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(1)Variety in Japan (1980― 2000) Nguyen Anh Thu. 1．Introduction Since the Meiji period, the composition of Japanʼs foreign trade has had many changes. Along with the development of the economy, more and more products are available for export and, at the same time, more varieties of goods are imported for domestic consumption and production. However, since the mid-1980s, specialization and the expansion of foreign direct investment became trends in the Japanese economy, which might reduce the range of exported products. The 1980s also witnessed solid developments of Japanʼs economy, which might have the opposite effect on variety. From 1993, Japanʼs economy entered a period of economic stagnation. We expect that varieties of imports and exports might decrease in this period. Also the conclusion of many bilateral trade agreements in these periods might affect Japanʼs trade composition as well as import and export varieties. Therefore, it is interesting to access the real changes of variety in Japan during these two periods: the 1980s with an economic boom and the 1990s with an economic slowdown. In this paper we present calculations of variety of Japanʼs import and export for 21 industries over 21 years with a method developed by Feenstra (1994). Many papers on economic growth theory have confirmed the importance of product variety (Romer, 1990; and Grossman and Helpman, 1991) and a number of empirical studies have tested this theory. These studies analyze the relationship between an increase in variety and total factor productivity (TFP) as in Feenstra et al. (1999a), between an increase in variety and Gross Domestic Product (GDP) in Funke and Ruhwedel (2005), between variety and business groups in Feenstra et al. (1999b) or between an increase in variety and welfare gains as in Broda and Weinstein (2006). A careful study of Japanʼs product variety, therefore, will be significant for other empirical studies of economic growth theory. Firstly, we have to consider Japanʼs trade composition as well as trade policy to have the overall picture of Japanese foreign trade, which are the main factors affecting the variety of imported and exported goods. Japan’s trade composition In the early Meiji period, Japanʼs major exports were coal and silk, and its major imports were manufactured goods, wool and cotton. From the late nineteenth century until the Pacific War, Japanʼs major export was textiles and its major imports were primary products including fuel. From 1960, Japanʼs major exports changed to automobiles, electronics goods and other manufactured goods. From 1945, its major imports have been petroleum and other natural resources. The changes of Japanʼs trade composition are in accordance with the principle of comparative advantage (Saxonhouse, 1982). In the Meiji period, Japan had comparative advantages in producing coal and silk, which had a lower autarky price than in other countries. At the same time, it imported manufactured goods, wool and cotton, which.

(2) 96. （288）. 横浜国際社会科学研究第 14 巻第 3 号（2009 年 9 月）. had higher autarky prices (Huber, 1971). As Japan industrialized and accumulated physical and human capital, its trade composition has changed. Japan has gained expanded production possibilities in producing automobiles, electronic goods and other manufactured goods and therefore it became the exporter of those goods and the importers of natural resources. From 1980 to 2000, the basic trade composition of Japan remains, but with the conclusion of many bilateral trade agreements, we can expect changes in trading partners as well as in the trading pattern, which directly leads to changes in import and export varieties. In the next section, I would like to give an overview of Japanʼs trade policy during this period. Japan’s trade policy Since the establishment of the General Agreement on Tariffs and Trade (GATT) in 1947, a number of multilateral trade policy agreements have cumulatively reduced the developed nationsʼ ad valorem tariff rates from 40% in 1947 to 4% in 1994. Japanese trade policy also followed this liberalization trend. However, the elimination of protectionist trade policies of Japan is substantially due to foreign pressure (gaiatsu) (Lincoln, 2001). Japan joined the GATT in 1955, however, it still maintained its system of foreign trade rationing and trade quotas in agricultural commodities. Only in 1963 were those quotas converted to tariffs and in 1964, foreign exchange restrictions on current transactions were abandoned. The liberalization of Japanʼs trade was largely due to the successive GATT rounds, especially the Tokyo Round concluded in 1979 and the Uruguay Round concluded in 1995. In 1988, Japan began lowering tariffs on many goods three or six years ahead of schedule. By 1992, all Uruguay Round concessions and more were made. By this year, Japanʼs average tariff rate for all imports was about 7% (GATT, 1994). Most of the manufactured products were duty free. Although Japan is a full member of GATT, Japan has often been accused by the United States and Europe as having a closed market (Prestowitz, 1988). This criticism arises partly from the trade surplus of Japan with other countries, especially with the US (Flath, 2005). Before 1980, many US industries including textiles, steel, televisions and automobiles were seeking protection from Japanʼs imports. The Japanese Government then agreed to voluntary export restraints of the above mentioned and other disputed commodities. The restraints of Japanese exports to US were then followed by similar restraints requested by the EU. Consequently, by the mid-1980s, a substantial part of Japanʼs exports to the US were subject to Japanese government restraints. However, the protectionist pressures seem to grow (Lincoln, 2001). Since 1985, many bilateral negotiations between US and Japanese governments, which benefit American exporters to Japan, were obtained. The US industries which benefited included semiconductors, beef, oranges, wood products, insurance, telecommunications, auto parts and other items. Table 1 reports important Japan-US bilateral agreements on agriculture and manufactured products. In the 1980s, although Japan lowered barriers to trade, Japanʼs trade surplus rose sharply. This was partially due to the liberalization of its foreign investment law beginning in 1980. Later, in 1992, after a long period of steady growth, Japan entered a period of economic stagnation. The GDP growth fell and in 1993, the GDP real growth was zero. This stagnation led to the decrease in nominal imports and thus leading to a higher trade surplus (Parsons, 2000). The above overview of trade policy in Japan helps us to understand the import and export activities of Japan in the period 1980─2000 and thus, can help us to explain the changes in import and export varieties of Japan during this period. Feenstra (1994) created a method to measure product variety. This method was used in many empirical studies to estimate the effects of variety on economic growth or other economic indices. In the following part of this paper, I will.

(3) Variety in Japan (1980―2000)（Nguyen Anh Thu）. （289）. 97. Table 1 Major Bilateral Trade Agreements between Japan and the US (1980―1996) Year Telecommunications NTT Procurement Telecomm.Equip. & Services- MOSS Telecomm.-Cellular &Third-Party Radio Telecomm.-Cellular & Third Party Radio. 1980 1986 1989 1994. Computers & High Technology Electronics – MOSS Medical/Pharmaceutical Products-MOSS Medical Technology Procurement Non-R&D Satellite Procurement Supercomputer Procurement Computer Products Procurement Semiconductors Semiconductors. 1986 1986 1994 1990 1990 1992 1991 1996. Transportation Auto and Auto Parts –MOSS Auto and Auto Parts Auto and Auto Parts. 1987 1992 1995. Food and Agriculture Agriculture – Beef and Citrus Agriculture – Other Products Leather and Leather Footwear Wood Products – MOSS Wood Products Paper Products. 1988 1988, 1992 1985 1986 1990 1992. Building and Construction Flat Glass. 1995. Source: ACCJ 1997. try to analyze and extend the product variety index in Feenstra (1994) to clearly separate import and export variety. The third part will describe the data used in this paper, which is Japanʼs trade data for 21 years, from 1980 to 2000. The result of the second part will then be applied in the fourth part of this paper to measure Japanʼs export and import varieties. Section 5 concludes the paper. 2．The measurement of import and export varieties Generally, a product variety is defined as the brand produced by a firm, the output of a firm, the output of a country or the output within an industry in a country. In order to measure product variety, Feenstra (1994) and Feenstra and Markusen (1994) proposed a solution, in which new product varieties enter a constant-elasticity-of-substitution (CES).

(4) 98. 横浜国際社会科学研究第 14 巻第 3 号（2009 年 9 月）. （290）. aggregator function. The change of product variety between two periods is a function of the total expenditure and the expenditure on new varieties of the two periods. In this paper, I extend Feenstraʼs (1994) variety index by incorporating import variety or export variety. The production function will take the form. V /(V 1). V /(V 1). , zt , I t , J t ). ª º V /(V 1) ª º (V 1)/V aªi xit(V 1)/V (V1)/ b z (V 1)/V (»V 1)/V º ¦ V j jt (1) ¦ b j z jt (yVt1)/Vfy»( xt , zf t(,xI t,, zJ t,)I , J« ¦ « ¦ ai xit )I « ¦ ai xit iJ ¦ b j z jt ¼ » t t t t ¬ti iJ t ¬ iIt ¼ iJ ¬ iI ¼ t. t. t. (1). ⑴ . (1). t. where ai ! 0 and b j ! 0 are parameters, V ! 1 is the elasticity of substitution, I t VV/(/(VV1) 1) V /(V 1) ! 0 and b j1!ªis0I tthe are parameters, V !substitution, 1 is the elasticity of substitution, 0 and b j ! 0 are parameters, 1 is the ofaisubstitution, > 0! and 0 arewhere parameters,σ> elasticity the set Iof domestic inputs in bj >elasticity t where ai V º It denotes º of (((V VVV (V 1)/V the set denotes ythe ªªset of domestic t ºand Jbt zdenotes of imported(1) ((VV1)/ 1)/VV inputs in period VV1)/ 1)/ 1)/ f ( x , z , I , J ) a x y y f f ( ( x x , , z z , , I I , , J J ) ) a a x x b b z z (1) (1) « » t t t t t i it j jt « « » » t t t t t t t t t t i i it it j j jt jt denotes set inputs in period tproduction and J t denotes the set yof imported ª period set ofthe imported inputsiin period of output of t and Jtt denotes t. The of domestic inputs in period andinputs J t the denotes the set ofofdomestic imported t requires not only varieties It output y requires of domestic in period ¬JJof ¼ ii t yt f ( xt , zt , I t , J t ) « ai xit(V 1)/V b j z jt (V tt ¬¬iiIIttt . The production ¼¼iJt not only varieties inputs in period t . The production of output y requires not only of domestic Vwith /(V varieties 1) the production domestic inputs , but also varieties of imported goods . This is different function in Feenstra t x z iJ t t. The production of output yt requires notxitonly of domestic it inputs ¬ iIt , butvarieties also varieties ofª imported jtgoods z jt . This is ºdifferent with the (V 1)/V 1)/V inputs xfita(i, x!domestic but imported is substitution, different with where 0 and ! parameters, V 1 is the I t the y00t are ,also I t ,bJj tvarieties )VV0 !are aof b jsubstitution, z jtz(Velasticity (1) !goods jt . This which does not distinguish and inputs. «imported » of t , ztin i xitwhich where where aagoods ! ! 0 0 and and b b ! ! are parameters, parameters, ! 1 1 is is the the elasticity elasticity of of substitution, I I also varieties of(1994) imported z . This is different with the production function Feenstra (1994) does not distinguish domestic and ii jj tt jt iJ t ¬ iIt in(1994) ¼ the set where ai ! 0 and b j(derived ! 0 are parameters, production function in Feenstra not distinguish domestic and denotes the of of domestic inputs t and Jdoes imported firm will minimize its set cost production and period come which up with following CESofunit-cost function in the V ! 1 is the ela t denotes imported inputs. The tion in Feenstra (1994)the which does notimported distinguish domestic and denotes denotes the set set of of domestic domestic inputs inputs in in period period t t and and J J denotes denotes the the set set of of imported imported tt inputs. denotes the set of domestic inputs in period t and J t den The firm will minimize its cost of production and come up with following CES inputs in period t. The production of output yt requires not only varieties of domestic Appendix) where ! 0 and 0 are its parameters, Vvarieties ! 1 is theand elasticity of with substitution, iof jy! requires Theaof firm will bminimize cost production up followingI t CES inputs inputs in in period period tt.. The The production production output output yin requires not not of only only varieties of ofcome domestic domestic unit-cost function (derived Appendix) tt the inputs with in period inputs xit up , but also varieties CES of imported goods z jt . This is different the t. The production of output yt requires not o will minimize its cost of production and come with unit-cost function (derivedinputs in thein Appendix) denotes the set of following domestic period t and J1/(1 the set of imported V ) t denotes inputs inputs xxitit ,, but but also also production varieties varieties of of imported imported goods goods (1994) zzjtjt .. This This is is does different different with with the theinputs x , but also varieties of imported goods z jt . Th ª º function in Feenstra which not distinguish domestic and 1/(1 V ) it n (derived in the Appendix) V 1V 1V production of output y Vrequires not only varieties of domestic inputs c (inptperiod , qt , I tt,. JThe (2) ªdoes « adoes t) i pit V 1V bt i q jt V» 1V º imported production production function function in in Feenstra Feenstra (1994) (1994) which which not not distinguish distinguish domestic domestic and and 1/(1 V ) inputs. production function cbut ( pt ,also qt , I tvarieties , J¬ti) It «of imported ai pitjJt goodsbiz¼q .jt This » is different with the(2) in Feenstra (1994) which does not d inputs xit ,firm ª imported º The jt come up will minimize its cost of production followinginputs. CES imported ⑵ V 1V inputs. V 1V i It jJ t and imported inputs. ¬ ¼ ofwith I t , J t ) « ai pit bi q jt unit-cost (2)Appendix) pfunction is the(derived price ofindomestic inputwhich i, and does q is the price imported input and j. » wherefunction production in Feenstra (1994) not distinguish domestic the The firm willj. minimize its cost of production and com The The firm firm will will minimize minimize its its cost cost of of production production and and come come up up with with following following CES CES where p is the price of domestic input i , and q is the price of imported input i I j J t ¬ t ¼ we consider Now toVanalyze the impactsfunction of ) imported inputs. two successive periods 0,1. In order1/(1 unit-cost (derived in the Appendix) unit-cost unit-cost function function (derived (derivedNow in in the the Appendix) ª input º order weAppendix) consider two successive to analyzeover the time, impacts of Vcost V periods V0,1. 1 VIn come varieties, IIimported assume that the domestic input variety is unchanged the price of domestic input i, and qimport is theThe price of j . 1of firm will minimize its production and up with following CES 1/(1V c ( p , q , , J ) a p b q (2) « t varieties, t t t I assume i itthe jt » variety is unchanged over time, 1/(1 1/(1domestic VV )) i input import that ª successive º I 0 I .(derived The set¬in imported input over time, there are themeaning price domestic input and the of imported inputbut we consider two where V 1V V 1V p is In i,of q ºis j. Now unit-cost function Appendix) iIthe jprice J t is changing ªªtoofI1 analyze º t ¼ er two successive periods 0,1. order the impacts of c ( p , q , I , J ) a p b q VVI 11IVV I . The VVset11of « t are t t i it i jt » input is changing over time, but tthere meaning 1p 0 cc(( p0,1. ptt ,,qqIn ,, IIorder Jsome aaavailable p impacts bbiidomestic qqjtjtVV »imported (2) (2) in over 1/(1V ratio ) ««where »Jinput ttinput tt ,, J tt ))to analyze iipthe inputs both periods J0 between theinput two iI tunchanged jJ t periods import varieties, thatof the domestic input isititthe price i, Jand qassume isºcost the price imported j. variety¬is ¼ 1 . IThe I assume that the domestic variety is unchanged time, ªofof V 1 V V 1 V i i I I j j J J some inputs available in both periods J J J . The cost ratio between the two tp t ,q ,I , J ) tt ¬¬we ¼¼ 0,1. 0q 1 ccan (over bi In (2) periods measured by theaare price developed bytime, Sato (1976) and Vartia « » tbe ttime, t of timported i pperiods it index jtorder consider two successive to analyze the impacts of where p is the price of domestic input i , and q is the p I . The set of imported is changing but there over time,input meaning = = The set input is changing over but there are some inputs available in both INow I I. 1 0 i I t byq jindex Jt periods can be measured priceprice Satojj..(1976) and Vartia ¼ where where pp is is the the(1976) price price of ofvarieties, domestic domestic input ii¬,,that and and qthe is isdomestic the the price of ofdeveloped imported imported input input import I input assume the input variety is by unchanged over time, Now we consider two successive periods 0,1. In order to periods = . The cost ratio between the two periods can be measured by the price index developed by Sato (1976) ilable in both periods JJ JJ00 J11 . The (1976) cost ratio between thedomestic two w j (imported J) where the price0,1. of i, and is)the theimpacts price inputarej. I assume that the domestic input variety 1/( V 1) input wq i ( I the I pI isperiods I . The set ofIn is changing over of time, but there meaning Now Now we we consider consider two two successive successive periods 0,1. Inimported order order to toinput analyze analyze impacts of of import varieties,. ¦. ¦¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. ¦. § · , J1 ) §and O1 (Vartia c ( p1 ,Sato q1 1 , I10 (1976) J) · wj (J ) 1/(V § 1) pi1 · wi ( I ) q j1 and Vartia (1976) measured by the price index developed Nowby we two ¨successive In to analyze the · impacts ¨över ¸¸§time, qbetween import import varieties, varieties, II assume assume that that domestic domestic input input variety is unchanged unchanged over time, I(3) Iof I . The set of imported input is changing § Operiods · cost ¸1 (variety ¸§ porder ( the ) ·Jis cconsider pthe Jperiods some inputs available J¨0,1. ratio the j1meaning 1 two 0 i1 1 , ,qJ 1 , I)1 , Jin 1 )Oboth 0 J1 . The ( , , ( ) c p q I J p q J © is ¨¨ ¸¸ over time, (3) 0 0 i0 ¹ j unchanged 0 ¹ © 0 that ¹the domestic import 0varieties, I0 assume input variety ïs ¸ iI ©over ¨time, ¸jbut The set set can of of imported input input is changing changing over time, but there there are are meaning meaning II11 II00 II .. The some inputs available in both periods J J 0 J1 . The cos , , , ) O ( ) c ( pimported q I J J p q periods be measured by the price index developed by Sato (1976) and Vartia iI © i 0 ¹ jJ © j 0 ¹ 0 0 0 © imported ¹ I1 weights I 0 w0jI( .J 0)The of is changing overexpenditure time, but there are 1/(V 1) wmeaning ) wi ( I set w j ( J ) are input constructed from the shares the ) and i ( Iwhere (1976) § · q periods can be measured by the price index developed by § · § · pi1 , J1 ) O1 ( Jsome ) some inputs inputs available available in in both both periods periods JJ JJ00 The Thewcost cost ratio ratio between betweenfrom the the two twoexpenditure shares wi (JJI11).. and ( J ) are constructed the where j1 the weights inputs in both periods Jj J 0 J1 . wThe cost ratio wbetween the two (3) J) ¨N t zN t /available ¸¸ qN t zN t as: 1/(V 1) j ((1976) ¨ ¸ ¨ ¸sNsome i (I ) ¦ t (. ) { q¨ § qVartia · § pi1(1976) · , J 0 ) © O0 ( Jperiods )¹ periods can can be measured by by the price index developed by by Sato Sato (1976) and and Vartia ( p. ,q ONdeveloped (the J ) ·price index NI. j1 ) q{j1be z,NJt /1 )index qN§t zby iI be jsc 1the i 0 ¹ periods 0,qprice © pmeasured ¦ NJt (© N¹t1measured t1 as: can by ¨Sato 1/(V 1) wi ( I ) (3) ¸(1976) and Vartia ¸ ¨ developed ¸ N . ¨ ¨ (1976) (1976) ( , , , ) O ( ) c p q I J J p q §0 expenditure iI§ © siN01 (¹. ) jsNJ0 © c ( p1 , q1 , I1 , J1 ) § O1 ( J ) · ⑶ § pi1 · (1976) (. ) ¹ · (. )j 0 ¸¹· 0 the 0sN 1 (0. ) ©sN 00shares w j ( J ) are constructed from eights wi ( I ) and ¨ ¸ ¨ ¸ wN (. ) { ¨ 1/( ¸w j )( J ) ·Nc (=pi, ,j q , (4) § sN 1 (. ) sN 0ww1/( wjj (s(JJ)) (. ) sN 0 (. (¸(IVI)))1)¦· ¨ ln s § (w ) © O0 ( J ) ¹ )wi (ln )(iji. ln s§N 0the (. )expenditure iI © pi 0 ¹ jJ w ())©.,·ln )I1/({s,VVNJ¨1(1)1). N =0 i,I 0j , J 0(4) I§) sp and w where weights . N 0 (. N¨ 1· ¹( J ) Nare ··.wi )( NI)1from ¸§©§constructed qq¦ Nthe ·¹ (. ) ¸ 0shares § § · § · · q p § · § ( ( , , , , , , ) ) O O ( ( c c p p q q I I J J J J p ( , ) O ( ) c p q J j j 1 1 j 1 q z as: i i 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 ln s ( ) ln s ( ) ln s ( ) ln s . . . ¦ Nt Nt N1 © ¹¨¨ ¨N . ©¸¸¸ N 1 ¨ ¹ (3)weights w ( I ) and w ( J ) are constructed from (3) (3) ¸¸N 0 ¨¨¨ ¸ N0 ¨ ¨ ¸ ¸ ¸ ¸ where the . i j ¨ ( ) / s . { q z q z as: Ï¨ ©qqpi 0¸¸¹ (Op00(0(,JNJqt ))0N,t¹¹I 0¦ , J N)t N t II©©©O0pp(iiJ00 )¹¹¹ cO cc(( pp00,,qq00,, II00,, JJ00)) N t ©©The jJ © q j 0 ¹ jj JiJ© © jj00 as: ¹¹ value ofN .O1 (0J )iiand O0 ( J ) are constructed the (I) and (J) are constructed from the expenditure shares sN t (. ) { qN t zN t / ¦ qN t zN t as: as: w § weights · sN 1 (. ) sN 0 (. where ) · sN 1 (. )w s ( ) . i i The value of O ( J ) and O ( J ) are constructed as: N 0 I= ( J·)from are constructed from the expenditure shares N . thew ) iand wiiwhere and J¸sqN))1 (are are from the expenditure shares shares where where the¨weights weights w ((II)) and §wweights §the · sN ,0 (j.§)w0j (4) sexpenditure .w)i1N·(constructed constructed jj((J ¸ the § · N 1 (. ) sN 0 (. ) q z z ¦ jt¨ jt q¸ z · ¦)J ¹s§qjt(.z jt)qas: w ln (.s) {(. N =i, j (4) n sN 1 (. ) ln sN 0 (. ) ¹ N . © ln sN 1 (. ) s (. N) { qNNt0z¨N t¨©j/ln z jtsN·0 (¨.j) J¸¹t ,§jNJ¦ § sN 1 (. ) sN 0 (. ) · § sN 1 (. ) s jt ln ¦ N 1N¦ ¦ ln s jt (.jt ) ln sN 0 (. ) ¸¹ w (. (5) t Nt ¸ . ssNNtt((. .)) {{ qqNNttzzNNtt // ¦ qqNNttzzNNNttO as: 1 ¸ ¨ t as: ){¨ N .¨ j J ¸ ¨ j J t ,©jJ ¸N 1, t¸ 0,1 t (J ) ¨ ¸ ¦¨ N NN. . q z Ot ( ¨J )¦ q¨ jt z jt ¸ 1 , 0,1 (5) t ln s ( ) ln s ( ) . . ¦¨ jt §jtq s¸z (. )¸ s (. ) · N1 N0 © ¹ N . © ln sN 1 (. ) ln ¸ §jof ((. )qand jt szNOjt0 (¸(.J¨©)) arej· Jconstructed J t sN 1¦ of O1 ( J ) and O0 ( J ) are constructed as: ¦ t © ¹ jt¹ Nas: 1 jt N0 The value O J ) ¨ ¨ ¸ 1 0 w ( ) = i , j (4) N . { ⑷ §§ ss ((. sNNj00(¨J(. .)) NssNN00((. .)¨) ··© j J t §§ ss¹NN11((. .)¸) .)) ·· ¹ ¸ t © s¦ w wNN ((. (4)The value of O ( J ) and O ( J ) are constructed as: .)) {{ ¨¨ NN11 © ln ¸s¸N 1 (. ) ¨¨ln sN 0 (. ) ¹ N . © ln sN 1 (¸. ¸ ) lnNNs=N=0ii(,,.jj) ¹ (4). ¦q ¦q. j J. J t. . . . . ¦. z jt · ¸ ¸ z jt jt ¸ ¹. jt. ¦. ·lnln ss ((§..))¦ § ¦ q©©jtln · lnz sjtsNN11·((. ln ssNN00((§. )) ¹¹ q jtNNz. ln ssqNNjt00(z(. .)) ln .¦ ln . jt )) ¹¹ jt ©© NN11 ¨ j J ¸ ¨ j J , j J ¸ ¨ j J t , j J ¸ O ( ) 1 J 1 ¨ , 0,1 (5) t as: tThe value ¨ of Oq1 ( Jz) and ¸ O0 ( J ) äre constructed ¸, t ¸ q z q z ¦ ¦ jt jt ¸ jt jt ¦ ¨ ¨ ¸ jt jt (J) and (J) are constructed as: The The value value of of O O ( ( J J ) ) and O O ( ( J J ) ) are are constructed constructed as: as: The ¨ j J 1¸ 1 00 j J j J ©§ ¦ ©§ ¦ q jt z jt ¹· q jt z jt ¹· t © ¹ ¸ §§ ¦ qq jtjt zz jtjtOt··( J ) ¨¨§§jJ ¦ qq¸¸jtjt zz1jtjt··¨¨ jJ , jJ ¸, t q z q z ¨¨ jjJJ ¸¸ ¨ ¨ ¸ ¸ ¦ ¦ j j J J , , j j J J jt jt jt jt ¨ j J tt ¸ ¨,, jttJ 0,1 ¸ OOtt ((JJ )) ¨¨ 1 1 0,1 ©¨¨ ¹ ¹ ¸¸ ¸¸© q q z z q q z z ¦ ¦ jt jt jt jt jt jt jt jt ¨¨ jjJJ ¸¸ ¨¨ jjJJ ¸¸ tt ©© tt ¹¹ ©© ¹¹ t. t. 0,1. Ot ( J ). t. t. t. 1. t. 0,1. (5) (5). (5)§ ¦ q jt z jt ¨ j J ¨ q jt z jt ¨¦ © j J t (5). 0. · ¸ ¸ ¸ ¹. § ¨ 1 ¨ ¨ ©. ¦. q jt z jt · ¸ , q jt z jt ¸¸ ¦ j J t ¹. j J t , j J. t.

(5) iI 0,1. jJ ©to janalyze 0 0 0 two 0 successive 0 ¹ Now we consider the impacts of © 0 ¹ periods © i 0 In ¹ order I1i ( Ithat Iw. j (domestic The setconstructed ofinput imported is changingshares overtime, time, but there are import where varieties, I assume variety is unchanged over w J ) are frominput the expenditure themeaning weights )I 0andthe of imported input periods is changing meaning in both J J 0over J1time, . Thebut costthere ratioare between the two /I . The s (. I)1{ q I 0z some qinputs z set as: available Nt. Nt Nt. ¦. N .. Nt Nt. some inputs available J byJ 0 the J1price . Theindex cost developed ratio between the two periods incanboth be periods measured by Sato (1976) and Vartia § sN 1 (. ) sN 0 (. ) · § sN 1 (. ) sN 0 (. ) · (1976) periods wcan by the price by Sato ¸(1976) ) { measured i, j Vartia (4) N =and ¦ ¨ developed ¨ ¸ index N (.be (.V)1) ln sN 0 (. ) ¹ w ( I ) wj (J ) © ln sN 1 (. ) ln sN 0 (. ) ¹ N . © ln sN 1 1/( i (1976) Variety in Japan (1980―2000)（Nguyen Anh Thu） § q j1 · （291） 99 § p · c( p , q , I , J ) § O ( J ) ·. i1 1 1 1 1 1 1/(V 1) ¨ (3) ¸¸ ¸as:· wi ( I ) §¨ q ·¸w j ( J ) ¨¨ § p , q1value , I1 , Jof1c)O(1 (pJ0)§, and c ( p1The ) constructed O ( ) qO01,(OIJ00(),JJ·) 0are J p iI © ji10 ¹ jJ © q j 0 ¹ © 0 i1¹ (3) ¨¨ ¸ ¨ ¸ ¨ zp ·¸ O·0 (weights c ( p0 , q0 , I 0§, ¦ Jwhere J ) ¹§ ¦ q j 0 ¸¹ jJ constructed 0 )q jt z©jtthe ©jt jti 0w¹j ( J ) are wi (iI)Iqand from the expenditure shares © ¨ j J ¸ ¨ j J , j J ¸ expenditure(5)shares ⑸ Ot (the 1 0,1the J ) weights where ¸ , t from / wq¨j ( Jz ) are s¨ (. ) {wiq( I )z¸ and as: constructed t. t z Njtt ¸N t ¦ ¨N t N¦ q jt z jt ¸ © jqJNt t zN t as: ¹ N . © j J t ¹ sN t (. ) { qN t zN t / ¦ N . § · § sN 1 (.in) the s ( ) s ( ) ) · . . sNset N 0 on the imported inputs 0 (. The term Ow ) is the periodN 1t expenditure J, N =i, j (4) t (J ( ¨ the imported inputs ¸ the¦ ¨ J, ¸ expenditure N . ) {on The term Ot (J) ( J ) is the the period period §tt expenditure expenditure J , in set relative to that periodʼs The ln s ( ) ln s ( ) ln s ( ) ln s ( . . . · § · s ( ) s ( ) s ( ) s ( ) . . . . N .Ninputs. N1 N 0 Nimported N 1It can also Nbe 0 .) ¹ © Nperiod’s 1 N© 0 1 ¹ 0 relative to that expenditure on the total wN (. ) { ¨ =i, j (4) ¦ ¸ 1inputs. ¨ the ¸ onNthe on the total imported inputs. It canto also bethe to be minus relative to that period’s expenditure imported can also t expenditure son ) total ln sItN 1the (period ) lnimported sbe .understood . new understood be thesperiod N . © ln on N1 1 (minus N 0 (. )t ¹expenditure N 0 (. )input, © ln ¹ relative new imported input, understood 1 minus onoftheon imported relative relative to to thebeperiod expenditure onexpenditure import. there is a as: greater number of new imported value O1new ((J) J ) will and ( Jlower ) input, are if constructed t total tothetheperiod periodt texpenditure totalThe import. OObe 10( J ) will be lower if there is a greater toinputs the period t total expenditure import. )lead there a first greater in period 1. The lower a lower lower thelead right side of equation The value of O1 (J) ( J )Owill and O§will )tobe are constructed as:isthe number ofonnew imported inputs period 1. The lower value ofratio O1 ( J )on to hand a 1(J 0 ( J in · ifvalue §of ·will. ¨¦q Nt. jt. ¦ q z ¦q z q z 1 ¨ 0,1 ¦equation ¸ variety ¸ , tthe unit . In conclusion, new period !¨0 the V 1

(6) on ¸ ¨ any ¨q ofzimport ¸in ¦ q 1zwill reduce to thatvalue of period 0. first1/ratio lower of the right hand side (3), because ¦ ¨ ¸ ¨ ¸ Ocost( Jof) period 1 , 0,1 (5) t ¨the1change ¸import compared period 0. ©thatinof¨variety ¹1qofwill ©¸ t-1 ¹ to be defined as follows: any import period theand unitt, and 1/ q z variety z reduce ∆VAR this case will benew in to two years V 1

(7) ! 0 . Inin conclusion, ¦ ¦ ¨ ¸ ¨ ¸ ¨VAR in this case will be the change in import variety of two years t-1 and t, jt. jt. jt. jt. ¨ j Jon§value ¸ (3), value of any the1.new first ratio the right equation (3), because 1/(s-1) > 0 . lower In conclusion, variety unitbecause cost of period 1 compared number of new imported inputs in§period The lower of¸inO1period (hand J ) ¨will to a the , jof Jreduce j1 Jwill tlead · import ·side. ¦ Oq tjt(zJjt) j J. t. t-1,t. jt. j J t. jt. jt. , j J jjt J t jt. jt. jt. jt. j J t. jt. © ¹ cost of period 1 compared to that of© period 0. ¹ and to be defined as follows: ¨VARt-1,t in this case will be the change in import variety of two years t-1 and t, § q jt z jt ¦ q jt z jt ¦ and to be defined as follows: § O (J ) · ¨ j J t j J ' VARt 1,t ln ¨ t 1 ln ¸ ¨ O ( ) J q z q z § · © t q jt z jt¹ ¨qj¦ jt z jt jt 1 jt 1 ¦ jt 1 jt 1 J t 1 j J § Ot 1 ( J ) · ¨ ¸ j J t j J© t-1,t j J t. ' VARt 1,t. ln ¨ ¸ © Ot ( J ) ¹. ln ¨. j J t. ¦. ¦. q. ¦. z. ¦q. z. ¸. (5). jt. · ¸ ¸ ¸ ¹. (6). ⑹ . (6). jt 1 jt 1 jt 1 jt 1 ¸ ¨ derive can the index as in (6) forwith export variety, withfollowing V <0. In part of the paper, I variety as same in (6)variety for In the We can derive the same We σ<0. J t 1 j J export variety, © jindex ¹ the following part of the paper, I will use these indices to measure the changes in will use these indices to measure the changes in import and export varieties of Japan. import and export varieties of Japan.. We can derive the same variety index as in (6) for export variety, with V <0. In the following part of the3.paper, to measure the changes in Data I will use these indices3．Data import and export varieties of Japan. I will use disaggregated trade data of Japan for the period 1980-2000 to trade data ofand Japan forvariety the period construct import I will use disaggregated construct the import export indices.1980─2000 Figure 1 and to figure 2 show the the total of and export variety. 2 show the total of import andfrom export Japan from 1980 2000. Import volumes import and export volumes of Japan 1980volumes to 2000. of Import volumes were to quite 3.indices. Data Figure 1 and figure stable in the 1980s. However, during the 1990s, there were significant changes in the I will use disaggregated trade data of Japan for the period 1980-2000 to were quite stable in the 1980s. However, during the 1990s, there were significant changes in the import volume of import variety volume indices. of Japan Figure with a sharp increase inshow 1993-1995 andofa fall in 1997 and construct theaimport export figure the total Japan with sharp and increase in 1993─1995 and a fall 1inand 1997 and21998. For exports, in the 1980s, the volumes steadily 1998. For exports, in the 1980s, the volumes steadily increased. In the early 1990s, import and export volumes of Japan from 1980 to 2000. Import volumes were quite increased. In the early despite 1990s,stagnation, despite stagnation, Japanʼs export volume still increased. However, there was some Japan’s export volume still increased. However, there was some stable in the 1980s. However, during the 1990s, there were significant changes in the slowdown in exports in the late 1990s. slowdown in exports in the late 1990s. import volume of Japan with In a sharp in 1993-1995 and aand falltoinmaintain 1997 and order increase to construct variety indices consistency in the to construct variety and to maintain consistency in the1990s, classification of goods, I use the highly In 1998. Fororder exports, in theclassification 1980s, theindices volumes increased. In the early of goods, Isteadily use the highly disaggregated trade data at the five-digit level disaggregated trade data at therevision five-digit level of SITC revision 2classification forwas Japan from 1980─2000. despite stagnation, Japan’s export volume still increased. However, there some of SITC 2 for Japan from 1980-2000. The distinguishes 1,473 The classification commodities according to the Standard International Trade Classification (SITC slowdown in exports in the late 1990s. distinguishes 1,473 commodities according to the Standard International Trade Classification (SITC Revision 2). Each Revision 2). Each commodity will also differ if it in is produced in a different In order to construct variety and tocategory maintain consistency commodity category will also differ indices if it is produced in a different country. In the other words, the origin of the product country. In otherdisaggregated words, the origin of the an important classification of goods, I use the highly trade dataproduct at the plays five-digit level role in defining plays an important role in the characteristics the product. Therefore, to be a four or five digit thedefining characteristics of the product. of Therefore, I define a good to Ibedefine a four aorgood five digit of SITC revision 2 for Japan from 1980-2000. The classification distinguishes 1,473 SITC-2 category, and aof variety is the import a particular good country from a particular SITC-2 category, and a variety is the import a particular good of from a particular (as in Armington, 1969 and commodities according to the Standard International Trade Classification (SITC country (as in Armington, 1969 and Broda and Weinstein, 2006). Broda and 2006). Revision 2).Weinstein, Each commodity category will differ if it is produced a different All the trade dataalso are collected from the United in Nations’ COMTRADE database. tradewords, data are collected the United Nationsʼ COMTRADE database. I have divided the industries into AllIntheother country. the origin of from thetheproduct plays an 21 important role in defining I have divided industries into sectors, including primary and secondary the of the product. I industries. define good be a four or five digit industries. Table 2 and table 3 ashow thetocomparison of 3simple count-based varieties 21 characteristics sectors, including primary andTherefore, secondary Table 2 and table show the comparison of simple count-based SITC-2 a variety thedefinition import ofofavariety) particular a particular varietiescategory, of those and sectors (usingisour andgood total from varieties between 1980 and 2000. We can see a sharp country (as in Armington, 1969 and Broda and Weinstein, 2006). increase in import varieties in this period, from a total of 23885 1980 to 36684 varieties in 2000, implying 5 varieties in All the trade data are collected from the United Nations’ COMTRADE database. an increase of more than 50%. In contrast, export variety by the simple count-based method decreased quite sharply, I have divided the industries into 21 sectors, including primary and secondary from 58403Table varieties in table 19803toshow 43552 in 2000, meaning a decreasevarieties of nearly 30%. industries. 2 and thevarieties comparison of simple count-based. 5.

(8) 横浜国際社会科学研究第 14 巻第 3 号（2009 年 9 月） Figure 1. Japan’s imports (1980-2000). 100 （292）. 400,000 350,000. millions USD. 300,000 250,000 200,000 150,000 100,000 50,000 0 1975. 1980. 1985. 1990. 1995. 2000. 2005. 2000. 2005. Source: UN’s Comtrade database. Figure 1 Japan s imports (1980―2000) 600,000 500,000. millions USD. 400,000 300,000 200,000 100,000 0 1975. 1980. 1985. 1990. 1995. Source: UN’s Comtrade database. Source: UN’s ComtradeFigure database2 Japan s exports (1980―2000). 4. 4．Import and export varieties of Japan Table 2 and table 3 are only the simple count-based varieties, which provide us with a rough estimate of the changes in variety. In this section, I will use the variety index calculation as developed in previous section to provide more comprehensive results. The variety index calculation also includes the volume of the imported or exported goods (pit xit) thus giving the weights to each variety. To compare the changes of variety between two years t and t-1, I will calculate ∆VARt-1,t by using equation (6) and multiplying it by 100..

(9) Variety in Japan (1980―2000)（Nguyen Anh Thu）. （293） 101. Table 2 Simple count-based variety in Japan s imports (1980―2000) 1980. 2000. 1. Agriculture. Industry. 1607. 2292. 2. Food and kindred products. 1536. 2330. 3. Textile mill products. 2363. 3146. 4. Apparel. 2036. 4015. 5. Lumber and wood. 648. 891. 6. Furniture and fixture. 237. 354. 7. Paper and allied. 499. 742. 8. Printing, publishing and allied. 9. Chemicals. 10. Petroleum and coal products. 398. 444. 2977. 4364. 278. 337. 11. Leather. 419. 462. 12. Stone, clay, glass. 1047. 1696. 13. Primary metal. 1427. 1960. 14. Fabricated metal. 1174. 1699. 15. Machinery, non-elect. 2780. 4402. 16. Electrical machinery. 1382. 2466. 17. Motor vehicles. 220. 417. 18. Transportation equipment and ordnance. 147. 213. 19. Precision instruments. 630. 1617. 20. Rubber and misc. plastics. 534. 859. 21. Misc. manufacturing. 1546. 1978. 23885. 36684. Total Source: UN’s Comtrade database, counts compiled by author. Figure 3 and figure 4 show the changes in import and export varieties for 21 sectors of Japan during period 1980─2000. The index ∆VARt-1,t presents the percent change of variety between two years t and t-1. A positive value of the index shows an increase in variety and a negative value shows a decrease in variety. In figure 3, 11 industries show downward trends of import varieties, with many variety indices below zero. Those industries are food and kindred products, apparel, lumber and wood, furniture and fixture, paper and allied, printing, publishing and allied, leather, stone, clay, glass, primary metal, non-electrical machinery and precision instruments. As mentioned in the introduction, the period 1980─2000 witnessed the conclusion of many bilateral trade agreements between Japan and the US. We expect that these agreements, with the desire of the US to increase exports to Japan, would increase import variety of Japan during the period. However, the graph does not show an increase in the varieties of targeted industries like paper products, wood products, leather and electrical products. This can be explained more clearly in Greaney (2001), in which the author studies the impacts of the US-Japan Trade Agreements during 1980─1995 and concludes that the expansion of the US exports to Japan created by these agreements was very limited..

(10) 横浜国際社会科学研究第 14 巻第 3 号（2009 年 9 月）. 102 （294）. Table 3 Simple count-based variety in Japan s exports (1980―2000) Industry. 1980. 2000. 756. 689. 1. Agriculture. 2. Food and kindred products. 958. 923. 3. Textile mill products. 5915. 3846. 4. Apparel. 2642. 1839. 5. Lumber and wood. 606. 338. 6. Furniture and fixture. 589. 433. 7. Paper and allied. 1309. 992. 8. Printing, publishing and allied. 9. Chemicals. 10 11 12. 876. 662. 7807. 6424. Petroleum and coal products. 427. 272. Leather. 179. 105. Stone, clay, glass. 1648. 1284. 13. Primary metal. 4091. 2861. 14. Fabricated metal. 4950. 3419. 15. Machinery, non-elect. 9436. 7844. 16. Electrical machinery. 5279. 3818. 17. Motor vehicles. 478. 353. 18. Transportation equipment and ordnance. 447. 372. 19. Precision instruments. 4480. 3074. 20. Rubber and misc. plastics. 1531. 1374. 21. Misc. manufacturing Total. 3999. 2630. 58403. 43552. Source: UN’s Comtrade database, compiled by author. Table 3 shows the decrease of export variety by the simple count-based method. If we look at figure 4, we can find the same result: 9 among 21 industries show downward trend of export varieties, with a lot of variety indices below zero. Those industries are food and kindred products, furniture and fixture, printing, publishing and allied, chemicals, leather, primary metal, fabricated metal, non-electrical machinery and motor vehicles. Only two industries, which are electrical machinery and miscellaneous manufacturing, show an upward trend of export varieties from 1980 to 2000. 5．Conclusion This paper provides a complement to Feenstraʼs variety index, with a focus on import and export varieties. Based on this calculation method, we measure Japanʼs export and import varieties over 21 years, from 1980 to 2000. The result suggests that both export and import variety of Japan show downward trends in many industries. Specialization and the expansion of foreign direct investment from mid-1980s might have reduced the range of imported.

(11) Figure 3. Changes in Japan’s import varieties for 21 industries (1980-2000) Variety in Japan (1980―2000)（Nguyen Anh Thu） VAR1 6 4. VAR2 2.5. 1.0. 2.0 1.5 1.0. 0.0 0. -4. 0.5. -0.5. -2. 0.0. -1.0. 82 84 86 88 90 92 94 96 98 00. -0.5. -1.5. 82 84 86 88 90 92 94 96 98 00. VAR4 1.5. VAR6. 1. 2. 0.0. 0 0. -0.5. -1. -2. -1.0 -1.5. 82 84 86 88 90 92 94 96 98 00. 2. 4. 0.5. -1.0. VAR5 6. 1.0. VAR3. 1.5. 0.5. 2. （295） 103. 82 84 86 88 90 92 94 96 98 00. -4. 82 84 86 88 90 92 94 96 98 00. VAR7 3 2. -2. 82 84 86 88 90 92 94 96 98 00. VAR8. VAR9. 2. 6. 1. 4. 0. 2. -1. 0. 1 0 -1 -2. 82 84 86 88 90 92 94 96 98 00. -2. Figure 3 continued 82 84 86 88 90 92 94 96 98 00. VAR10 12. -2. 82 84 86 88 90 92 94 96 98 00. VAR11 2. VAR12 2. 1 8. 0 0. 4. -1 -2. -2. 5. 0. -4 -3. -4. 82 84 86 88 90 92 94 96 98 00. -4. 82 84 86 88 90 92 94 96 98 00. -6. 82 84 86 88 90 92 94 96 98 00. Figure varieties for 21 industries (1980―2000) VAR13 3 Changes in Japan s import VAR14 VAR15 2. 4. 4. 1. 3. 3. 0. 2. 2. -1. 1. 1. -2. 0. 0.

(12) 0 4. -1. -2. -2 0. -4 -3. 横浜国際社会科学研究第 14 巻第 3 号（2009 -6年 9 月） -4. 104 -4（296）. 82 84 86 88 90 92 94 96 98 00. 82 84 86 88 90 92 94 96 98 00. VAR13. 82 84 86 88 90 92 94 96 98 00. VAR14. VAR15. 2. 4. 4. 1. 3. 3. 0. 2. 2. -1. 1. 1. -2. 0. 0. -3. -1. -1. -4. 82 84 86 88 90 92 94 96 98 00. -2. VAR16 4. 82 84 86 88 90 92 94 96 98 00. VAR17 1. VAR18. 4. 0 2. 0. 1. -1 -4. 0 -2. -8. -1. 82 84 86 88 90 92 94 96 98 00. -3. VAR19 8. 82 84 86 88 90 92 94 96 98 00. 82 84 86 88 90 92 94 96 98 00. VAR21 8 6. 2. 4. -12. VAR20 4. 6. 4. 0. 2. 2 -2. 0. 0. -4. -2 -4. 82 84 86 88 90 92 94 96 98 00. 8. 3. -2. -2. 82 84 86 88 90 92 94 96 98 00. -6. -2. 82 84 86 88 90 92 94 96 98 00. -4. 82 84 86 88 90 92 94 96 98 00. Note: The numbers 1 to 21 stand for the names of the 21 industries as presented in table 2 and table 3. Note: The numbers 1 to 21 stand for the names of the 21 industries as presented in table 2 and table 3 Figure 3 continued and exported goods, as we expected. These negative effects on variety might be larger than the positive effects of more 6 expenditure on R&D and the expansion of foreign markets during the period. The variety indices calculated in this paper are the percent change of variety between two years. This paper provides import and export variety indices of Japan during period 1980─2000. As suggested by endogenous growth theory, the changes of variety may have effects on other economic indices or measures, such as Total Factor Productivity, Gross Domestic Product or welfare gains. The results of this paper, therefore, can be used for further empirical studies ..

(13) Figure 4. Changes in Japan’s export varieties for 21 industries (1980-2000). Variety in Japan (1980―2000)（Nguyen Anh Thu） VARE1. VARE2. 30. 2. 20. 1. 10. 0. （297） 105 VARE3. 1.5 1.0 0.5 0.0. 0. -10. -1. 82 84 86 88 90 92 94 96 98 00. -2. -0.5. 82 84 86 88 90 92 94 96 98 00. VARE4. -1.0. VARE5. 3. 12. 2. 8. 1. 4. 0. 0. -1. -4. 82 84 86 88 90 92 94 96 98 00. VARE6 2. 1. 0. -2. 82 84 86 88 90 92 94 96 98 00. -8. -1. 82 84 86 88 90 92 94 96 98 00. VARE7 2. VARE8 1. 1. 0. 0 -2. -1. -1. -3. Figure 4 continued. 82 84 86 88 90 92 94 96 98 00. -4. 82 84 86 88 90 92 94 96 98 00. VARE10 20. 82 84 86 88 90 92 94 96 98 00. VARE12. 2. 4. 1. 2. 0 0. -10. -1. -2. 82 84 86 88 90 92 94 96 98 00. -4. -2. 82 84 86 88 90 92 94 96 98 00. -3. 82 84 86 88 90 92 94 96 98 00. VARE13 VARE15 Figure 4 Changes in Japan s exportVARE14 varieties for 21 industries (1980―2000) 3 2. 7. 1 1 0. 2 1 0. 0 -1. -1 -1. -2. -2 -2. -3. 3. 0. 2. -2. VARE11 6. 10. -20. VARE9. 2. -1. -2. 82 84 86 88 90 92 94 96 98 00. 3. 0. 1. -2. 82 84 86 88 90 92 94 96 98 00. -3. 82 84 86 88 90 92 94 96 98 00. -3. 82 84 86 88 90 92 94 96 98 00.

(14) 4. 10. 1. 2 0. 0 0. -10. -2. 横浜国際社会科学研究第 14 巻第 3 号（2009 年 9 月）. 106 （298） -20. -1. -2. 82 84 86 88 90 92 94 96 98 00. -4. 82 84 86 88 90 92 94 96 98 00. VARE13 2. 2. 1. 1. 0. 0 -1. -1 -1. -2. -2. 82 84 86 88 90 92 94 96 98 00. -3. 82 84 86 88 90 92 94 96 98 00. VARE16 3. 82 84 86 88 90 92 94 96 98 00. VARE18 12. 0.4. 8. 0.0. 1. -0.4. 4. -0.8. 0. -1.2. 0. -4. -1.6 82 84 86 88 90 92 94 96 98 00. -2.0. 82 84 86 88 90 92 94 96 98 00. VARE19 2. 3. 1. 2. 0. 1. -1. 0. -2. -1. -3. 82 84 86 88 90 92 94 96 98 00. -8. 82 84 86 88 90 92 94 96 98 00. VARE20. 4. -2. -3. VARE17 0.8. 2. -1. VARE15 2. 1. -2. 82 84 86 88 90 92 94 96 98 00. VARE14 3. 0. -3. -4. VARE21 3 2 1 0 -1. 82 84 86 88 90 92 94 96 98 00. -2. 82 84 86 88 90 92 94 96 98 00. Note: The numbers 1 to 21 stand for the names of the 21 industries as presented in table 2 and table 3. Note: The numbers 1 to 21 stand for the namesFigure of the 421continued industries as presented in table 2 and table 3. Acknowledgement. 8. This paper is a part of the authorʼs doctoral dissertation at Yokohama National University. The author would like to thank Prof. Craig Parsons─her academic advisor─for his valuable ideas and comments..

(15) Variety in Japan (1980―2000)（Nguyen Anh Thu）. （299） 107. References American Chamber of Commerce in Japan (ACCJ) 1997. Making Trade Talks Work: Lessons from Recent History. American Chamber of commerce in Japan: Tokyo. Armington, P., 1969. A Theory of Demand for Products Distinguished by Place of Production. International Monetary Fund Staff Papers 16, 159-178. Broda, C., Weinstein, D. E., 2006. Globalization and the Gains from Variety. Quarterly Journal of Economics 121(2), 541-585. Feenstra, R. C., 1994. New Product Varieties and the Measurement of International Prices. The American Economic Review 84(1), 157-175. Feenstra, R. C., Markusen, J., 1994. Accounting for Growth with New Inputs. International Economic Review 35, 429-447. Feenstra, R. C., Madani, D., Yang, T., Liang, C., 1999. Testing Endogenous Growth in South Korea and Taiwan. Journal of Development Economics 60, 317-341. Feenstra, R. C., Yang, T., Hamilton, G., 1999. Business Groups and Product Variety in Trade: Evidence from South Korea, Taiwan and Japan. Journal of International Economics 48, 71-100. Flath, D., 2005. Distribution Keiretsu, Foreign Direct Investment, and Import Penetration in Japan. The Japanese Economy 33(2), 26-53. Funke, M., Ruhwedel, R., 2005. Export Variety and Economic Growth in East European Transition Economies. Economics of Transition 13(1), 25-50. Greaney, T., 2001. Assessing the Impacts of US-Japan Bilateral Trade Agreements, 1980-1995. The World Economy 24(2), 127-157. Grossman, G. M., Helpman, E., 1991. Innovation and Growth in the Global Economy. MIT Press, Cambridge, MA. Huber, R., 1971. Effects on Prices of Japanʼs Entry into World Commerce after 1858. Journal of Political Economy 79, 614-628 Lincoln, E. J., 2001. Arthritic Japan – The Slow Pace of Economic Reform. Brookings Institution Press, Washington D.C. Nguyen, A. T. 2009. Variety and Productivity in Japan. Doctoral Dissertation, Yokohama National University. Parsons, C. R., 2000. Market-share Voluntary Import Expansion (VIE) and Import Promotion with an Application to Japan. Doctoral Dissertation, University of Hawaii, Manoa. Prestowitz, C. V., Jr., 1988. Trading Places: How We Are Giving Our Future to Japan and How to Reclaim It. New York: Basic Books. Romer, P. M., 1990. Endogenous Technological Change. Journal of Political Economy 98(5), S71-S102, Part 2. Sato, K., 1976. The Ideal Log-change Index Number. Review of Economics and Statistics 58 (2), 223-228. Saxonhouse, G. R., 1982. Evolving Comparative Advantage and Japanʼs Imports of Manufactures. In: Yamamura, K. (ed.). Policy and Trade Issues of the Japanese Economy. University of Washington Press, London, 239-270. Vartia, Y. O., 1976. Ideal Log-change Index Numbers. Scandinavian Journal of Statistics 3(3), 121-126.. Appendix. Appendix Unit-costAppendix function derivation Unit-cost function derivation Unit-cost function derivation. its profit producing the production function in (1)onasthe described in section 2: In each period t, the firm y based In maximizes each period t, the infirm maximizes its on profit in producing y based. In (1) each period t, the firm maximizes its profit in producing y based on the production function in as described in section 2: V /(V 1) production function in (1) as described in section ª º 2:. V /(V 1) f ( x, z , I , J ) « ¦ ai xi(V 1)/V ¦ b j z j (V 1)/V » (A1) ª iJ (V 1)/V º (V 1)/V iI ¬ ¼ ¦ bj z j y f ( x, z , I , J ) « ¦ ai xi » iI iJ The firm faces the following budget ¬constraint: ¼. y. (A1) . (A1). The firm faces the following budget constraint: The firm faces the following budget constraint:. B. ¦ p x ¦q z ¦ p x ¦q z i i. iI jJ B. j. (A2). j. iI. i i. jJ. j. (A2)(A2) . j. Then the firm will produce product y according to the production function (A1) Then the firm will produce product y according to will the production function (A1) with the budget constraint (A2). The maximization problem of the firm be: V /(V 1). L. wL wxi. with the budget constraint (A2). The ª º § maximization problem · of the firm will be: (V 1)/V V /(V 1)p x ¦ b j z j (V 1)/V » O¨B qjzj ¸ « ¦ ai xi ¦ ¦ i i ª º § jJ · iJ ¬ iI ¦ p¹i xi ¦ q j z j ¸ L «¦ ai xi(V 1)/V ¼¦ b j z j (V 1)/©V » iI O ¨ B i I i J i I j J © ¹ ¬ V /(V 1) ¼. ª º 1 (V 1)/V (V 1)/V ai xi V V/(OV p1)i 0 « ¦ ai xwi L ª ¦ b j z j » º 1 iJ ¬ iI a x (V 1)/V ¼ b z (V 1)/V a x V Op. 0.

(16) production function as firm described in section In each periodint(1) , the maximizes its 2: profit in producing y based on the V /(V 1). production function in (1) asª described in section 2:. º (V 1)/V ¦ b j z j (V 1)/V »V /(V 1) « ¦ ai xi ª¬ iI º iJ (V 1)/V ¦ b j z j (V 1)/V ¼» « ¦ ai xi The firm faces the following iJ ¬ iI budget constraint: ¼ y y. f ( x, z , I , J ) f ( x, z , I , J ). (A1) (A1). 14 巻第 3 号（2009 年 9 月） The firm横浜国際社会科学研究第 faces the following budget constraint:. 108 （300）. ¦ p x ¦q z ¦ ¦. B. i i. iI. j. jJ. (A2). j. B pi xi y qaccording (A2) constraint (A2). The product to the production function (A1) with the budget Then the firm will produce jzj iI maximization problem of the firm will be: jJ Then the firm will produce product y according to the production function (A1) with the budget constraint (A2). The maximization problem the firm will be: (A1) Then the firm will produce product y according to theof production function V /(V 1). with ªthe budget constraint (A2). Theº maximization § problem of the firm will · be:. L. . L. wL wxLi wxi wL w wzLj wz j. «¦ a x ª¬ iI «¦ a x ¬ iI. (V 1)/V i i (V 1)/V i i. ¦ bj z j. »V /(V 1) O ¨ B ¦ pi xi ¦ q j z j º § iJ iI jJ ¦ b j z j (V 1)/V ¼» O ©¨ B ¦ pi xi ¦ q j z j iJ iI jJ ¼ V /(V 1)© (V 1)/V. ª º 1 ai xi(V 1)/V ¦ b j z j (V 1)/V »V /(V 1) ai xi V O pi 0 ª«¬ ¦ º 1 iI J (V 1)/V b j z j (V 1)/V ¼» ai xi V O pi 0 i¦ « ¦ ai xi iJ ¬ªiI ¼ºV /(V 1) 1 (V 1)/V (V 1)/V V a x b z «ª ¦ i i »ºV /(V 1) b j z j 1 O q j 0 ¦ j j ¬« iI a x (V 1)/V iJ b z (V 1)/V ¼» bj z j V Oq j 0 ¦ ¦ i i j j i I i J ¬ ¼. . From the above maximization problem, we have: From the above maximization problem, we have: From the above maximization problem, we have: V. § a1 p2 · x1 ¨ ¸V , x13 §© a12 pp21 ·¹ ¨ ¸ , x2 © a2V p1 ¹ xV § p1 · § p ·3 ¨ ¸V x1 ¨ 2 ¸V § ap · § ap · ©¨ 11 ¹¸ x1 ©¨ 22 ¹¸ a © 1¹ © a2 ¹ x1 x12. V. § a1 p3 · ¨ ¸V ,... §© a13 p31 ·¹ ¨ ¸ ,... © a3 p1 ¹§ q ·V x2 ... ¨ 1 ¸V § qb · x2 ... ©¨ 11 ¹¸ © b1 ¹. V. § a1q1 · x1 ¨ ¸V , zx21 §© ba11qp11 ·¹ ¨ ¸ , z1 © b1 Vp1 ¹ z2 § q2 · z1 ¨ ¸V z2 ... § qb · z1 ©¨ 22 ¹¸ z2 ... © b2 ¹ x1 xz11. ¸ ·¹ ¸ ¹. V. § a1q2 · ¨ ¸V ,... §© ba21qp21 ·¹ ¨ ¸ ,... © b2 p1 ¹. (A3) (A3) (A4). Substituting (A3), (A4) into the budget constraint in (A2), we obtain:. Substituting (A3), (A4) into the budget constraint in (A2), we obtain: Substituting (A3), (A4) into the budget constraint in (A2), we obtain:. V. V. V. V. §a p · §b q · §a p · §bq · p1 ¨ 1 2 ¸ x2 p2 ¨ 2 3 ¸ x3 ... q1 ¨ 1 2 ¸ z2 q2 ¨ 2 3 ¸ z3 ... B a p a p b q © 2 1¹ © 3 2¹ © b3 q2 ¹ 9 © 2 1¹ V. V. V. 9. V. §a · §p · §a · §p · p1 ¨ 1 ¸ ¨ 1 ¸ x1 p2 ¨ 2 ¸ ¨ 1 ¸ x1 ... © p1 ¹ © a1 ¹ © p2 ¹ © a1 ¹ V. V. V. V. §b · § p · §b · § p · q1 ¨ 1 ¸ ¨ 1 ¸ x1 q1 ¨ 2 ¸ ¨ 1 ¸ x1 ... B © q1 ¹ © a1 ¹ © q2 ¹ © a1 ¹ V. § · §p · ¨ 1 ¸ x1 ¨ ¦ aiV pi1V ¦ bVj q1jV ¸ a jJ © 1¹ © iI ¹. x1. B § V 1V V 1V ¨ ¦ ai pi ¦ b j q j i I j J ©. B. V. § a1 · ¨ ¸ · © p1 ¹ ¸ ¹. Similarly for other values of xi and z j , we have the following expressions for xi . and z j. xi. zj. B § V 1V V 1V ¨ ¦ ai pi ¦ b j q j jJ © iI B § V 1V V 1V ¨ ¦ ai pi ¦ b j q j jJ © iI. V. § ai · ¨ ¸ · © pi ¹ ¸ ¹ § bj ¨ · ¨© q j ¸ ¹. V. · ¸¸ ¹. (A3) . (A4) (A4) .

(17) V. § § p1 · V 1V V 1V · ¸ x1 ¨ ¦ ai pi ¦ b j q j ¸ B V ¨ a i I j J 1 © ¹ § · © ¹ §p · ¨ 1 ¸ x1 ¨ ¦ aiV pi1V ¦ bVj q1jV ¸ B jJ © a1 ¹ © iI ¹ V § a1 · B x1 ¨ ¸ V § B V(1980―2000)（Nguyen 1V § Va 1·V · © p1 ¹Anh Thu）（301） 109 Variety in Japan ¨ ¦ ai pi ¦ ¨b j 1q j¸ ¸ x1 iI j·J p § © ¹ V 1V V 1V © 1 ¹ ¨ ¦ ai pi ¦ b j q j ¸ Similarly values of xxi i and andzi z j , we have the following expressions for xi Similarly for other values of xi and zi, we have following expressions for jfor J other © iI the ¹ and zfor Similarly other values of xi and z j , we have the following expressions for xi j and z j. V. § ai · ¨ ¸ V § B V 1V · § V 1·V © pi ¹ ¨ ¦ ai pi ¦¨baj iq¸j ¸ xi jJ © iI ¹ § V 1V V 1V · © pi ¹ ¨ ¦ ai pi ¦ b j q j ¸ jJ © iI ¹ V § bj · B zj ¨ ¸ V ¨ ¸ § B V 1V § bV 1·V · © q j ¹ ¨ ¦ ai pi ¦¨b j jq¸j ¸ zj ¸ ¹ jJ ¨ © iI § V 1V V 1V · © q j ¹ ¨ ¦ ai pi ¦ b j q j ¸ jJ © iI ¹ With the above equations for xi and z j , the firm will come up with the following the will comeasupin with unit-cost function as in the (2) following With the above equations for xi and zi,unit-cost function (2)x the With the firm above equations for andfollowing z , the firm will come up with xi. B. i. j. unit-cost function as in (2). ª º c ( pt , qt , I t , J t ) « ¦ aiV pit1V ¦ 1/(1 biV qV1jt)V » ª iI jJº ¼ c ( p , q , I , J ) « ¦ aV p¬1V t ¦ bV q1V »t t t t t i it i jt jJ t ¬ iIt ¼. . 1/(1V ). (A5) (A5). (A5). ［グェンアントウ横浜国立大学大学院国際社会科学研究科博士課程修了］. 10 10.

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