagnosis and therapy of interregional feedback effects",In:Hewings,G.J.D.,Sonis,M.,Madden,M.and Kimura,Y., eds, Understanding and InterpretingEconomicStructure(Springer, Berlin), pp91-112.

Jurcat, W.D. and Ryser, H.J. (1967) "Termranks and permanents of nonnegative matrices", Journalof^{Algebra 5,342-357.}

Krugman,P. (1991) "Isbilateralismbad",In: Helpman, E.and Razin,A., eds, International Trade and Trade Policy(MIT Press, Cambridge), pp9-23.

Krugman, P. (1993) "Regionalism versus multilateralism: analytical notes", In:Melo, J.D.E.and Panagaria,A., eds,NewDirections in Regional Integration(Cambridge University Press, Cambridge), pp 58-79.

Ministry of International Trade and Industry of Japan, 1980-1995:

"1980, 1985, 1990 InterregionalInput-OutputTables."

Richardson, L.E (1922) Weather Prediction by Numerical Process (Cambridge UniversityPress,Cambridge),p 66.

Slater,D.B. (1981) "Combinatorialproceduresfor structuringinternal migration and other transaction flows", Quality and Quantity 15, 179-202.

Sonis,M. (1980)"Locationpush-pullanalysis of migrationstreams", Geographical Analysis12,80-97.

Sonis,M., (1982)"The decomposition principleversusoptimizationin regionalanalysis--the invertedproblemofmultiobjectiveprogram- ming",In:Chiotis,G.P.etal.,eds, The Regions and Enlargementof European Economic Community (Athens Meeting of Regional ScienceAssociation,September, 1981).Athens:Eptalofos,35-60.

Sonis,M.andHewings, G.J.D. (1990)"The "Matrioshka"principleinthe hierarchical decomposition of multiregional social accounting systems",In: Dewhest,J.J.LI., Hewings, G.J.D. andJensen, R.C., eds, Regional Input-Output Modeling: New Developments and Interpretations(Aldershot, Avebury),pp 141-158.

Sonis, M., Oosterhaven, J. and Hewings, G.J.D. (1993) "Spatial economicstructureand structuralchangesintheEuropeancommon market: feedback loop input-output analysis",EconomicSystems Research5, 173-184.

Sonis, M., Hewings, G.J.D. and Gazel, R. (1995a)"The structure of multi-regionaltradeflows: hierarchy feedbacks andspatiallinkages", The Annalsof^{RegionalScience29(4),409-430.}

Sonis,M., Guelhoto,J.J.M. andHewings, G.J.D. (1995b) "TheAsian economy: trade structure interpretedby feedback loop analysis", Journalof^AppliedInput-OutputAnalysis2(2),24-40.

Sonis,M.,Hewings,G.J.D., Guo, J.and Hulu,E. (1997)"Interpreting spatial economic structure: feedback loops in the Indonesian economy 1980-1985", RegionalScienceand UrbanEconomics27, 325-342.