Aoki Horizonal vs Vertical Info Structure

8/13/2019 Aoki Horizonal vs Vertical Info Structure

1/14

American Economic Association

Horizontal vs. Vertical Information Structure of the FirmAuthor(s): Masahiko AokiSource: The American Economic Review, Vol. 76, No. 5 (Dec., 1986), pp. 971-983Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1816463Accessed: 06/04/2009 09:40

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=aea .

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform thatpromotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review.

http://www.jstor.org
http://www.jstor.org/stable/1816463?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=aeahttp://www.jstor.org/action/showPublisher?publisherCode=aeahttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/1816463?origin=JSTOR-pdf


2/14

Horizontal vs. Vertical Information Structure of the Firm

By MASAHIKO AOKI*

This paper compares the efficiency of two information structures, hierarchical andvertical, of the firm in coordinating operational decisions among technologicallyinterrelated shops whose costs are uncertain. In the first, the capability ofmanagement to monitor and respond to emergent events at the shop level isbounded. In the second, production decisions are coordinated among shops withoutthe centralization of information, whose capability of semiautonomous problemsolving improves through learning by doing. This study is motivated by aU S. - Japan comparison of industrial organization.

The objective of this paper is to comparethe efficiency of two informational structuresof the firm in coordinating operational deci-sions among interrelated units (shops) whosecost conditions are uncertain. One informa-tional structure is hierarchical-manage-ment possesses a perfect a priori knowledgeof the technological possibilities of shops,but is incapable of perfect monitoring ofemerging events affecting these technologies,and/or

having rapid corrective actions im-plemented at shops. The second structure ishorizontal-production decisions are coordi-nated among semiautonomous shops thathave only incomplete knowledge of technol-ogy at the outset, but gradually become ca-pable of responding to emerging events morequickly by better uses of on-the-spot knowl-edge. This paper is exclusively concernedwith efficiency properties of the two infor-mational structures; and the issue of theirincentive compatibilities is relegated to other

work.' The comparison of the two structuresis purely analytical, but I hope to providea conceptual framework for a U.S.-Japancomparison of industrial organization (suchas workshop organization, internal firmorganization, manufacturer-suppliers rela-tions, etc.). Another obvious applicationwould be to production coordination in thesocialist economy. In this application, themanagement should be read as the ministry

of industry and shops as firms.I. Motivation f the Study

This section, as a way of motivating thepresent study, describes several stylized con-trasts between Japanese and U.S. firms perti-nent to the operation of the internal organi-zation, as well as to the degree and mode ofintegration. These references are mainly di-rected toward large unionized firms in themanufacturing industry.

A. Specialization vs. Learning

There is a distinct difference in the waywork is organized on the shop floor in thetypical Japanese firm (denoted J firm) andthe typical American (unionized) firm (de-noted A firm). In the A firm, workers' jobsare specified according to a job classificationscheme stipulated in a collective agreement,

*Professor of Economics, Stanford University, Stan-ford, CA 94305 and Kyoto University, Kyoto, Japan,606. I thank Kazuo Koike for discussions which in-spired the present study. I am indebted to readers of anearlier version for helpful comments: Kenneth Arrow,James Hamilton, Hideshi Ito, Burton Klein, HajimeMiyazaki, David Mowrey, Michael Riordan, and OliverWilliamson; to referees of this Review, and to par-ticipants of seminars at Stanford, UC-San Diego, BritishColumbia, Washington, Tokyo, Ohio State, and theStockholm School of Economics. Research leading tothis manuscript was partially supported by grants fromthe Center for Economic Policy Research and the Centerfor Research in International Studies at Stanford Uni-versity.

'See my 1985 paper for an exploratory attempt onthis issue.

971


3/14

972 THE AMERICAN ECONOMIC RE VIEW DECEMBER 1986

and each worker is required to perform his(her) own specialized task according to for-mal or informal rules, operation manuals,

supervisor's directives, etc. When irregularevents happen, such as the absenteeism ofworkers, breakdown of machinery, or pro-duction of an abnormally high rate of defec-tive products, remedies are usually sought bysupervisors, reliefmen, repairmen, engineers,and the like. Manual workers are not specifi-cally responsible for coping with unexpectedemergent events.

In contrast, in the J firm, workers' jobsare not specified in detail and workers ro-tate among various jobs with some frequen-

cy within, as well as beyond, workshops.Through this practice, workers are graduallymade familiar with the whole work processand become capable of coping with unex-pected emergencies. As Kazuo Koike con-vincingly argues, such capability constitutesone of the most important components ofthe workers' skills.2 In fact, there is a consid-erable degree of delegation of decision-mak-ing power to the group of workers on theshop floor. They are encouraged to solveemergent problems by themselves and im-provise improvements on designed workprocesses. When needed, the repairmen, in-spectors, and engineers are willing to cooper-ate with the workers in joint problem solv-ing.

The emphasis at the A firm is on theefficiency attained through job specializationand rational hierarchical control, whereas atthe J firm, it is on the workers' grass rootscapability to cope with emergent events fos-tered by collective learning by doing. TheJapanese approach has proved to be effectivefrom a quality- and cost-control point ofview in industries such as steel and automo-tive manufacturing where cost reduction hasbeen attained largely through improvementson fairly established technology. But, will it

be equally effective in the high-tech industrywhere the speed of technological obsoles-cence is likely to be high, and general educa-

tional training seems to be gaining impor-tance as a component of workers' skills?

B. Hierarchical Control vs.Horizontal Coordination

In the uncertain world where completecontingent contracts cannot be written be-cause of bounded rationality of concernedagents, emergent events have often to bedealt with, ex post. Different modes of trans-actions would emerge, depending upon how

and by whom they are dealt with. In the Afirm, decisions involving discretion are nor-mally hierarchically organized according totheir importance. In fact, some authors arguethat the layering of specialized decision mak-ing in order to cope with emergent events forwhich detailed specification of appropriateactions cannot be formulated ex ante is theessence of hierarchy.3

In the J firm as well, decisions involving ahigh degree of uncertainty, such as invest-ment and research and development, as wellas those responding to a high degree ofirregularity are placed under hierarchicalcontrol. However, once an overall frame-work for production is laid down by suchstrategic decisions, horizontal informationalexchanges and semiautonomous coordina-tion of operations by relevant subordinatesare emphasized. In contrast to the prominentrole played by the expediter in the A firm,the coordination of production between Jfirm workshops to facilitate a smooth pro-duction flow along the production stream isoften done by horizontal communicationwithout the intervention of a supervisor, asthe highly publicized kanban-system atthe Toyota factory exemplifies. A kanban isa tag-like card put in a vinyl envelope whichorders from the immediately upstream shop(or the supplier) a particular amount ofmaterials, tools, parts, or processed goods ata particular time. Robert Cole aptly drawsan analogy between this practice and the

2The practice of job rotation in the Japaneseworkshop is described and its implication to skill for-mation is thoroughly discussed in Koike (1984). Basedupon his own extensive field work, Koike (1985) alsomaintains that an important part of the workers' skillsconsists of their ability to cope with unexpected emer-gencies. 3See for example, David Kreps (1984).


4/14

VOL. 76 NO. 5 AOKI: STRUCTURE OF THE FIRM 973

system we use in restocking supermarkets(1985, p. 106). Although apparently crude,the kanban system is considered to have

contributed greatly to reducing inventory andwaste, uncovering bottlenecks, allowing forrapid adjustment of product lines, and re-ducing managerial personnel.4

The emphasis at the A firm is on theefficiency attained by rational technocraticcontrol, whereas, in the J firm, it is theefficiency attained through the use of on-the-spot knowledge and rapid problem solv-ing through learning by doing. In the former,decisions may be made consistently and ra-tionally from the organizational point of

view, once an emergent problem is recog-nized. However, if the quality of informationis poor, the manager may be slow and im-precise in recognizing the problems to behandled. Also, subordinates, by not beingincluded in decision making, may lack themotivation to report problems and to imple-ment the hierarchical order in a precise andswift way. Thus using the hierarchical sys-tem involves the cost of monitoring due tothe bounded rationality of the supervisors,and the cost of implementation due to thelack of incentives of the subordinates.

On the other hand, in the J firm, sub-ordinates may be motivated to respond toemergent events swiftly in a way which theyconceive to be consistent with the organiza-tional purpose, provided that organizationalgoal is internalized by them. However, theability of subunits to coordinate their deci-sions between themselves in a way actuallyconsistent with the organizational purposewould be limited by their partial under-standing of the whole mechanism operatingwithin the firm. This understanding can beenhanced by learning by doing, but is costlyin terms of time. Also, the problem-solvingcapability of subunits through horizontal co-ordination would be limited by the lackof centralization of information concerningemergent events which affect various othersubunits.

Which of the two information and deci-sion-making structures, hierarchical or hori-zontal, is more effective for controlling the

total costs of the system in changing en-vironments? How does the complexity oftechnological interdependencies of subunitsaffect their relative efficiency performances?

C. Integration vs. Quasi Disintegration

The degree of integration of the A firm isnormally much higher than that of the Jfirm. A joint U.S.-Japan study of the auto-motive industry estimates that 45 percent ofa car's purchased value is provided by U.S.

manufacturers and their wholly owned sub-sidiaries, with 55 percent being provided byoutside suppliers. Only 25 percent of a car'spurchase value is made in-house for Japanesemanufacturers.5 This difference is due to anextensive reliance of Japanese major manu-facturers on suppliers which are normallysmaller in size and often referred to as sub-contractors. 6

A reason often cited for the extensive de-ployment of the subcontracting relations bythe J firm is that, since the rate of its growthwas so fast, it could not generate enoughinternal resources for integration to an ex-tent comparable to that which the A firmhad achieved over its longer course of growth.This may partially explain the genesis of theextensive subcontracting relations observedin the Japanese manufacturing industry. Butif this was the only reason, and there was nointrinsic comparative advantage of a subcon-tracting relationship over more complete in-tegration, the former would have been grad-ually replaced by the latter as the growthrate of the economy slowed down and the

4For more details on the kaban system, see Cole(1985) and Yashuhiro Monden (1983).

5See Cole and Taizo Yakushiji (1984, p. 153-54).6Precisely speaking, the subcontractor is a legal con-

cept in Japan. According to Basic Law for Medium andSmall Enterprises and Law for Preventing the Delay ofPayment of Subcontracting Fees, firms with 300 orfewer employees, or with 100 million yen or less paid-incapital, are classified as subcontactors when they havecontractual relations with larger firms for supplyingparts, processed products, matrials, etc. Excellent stud-ies on subcontracting relations in the Japanese automo-

tive industry are found in Banri Asanuma (1985) andCole and Yakushiji (ch. 9). Also see my book (1984a).


5/14

974 THE AMERICAN ECONOMIC REVIEW DECEMBER 1986

accumulation of internal resources of the Jfirm progressed in the 1970's and the early1980's. On the contrary, the degree of reli-ance of the J firm on subcontracting rela-tionships has increased over this period.7Furthermore, the relationship between theparent firm and its subcontractors has cometo be much more systematic and formalized.The large J firm maintains long-term, directrelations with primary subcontractors thatare loosely organized into associations ofcooperating firms (kyoryoku-kai); and thoseprimary subcontractors in turn maintain re-lations with secondary subcontractors, etc.Instead of a highly integrated, hierarchicalfirm, we observe a quasi-disintegrated, quasi-hierarchical group of firms (hereafter re-ferred to as the J-firm group) in whichsubcontractors maintain semiautonomouscontrol of production, although the mainmanufacturers typically have minority equityholdings in their first-tier suppliers, and ex-ercise substantial influence over the directionof research and development as well as overinvestment decisions by the latter.

The benefits of integration vis-'a-vis themarket have been discussed by many authors.

Integration may be able to reduce the cost ofmarket transactions caused by the opportun-istic and inefficient behavior of a seller andbuyer in situations where either the buyer orthe seller must make transaction-specificinvestments (Oliver Williamson, 1975, andBenjamin Klein et al., 1978), and/or whereit is too costly for one party to specify a longlist of the particular rights it desires overanother party's assets (Sanford Grossmanand Oliver Hart, forthcoming). Another mo-tive for integration may be to communicate

uncertain information regarding upstreamsupply conditions more efficiently (KennethArrow, 1976).

But as Grossman and Hart argue, thetransaction-cost and information-cost-basedarguments did not elucidate where the ben-efits of integration will stop. Ronald Coase(1937) states that the size of the firm islimited by the capacity of the single owner inthe number of activities he can manage. This

is unconvincing, however, because organiza-tional innovation such as the multidivisionalform may overcome this limit (Williamson,1975). Facing this problem, Williamson(1985) came to argue that excessive integra-tion may sacrifice the efficiency possible un-der the high-powered market incentive.Consequently, he states, if benefits of high-powered incentives are potentially high, whilethe transaction in question involves a sub-stantial degree of asset specificity, new hy-brid forms of organization other than thefirm may appear in response. I submit thatthe information costs may also increase fromexcessive integration and that may provideanother reason for the emergence of theJ-firm group, which is an example of such ahybrid form.

The J-firm group may combine some ofthe benefits of both integration and themarket. Since the relationship between theparent firm and subcontractors is of a long-term nature, both would come to have afairly good knowledge of each other's tech-nology, and inefficient price haggling wouldnot be a serious problem. In Williamson'sterminology, conditions of information im-

pactedness (1975, pp. 31-33) are more easilyovercome and, even when they appear, areless likely to give rise to strategic behavior.Also, since an implicit/explicit arrangementof profit sharing is the normal practice inthis long-term relationship,8 underinvest-ment in transaction-specific assets may beavoided to both parties' mutual advantage.On the other hand, since the long-term rela-tionship is maintainable only if it is benefi-cial to both parties, but is otherwise dis-solvable albeit at some cost, the midpower

market incentive would operate within theJ-firm group; that is, subcontractors wouldtake greater care in cost control and qualitycontrol of their production as compared toin-house supply divisions. But these relativeadvantages still remain hypothetical, unlessan efficient information system between theparent firm and its subcontrators for coordi-nating their operations is possible withoutconsistent hierarchical direction under an in-

7See my paper (1984b). 8See my paper (1985) and also Asanuma.


6/14


tegrated firm or the efficient signal of com-petitive prices.

As indicated above, one of the premisesfor the efficiency of the J-firm group is tech-nological knowledge sharing between theparent firm and its subcontractors for miti-gating the problem of opportunistic behav-ior. However, within a general framework ofknowledge sharing, day-to-day monitoringof emergent events affecting the cost ef-ficiency of productive operations and/orproduct quality may be delegated to subcon-tractors. Then the information exchange nec-essary for rapid corrective action can bemade more direct by coordination between

the relevant operational units (for example,between parts-supplying subcontractors andthe assembly shop of the parent firm, be-tween first-tier and second-tier subcontrac-tors, etc.), without the intermediary of anelaborate, centralized control mechanism

However, is this quasi-decentralized coor-dination within the J-firm group not a crudeinformation system? Is it not likely to be thecase that the administrative costs of a highlyintegrated firm will be reduced in the nearfuture by the rapidly growing information-

processing technology and more reliablerobotic technology? Or will the quasi-disin-tegrated group continue to exhibit highertransaction-cost savings in spite of these newdevelopments?

I have described three stylized contrastsbetween the A firm and the J firm/J-firmgroup. They include oversimplificationsinevitable in any stylized formalization.Neither a pure J firm nor a pure A firmexists. Any American or Japanese firm cancontain some aspects of both. There is alsomuch anecdotal evidence that many Ameri-can firms have recently been adopting someelements of the J firm, such as the simplifi-cation of the job classifications scheme, anincreased delegation of decision-making au-thority to line organizations, more sys-tematic relationships with suppliers, etc. Onemay also argue that the three issues dis-cussed above are only mildly related to eachother. I submit, however, that if these threestylized contrasting features are taken to-gether as a benchmark from the informa-tional structure point of view, one funda-

mentally common issue arises. That is theissue of relative efficiency of what I call

horizontal coordination based on learningby doing vs. rational hierarchical controlbased on specialism.

Suppose that strategic decisions (such asthose that involve investment as well as thedirection of research and development) aremade by superordinates (the management ofthe firm). Given these decisions, actual oper-ations of subunits (shops) must be adjustedand coordinated accordingly as emergentevents affect the efficiency of each unit. Inorder for efficient coordination to occur, themonitoring and identification of emergent

events affecting cost efficiency as well asquick implementation of corresponding op-erational decisions are imperative. In thehorizontal coordinating system, these tasksare delegated to subunits performing rele-vant operations that are limited in theircapacity to recognize a relevant emergencyat the outset. Even if they do, since thecentralized use of information concerningemergent events is absent, problem solvingat the subunit level may not satisfy the first-best condition. But, through learning by

doing, the subunits can improve their abilityto perceive emergent problems and to findcorresponding solutions. Once a problem isrecognized and a corresponding solutionfound, the subunits should be able to imple-ment it quickly.

On the other hand, in the hierarchicalcontrol system, management has a prioriknowledge of the overall production technol-ogy. But their capacity to identify emergentevents affecting production technology ofsubunits and to enforce the implementationof appropriate operational decisions uponsaid subunits may be limited and costly,simply because management is removed fromoperational activities. In other words, therationality of the superordinates is apt to be

bounded.Thus the relative efficiency of the two

systems depends upon the following factors:the ability of subunits to learn how technol-ogy is affected by emergent events and howthese events should be dealt with (the speedof learning); the initially endowed ability ofsubunits to understand the nature of tech-


7/14


nology as well as the speed of obsolesence oftechnology; and the ability of managementto identify emergent problems at the subunitlevel as well as to enforce the implementa-tion of operational decisions upon subunitsas quickly as possible (the quality ofhierarchical informational structure and thereward system). In the next section, I con-struct a simple analytical model of horizon-tal coordination in which learning by doingby subunits would play a significant role,and a model of hierarchical control whoserationality is bounded; I then analyze howthe factors affect the relative efficiency of thetwo models. As I have indicated, it is likelythat the aspects of hierarchical control andthose of horizontal coordination may coexistin any single firm. Therefore, the followingmodel comparison may be understood as ananalytical device for considering the problemof an optimal mix of the two approacheswithin a firm.

II. The Model

Let us employ the production model dueto Jacque Cramer (1980) and John Geana-

kopolos and Paul Milgrom (1985) as a basisfor the comparative analysis of the two in-formational structures of the firm. Let usconsider a system composed of n technologi-cally interrelated subunits called shops,identified by index i=1,...,n. Let xieRsdenote a vector of net production assign-ment of the ith shop, with the conventionthat negative components indicate inputs andpositive components outputs. Suppose thatthe cost incurred by shop i to realize aproduction assignment xi is represented bya quadratic cost function: 9

Ci(x,, Ui) = [Xi - UJI'Bi[xi - ui] + Ai

(iher .B.. n)where Bi is a positive semidefinite matrix

with at least one diagonal element beingstrictly positive, A, is a constant matrix, andui E RS is a random variable representingcost uncertainty with E[uJ]=0ut, E[(u,-u*(iU- *)']= var ui, and E[(ui - U*)(uj- = 0 for i $ j. The cost Ci may repre-sent the outlay from the system or theeffort expenditure level incurred by shop i torealize its production assignment.

The objective of the system is to realize anet output target:

*_X

with the expected minimum aggregate cost

E [C(x, u)] = Y.E [Ci(xi, ui)]

responding to emergent events ex post. Givenan observed event u = (ul,..., un , the solu-tion to this problem is

(1) xf= u?+ B,lB[x*-UI

where B= [YBI-1] ; U=Eui.

If the system can identify emergent eventsand implement corresponding cost-minimiz-ing solutions immediately, the expected totalcost under this perfect control is

CP = E{4[x*- U]'BBi?lB[x*- U]) + EAi

= C* + tr[ B var U]

where C*= [x*-U*]'B[x*-U*I?+Ai

U* = E0,

tr[B varU] = E{[U- U*]'B[U- U*]}.

On the other hand, if the system cannotidentify emergent events, the system rou-tinizes its production at the level

xn = U* + B7 lB[x*-U*]

so-1,..,n)

so as to realize the minimum expected total

9Arrow (1985) cautions against the use of a quadraticfunction for the study of information structure. As hestates, the use of the quadratic function sometimes leadsto strange analytical results. I assume that the quadraticrepresentation of technology is a local approximationfor nonlinear technology.


8/14

VOL. 76 NO. S AOKI: STRUCTURE OF THE FIRM 977

cost under no ex post information condition:

C' = YE{ [x n- ui]'Bi[Xn -u] }+ EAi

= C* + E tr[ Bivar ui],

where

tr[Bivar ui] = E -[ui-u*]'Bi[ui - u*]}).

The solution x n corresponds to MartinWeitzman's (1974) quantity solution in histreatise on price vs. quantity. We are inter-ested in two control mechanisms whose costperformances lie somewhere between the

perfect control case and the no ex post infor-mation case.

A. Bounded Rational Control

Let us consider a control mechanism inwhich the managing unit sends assignmentsto each shop. Management has perfecta priori knowledge concerning technologiesof shops (i.e., it knows Bi's) and is capableof calculating the optimal solution once anemergent event is identified, but its rational-ity is bounded in two respects: it can iden-tify emergent events only imprecisely, andcan have production assignments imple-mented only with some delay-meanwhile,events may change.

First, suppose that the perception ubrof management of an emergent event u1 iserrored in such a way that

ubr = u v (i=1,.. .,n)

where vi is a stochastic vector with E[vJ]= 0

and E[v v] = yE[(u - u)(uj - u*)'] forsome constant -y. Given the quadratic lossfunction, expected loss is minimized by set-

= brting ui u1 in equation (1). Production as-signments would therefore be

Xbr =br + B-1B[X* uz br]

Second, it is assumed that time \ elapses

between the perception of an emergent eventby the management and the implementation

of the corresponding production assignmentsand that emergent events constitute a first-order autoregressive process defined by

dui(t) + hui(t) dt = dM1(t)

(i=l, ... , n),

where h is a positive parameter representingthe rate at which the environment forgets thepast history of ui and {f,} is a randomprocess with orthogonal increments. It canbe shown that the process ui(t) defined bythe above equation satisfies the followingrelation:10

E{[ui(t)- u*[ui(t + A)- u]'}

e-hAvar ui(t).

When an event Uir(t) (i =1,. ..,n) is per-ceived by management and the correspond-ing production assignments are implementedafter time A, the expected instantaneous totalcost at the time of implementation would be

Cbr=[xbr

(t)- u,(t+

A)I'Bix [Xbr(t) _Ui(t + A)] + Y.Ai

= C*+tr[B var U]+(y +2(1- e-hA))

x {2 tr[Bivar ui]-tr[B var U]}

= C'n + (y + 1-2e hA)(Cn - CP).

Actually the production assignment xi(i = 1 .. .,

n)does not minimize the expected

cost given the perception error and the timelag in response to emergent events. This canbe easily seen from the observation that if -yor hA is sufficiently large, Cbr can exceedthe cost C' under no ex post information.In such cases it is better not to react tochanging events, but to make routine thenoninformation solution (i.e., the Weitzmansolution).

10See A. M. Yaglom (1962, chs. 2 and 3).


9/14


If management is rational enough to rec-ognize its bounded rationality, what it oughtto do to reduce the expected cost is to mixthe production assignments x' and xbr.ll Inother words, before utilizing perceived infor-mation u br, management ought to shrink itto the expected value. Let

x r(t + A) = aXxbr(t) + a1()Xn

(i-1,... , n).

Then the aggregate instantaneous cost wouldbe

cr = Cn + {(1 + y)a22ae-hA }(Cn-CP).

By choosing a= e-hA/(I + y), the expectedcost would be minimized at the level

cr = C -e- 2h(Cn - CP)/(1 + y)

Suppose that the time discount rate of thesystem is 8. (It is assumed that the rate ofdiscount captures the effect of technologicalobsolescence as well.) Then the sum ofdiscounted expected costs from the present

to the infinite horizon would be

fe -8tCrdt

= (1/i){ cn-e 2hA(CnCP)/(1 +y)}.

B. Learning by Doing

An alternative mechanism in controllingthe system is the horizontal coordination inwhich decisions on inputs and outputs ofshops are coordinated among relevant shops.But the shops capacity to coordinate islimited in two respects: the ability to iden-tify emergent events is initially limited andcan only be improved upon over time throughlearning by doing; and the horizontal coor-dination by shops is imperfect as each shoplacks information concerning technologies ofother shops except for those directly related.

However, once shops acquire the skill toidentify emergent events affecting heir ownand their transaction partners' cost condi-tions, they can implement at least locally)an appropriate production plan without de-lay. First, let us concentrate upon the effectof learning by doing by assuming hat shopscan somehow find and implement he opti-mal solution of production orresponding oa perceived emergent event. Let us call thismechanism-in which the perceptive abili-ties of shops improve over time and theybecome perfectly capable of calculating pti-mal solutions-quasi-horizontal coordina-tion. The problems arising from imperfectcoordination due to the lack of centralizedtechnological nformation will be consideredlater.

Assume that the shops' perceptive bilitiesare represented by the probability of iden-tifying true emergent events. Suppose that,if the shops identify a situation, an opti-mal solution correspondent o it is imple-mented. If not, the no ex post informationsolution x7 (i ..., n) is routinized. Thenthe instantaneous expected total cost of thesystme under this quasi-horizontal oordina-

tion would be

Ch Cn f(Cn Cp).

Suppose that the probability of problem re-cognition improves over time through earn-ing by doing according o

df(t)/dt = kf(t){log[l/f(t)] }

where k is a positive parameter epresentingthe rate of learning. Upon integration, weobtain the Gomertz growth model

f(t) =-exp{-Pe-kt } .

When t = 0, f(0) = e- so that the inverseof / may be identified with the initial abilityof shops as regards to problem identifica-tion. As t goes infinity, f approaches ne.

The sum of expected discounted costs un-der the quasi-horizontal oordination rom

Since I am concerned with a quadratic program-ming, the optimal solution is a linear function of xi's.


10/14


the present to the infinite horizon is

fe-8tCqh(t) dt = (IIS)Cn00

- exp( St - Pe-kt) dt(Cn _ CP)

= (1,/)Cn-(1/k) exp{(Slk)y

-/e-Y} dy(Cn-CP).

By setting S/k = 0

= (1/8) { Cn - f v(o, ,)(Cn _ Cp)}

where v is the incomplete gamma function:'2

v(O,1 ) =fpe-sse-1ds.

The value of 0fl-3e(0, /) is monotonicallydecreasing in both 0 and ,B. By comparingthe sum of expected discounted costs underthe bounded rational control and the quasi-horizontal control, we have the followingproposition.

PROPOSITION 1: The sum of discountedexpected costs under quasi-horizontal coordi-nation is smaller than that under boundedrational control if and only if

e-2hA/(I + y) < 0j-ev(0, ,B).

Thus the relative advantage of quasi-horizontal coordination is positively relatedto the lag in hierarchical adaptation to emer-gent new events represented by A, to thedegree of imprecision of management's per-ception represented by y, to the relativeratio of the rate of learning of shops to thetime discount rate represented by 0, and tothe initial ability of shops to perceive emer-gent events represented by the inverse of ,B.This is independent of technological datarepresented by B.'s and var u 's. Specifically,

inncreased 0

e_2hA1+ Y

OS-

v(O,0)

FIGURE

if 0=1, then v(1,f3)=1-e- so that thecondition can be simply written as

e-2hA/(1 + y) < -I [I- f (O)].Since lim ---0f3(0 ,B) =I1 andlim. f,B -e v (0, ,) = 0, it holds that

COROLLARY 1: The value of ,B must besmaller than a certain strictly positive maxi-

mum value in order for the quasi-horizontalcoordination to be relatively advantageous.This maximum value of ,B decreases as h, y,and A decrease and as 0 increases. (SeeFigure 1.)

This corollary suggests that in order forthe quasi-horizontal coordination to be rela-tively advantageous, the initial ability ofshops to identify emergent events must behigher than a certain level. Even if the rateof learning is very high relative to the timediscount rate, learning alone cannot makethe quasi-horizontal coordination a superiormechanism.

C. Imperfect Horizontal Coordination

Let us now take into account the imper-fect ability of shops to coordinate their pro-duction decisions. Suppose that transac-tional decisions concerning any products arecoordinated between the relevant suppliershop(s) and the relevant user shop(s). Sup-pose that, with probability f evolving as12See I. S. Gradshteyn and I. M. Ryzhik (1980,pp. 308, 940).


11/14

980 THE A MERICA N ECONOMIC RE VIE W DECEMBER 1986

already specified, they are able to mutuallyidentify emergent events affecting eachothers' cost condition associated with thetransaction of that particular product, aswell as to share technological knowledgeconcerning mutual B 's. When they do so,they agree upon the particular amount of thetransaction of that product which minimizesthe joint costs, assuming other inputs andoutputs are fixed at the solution under no expost information. If they cannot share infor-mation, they routinize the transaction at thelevel of the no ex post information solution.For example, suppose that product k istransacted between shop i and shop j. Fur-

ther, suppose that it is only these two shopsthat either produce or use the product k.Then shop i and shop j, mutually recogniz-ing the true value of uik and Ujk with prob-ability f, choose xik and Xjk which wouldminimize the joint costs subject to the con-straint x ik + Xjk = x , assuming that othercomponents of xi and xj are fixed at thelevel specified by xn and xj7 and those of uiand Uji are fixed at the level specified by u*and uj*.

In general, the local joint cost minimizing,

when ex post information is shared by rele-vant shops, requires that

B. (X. -u + B' [(Xi-ui

-(Xn U*)]=A (i=1,...,n)

and Exi = x* for some intrafirm shadowprice X, where

Bi= bKJ, b1, ss

From this, the imperfectly coordinated solu-tion xlP satisfies

xi ui + B7'lB[x* U*]-B7lB[u-u*I

= xP + [B-'B-B A7B] [U-U*]

wi=ls...,i n),A

where Bi- is a diagonal matrix with the jth

element being 1/b 'jj if bi jj is positive andzero otherwise. Then the total instantaneousexpected cost under the imperfect horizontalcoordination when the true event is per-ceived is

C -P = CP + tr[(BAB'i-BiB'i- - B)var U]

= - 2 {tr[(Bi - BB7'B B7'B)var ui] }.One can define efficiency ratio of the imper-fect horizontal coordination relative to per-fect control by

'q(B) = (Cn - Cip)(Cn _ Cp)

z {tr [B(-

BBi 'Bi.BiB)var u] }E {tr[(Bi - B)var u1] }

Following the same reasoning as in the caseof the quasi-horizontal coordination, we canderive

PROPOSITION 2: The imperfect horizontalcoordination based upon learning is superior tothe bounded rational control if and only if

e-2h/(l + y) < of3-pv(O,f )rq(B).

As all off-diagonal elements of Bi (i=1,..., n) approach zero, q(B) approachesone. Therefore, somewhat loosely we canclaim

COROLLARY 2: Given other parameters,the relative advantage of the imperfect hori-zontal coordination would increase vis-a-visthe bounded rational control, as the techno-logical matricies, Bi, become more stronglydominant-diagonal.

Roughly speaking, the more strongly dom-inated the marginal cost of each output is bythe output level of that product than any-thing else, the more the relative advantage ofthe imperfect horizontal coordination wouldincrease vis-a-vis the bounded rational con-trol. This means that if the technology ischaracterized by near-constant returns to

scale,the

imperfecthorizontal coordination

would not perform well. On the other hand,


12/14

VOL. 76 NO. S AOKI: STRUCTURE OF THE FIRM 981

it would perform relatively well when thereis a separate capacity constraint for eachoutput.

III. Concluding emarks

Section II above formalizes the intuitivenotion that decision-making power in theJapanese industrial organization is, as far asoperational decisions are concerned, rela-tively widespread. This decentralized ten-dency is to use the on-the-spot knowledge ofsubunits (workers, in-house shops, and rela-tively smaller subcontractors). Also, in orderthat the localized use of on-the-spot knowl-

edge would not lead to inefficient strate-gic haggling between subunits, sharing ofknowledge among neighboring subunits(among workers, among shops, and betweenprime contractors and subcontractors) is em-phasized. The accumulation of on-the-spotknowledge as well as sharing of knowledgecan be, needless to say, fostered only overtime. That is one of the primary reasons whythe Japanese tend to emphasize long-termrelations such as lifetime employment andstable relational contracts with subcontrac-tors.

On the other hand, emphasis on spe-cialization in the United States seems tohave two consequences: First, as jobs be-come more specialized and standardized, aseparate market for each job tends to de-velop outside the firm, facilitating interfirmmobility of workers. Second, in order tointegrate specialized and compartmentalizedjobs within the firm, the integration itself hasbecome a specialized function of manage-ment. Thus American industrial organizationis characterized relatively more by interfirmmobility of workers cum vertical control,whereas Japanese industrial organization ischaracterized relatively more by intrafirmmobility (rotation) cum horizontal coordina-tion. Needless to say, this difference is only amatter of relative degree and should not betaken as an absolute principle.13 I simply

suggest that there may be a close connectionbetween labor market characteristics and in-formation systematic characteristics of the

firm from a comparative perspective.How does the relative difference betweenthe A firm and the J firm in their approachtoward coordination of operational decisionsinteract with the mode and direction of morestrategic decision making such as researchand development? This is an interestingquestion, however, it is beyond the scope ofthis paper. I believe that the distinction ofthe two types of knowledge emphasized intheir respective approaches may have somebearing upon this question.

As Hayek (1945) emphasized in the con-text of the price mechanism vs. central plan-ning, economically useful knowledge maynot be limited to that which can be de-scribed in terms of formal language (forexample, blueprints, books, patents), but mayalso include intangible skills, undefined tacitknowledge, etc., as generated and trans-mitted through experiences and on-the-spotcontacts. The Japanese firm that relies moreon collective learning by doing and informalknowledge sharing in its operations seems toplace relative emphasis in research and de-velopment efforts on systematizing and de-veloping potentially useful knowledge of thesecond kind, collectively accumulated withinthe firm through production experiences.Even when new knowledge is acquired fromoutside the firm in the form of patents andthe like, that new knowledge is often reinter-preted and developed in reference to thefirms' own productive experiences. For ex-ample, some of the firms most active in thedevelopment of biotechnology in Japan aretraditional food-processing firms that strivefor possible adaptation of their amino acidfermentation and/or brewing techniques toscreening and breeding of new micro or-ganisms that have been genetically modifiedby the use of recombinant DNA. On theother hand, the American firm based onprofessional specialization and managerialvertical control in its operations seems toplace relative emphasis on the scientificefforts of professionally trained researchers

in R&D under the entreprenurial directionof top management.

13This contrast of interfirm mobility vs. intrafirmmobility between American industry and Japanese in-dustry is well described in Cole (1979). See also MasanoriHashimoto and John Raisian (1985).


13/14


Of course, when the Japanese firm sys-tematizes and develops its own productionexperiences, the infusion of researchers' andengineers' expertise is indispensable. Buteven for researchers and engineers, on-the-job training is regarded as equally importantas formal training. Therefore, quitting byresearchers and engineers in midcareer isdiscouraged by a system of seniority salariesand retirement benefits contingent on life-time employment. As a consequence, therate of interfirm mobility is relatively loweven for researchers and engineers. Someargue that the low rate of interfirm mobilityof researchers deters rapid technologicaldiffusion without possible government assis-tance,14 but one may counterargue that thelower exit rate of researchers reduces the riskof premature leakage of research results outof the firm, thus inducing the firm to financeR&D more actively without fearing the freeriding of quitters.

Professional specialization in R&D in theUnited States makes professional communi-cations across the boundary of firms, as wellas interfirm mobility of researchers, rela-tively more frequent. Also, one of the possi-

ble implications of the vertical control ap-proach is the ease of adding new subunits toa system, or starting an entirely new system,by managerial initiatives. The relatively highmobility of researchers combined with therelative ease of structural reorganizationmakes it easier to commercialize new knowl-edge in the form of acquisition of smallinnovative firms by large established firms orspinoffs of venture businesses. In contrast,the internal diversification or spinoffs ofsemiautonomous subsidiaries by establishedfirms is the more dominant form of com-mercializing new knowledge in Japan.

Again I emphasize that the difference inthese two approaches to the generation, de-velopment, and commercialization of newknowledge is simply a matter of relativedegree, but I submit that it is not reasonableto neglect the subtle difference as irrelevantfor comparative studies of industrial organi-

zation between the two economies. Conven-tional wisdom may dictate, then, that theAmerican approach is more conducive toscientific research which may lead to a truebreakthrough in technology, whereas theJapanese approach is more consistent withapplied research and product development.But whether this conventional wisdom is anempirically supportable proposition or not isyet to be seen.

REFERENCES

Aoki, Masahiko, 1984a) The Economic Analy-sis

of the Japanese Firm, Amsterdam:North-Holland, 1984.9 (1984b) Innovative Adaptation

through the Quasi-tree Structure: AnEmerging Aspect of the Japanese En-trepreneurship, in D. Bos et al, eds., En-treprenurship, Zeitscrift ur National Okon-omie, 1984, supplementum 4, 177-98.

, Incentives to Share Knowledge andRisk, presented to Arne Ryde Sym-posium on Incentive Problems in SomeMajor Economic Systems, University of

Lund, August 1985.Arrow, Kenneth J., Vertical Integration andCommunication, Bell Journal of Econom-ics, Spring 1976, 6, 173-83.

, The Information Structure of theFirm, American Economic Review Pro-ceedings, May 1985, 75, 303-07.

Asanuma, Banri, The Organization of PartsPurchases in the Japanese Automotive In-dustry, Japanese Economic Studies, Sum-mer 1985, 9, 32-53.

Coase, Ronald, The Nature of the Firm,Economica, November 1937, 4, 386-405.

Cole, Robert E., Work, Mobility, and Par-ticipation: A Comparative Study of Ameri-can and Japanese Industry, Berkeley: Uni-versity of California Press, 1979.

Target Information for Competi-tive Performances, Harvard Business Re-view, May-June 1985, 63, 106-09.

and Yakushiji, Taizo, The Americanand Japanese Auto Industries in Transition,Ann Arbor: University of Michigan, 1984.

Cramer, Jacque, A Partial Theory of the Op-timal Organization of a Bureaucracy, Bell

14

Such an opinion is expressed and the followingcounterpoint is discussed by Gary Saxonhouse (1984).


14/14


Journal of Economics, Autumn 1980, i1,683-93.

Geanakopolos, ohn and Milgrom,Paul, A The-

ory of Hierarchies based on LimitedManagerial Attention, unpublished man-uscript, 1985.

Gradshteyn, . S. and Ryzhik, I. M., Table ofIntegrals, Series, and Products, New York:Academic Press, 1980.

Grossman, Sanford and Hart, Oliver, The Costsand Benefits of Ownership: A Theory ofVertical and Lateral Integration, Journalof Political Economy, forthcoming.

Hashimoto, Masanori and Raisian, John, Em-ployment Tenure and Earnings Profiles inJapan and the United States, AmericanEconomic Review, September 1985, 75,721-35.

Hayek, Friedrich, The Use of Knowledge inSociety, American Economic Review, Sep-tember 1945, 35, 519-30.

Klein, Benjamin, Crawford, Robert A. and Al-chian, Armen A., Vertical Integration, Ap-propriable Quasi-rents and the Competi-tive Contracting Process, Journal of Lawand Economics, October 1978, 21,297-326.

Koike, Kazuo, Skill Formation Systems in

the U.S. and Japan: A ComparativeStudy, in M. Aoki, ed., The EconomicAnalysis of the Japanese Firm, Amster-

dam: North-Holland, 1984, 47-76.,_ Human Resource Development in

the Japanese Industry, mimeo., 1985.Kreps, David, Corporate Culture and Eco-

nomic Theory, mimeo., Stanford Univer-sity, 1984.

Monden, Yasuhiro, Toyota Production System,Atlanta: Industrial Engineering and Man-agement Press, Institute of Industrial En-gineers, 1983.

Saxonhouse, Gary, Industrial Policy and Fac-tor Markets: Biotechnology in Japan andthe United States, mimeo., University ofMichigan, 1984.

Weitzman, Martin, 'Prices and Quantities,Review of Economic Studies, October 1974,44, 511-18.

Williamson, Oliver E., Markets and Hierarchies:Antitrust Implication, New York: FreePress, 1975.

, The Economic Institutions of Capi-talism, New York: Free Press, 1985.

Yaglom, A. M., An Introduction to the Theory

of Stationary Random Functions, Engle-wood Cliffs: Prentice-Hall, 1962.

Aoki Horizonal vs Vertical Info Structure

Documents