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1 econstor Make Your Publications Visible. A Service of Wirtschaft Centre zbwleibniz-informationszentrum Economics Miyazawa, Kenichi Working Paer An Analysis of the Interdeendence Between Service and Good-Producing Sectors Center Discussion Paer, No. 92 Provided in Cooeration with: Economic Growth Center (EGC), Yale University Suggested Citation: Miyazawa, Kenichi (1970) : An Analysis of the Interdeendence Between Service and Good-Producing Sectors, Center Discussion Paer, No. 92, Yale University, Economic Growth Center, New Haven, CT This Version is available at: htt://hdl.handle.net/10419/ Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch geseichert und koiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Oen-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and coied for your ersonal and scholarly uroses. You are not to coy documents for ublic or commercial uroses, to exhibit the documents ublicly, to make them ublicly available on the internet, or to distribute or otherwise use the documents in ublic. If the documents have been made available under an Oen Content Licence (esecially Creative Commons Licences), you may exercise further usage rights as secified in the indicated licence.

2 ECONOMIC GROWTH CENTER Yale University Box 1987, Yale Station CENTER DISCUSSION PAPER No. 92 AN ANALYSIS OF THE INTERDEPENDENCE BETWEEN SERVICE AND GOOD-PRODUCING SECTORS by Kenichi Miyazawa August 13, 1970 Note: Center Discussion Paers are reliminary materials circulated to stimulate discussion and critical comment. References in ublications to Discussion Paers should be cleared with the author to rotect the tentative character of these aers.

3 AN ANALYSIS OF THE INTERDEPENDENCE BETWEEN SERVICE AND GOOD-PRODUCING SECTORS by Kenichi Miyazawa I. INTRODUCTION There are two oosing views on the relationshi between the goods-roducing sector and the.service sector, and this divergence of views has an imortant meaning in light of the recent growth of service sectors in the economy. In the orthodox view (and robably in Marxian theory), service activities have only secondary standing after goods-roducing activities; the income of the former is seen as derived from the income of the latter, i.e., a "redistribution of income" originated in goods-roducing activities. The distinction between "roductive 11 and "unroductive" labors emloyed by A. Smith, and the concet of surlus value emloyed by K. Harx, exress some of the earliest tyical views of these orthodox aroaches. On the other hand, modern economics treats service activities on an equal basis as goods-roducing activities, since many services have the same utility as goods and thus have value in the market in terms of the exchange mechanism in the national economy. The methods of modern economics emhasize the demand factor by making much of the concets of utility and exchange, whereas the

4 -2- orthodox methods stress the suly factor by attaching imortance to the roduction-relationshi. The contrast between the two, i.e., modern economics taking a unified view of goods and services, while the orthodox method overlooks the two-dimensional relation in roduction and service activities, is thus very clear. These differences have been reflected in the oosing standoints of the 11 national economic accounting systems 11 in the resent day. The so-called SNA, i.e., the System of National Accounts of the United Nations, emloyed for the economic accounts of many caitalistic countries, includes both income from service activities and income from goods-roducing activities as art of the National Income. On the other hand, the so-called MPS, i.e., Material Product System, emloyed by the economic accounts in socialistic countries, does not include service income as art of the National Income or National Products. The one-dimensional aroach to the income-concet adoted by SNA has sueriority in the broad treatment of roblems. But if incomes from both goods-roducing and service activities have an internal relationshi rather than a arallel one, we must take this into account together with the modern economics concet. In this aer we shall resent some linkage for the gas just described and formulate the interdeendent models of the goodsroducing sector and the service sector both by methods of income analysis and of inut-outut analysis with some tentative emirical illustrations.

5 -3- II. INCOME AND EMPLOYl:lENT ANALYSIS OF INTERDEPENDENCY OF TWO SECTORS. Denoting by! the national income defined by the usual SNA concet, we divide Y into two comonents: Y, the income from the - goods-roducing activities, and Y, the income from the service s activities, i.e., y = y + y s where Y may be regarded as the national income defined by the MPS concet. If we define.9.. as the roensity to consume services, then the demand for services, i.e., qy, must be equal to the suly of services in equilibrium and we have (1) y s Substituting (1) in (2), we get = qy (2) y = 9. s 1 - q This equation (3) demonstrates that the level of service-income Y deends on two factors: s y (3) the activity level of goods-roduction and the roensity to consume services. The first factor reflects the correlation of the level of service activities with the level of goods-roducing activities so that the latter determines the former as argued by the orthodox economists. As shown by the equation, service activities will exand with a higher level of activities in goods roduction. The second factor reflects the structure of demand as asserted by many modern economists. Since the income-elasticity of demand for services is greater than that for goods, the degree of growth in the service sector would deend on the order of increase in the roensity to consume services. Higher roensity would generate a higher level of service activities.

6 -4- The form of exression (3) is very similar to the Keynesian multilier equation, and in effect we can interret it as the result of the roagation rocess caused by the goods-roducing activities through the exenditure of income. Justification for the existence of formula (3) as a result of the multilier rocess follows. First~ we make three assumtions: (i) the roensity to consume services.9.. lus the roensity to consume goods.e. lus the roensity to saving ~ are equal to one; (ii) saving equals investment in ex ost; and (iii) the level of goods roduction equals Y in ex ost. Given these assumtions, the following ro agation rocesses can be worked out: income from goods-roduction,y! saving total suly of goods demand for g:ods I = y l I II j' Consumtion of goods Consumtion of services = -~q-y 1 - q - demand for services income from service activities = g y 1 - q II su:y of J services National roduct y y + y s 1 y 1 - q

7 -5- Of course, the convergence conditions are generally verified by the assumtion that the values of _g_, E. and s are each less than one. We could define the multilier 1 ~ q as the "exansion multilier of service activities" accomanied by the multilicand Y Thus formula (3) interreted as a multilier equation may be one means of connecting the orthodox view of the relationshi between goods and services with the modern Keynesian exenditure viewoint. In any event the growth of the service sector must be exlained in terms of both demand and roduction. The last line of the above table, i.e., the equation on 1 national roduct, Y = --- Y, can also be obtained in another 1 - q way, namely, by substituting (2) in (1). This national roduct equation gives us a relationshi between the national income defined by SNA (i.e., Y) and the national income defined by MPS (i.e., Y ). Some oular exlanations for growth of the service sector in recent years are often exressed in terms of emloyment rather than in terms of income. Our formula (3), exressed in terms of the income base, could be transformed into the emloyment base so that y L q -12. L (3a) s 1 - q y s where L s' L are levels of the goods-roducing sector stand for the roductivity of each sector. 1 According to A. S. Dhalla, emloyment in the service sector and in y y s resectively, and -12. ys =- L ' y = L s in an attemt to exlain the relatively faster growth of emloyment in the service sector, three main aroaches have been considered, namely: (1) income

8 -6- and exenditure aroach, (2) roductivity aroach, and (3) emloyment aroach. These three aroaches can be dislayed in unified form with our formula (3a). The first element in (3a), i.e. 1 ~ q, shows a demand factor that reflects the degree of income-elasticities in demand for services, as tyically argued by Colin Clark and others. 2 second element, y /y, exlains emloyment growth in services through s a relatively slower growth of roductivity in the service sector, 3 as ointed out mainly by V. Fuchs. The And the third element, L, shows that growth of service emloyment is a function of the growth of 4 manufacturing emloyment, as argued esecially by W. Galenson. These conventional exlanations of emloyment growth in the service sector are often considered in isolation rather than in conjunction, but our formula (3a) ties together the above three main aroaches in a generalized attern, Now, we return to formula (3), roved in terms of income base, in order to examine its character and economic meanings. At least four oints should be noted reliminary to a generalized analysis based on the above formula. First, in order to understand our formula (3) as one of the multilier equations, we have to assume that the comonent of the multilier, i.e., _q, is indeendent of the multilicand Y; similarly, the multilier formula in general must make this assumtion. However, the assumtion does not hold for our case. In the modern industrial society, the value of Y includes costs such as advertisement and information, and the sum of these exenditures by firms influences the value of _g_, as asserted by

9 -7- K. Galbraith in terms of "deendence effects" or a shift from 11 acceted sequence" to 11 revised sequence" in the relation between demand and roduction in the markets of modern industrial society. 5 As we can see in the comment by R. Solow on Galbraith, the effects of advertising by various firms may offset each other. Still, we cannot overlook the existence of such effects. At any rate, this roblem leads naturally to the next oint. Second, the value of Y in (3) shows income originating in the.goods-roducing sector. To be sure, Y is value-added by manufacturing industries, but not received in the same industries. And Y contains not only costs of advertisement and information, but also interest costs, rent carriage, insurance rates, etc. These costs then will be transferred from the goods-roducing sector to the "tertiary sector" as income. The increasing trend toward such income-transfer coincides with the fact that growth in the goods-roducing industries reflects increased activities in the service sector. Then, denoting by..'.. this transfer of income from goods-roducing I to service sector, and by Y income received in the goods sector, we get y = y - T Here Y is income as defined by the MPS concet, whereas Y is the income of the goods-roducing sector in the usual sense emloyed by national accounts in caitalistic countries. Denoting by Y s I the income 0 service sector in the ordinary sense, namely, on an income received base, then we have So, if we ut a following form: y y + T s s = T/Y ', formula (3) would be rewritten in the (4)

10 -8- where a may be viewed as the ratio of transfer income. This revised formula (4) is exressed in terms of an "income-received base,;r and not an "income-originating base" as was the case in the revious formula (3). In this new exression, the fundamental assumtion of indeendence between the comonents of the multilier and the multilicand may also be imroved. An increase in arameter a i.e., the ratio of transfer income, will induce the increase, namely, the income of the service sector in the income- of Y s I received base. If we stand on the income-received base, the equation of the growth of service emloyment must also be rewritten as follows: Y' L q + a _E_ L (4a) s 1 - q i y s where the definitions of roductivity for each sector are revised Y' v Y' as y = s y = _E_ resectively. s L L s s The tendency toward increase in the arameter a could be illustrated by Table 1 of M. Shinohara's work. 6 Figures of Column (a) in the Table indicate the gross value-added in manufactures according to Industry Census statistics which show the manufactures' income in the income-originating base; whereas Column (b) reflects the income of the manufacturing sector by Income Statistics which show the manufactures' income in the income-received base. The increasing tendency toward discreancy in both sets of figures in the table clearly discloses one reason for the growth of the service sector in recent years.

11 -9- It may be worth noting that the recent growth tendency of service sectors is usually calculated on an income-received base and not on an income-originating base. latter base, namely (3) instead of (4)~ Then, if we choose the or (3a) instead of (4a), the weight of goods-roducing activities would be larger than is usually estimated. TABLE 1. Discreancy in Manufactures' Income Between Census and Income Statistics Industry Date (a) Gross value-added in manufactures (by industry census) (b) Income of manufactures (by Income Statistics) (b) (a) hundred million yen hundred million yen % 1952 S3 S4 SS 56 S7 S8 S ,000 11,629 16,864 13,092 18,9S9 1S,3S8 20,986 ls,348 2S,437 18,S7S 29,S22 24,082 31,748 24,SS6 38,467 27,138 S0,348 36,390 61,898 44,2S7 71,SOS 49,81S 81,709 SS,S09 94,619 63,93S 89.S l S S Source: M. Shinohara, Sangyokozoron (Industrial Structure), Tokyo, Figures in column (a) show the manufactures' income in 11 income-originating base," and those in column (b) show the manufactures' income in "incomereceived base."

12 -10- Third, the relationshi between the growth of the service sector and the activity level of the goods-roducing sector suggests that the latter determines the fonner, but this may reresent only one side of the roblem. The other side, showing that service activities determine the level of goods-roducing activities, also exists, articularly if we take into account the develoment of informationservice industries in recent years. The imortance of informationservice industries is great enough that it is not longer ossible to regard them as merely an accessory of goods-roducing activities. Rather we must recognize information-service industries as a necessary and imortant art of the modern economy. We leave the discussion on this roblem to other works and instead consider the twofold interaction betwc;;en these sectors from some other standoint. Fourth, the aroach to income analysis as shown in the formulae (3) and (4) hava one limitation, namely, they treat services only as final roducts. If these many scyvices did constitute final roducts, we could ut forr'1ard an a:-1alysis in income terms. It is true, however, that the growth of intcrmedi~te services in their magnitude and their content is a characteristic of the modern industrial society. It is thu:3 im)ortant to examine the intermediate services, not only because of their own significance, but also because of the interactions betwr:.en goods and service sectors and between final and inte-:::medl1te ro;:il!cts. The next section resents a tentative aroach based oe an :I.nrut-outµut analysis by which we can clarify some of these oints.

13 -11- III. INPUT-OUTPUT ANALYSIS OF INTERDEPENDENCY OF TWO SECTORS As an extension of the inut-outut analysis, we reviously introduced a formula of artitioned matrix multiliers showing the interaction 7 among two or more strategic industry grous. The method emloyed therein is to artition off the original Leontief inverse in terms of the combined effects of "internal multiliers," "external multiliers," and their "induced sub-matrix multiliers." Such an internal-andexternal matrix multilier model well may be alied to our resent roblems, because the usual Leontief inverse tells us only the ultimate total effects but not the disjoined effects searating into artial multiliers. We will reroduce a summarized version of these theoretical ideas and then introduce emirical illustrations showing some international comarisons on the interaction between the goods-roducing and the service sectors. We divide ~ industries in the usual inut-outut table into two subgrous designated P sector (goods-roducing) which consists of 1 industries, and S sector (service) which consists of m industries. Then the n x n matrix of inut coefficients is 1 m A 1 + m = n where P and P 1 are submatrices of coefficients showing the inut of P sector's roducts in the P and S sectors resectively, and s 1 and S are submatrices of coefficients showing the inut of S sector's roducts in the P and S sectors resectively. Among these submatrices, P and

14 S are square and P 1 and s 1 are rectangular. Since the n x n Leontief inverse -1 R = (I - A) tells us only the total ultimate effect but not the disjoined interdeendence of the above two activities, we must introduce some device consisting of artitioned matrix multiliers. In order to solve this roblem, we decomose the elements of the Leontief inverse into three asects of roagation as follows: (i) Internal roagation activhies inside the goods-roducing sector's industries. This asect will be shown as the "internal matrix multilier 11 of the P sector (having order 1 x 1): B = (I - P)-l (ii) Internal roagation activities inside the service sector's industries. This asect will also be shown as the "internal matrix rnultilier 11 of the S sector (having order m x m): T - (I - S)-l (iii) Intersectoral roagation activities between the P and S sectors' industries. This asect will be shown as four rectangular sub-matrix-multiliers which naturally follow from the oeration of internal multiliers B and T: B 1 = s 1 B... S-goods inut in P sector induced by internal roagation in P sector's industries (m x 1). B 2 BP 1... internal roagation in P sector's industries induced by P-goods inut in S sector (1 x m).

15 -13- T 1 P 1 T... P-goods inut in S sector induced by internal roagation in S sector's industries (1 x m). T 2 = TS... internal roagation in S sector's 1 industries induced by S-goods inut in P sector (m x 1). These four sub-multiliers reveal the coefficients of induced effects on outut or inut activities between two sectors and are called the roduction-generating rocess in succession. (iv) The above three asects of the interaction rocess naturally lead to another intersectoral multilier that we could call the "external matrix multiliers" of the P and S sectors according to their economic meanings. If we select the coefficient of the induced effect on roduction (i.e., B 2 and T. 2 ) as the base, then they will take the form -1 L = (I - B 2 T 2 ) K (I - T B )-l 2 2 Of course L, the external matrix multilier of the P sector, has the order 1 x.!_, and K, the external matrix multilier of the S sector, has the order ~ x ~'. 9 ma k e t h e new square matrices. because the multilications of rectangular matrices (v) Now then, we have arrived at the fact that the total of the roagation effects in the P and S sectors' industries, each generated by its own sector's activities, are exected to take the values LB and KT resectively, i.e., 11 the internal matrix multilier" remultilied by the "external matrix multilier." So, if we assume KT H LB = N

16 -14- then we can rove the following formula: -l l B + B2MB1 B2M ]\ R = (I - A) = \ ' >-! '. MB1 M ~-,.- I =I i N T + NT l 1 J T 2 NT 1 j In other words, we can break down the original Leontief inverse (R = (I - A)- 1 ) in terms of the combined effects of internal and external matrix multiliers and their induced sub-matrix-multiliers (the roof omitted). From which it is easily seen that the combined effects in the P and S sectors originated each in its own sector's activities and can be written in the additive form B + B MB or 2 1 T + T NT as well as the multilied form LB or KT. 10 In any case, 2 1 such analysis serves to elucidate some inherent roerties of the interaction between the P and S sectors. An emirical alication of our model was made for several countries by utilizing these countries' inut-outut tables, and the data arrangements and calculations were done by the staff of the Research Bureau of Economic Planning Agency of Jaan. Table 2 is a summarized version indicating the interaction between P and S sectors and esecia.lly emhasizing the relation between the cross-inut-coefficients of the two sectors (i.e. A and 1 s 1 ) and the internal roagation in the goods-roducing sector. By examining Table 2 -(1), we can see which country's goods-roducing sector generates more service activity because the figures in the table show the coefficients of service-inut generated by the

17 -15- internal roagation of goods-roducing sectors. They are obtained by adding u the values of B = 1 s B for each service sector. 1 One feature of these figures is of articular interest. Among the total values in the last line of Table 2-(1), the figure for the United States is distinctly high. It totals 0.24, while values for the other countries are in the range of about Among these other countries, Jaan and West Germany have relatively higher values. Thus, the caacity of the industrial sector to induce service activity is greatest in the United States, followed by Jaan and West Germany. Now, looking at the tables by category, we can see that the Trade category has a relatively high value in almost all of the countries cited above, but at the same time it may. be worth noting that the Other Services category in the United States also has significant value. This shows that goods-roducing activities, esecially in the United States, have a significant effect uon the Other Services category as well as on Trade. On the other hand, Table 2-(2) tells us what sort of service sector has more influence on the internal roagation in goodsroducing activity, because these figures indicate the coefficients of internal roagation in the goods-roducing sector induced by goods inut in the service sector. The coefficients obtained by summing u the values of n 2 = BP for each sector. 1 Looking at the table by category, the figures for Transortation are highest in every country but the United States; thus that category has the greatest caacity to induce goods-roducing activities. In the United States alone, the highest coefficient is found in the Other

18 -16- INTERNAL MULTIPLIERS IN THE GOODS-PRODUCING SECTOR AND LEVEL OF SERVICE ACTIVITIES (1) Coefficients of Service-Inut Induced by Internal Proagation in the Goods-Producing Sector Country United Jaan West France Italy Holland Belgium States Germany Category (1958) (1960) (1960) (1959) (1959) (1959) (1959) Trade Banking and Insurance Real Estate Transortation ( ( Communication ( Public Services Other Services All Service Sectors

19 -17- Table 2 (cont'd.) (2) Coefficients of Internal Proagation in Goods-Producing Sector Induced by Inut in Service Sector Country United Jaan West France Italy Holland Belgium States Germany Category (1958) (1960) (1960) (1959) (1959) (1959) (1959) Trade Banking and Insurance Real Estate Transortation ( ( Communication ( Public Services Other Services ( ( ( ( All Service Sectors

20 -18- Service category, and this fact, together with the above conclusions, suggeststhat the United States is the country having the most advanced "Service Economy. 11 Next, among total values in the last line of Table 2-(2), that for Jaan is the highest, but this is because of the relatively high value of the internal multilier in the goods-roducing sector in Jaan (on the average, the value for Jaan amounts to 2.298, while for the United States it is and for West Germany, 1.732). On the other hand, Jaan's total value in the revious Table 2-(1) was not the highest because of the relatively low service-inut coefficients in the goods roducing sector (S 1 ) in Jaan. On the average, the value for Jaan amounts to 7.3%; for the United States, 12.9%; and for West Germany, 9.3%. Viewing the service sector, we see that the sub-matrix-multiliers B 1 and B 2 oerate on that sector in an indirect manner. Of course, the final roagation effect on the service sector itself may be shown by the value of M or by the searate values of T and K, namely, the internal and external multiliers of the service sector. The summarized values of the elements of T and K are given in Table 3, which shows the owers of disersion of the service sector internally and externally. Table 3-(1) tells us the effects of internal roagation on the service sector starting from service-inut in the service activities. By examining the values for each category in that table, it is aarent that the service sector in the United States has the greatest effects of internal roagation. The values for Jaan are of about the same order as those for the Euroean countries. Such internal roagation in the service sector leads in turn to circular reercussions on the service

21 -19- sector itself through the goods-roducing activities that start with the consumtion of goods in the service sector. For examle, the United States' Trade sector has an internal multilier effect of on the average, and it leads to external reercussions through goods-roducing activities to the extent of an aroximate 2.68%-lus average. We see then that the total effect on the Trade sector is equal to x = on the average. Thus do the internal roagation atterns together with the external reercussion atterns deict the characteristics of intersectoral roagation in the service sector. Among the round-about external effects in Table 3-(2), the Transortation sector has the highest values for all countries excet the United States. Again, the United States alone finds its highest value in the Other Service category. This fact reinforces our conclusion that the United States of America is the country with the most advanced Service Economy f~om the viewoint of the interaction of goods-roducing activities and service activities. A comment is needed to evaluate the figures in the above tables because international standards for calculating inut-outut tables are not yet established. In articular, inconsistency in the arrangement of data from the service sector may lead to some estimation errors, and only rough international comarisons of figures can be achieved. is because we are restricted, when citing the calculated figures~ This to some summarized and aggregated values only. Under these circumstances, we must resign ourselves to the test of column sum or row sum values instead of using the details of cross-effects determined by testing the figures of elements in matrices themselves.

22 Table 3. INTERNAL AND EXTERNAL MULTIPLIERS IN SERVICE SECTOR (1) Internal Multilier of Service Sector ~ntry United Jaan West France Italy Holland Belgium Categ y States Germany Trade Banking and Insurance Real estate Transortation ( ( Connnuni.cation ( Public services I 0 Other services N I - (2) External Multilier of Service Sector Trade Banking and Insurance Real estate Transortation ( ( Communication ( Public services Other services

23 NOTES AN ANALYSIS OF THE INTERDEPENDENCE BETWEEN SERVICE AND GOOD-PRODUCING SECTORS by Kenichi Hiyazawa 1. A. S. Bhalla, "Role of the Services Sector in Emloyment Exansion," International Labour Review, May 1970, and "A Disaggregative Aroach to LDCs Tertiary Sector," Yale University Economic Growth Center Discussion Paer, Aril, Colin Clark, The Conditions of Economic Progress, 1940 and Victor Fuchs, The Service Economy, Walter Galenson, "Economic Develoment and the Sectoral Exansion of Emloyment," International Labour Review, June J. K. Galbraith, The New Industrial State, Miyohei Shinohara, Sangyokozoron (Industrial Structure), Tokyo, K. Miyazawa, "Internal and External Matrix Multiliers in the \ _ Inut-Outut llodel, 11 Hitotsubashi Journal of Econor.1ics, June This dividing of matrix means that we use the following system: PX + P 1 X + Y s s 1 x + sx + Y s s Where X, X are outut vectors of P and~ sector's industries, s and Y, Y are the final demand vectors of the P and S sectors s r.esectively.

24 -2-9. Another formulation of the external matrix multiliers based on the coefficients of induced effect on intersectoral inut activities (i.e., T and B ) could be 1 1 L = (I - Tl Bl) -1 (1 x 1) K = (I - Bl Tl) -1 (m x m) We can rove the existence of the following relations: KT = TK LB BL 10. Thus the searate intersectoral activities may be viewed in two ways: (a) the first exression of the formula shows it from the P sector viewoint and (b) the second exression constitutes the S sector viewoint. The solution of our system shown in Note 8 is stated as [ x 1 IB + BlIB1 B2Mj x:j 3:-] = MB M l. 1 = r- N J r~j NT t 1 T 2 N T + T NT 2 1 \y L s