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1 *1, *2, *1 (*1, *2 ) Comparative study of Input-Output Table of Ministries with Input-output table compiled with private business data. K. Akagi*1 T. Ohsato*2 and H. Deguchi*1 (*1:Tokyo Institute of Technology, *2:Teikoku Databank, Ltd.), (SNA ),,.,,., TDB -SNA,. :,,,, 1, (,TDB ) (,TDB ), (.SNA ),TDB., = ( ),, (SNA:System of National Accounts). Fig.1 1,,,.,,. 1.1.,.,,, 2.,5, tdb.dis.titech.ac.jp/en/index.html. 1 HP(: 2016/1/26), , 4, ( ) pp.75 toukatsu/data/io/011index.htm 2 (2010), pp17 Fig. 1: ( ), 5.,,., 2, 2 3.,, RAS,,. 4)4.,, 3 HP ( 2016/01/26), toukatsu/data/io/c_method.htm 4, (2010),pp258 第 10 回社会システム部会研究会 (2016 年 3 月 16 日 -18 日沖縄 - ) 1 - PG0002/16/ SICE

2 ,.,, 10),.,2011,,,.,, 5,.,., 7 (1995 ),,., 10).,,,,,.,,,,., (2015) 1), (2015) 5) TDB,. TDB,., 1-3 TDB., TDB,,.,TDB,., TDB (BS, PL), (2000) 9),,.,,,,,.,,,.,,, 5 (2010), 2005 Inter-Regional Input-Output Table,.,TDB,TDB, SNA,,., AADL(Algebraic Accounting Description Language), FALCONSEED 6,. TDB,.,,TDB,,. 2 TDB SNA TDB TDB 23 (2011 ).TDB, (2015) 1), (2015) 5),,. 2.1 TDB..,,.,,,,.,,. TDB, ,TDB 1,200, 90%.,TDB,. Table.1. Fig2,TDB (TRD), (COSMOS2). TDB, HP(: 2016/1/26), 24, 1,

3 Table 1: TDB (COSMOS1) (COSMOS2).,. (TRD),, ( ),70 ( ),, , : SNA, 8,.,TDB,.,,, , :, ( ),,, 2 9.TRD,,. 2.2 TDB TDB TDB 10.,TDB,. 2.3 TDB TDB,TDB 4. 1) : TSCA(Two Side Classification Algoritum),TRD 8., HP ( 2016/01/26), exam.html 9 HP(: 2016/1/26), ) (1) ( ),pp91, io/011index.htm 10 HP(: 2016/1/26),TDB, X. 2) : TRD,,.,TRD,. 3) :,,. 4) : 3, , ( ) (,X ), TDB X.TRD,,,, X.TRD TDB. TDB, 91. TRD, TDB TSCA(Two Side Classification Algorithm),. TSCA 2. 1),,., ( ).,,,. 2) (1) (= ), TDB

4 , TSCA. TDB. : I = {1, 2, 3,,,,, } 2 : Ind 2 = {d i i = 1, 2,,,,, 91} : G = {α k K = 1, 2,,,,, 780, 000} TRD : T RD = {< x, y, z, i > x, y Ind 2, z G, i I} Ind 2 Ind 2 G I, function; Selection : G G Ind 2 α G Selection[α], ( ): Ex[α] = {< q, α, i > (< q, y, α, i > T RD < x, q, α, i > T RD), q Ind 2, α G} ( ): Count[α] = {< n, q, α > q Ind 2, < q, α, i > Ex[α], n N, i I [n = < q, α, i > ]} : CountedN umber[α] = {x < x, q, α > Count[α]} : F irstsecondnumber[α] = {< x, y > x, y CountedN umber[α], x > y, ( z)(z CountedNumber[α] y > z)} : Selection[α] = {< x, q, α >, < y, p, α > < x, y > F irstsecopndnumber[α], < x, q, α >, < y, p, α > ContedNumber[α]} TRD,.,,.,,,,... (Order): O = {O i i = 1, 2,...n} (Cost): C = {c i i = 1, 2,...n} (Reciever): (Profit): (Exchange): R = {r j j 1, 2,...m} P = {p j j = 1, 2,...m} Ex = {< O i, r j >} O R :DivC[o i ] = {dvc i divc i = c i (P j / c [p i C j], p j P, c i C, < o i, r j > Ex[o i ])} :DivP [< r j, o i >] = {dvp l divp l = p j (DivC[o i ]/ divc i DivC[O i ] divc i), < o i, r j > Ec[o i ], o i O, r j R} :SelectionProfit={< o i, divc i, r j, divp j > o i O, r j R, divc i DivC[o i ], (divp j DivP [r j ] divp j = divc i DivC), < o i, r j > Ex, divc i divp j } 3.2, (91 91) ( ), ( ). A, B,, A.,,,., (,,,, ) TDB 0.,,.,,2, -... (Goods): G={g i i = 1, 2,...n 1 } = α G Selection[α], n 1 N (Orders): O={o j j = 1, 2,...n 2 }n 2 N (Receivers): Re={r k k = 1, 2,...n 3 }, n 3 N (Exchange): Ex={< o j, r k > o j O, r k Re, } O Re (Divided Profit): DivP [< o j, r k >] = {divp l o j O, r k R, < o j, divc i, r j, divp l > SelectionP rofit} cf - 4 -

5 DivP= {divp l divp l <o j,r k > Ex DivP [< o j, r k > ]} (Company): COM ={co s s = 1, 2,...n 4 }n 4 N, G, O COM (ForConsummer): F C COM (Buisinsess): B={< o j, r k, g i, divp l > < o i, r k > Ex, g i G, divp l DivP } Ex G DivP (Department of Industory): Ind 2 = {I z z = 1, 2,...n 1 } (Department of companies): DC={< Co s, I s > Co s COM, I s Ind 2 } COM timesind 2 1 (Produser):P [g i ] = {p t p t Re, g i G, < o i, r k > Ex, o j O, divp l divp } 1 (Demand Side Orders):D[g i ] = {d u d u O, g i G, p t P [g i ], < d u, p t, g i,, divp l > B} 2 (Second Produce): S[g i ] = {< g i, Sg v, SumSdivP v > g i, Sg v G, SdivP v DivP, d u D[g i ], o j O, < o j, d u, Sg v, SdivP v > B (< g i, I z, Sg v, SdivP v > averagep [< g i, I z, Sg v > ] < d u, I z > DC), averagep [, < g i, I z, Sg v >.] = {< g i, Co s, I w, Sg v, avep [< g i, I w, Sg v >] > g i, Sg v G, < Co s, I w > DC, avep [< g i, I w, Sg v >] = {ap d w D[g i ], < d w, I w > DC, ap = isdp α IndSdivP [<gi, I w,sg v >] isdp α / IndSdivP [< gi, I w, Sg v >], IndSdivP [< gi, I w, Sg v >] = {isdp α isdp α DivP, o j O, r k R, g i G, divp l DivP, < o j, r k, g i, divp l > B, < o j, I w > DC, O j D[g i ], < o j, o j, Sg α, SdivP α > B, isdp α = SdivP α } } } sumsdivp v = sdivp w SDivP [Sg w sdivp w, SDivP [Sg w ] = {SdivP w Sg w G, SdivP w DivP, o j ino, d u D[g i ], < o j, d u, Sg w, SdivP w > B, d u F C SdivP w = 0} } SumP [g i ] = {< g i, sump i > g i G, DivP [g i ] = {divp l < o i, r k, g i, divp l > B[g i ]}, sump i = divp l DivP [g i] } 2 (Total Second Produce): T S[g i ] = sumsdivp y SumSDivP [g i ] sumsdivp y SumSDivP [g i ] = {sumsdivp y < g i, Sg v, sumsdivp y > S[g i ], g i, Sg v G} 2 (Rate of Second Produce): RS[g i ] = {< g i, Sg z, RS z > g i, Sg z G, RS z = sumdivp z /T S[g i ], < g i, Sg z, sumsdivp x > S[g i ]} 2 (Demand by Second Produce): DS[g i ] = {< g i, Sg x, ds x > g i, Sg x G, < g i, Sg x, sumsdivp x > S[g i ], < g i, sump i > SumP, RS x = SumdivP x /T S[g i ], ds x = RS x sump i },,. SelectionDemand = g i g DS[g i] 4 TDB,,,, TDB SNA. 4.1 TSCA,., (= )., 1 ( ), ( :,, ). 10 Tabale.2. Table 2: 10 33% 21% 20% 20% 19% 19% 18% 16% 15% 15% 7%,7%,Table.2,.,,

6 : 4., SNA.,, :,,,.,,,.,,,. 4.2 TRD,., 4931, 100. Table 3: ( - ) (/) ,,, (1),(2),. (1),.,.,. (2),,,.,.,0.698,.(, ). TRD,.,.,.,,. Estimated value SNA,TDB 3,.,, TDB.,TDB, SNA. X 19), 22)21), 23, TDB,, Actual value Fig. 2: Table.3,Fig , ,,. 5.1 TDB,SNA,,.,,. - 21), () 22), TDB -, TDB -, 47 TDB-SNA (::).,TDB,SNA,., - 6 -

7 .TDB,SNA,. ( ),, 12).,TDB,.,, 11)11.,TDB,SNA TDB SNA,.. Table 4: TDB,SNA, SNA TDB TDB/SNA ( 257 ) TDB 3.439,TDB SNA., SNA TDB 20,TDB. TDB,.,TDB,., %, 59%. (433/(0.59*((0.0485/0.0759))*334)),SNA TDB ,TDB TDB,,. TDB SNA,.,,TDB,SNA., TDB 476, 40 11, (2012) 6). 12,., HP(: 2016/1/26), 24, 1, pdf/gaiyo.pdf,, HP (: 2016/02/23), tokei/kokuzeicho/kaishahyohon2011/kaisya.htm., TDB. TDB,,, ,.,,,.,,.,,.,,,.,TRD, TRD,,. SNA, 1023,SNA 463 (SNA /(SNA -) ) ,,, SNA TDB (3.439*0.4529),TDB TDB.,,., (GDP)=- (-),,,., -( +) = - =.,,..,,. SNA 940, - 7 -

8 1300.TDB,TDB 1200 SNA.,TDB.,,TDB,TDB , ,1.542.,0.698,.,,,, ,, TDB,1.658.,, ,TDB,,.,.,,,,,,,.,TDB SNA,),, ),,,.,,,., 0, ,,, , (,,,, ) TDB 0.,, SNA TDB,TDB,TDB.TDB, ,, , TDB,TDB,,.,TDB,,.,,.,,.,,,,.,, SNA,TDB,.,, 1, x, y a x,y HP(: 2016/1/26), ) 5, toukatsu/data/io/011index.htm - 8 -

9 x y a x,y = x,,,.,augustinovics(1970) 2),, (2000) 13),Wolff (2002) 3), (2008) 8),,,,..,a T, a S,TDB,SNA,a i 1 1,n n,i. S at a T = a T 2 i ( a T i )2 n S a S a S = a S2 i ( a S i )2, n S a T a S = a T i a S i ( a T i a S i ), n r at a S = S at a S SaT a T S a S a S,, 1, 0. d(a T i, a S i ) = n i=1 (at i a S i )2 Wolf(2002),,,,,,i ( ) : W i j ( ) : W j, (, ). W i, W j, W i =, n i n n i x ij n j x, W i = ij n i n j x ij n j x ij n cos(wk T, Wk S k ) = (W k S W k S ) n k W n, k = i j T 2 k k W T 2 k.,( )0 1, 1, Table.. 5 Table 5: ( 2011SNA 2005SNA ) (r at a S ) ( ) (d(a T i, as i ) ) 0.118(0.0185) cos(wi T, W i S )) ( ) ( cos(wj T, W j S )) ( ),,,2005 SNA 20) 2011 SNA. 14,TDB,SNA,Fig,2.,TDB. TDB Fig. 3: SNA TDB , 0.1,Fig.3. SNA,TDB SNA.,SNA TDB TDB., 14,2011SNA 2005SNA, 2016/1/26.,,.,.2005SNA,.2005SNA,.2005SNA,.2005SNA,,,,., 2005SNA 2011SNA, 2. SNA - 9 -

10 ,TDB,TDB., SNA,TDB. TDB 10 Table.6. Table 6: TDB / - () TDB SNA SNA-TDB () TDB SNA SNA-TDB TDB 19,TDB.,,.,SNA,,,,,,,TDB. TDB,., -, -,.,SNA,TDB, TDB SNA,, SNA TDB,.,,,Wk T, W k S. Table.6,,,,TDB,,.,TDB,,,, Table 7: TDB / , TDB, TSCA (: ), (: ). TDB,,TDB,Table. 8. Table 8: TDB / ,,,.,

11 .,, (,, ),,.,,,.,,., ( ),,.,,, ( NPO,NGO ).,,. Table 9: - () ( - ) ( - ) Table.9 10.Table.9, -,.,,.,,,,,,,,. 5.3 SNA,TDB,.,,, 1. y, x b v,x,. b y,x = y x y,,,,. SNA TDB,,. Table.10, Table.11. Table 10: () () SNA TDB,.( 2 ) SNA, ,TDB,0.002,, ,,TDB,., SNA, ,TDB ,, ,,TDB

12 ,. Table 11: () () SNA TDB,.( 2 ) : SNA,, ,TDB , Table.6 TDB 2.,,, : SNA 0.999,TDB 0.02, ,, ,. TDB,,,,, ,,,.,,. 6,TDB,. TDB, TDB, 2.,,,. Table.12. Table 12: TDB Table.12,,TDB.,,,,.,3.439, ,.,, -,,.,,, TSCA,TDB,.TSCA,.TDB, ( ).,,,.,TDB. 6.1,,,

13 .,,,,.,,, TDB,,,TDB,.,TDB,, TDB., TDB,TDB,TDB,.,,.,,,.,,.,, TDB.TDB TDB,,.,,,,., TDB,,,,.,.,,,,,,TDB,.,,,,. 2) M,Augustinovics: Methods of International and Inter temporal Comparison of Structure, in A. P. Carter and A. Brody, Contribution to Input-Output Analysis, Amsterdam, North- Holland, 249/269 (1970) 3) Wolff, E. N. : Computerization and Structural Change, Review of Income and Wealth, Series 48, No. 1, 59/75(2002) 4) : :RAS, = THE ECONOMIC STUDIES, 30(1): 121/142(1980) 5), :, 2015 (2015) 6) :SNA, (148), 101/108 (2012) 7) :,258/258, (2010) 8) :, -20 (2008) 9) :, (2000) 10) :,,9-2 (2002) 11) :,,-76 77,77/77 (1992) 12) :SNA,, 9-4, 23/23 (2000) 13) :,, -58 (2001) 14), : -2000,, -44, 39/64 (2009) 15) : 2005 Inter-Regional Input-Output Table, (2010) 16) :, (2012) kaishahyohon2011/kaisya.htm 17) : 24, (2012) go.jp/data/e-census/2012/kakuho/pdf/gaiyo.pdf 18) : , (2009), 011index.htm 19) : 23 (2011 ) () (108 ), (2016), SG1/estat/List.do?bid= &cycode=0 20) : 17 (2005 ) () (108 ), do?bid= &cycode=0 21) : 2 17 (2005 ) -, jp/main_content/ pdf 22) : 23 (2011 ) (), (2016) bid= &cycode=0 23) : toukatsu/data/io/exam.html 24) :TDB, pdf/tic.pdf 7 1) Kaya Akagi,et al:input-output Table constructed with private business data and its algebraic description, 2015 IEEE/SICE International Symposium on System Integration (2015)

14 Table 13: TDB TDB Table 14: SNA

= /

= / [ ( 3)] 1 System of National Accounts SNA SNA 1993 93SNA 2008SNA 1.1, Gross Domestic Product (GDP) SNA GDP. 1 (Gross Value Added), (1) (2) (3) 1 1 1 1 1 5 100 75 1 20 30 1 100 500 1500 3000 1 500 +1500