24 212 1 24 NO.212-1 GDP 2 8 4.3%9 7.6%2 1.% 7 47 2 2 8 9 1
1 2 GDP 196 8 7 9 1 8 4.3%9 7.6%2 1 1.%7 11.5% 2 8 2 GDP 7 8 9 7 3 2 7 8 15 1 1GDP 1 5 2GDP 5-5 -5-1 -1 55 6 7 8 9 1 UFJ -15 1 2 3 4 5 6 7 8 9 1 11 UFJ 3.5 3. 3GDP 7 4GDP 4 11/7-9 1/1-12 9/1-12 3 2.5 2. 1.5 2 9 8 6 195 1. 2 4 6 8 1 12 1951956221 UFJ 2 1 2/7-9 2/1-3 5/7-9 7/1-12 -.5..5 1. 1.5 2. 2 UFJ 2
4 6 8 7 29 3 GDP 1 2 1 9 3 197 71 12 75 3 86 11 93 1 2 54 8 2 3 1GDP GDP GDP GDP 195411 19586 43 7.5 1.5 195411 19576 31 7.2 1.7 19576 19586 12 7.8 1.1 19586 19621 52 1. 2.8 19586 196112 42 1.4 2.9 196112 19621 1 9.3 1.9 19621 19651 36 8.4 2.8 19621 19641 24 9.6 2.5 19641 19651 12 6.2 1. 19651 197112 74 9.8 3. 19651 1977 57 11.1 1.8 1977 197112 17 5.9 2.6 197112 19753 39 4.8 4.4 197112 197311 23 7.8 1.8 197311 19753 16.4 2.6 19753 19771 31 3.8 1. 19753 19771 22 3.6 1. 19771 19771 9 4.4.5 19771 19832 64 4.2 1.4 19771 1982 28 5.2.6 1982 19832 36 3.4 1.2 19832 198611 45 4.2 1.6 19832 19856 28 4.2 1.2 19856 198611 17 4.4 2.2 198611 19931 83 3.7 2.8 198611 19912 51 5.4 2.1 19912 19931 32 1.5 1.8 19931 19991 63.9 1.9 19931 19975 43 1.8 1.4 19975 19991 2.7 1.5 19991 221 36.6 1.3 19991 211 22 1. 1.3 211 221 14.3 1.3 221 293 86.9 2.5 221 282 73 1.6 1. 282 293 13 2.7 3.9 293.6 4.7 293.6 4.7 1. GDP 2. 19541119561-32932117-9 UFJ 3
2 GDP N N 2 N 47 47 47 var(g JPN )=w i2 *var(g i )+w i *w j *cov(g i,g j ) -----(1) i=1 i=1 j=1,j i var(g JPN ) GDP %G JPN var(g i ) i GDP G i cov(g i,g j ) i j 2 w i w j i j GDP % w i (1) 1 2 197 8 9 (1) 2 9 2 8 9% 3.13.48 4
2GDP 195 1.4.7.8 6 3.1.8 2.4 7 32.9 2.3 3.6 8 1..1.9 9 3.4.3 3.1 2 3.4.3 3.1 1. (1) 2. 19519562287585 UFJ 1 GDP 1 2 199 2 5 9 97.5% 1,81 1,54 2 98.4% 1,64 7 99.4% 9 2 6 8 9 77.7% 84 61.1% 66 2 82.1% 887 64.% 692 2 5 6 2 1 9 8 7 6 5 4 3 2 1 5 195 6 7 8 9 2 1. 21,81 2. 195195622875 85 UFJ 1 9 8 7 6 5 4 3 2 1 6 9 2 9 2 9 2 195 6 8 1. 21,81 2. 195195622875 85 UFJ 5
2 47 7 198 86 9 33 7 2 8 33 9 31 GDP 7 3 2 15 7GDP 198 9 2 1 5-2 2 4 6 8 1981986228 UFJ 3198 GDP 9 46 2 47 9 2 39 8 9 2 9 2 3 199 6
GDP 6 89 2 IT 28 3.5 3. 2.5 2. 8GDP 195 8 7 2 4 3 2 11/7-9 9GDP 9/7-9 1995/1-3 3/4-6 1.5 9 6 1 5/1-12 8/1-3 2/1-12 1. 1 2 3 4 5 221 UFJ 1 2 3 4 5 2 UFJ GDP 51 D.C.(2) 51 51 51 var(g US )=w i2 *var(g i )+w i *w j *cov(g i,g j ) -----(2) i=1 i=1 j=1,j i var(g US ) GDP %G US var(g i ) i GDP G i cov(g i,g j ) i j w i w j i j GDP % 1988 9 9 2 21 3 9 3 2 1,275 2 9 752 59.% 2 1,35 81.2% 1 9 19.7% 28.9%2 9 78.8%67.2% 11 7
3GDP 199 3..2 2.7 9.3.1.3 2 3.2.3 2.9 1. (2) 2. 1991988221 UFJ 1 9 8 7 6 5 4 3 2 1 1 199 9 2 1. 21,275 2. 1991988221 UFJ 1 9 8 7 6 5 4 3 2 1 11 9 2 2 199 9 1. 21,275 2. 1991988221 UFJ 1999 2 GDP 12 8 13 (3) 17 4 8 7 86.8%8 92.6% 136 1 92.6%88.2% 17 17 17 var(g EUR )=w i2 *var(g i )+w i *w j *cov(g i,g j ) -----(3) i=1 i=1 j=1,j i var(g EUR ) GDP %G EUR var(g i ) i GDP G i cov(g i,g j ) i j w i w j i j GDP % 8
3 2 12GDP 811 3 2 13GDP 11/7-9 9/1-3 1 27 199 1 5/1-12 2/ 8/4-6 1-12 1/ 7-9 -1 1 2 3 1. 2. 19919961-38112117-9 UFJ 1 2 3 2 UFJ 4GDP 21 4.2.9 3.3 99 7.9.3.6 87 8 7.3 1.6 5.7 93 1. (3) 2. 2136 3. 82117-9 UFJ 78 93 88 4 47 7 GDP 4 199 85.7% 87.9%2 8 86.1%88.5% 14 9 82.9% 85.8%2 9 83.7%86.5% 15 1% 6 7 8 8 9 9
1 14 GDP 1 15 GDP 9 9 8 8 7 195 6 7 8 9 2 1. 4 2. 19519552287 7589 UFJ 7 196 7 8 9 2 979 1. 4 2. 19619639 9792979 UFJ 447 51 (4) 7 21 8 28 (5)2 %1% X Y 1 1% 2 2% 3 97% 1 3% 2 96% 3 1%4% =1%+2%+1% 2% 3% 5%22% 32% 46% 96% =2%+3%+46% (4) min(x i /X,AX i /AX) X i GDP i %X i /X i AX i /AX (5) min(x i /X,Y i /Y) X i GDP X i /X i Y i Y i /Y GDP 16 2 8 4 15% 2.7%196 7 5 22%2 1 17 2 3 18%4 15% 1
5 16GDP 5 17GDP 4 3 1/714.3 4 3 1/812.5 2 2 1 1 195 6 7 8 9 2 1951955228 UFJ 196 7 8 9 2 1961963221 UFJ 5Southeast Far West Mideast D.C.Great Lakes 9 11
GDP GDPG JPN GDPw i GDPG i 147 47 G JPN = w i * G i i=1 = w 1 *G 1 +w 2 *G 2 +w 47 *G 47 47 E(G JPN ) = w i * E(G i ) i=1 = w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 ) GDPvar(G JPN ) var(g JPN ) = E{G JPN -E(G JPN )} 2 = EG JPN2-2G JPN *E(G JPN )+E(G JPN ) 2 = E{w 1 *G 1 +w 2 *G 2 +w 47 *G 47 } 2-2*(w 1 *G 1 +w 2 *G 2 +w 47 *G 47 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )} + {w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )} 2 = E(w 1 *G 1 ) 2 +(w 2 *G 2 ) 2 +(w 47 *G 47 ) 2 + (w 1 *G 1 )*{(w 2 *G 2 ) +(w 47 *G 47 )}+(w 2 *G 2 )*{(w 1 *G 1 )+(w 3 *G 3 ) +(w 47 *G 47 )} + (w 47 *G 47 )*{(w 1 *G 1 )+(w 2 *G 2 ) +(w 46 *G 46 )} - 2*[(w 1 *G 1 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )}+(w 2 *G 2 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )} + (w 47 *G 47 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )}] + {w 1 *E(G 1 )} 2 +{w 2 *E(G 2 )} 2 +{w 47 *E(G 47 )} 2 + {w 1 *E(G 1 )}*[{w 2 *E(G 2 )} +{w 47 *E(G 47 )}]+{w 2 *E(G 2 )}*[{w 1 *E(G 1 )}+{w 3 *E(G 3 )} +{w 47 *E(G 47 )}]} + {w 47 *E(G 47 )}*[{w 1 *E(G 1 )}+{w 2 *E(G 2 )} +{w 46 *E(G 46 )}] = w 12 *E{G 1 -E(G 1 )} 2 +w 22 *E{G 2 -E(G 2 )} 2 +w 472 *E{G 47 -E(G 47 )} 2 + w 1 *w 2 *E{G 1 -E(G 1 )}{G 2 -E(G 2 )}+w 1 *w 3 *E{G 1 -E(G 1 )}{G 3 -E(G 3 )} +w 1 *w 47 *E{G 1 -E(G 1 )}{G 47 -E(G 47 )} + w 2 *w 1 *E{G 2 -E(G 2 )}{G 1 -E(G 1 )}+w 2 *w 3 *E{G 2 -E(G 2 )}{G 3 -E(G 3 )} +w 2 *w 47 *E{G 2 -E(G 2 )}{G 47 -E(G 47 )} + + w 47 *w 1 *E{G 47 -E(G 47 )}{G 1 -E(G 1 )}+w 47 *w 2 *E{G 47 -E(G 47 )}{G 2 -E(G 2 )} +w 47 *w 46 *E{G 47 -E(G 47 )}{G 46 -E(G 46 )} 47 = w i2 *var(g i ) i=1 47 47 + w i *w j *cov(g i,g j ) i=1 j=1,ji cov(g i,g j )G i G j cov(g i,g j )=E{G i -E(G i )}*{G j -E(G j )} H24.1.24 yasuhiro_ishimaru@mufg.jp UFJ 1-8388 2-7-1 12