Fiscal sustainability in Japan: What to tackle?

Journal Pre-proofs Full length article Fiscal sustainability in Japan: what to tackle? Selahattin İmrohoroğlu, Sagiri Kitao, Tomoaki Yamada PII: DOI: Reference:

S2212-828X(19)30092-1 https://doi.org/10.1016/j.jeoa.2019.100205 JEOA 100205

To appear in:

The Journal of the Economics of Ageing

Please cite this article as: S. İmrohoroğlu, S. Kitao, T. Yamada, Fiscal sustainability in Japan: what to tackle?, The Journal of the Economics of Ageing (2019), doi: https://doi.org/10.1016/j.jeoa.2019.100205

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© 2019 Elsevier B.V. All rights reserved.

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i2`K +`2 BMbm`M+2 M/ UBpV BMi2`2bi TvK2Mi QM i?2 Tm#HB+ /2#i- rBHH #2 M2`Hv 2[mHHv BKTQ`iMi BM ;2M2`iBM; i?2 Ti? Q7 `BbBM; ;Qp2`MK2Mi /2#i /m`BM; i?2 +QKBM; /2+/2bX a2+QM/- i?2`2 `2 bi`QM; M/ TQbBiBp2 2z2+ib 7`QK ?B;?2` T`Q/m+iBpBiv ;`Qri? M/ BM+`2b2b BM 72KH2 2KTHQvK2Mi UrBi? r;2 BM+`2b2 M/ 2KTHQvK2Mi `2;mH`BxiBQMVX JQ`2 72KH2 T`iB+BTiBQM M/ BM+`2b2/ 2`MBM;b rBHH MQi QMHv BM+`2b2 BM+QK2 it `2p@ 2Mm2b #mi HbQ i?2 #m/;2ib Q7 HH i?`22 bQ+BH BMbm`M+2 T`Q;`KbX  H`;2 2z2+i Q++m`b #2+mb2 Q7 +?M;2b BM i?2 +QMi`B#miBQM i?2v KF2 iQ BMbm`M+2 T`Q;`Kb- i?2 KQmMi Q7 r?B+? Bb iB2/ iQ p`BQmb BM/BpB/mH bii2b M/ KQbi BKTQ`iMiHv iQ i?2 2KTHQvK2Mi biimb BM CTMX 1zQ`ib Q7 TQHB+vKF2`b BM bm+? /B`2+iBQMb rBHH #2 2bb2MiBH 7Q` i?2 }b+H bQmM/M2bb BM i?2 HQM;@`mMX q2 MQi2- ?Qr2p2`- i?2b2 irQ Bi2Kb Kv #2 i?2 KQbi /B{+mHi iQ BM~m2M+2 rBi?  bBKTH2 TQHB+v iQQH M/ i?2v `2[mB`2 bB;MB}+Mi bi`m+im`H `27Q`KbX h?B`/- BM+`2bBM; i?2 +QMbmKTiBQM it `i2 7`QK i?2 +m``2Mi 3W iQ RyW BM kyRN `2/m+2b }b+H T`2bbm`2b BM i?2 b?Q`i `mMX  7m`i?2` BM+`2b2 iQ  H2p2H i?i Bb +QKT`#H2 iQ Qi?2` /pM+2/ 2+QMQKB2b rQmH/ ?2HT HH2pBi2 ++mKmHiBQM Q7 /2#i bB;MB}+MiHvX 6Qm`i?- +?B2pBM; }b+H bmbiBM#BHBiv Bb /B{+mHi #mi MQi BKTQbbB#H2X 6Q` 2tKTH2 +QK#BMiBQM Q7 TQHB+B2b- `BbBM; i?2 7mHH `2iB`2K2Mi ;2 iQ ed- +miiBM; T2MbBQM #2M2}ib #v RyW- `BbBM; i?2 +QTvb BM Tm#HB+ K2/B+H 2tT2M/Bim`2b M/ HQM;@i2`K +`2 bT2M/BM; iQ kyW- BM+`2bBM; i?2 72KH2 2`MBM;b M/ 2KTHQvK2Mi +?`+i2`BbiB+b iQ i?Qb2 Q7 K2MM/ `BbBM; i?2 +QMbmKTiBQM it `i2 iQ R8W- +?B2p2b }b+H bmbiBM#BHBiv p2`v [mB+FHv M/ H2/b iQ bB;MB}+Mi }b+H +QMbQHB/iBQM rBi?  HQr2` /2#i iQ :.S `iBQ BM ky8y i?M i?i BM kykyX PM2 b?Q`i+QKBM; Q7 Qm` TT2` Bb i?i r2 /Q MQi KQ/2H BM/BpB/mH /2+BbBQMb QM +QM@ bmKTiBQMfbpBM; M/ H#Q`fH2Bbm`2 +?QB+2bX h?2`27Q`2- Qm` KQ/2H Bb MQi bmBi#H2 iQ +QM@ /m+i  r2H7`2 MHvbBb iQ bim/v i?2 2z2+ib Q7 `27Q`Kb Q` i?2 /2KQ;`T?B+ +?M;2X q2 2biBKi2 HB72@+v+H2 T`Q}H2b Q7 +QMbmKTiBQM- H#Q` bmTTHv M/ 2`MBM;b 7`QK i?2 KQbi `2+2Mi CTM2b2 KB+`Q /i- /2`Bp2 BM/BpB/mHbǶ +QMbmKTiBQM i 2+? ;2 mbBM; i?2b2 2biBKi2b M/ i?2 T`2b2Mi pHm2 Q7 HB72 iBK2 `2bQm`+2b +QMbi`BMi mM/2` i?2 +QKTH2i2 K`@ F2ib bbmKTiBQM- #+F Qmi i?2 bb2i ?QH/BM;b 7`QK i?2 T2`BQ/ #m/;2i +QMbi`BMi- M/ mb2 i?2 kyRd ASaa /2KQ;`T?B+ T`QD2+iBQMb iQ T`Q/m+2 7Q`2+bib Q7 7mim`2 }b+H M/ K+`Q2@ +QMQKB+ BM/B+iQ`bX PM i?2 QM2 ?M/- i?Bb Bb +H2`Hv  b?Q`i+QKBM; Q7 Qm` TT`Q+?X PM i?2 Qi?2` ?M/- i?Bb #bi`+iBQM HHQrb mb iQ BM+Q`TQ`i2 bB;MB}+Mi /2iBHb Q7 i?2 T2MbBQM M/ ?2Hi? BMbm`M+2 bvbi2Kb BM CTM- BM+Hm/BM; i?2 /BbiBM+iBQM Q7 /Bz2`2Mi +i2;Q`B2b Q7 bQ+BH BMbm`M+2 T`Q;`Kb UTm#HB+ T2MbBQM- ?2Hi? BMbm`M+2 M/ HQM;@i2`K +`2 BMbm`M+2V- 2HB;B#BHBiv- MQM@HBM2` 7mM+iBQMb Q7 #2M2}ib M/ +QMi`B#miBQMbfT`2KBmK BM 2+? T`Q;`KX AM //BiBQM- r2 +Tim`2 i?2 mMB[m2 M/ BKTQ`iMi ?2i2`Q;2M2Biv KQM; i?2 H#Q` 7Q`+2- KH2 p2`bmb 72KH2- `2;mH`- B``2;mH` U+QMiBM;2MiV M/ b2H7@2KTHQvK2Mir?B+? ?p2 p2`v BKTQ`iMi BKTHB+iBQMb 7Q` i?2 +b? ~Qr Q7 i?2 T2MbBQM M/ Tm#HB+ ?2Hi? M/ Gh* T`Q;`Kb M/ 7Q` i?2 T`QD2+iBQMb Q7 }b+H p`B#H2b BM i?2 7mim`2X "v BM+Q`TQ`iBM; bm+? /2iBHb- r2 `2 #H2 iQ bim/v 2z2+ib Q7  MmK#2` Q7 TQHB+v +?M;2b i?i `2 +m``2MiHv /2#i2/ BM i?2 TQHB+v +B`+H2- bm+? b M BM+`2b2 BM i?2 MQ`KH `2iB`2K2Mi ;2 M/ +?M;2b BM i?2 +QTv bvbi2K Q7 ?2Hi? M/ HQM;@i2`K +`2 BMbm`M+2 T`Q;`Kb- b r2HH b bQK2 i`2M/b i?i ?p2 bi`i2/ iQ iF2 TH+2- bm+? b  `Bb2 BM 6G6S+?M;2b BM i?2B` 2KTHQvK2Mi ivT2b M/  `Bb2 Q7 i?2B` `2HiBp2 r;2X h?2 `2KBM/2` Q7 i?2 TT2` Bb Q`;MBx2/ b 7QHHQrbX q2 T`2b2Mi i?2 KQ/2H BM b2+iBQM kX d

.2iBHb Q7 i?2 +HB#`iBQM M/ 2biBKiBQM bi`i2;v `2 ;Bp2M BM b2+iBQM jXh?2 #2M+?K`F `2bmHib- b2MbBiBpBiv MHvb2b M/ TQHB+v 2tT2`BK2Mib `2 /Bb+mbb2/ BM b2+iBQM 9X a2+iBQM 8 +QM+Hm/2bX

k Pp2`HTTBM; :2M2`iBQMb ai`m+im`2 kXR .2KQ;`T?B+b M BM/BpB/mH i iBK2 t Bb +?`+i2`Bx2/ #v  bii2 p2+iQ` {i, j, e}X i `2T`2b2Mib i?2 ;2 Q7 M BM/BpB/mH- j ∈ {m, f } /2MQi2b i?2 ;2M/2` UKH2 Q` 72KH2V M/ e BM/B+i2b i?2 2KTHQvK2Mi biimbX h?2 ;2 Q7 M BM/BpB/mH BM+Hm/BM; ;2b Q7 /2T2M/2Mi +?BH/`2M Bb /2MQi2/ b ei- /Bz2`2MiHv 7`QK i?2 /mHi ;2 iX AM/BpB/mHb +M HBp2 mT iQ Ie v2`bX GB72@iBK2 Bb mM+2`iBM M/ ;2Mib Q7 ;2 ei M/ ;2M/2` j i iBK2 t 7+2  +QM/BiBQMH T`Q##BHBiv Q7 sei,j,t iQ bm`pBp2 7`QK ;2 ei i iBK2 t iQ ;2 ei + 1 i iBK2 t + 1X h?2 72`iBHBiv `i2 Ui?2 MmK#2` Q7 +?BH/`2M T2` rQKM BM  v2`V Q7 M ;2 ei 72KH2 i iBK2 t Bb ;Bp2M b φei,t X AM/BpB/mHb #2+QK2 /mHi M/ 2Mi2` i?2 K`F2i 2+QMQKv i ;2 IA M/ #2;BM 2+QMQKB+ +iBpBiB2b- T`iB+BTiBM; BM i?2 H#Q` K`F2i M/ bi`iBM; iQ +QMbmK2 M/ bp2 /BbTQb#H2 BM+QK2X q2 /2MQi2 #v n eei,j,t i?2 MmK#2` Q7 BM/BpB/mHb Q7 ;2 ei M/ ;2M/2` j i iBK2 tX h?2 /mHi ;2 i bi`ib i ;2 IA - M/ i?2 ;2 Q7 M BM/BpB/mH ei ≥ IA Bb i ≡ ei − IA + 1X h?2 KtBKmK /mHi ;2 Bb /2}M2/ b I = Ie − IA + 1X

kXk G#Q` 7Q`+2 T`iB+BTiBQM M/ 2`MBM;b AM CTM- BM/BpB/mHb `2 ?B`2/ b- BKTHB+BiHv Q` 2tTHB+BiHv- 2Bi?2`  `2;mH` rQ`F2` Q` M B``2;mH`f+QMiBM;2Mi rQ`F2`X h?2 7Q`K2` Bb 7mHH@~2/;2 2KTHQvK2Mi Ub2Bb?BM Q` b2BFB@ FQvQmV M/ rQ`F2`b `2 `2iBM2/ b2KB@T2`KM2MiHv ivTB+HHv rBi? M ++2bb iQ Tm#HB+ T2MbBQM M/ ?2Hi? BMbm`M+2 i?`Qm;? 2KTHQv2`bX h?2 Hii2` Bb 2KTHQvK2Mi i  MQM@ `2;mH`- i2KTQ``v Q` /BbTi+? DQ# U?B@b2Bb?BM Q` ?B@b2BFB@FQvQmV M/ DQ#b `2 H2bb bi#H2 M/ /Q MQi Hrvb +QK2 rBi? Tm#HB+ BMbm`M+2 +Qp2`;2 i?`Qm;? 2KTHQv2`bX3 MQi?2` 7Q`K Q7 rQ`FBM; Bb iQ `mM QM2Ƕb QrM #mbBM2bb b b2H7@2KTHQv2/ rQ`F2`X q2 bbmK2 i?i BM 2+? T2`BQ/ M BM/BpB/mH Bb 2KTHQv2/ i  `2;mH` DQ# U_V-  +QMiBM;2Mi DQ# U*V- b2H7@2KTHQv2/ UaV Q` MQi@rQ`FBM; Ul VX h?2 2KTHQvK2Mi biimb Bb /2@ MQi2/ b  bii2 e ∈ {R, C, S, U }X 1`MBM;b Q7 ivT2 {i, j, e} BM/BpB/mHb i iBK2 t Bb yi,j,e,t X ni,j,e,t `2T`2b2Mib i?2 MmK#2` Q7 BM/BpB/mHb Q7 /mHi ;2 i- ;2M/2` j- M/ 2KTHQvK2Mi ivT2 e i iBK2 tX AM b2+iBQM j- r2 rBHH /2b+`B#2 BM /2iBH ?Qr r2 2biBKi2 ;2@2`MBM;b T`Q}H2b 7Q` j ivT2b Q7 rQ`F2`b Q7 2+? ;2M/2` mbBM; CTM2b2 KB+`Q /iX h?2b2 T`Q}H2b rBHH 7Q`K 3

h?2 /BbiBM+iBQM Bb /Bz2`2Mi 7`QK i?i Q7  T`i@iBK2 DQ# pb  7mHH@iBK2 DQ# BM i?2 lXaX Ai /Q2b MQi M2+2bb`BHv K2M i?i M BM/BpB/mH rBi?  +QMiBM;2Mi DQ# rQ`Fb H2bb i?M 7mHH@iBK2 2[mBpH2Mi ?Qm`bX Ai Bb 2KTHQvK2Mi mM/2`  /Bz2`2Mi ivT2 Q7 +QMi`+i i?M BM  `2;mH` DQ#- r?2`2 2KTHQvK2Mi Bb ;m`Mi22/ QMHv  }t2/ T2`BQ/ M/ Q7i2M i?2 bH`v Bb bB;MB}+MiHv HQr2`X h?2 Hbi 2KTHQvK2Mi biimb- MQi@rQ`FBM;BM+Hm/2b #Qi? mM2KTHQvK2Mi M/ MQi@BM@i?2@H#Q` 7Q`+2X

3

i?2 #bBb Q7 Qm` +H+mHiBQM Q7 BM/BpB/mHbǶ +QMbmKTiBQM M/ bb2i T`Q}H2b- BM //BiBQM iQ +H+mHiBM; T2`bQMH BM+QK2 it `2p2Mm2b- T`2KBmKb 7Q` Tm#HB+ T2MbBQM M/ BMbm`M+2 T`Q;`Kb M/ i?2B` #2M2}ibX

kXj *QMbmKTiBQM M/ bb2i T`Q}H2b AM Q`/2` iQ +H+mHi2 `2p2Mm2b 7`QK +QMbmKTiBQM M/ +TBiH BM+QK2 itiBQM- Bi Bb M2+@ 2bb`v iQ +QKTmi2 i?2 Ti? Q7 +QMbmKTiBQM M/ r2Hi? 7Q` 2+? BM/BpB/mH Qp2` iBK2;Bp2M i?2B` BM+QK2 T`Q}H2bX q2 bbmK2 i?i M BM/BpB/mHǶb ;2@+QMbmKTiBQM T`Q}H2 `2HiBp2 iQ i?2 HB72@iBK2 r2Hi?- /2}M2/ b i?2 /Bb+QmMi2/ bmK Q7 /BbTQb#H2 BM+QK2- Bb iBK2@BMp`BMiX q2 HHQr?Qr2p2`- i?2 MmK#2` Q7 /2T2M/2Mi +?BH/`2M iQ z2+i i?2 +QMbmKTiBQM HHQ+iBQMbX h?2 7+iQ` Q7 /DmbiK2Mi #v M //BiBQMH /2T2M/2Mi +?BH/ rBHH #2 iBK2@BMp`BMi- #mi i?2 iQiH /DmbiK2Mi rBHH p`v b i?2 72`iBHBiv `i2b M/ i?2 MmK#2` Q7 /2T2M/2Mi +?BH/`2M i 2+? ;2 2pQHp2 Qp2` iBK2X q2 bbmK2 i?i i?2 +QMbmKTiBQM Q7 #Qi? KH2 M/ 72KH2 BM/BpB/mHb Q7 i?2 bK2 ;2 rBHH #2 /Dmbi2/ #v i?2 bK2 7`+iBQM iQ ++QmMi 7Q` i?2 +QMbmKTiBQM Q7 /2T2M/2Mi +?BH/`2MX AM/BpB/mHb `2 bbmK2/ iQ #2 /2T2M/2Mi +?BH/`2M 7Q` IA − 1 T2`BQ/bX 1+? /2T2M/2Mi Bb bmTTQ`i2/ #v  TB` Q7 KH2 M/ 72KH2 UT`2MibV Q7 i?2 bK2 ;2 7Q` i?2B` +QMbmKTiBQMX G2i d˜t,ei,k /2MQi2 i?2 MmK#2` Q7 /2T2M/2Mib Q7 ;2 k i?i T`2Mib Q7 ;2 ei bmTTQ`i i iBK2 t- r?B+? +QBM+B/2b rBi? φei−k+1,t−k+1 XN h?2 iQiH MmK#2` Q7 +?BH/`2M 7Q`  KQi?2` Q7 ;2 P ei i iBK2 t Bb ;Bp2M b d e = IA −1 d˜ e X t,i t,i,k k=1 ˜i q2 2biBKi2 i?2 ;2@bT2+B}+ 7`+iBQM Q7 i?2 /Bb+QmMi2/ T`2b2Mi pHm2 Q7 BM+QK2 λ +QMbmK2/ i 2+? ;2 i 7`QK i?2 +QMbmKTiBQM /i 7Q` BM/BpB/mHbX h?2 7+iQ` λi,t iF2b BMiQ ++QmMi i?2 2[mBpH2M+2 /DmbiK2Mi BM +QMbmKTiBQM HHQ+iBQM 7Q` +?BH/`2M BKTHB2/ ˜ i (1 + dt,i ν)- r?2`2 ν `2T`2b2Mib /mHi +QMbmKTiBQM #v i?2 Ti? Q7 72`iBHBiv `i2bX λi,t = λ 2[mBpH2M+2 7Q` /2T2M/2Mi +?BH/`2MX AM/BpB/mHb `2 bbmK2/ iQ QrM x2`Q r2Hi? b i?2v 2Mi2` i?2 2+QMQKv M/ bi`i 2+QMQKB+ +iBpBiB2bX 6Q` bBKTHB+Biv- r2 HbQ bbmK2 i?i i?2 +QMbmKTiBQM T`Q}H2 Bb /2@ i2`KBM2/ #b2/ QM i?2 2tT2+i2/ HB72@iBK2 BM+QK2 r?2M i?2v #2+QK2 2+QMQKB+HHv +iBp2 M/ i?i BM/BpB/mHb Q7  ;Bp2M +Q?Q`i M/ ;2M/2` BMbm`2 KQM; i?2Kb2Hp2b ;BMbi 2K@ THQvK2Mi `BbFbX h?2`27Q`2- +QMbmKTiBQM Q7 M BM/BpB/mH Q7 ;2M/2` j i?i #2HQM;b iQ +Q?Q`i t+1 Ui?i Bb- M BM/BpB/mH dz#Q`MǴ i i?2 }`bi /mHi ;2 i = 1 i iBK2 t + 1V Bb ;Bp2M b 7QHHQrbX bi,t ci,j,t+i (1 + τc,t+i ) = λ

X e

h

I X s=1

Qs

k=1 [1

1 + ra,t+k (1 − τa,t+k )]

i n e s,t+s , P s,j,e,t+s ys,j,e,t+s − τs,j,e,t+s + ps,j,t+s + trt+s + bt+s − m e s,t+s − lc e ns,j,e,t+s

URV

N AM i?Bb +QKTmiiBQM- r2 #bi`+i 7`QK i?2 MQM@bm`pBpH Q7 +?BH/`2M ;Bp2M i?2 p2`v HQr KQ`iHBiv `i2b Q7 M BM7Mi M/ +?BH/`2MX

N

r?2`2 bi,t = λi,t / λ

M/

i Y

[1 + ra,t+k (1 − τa,t+k )],

UkV

k=1

τi,j,e,t = τl,t yi,j,e,t + τls,t + τp,t (yi,j,e,t ) + τm,t (yi,j,e,t ) + τlc,t (yi,j,e,t ).

UjV

τi,j,e,t /2MQi2b M BM/BpB/mHǶb it M/ T`2KBmK TvK2Mi iQ i?2 ;Qp2`MK2Mi- +QMbBbiBM; Q7 H#Q` BM+QK2 it2b i `i2 τl,t - HmKT@bmK it2b τls,t M/ T`2KBmKb Q7 Tm#HB+ T2MbBQM τp,t (yi,j,e,t )- ?2Hi? BMbm`M+2 τm,t (yi,j,e,t )- M/ HQM;@i2`K +`2 BMbm`M+2 τlc,t (yi,j,e,t )- b b?QrM BM UjVX pi,j,t - trt M/ bt `2T`2b2Mi Tm#HB+ T2MbBQM #2M2}ib- ;Qp2`MK2Mi i`Mb72`b e j,t /2MQi2 BM/BpB/mHǶb K2/B+H M/ HQM;@ M/ T`Bpi2 i`Mb72`b- `2bT2+iBp2HvX m e j,t M/ lc Ry i2`K +`2 +QTvb- `2bT2+iBp2HvX h?2 ;2@bT2+B}+ T`Q}H2 Q7 bb2ib +M #2 +QKTmi2/ `2+m`bBp2Hv ;Bp2M i?2 HB72@+v+H2 T`Q}H2 Q7 BM+QK2 M2i Q7 it2b M/ i`Mb72`b M/ i?2 Ti? Q7 +QMbmKTiBQM- b b?QrM #2HQrX bb2i ?QH/BM;b rBHH #2 mb2/ iQ +QKTmi2 i?2 it #b2 7Q` +TBiH BM+QK2 itiBQMX ai+1,j,t+i+1 =

X e

n P i,j,e,t+i {yi,j,e,t+i − τi,j,e,t+i + pi,j,t+i + trt+i + bt+i e ni,j,e,t+i

e i,t+i + [1 + ra,t+i (1 − τa,t+i )]ai,j,t+i − (1 + τc,t+i )ci,j,t+i }. −m e i,t+i − lc

kX9 :Qp2`MK2Mi M/ }b+H TQHB+B2b

AM 2+? T2`BQ/ i?2 ;Qp2`MK2Mi }MM+2b Bib Tm`+?b2b Q7 UMQM@?2Hi?V ;QQ/b M/ b2`pB+2b Gt - UMQM@T2MbBQMV i`Mb72` TvK2Mib iQ BM/BpB/mHb T Rt - T2MbBQM #2M2}ib iQ `2iB`22b Pt K2/B+H BMbm`M+2 #2M2}ib Mtg - HQM;@i2`K +`2 BMbm`M+2 #2M2}ib LCtg M/ i?2 +Qbi Q7 /2#i b2`pB+BM;- i?`Qm;? itiBQM QM BM/BpB/mHb Tt M/ QM +Q`TQ`iBQMb T Ct - BbbmM+2 Q7 M2r /2#i Bt+1 - M/ +QHH2+iBQM Q7 T`2KBmKb P Rt 7Q` Tm#HB+ T2MbBQM- K2/B+H BMbm`M+2 M/ HQM;@i2`K +`2 BMbm`M+2 T`Q;`KbX i i?2 #2;BMMBM; Q7 T2`BQ/ t- i?2 ;Qp2`MK2Mi Qr2b /2#i Bt M/ ?QH/b bb2ib BM i?2 T2MbBQM 7mM/ /2MQi2/ b Ft - r?B+? +M #2 mb2/ iQ Tv 7Q` T2MbBQM #2M2}ibX h?2`27Q`2 i?2 M2i /2#i Q7 i?2 ;Qp2`MK2Mi Bb Bt − Ft X h?2 M2i /2#i 2pQHp2b b 7QHHQrbX Bt+1 − Ft+1 = (1 + rb,t )Bt − (1 + rf,t )Ft +Gt + T Rt + Pt + Mtg + LCtg − Tt − T Ct − P Rt .

U9V

(1 + rb,t )Bt Bb i?2 T`BM+BTH M/ BMi2`2bi TvK2Mib QM i?2 biQ+F Q7 ;Qp2`MK2Mi /2#iX q2 bbmK2 i?i i?2 ;Qp2`MK2Mi Bbbm2b QM2@T2`BQ/- `2H #QM/b i BMi2`2bi `i2 rb,t - M/ r2 #bi`+i 7`QK KQM2v +`2iBQM M/ BM~iBQMX rf,t /2MQi2b i?2 `2im`M QM i?2 T2MbBQM 7mM/X Pm` Q#D2+iBp2 Bb iQ +H+mHi2  iBK2 Ti? 7Q` Bt+1 #2ir22M kyR8 M/ kRyy mM/2` p`BQmb bbmKTiBQMb QM i?2 2+QMQKB+ 2MpB`QMK2Mi BM+Hm/BM; }b+H TQHB+B2b- /2KQ;`T?B+b- H#Q` 7Q`+2 T`iB+BTiBQM M/ /Bbi`B#miBQM Q7 2KTHQvK2Mi ivT2bX Ry

m e j,t Kv BM+Hm/2 ?2Hi? BMbm`M+2 +QTv 7Q` /2T2M/2Mi +?BH/`2M- /2T2M/BM; QM i?2 ;2 Q7 M BM/B@ pB/mH- b /Bb+mbb2/ BM b2+iBQM jX

Ry

q2 /2b+`B#2 #2HQr ?Qr i?2 ;;`2;i2 p`B#H2b BM U9V `2 +QKTQb2/ Q7 BM/BpB/mH p`B#H2bX h?2 ;Qp2`MK2Mi ++QmMib `2 ;Bp2M #v X X X X Tt = τc,t ci,j,t ni,j,e,t + τa,t ra,t ai,j,t ni,j,e,t + τl,t yi,j,e,t ni,j,e,t + τls,t ni,j,e,t , T Rt =

X

i,j,e

i,j,e

i,j,e

i,j,e

trt ni,j,e,t ,

i,j,e

Gt =

X

gt ni,j,e,t ,

X

pi,j,t ni,j,e,t ,

i,j,e

Pt =

i,j,e

Mtg =

X

LCtg =

X

P Rt =

X

ei,j,e

m (1 − ηei,t )mei,t n eei,j,e,t , lc )lci,t ni,j,e,t , (1 − ηi,t

i,j,e

[τp,t (yi,j,e,t ) + τm,t (yi,j,e,t ) + τlc,t (yi,j,e,t )] ni,j,e,t .

i,j,e

Tt `2T`2b2Mib it2b +QHH2+i2/ 7`QK BM/BpB/mHb QM 7Qm` bQm`+2b Q7 `2p2Mm2bc +QMbmKTiBQM i `i2 τc,t - +TBiH BM+QK2 Q` `2im`Mb 7`QK bpBM; i τa,t - H#Q` BM+QK2 i τl,t M/  HmKT@ bmK it Q7 τls,t X T Ct /2MQi2b it2b +QHH2+i2/ 7`QK +Q`TQ`iBQMb- r?B+? 2pQHp2 2tQ;2MQmbHv BM i?2 KQ/2HX trt `2T`2b2Mib 2tQ;2MQmb MQM@T2MbBQM T2`@+TBi i`Mb72` TvK2Mib ;Bp2M iQ BM/BpB/mHbX gt /2MQi2b 2tQ;2MQmb T2`@+TBi ;Qp2`MK2Mi Tm`+?b2b 7Q` BM/BpB/mHb i iBK2 tX pi,j,t `2T`2b2Mib T2MbBQM #2M2}ib iQ 2+? `2iB`22X mei,t M/ lci,t /2MQi2 ;`Qbb K2/B+H m lc ) `2T`2b2Mi i?2 7`+iBQM TB/ M/ HQM;@i2`K +`2 2tT2M/Bim`2b M/ (1 − ηei,t ) M/ (1 − ηi,t #v 2+? Tm#HB+ BMbm`M+2 T`Q;`KX q2 bbmK2 i?i i?2 T`i Q7 K2/B+H 2tT2M/Bim`2b BM+m``2/ #v /2T2M/2Mi +?BH/`2M ei < IA M/ MQi +Qp2`2/ #v i?2 ?2Hi? BMbm`M+2 T`Q;`K Bb TB/ 2[mHHv #v /mHib i ;2 ky@e9X AM/BpB/mHbǶ +QTvb 7Q` ?2Hi? M/ HQM;@i2`K +`2 e i,t - `2 ;Bp2M b BMbm`M+2b- m e i,t M/ lc m m e i,t = ηi,t mi,t + I1≤i≤45 · mdt , e i,t = η lc lci,t . lc i,t

mdt h/2MQi2b i?2 TQ`iBQM Q7 ?2Hi? BMbm`M+2 +QTv 7Q` /2T2M/2Mi +?BH/`2Mc mdt = i PI A −1 m P P ηei,t mei,t j,e n eei,j,e,t / j,e,1≤k≤45 nk,j,e,t - BM+m``2/ QMHv B7 i?2 ;2Mi Bb i ;2 ky@e9X ei=1 τp,t (yi,j,e,t ) Bb i?2 +QMi`B#miBQM iQ i?2 Tm#HB+ T2MbBQM bvbi2K #v 2+? rQ`FBM;@;2 BM@ bm`2/ BM/BpB/mH- r?B+? /2T2M/b QM 2`MBM;b yi,j,e,t . τm,t (yi,j,e,t ) M/ τlc,t (yi,j,e,t ) /2MQi2 T`2KBmKb iQ i?2 K2/B+H M/ HQM;@i2`K +`2 BMbm`M+2 T`Q;`KbX Sm#HB+ T2MbBQM bvbi2K, h?2 Tm#HB+ T2MbBQM bvbi2K BM CTM +QMbBbib Q7 irQ T`ibc i?2 #bB+ T2MbBQM UEBbQ L2MFBMV M/ i?2 2KTHQv22bǶ T2MbBQM BMbm`M+2 UEQb2B L2MFBM

RR

>QF2MVXRR AM/BpB/mHb #2ir22M i?2 ;2b Q7 ky M/ 8N `2 2HB;B#H2 M/ `2[mB`2/ iQ T`@ iB+BTi2 BM i?2 #bB+ T2MbBQM M/ i?2 #2M2}i Bb  }t2/ KQmMi B7 M BM/BpB/mH ?b #22M BMbm`2/ i?`Qm;?Qmi i?2 T2`BQ/ Q7 2HB;B#BHBiv M/ /Dmbi2/ 7Q` T2`BQ/b Q7 MQ BMbm`M+2 M/ MQ T`2KBmK TvK2MiX h?2 #2M2}ib 7`QK i?2 2KTHQv22bǶ T2MbBQM BMbm`M+2 `2 #b2/ QM M BM/BpB/mHǶb +QMi`B#miBQM iB2/ iQ +`22` 2`MBM;b Q7 M BM/BpB/mHX hQ TT`QtBKi2 i?2 bvbi2K- r2 bbmK2 i?i i?2 T2MbBQM #2M2}ib pi,j,t +QMbBbi Q7 irQ T`ib-  HmKT@bmK +QKTQM2Mi- r?B+? `2T`2b2Mib i?2 #bB+ T2MbBQM M/  T`i i?i Bb T`QTQ`iBQMH iQ p2`;2 2`MBM;b Q7 M BM/BpB/mH- r?B+? TT`QtBKi2b i?2 2KTHQv22bǶ T2MbBQM BMbm`M+2X JQ`2 /2iBHb `2 T`QpB/2/ BM b2+iBQM jXjX h?2 TvK2Mi Q7 Tm#HB+ T2MbBQM #2M2}ib Bb }MM+2/ #v i?2 +QK#BMiBQM Q7 i?2 T`2KBmK TB/ #v i?2 BMbm`2/- +QMi`B#miBQM 7`QK i?2 ;2M2`H ;Qp2`MK2Mi #m/;2i M/ i?2 T2MbBQM 7mM/X h?2 Hr Q7 KQiBQM 7Q` i?2 T2MbBQM 7mM/ Bb ;Bp2M b 7QHHQrbX Ft+1 = (1 + rf,t )Ft + P Rt + Xt − Pt .

U8V

>2`2 Xt /2MQi2b i?2 +QMi`B#miBQM 7`QK i?2 ;2M2`H ;Qp2`MK2Mi #m/;2i iQ i?2 TvK2Mi Q7 T2MbBQM #2M2}ibX h?2b2 +QKTmiiBQMb `2Hv QM 2biBKi2b Q7 BM+QK2 #v M ;2 i BM/BpB/mH Q7 ;2M/2` jrBi?  ivT2 e 2KTHQvK2Mi i iBK2 t M/ ?Qr i?Bb Q#D2+i Bb `2Hi2/ iQ i?2 +QMbmKTiBQM M/ bb2i ?QH/BM; Q7 i?2 bK2 BM/BpB/mHX PM+2 r2 bT2+B7v i?2b2 Q#D2+ib- i?2M Qm` ;;`2;iBQM `mH2b #Qp2 rBHH vB2H/ i?2 KQ/2HǶb BKTHB+iBQMb QM i?2 7mim`2 Ti? Q7 ;Qp2`MK2Mi /2#i Bt+1 X

j S`K2i2`BxiBQM Q7 i?2 KQ/2H h?2 KQ/2H T2`BQ/ Bb QM2 v2`X q2 bi`i i?2 bBKmHiBQM Q7 i?2 KQ/2H BM kyR8 M/ +HB#`i2 T`K2i2`b iQ TT`QtBKi2 KB+`Q M/ K+`Q +?`+i2`BbiB+b Q7 i?2 CTM2b2 2+QMQKv BM kyR8X q2 rBHH 7Q+mb QM i?2 bBKmHiBQMb #2ir22M kyR8 M/ kRyyX

jXR .2KQ;`T?B+b q2 bbmK2 i?i BM/BpB/mHb 2Mi2` i?2 2+QMQKv M/ +M bi`i rQ`FBM; i i?2 ;2 Q7 kyX h?2 KtBKmK ;2 Q7 M BM/BpB/mH BM i?2 KQ/2H Bb Ry8X ;2@bT2+B}+ bm`pBpH T`Q##BHBiB2b M/ 72`iBHBiv `i2b `2 #b2/ QM i?2 2biBKi2b M/ T`QD2+iBQMb Q7 i?2 LiBQMH AMbiBimi2 Q7 SQTmHiBQM M/ aQ+BH a2+m`Biv _2b2`+? UASaaVX h?2 Q{+BH T`QD2+iBQMb Q7 i?2b2 p`B#H2b `2 pBH#H2 mT iQ kye8 M/ r2 bbmK2 i?i i?2v `2KBM i i?2 bK2 pHm2b 7i2` kye8X h?2 MmK#2` Q7 /2T2M/2Mi +?BH/`2M Bb +H+mHi2/ rBi? i?2 T`QD2+i2/ ;2@bT2+B}+ 72`iBHBiv `i2bX RR

LQi2 i?i i?2 i2`KBMQHQ;v- i?2 MiBQMH T2MbBQM UEQFmKBM L2MFBMV Bb HbQ mb2/ iQ `2T`2b2Mi i?2 BMbm`M+2 T`2KBmK TvK2Mi iQ `2+2Bp2 i?2 #bB+ T2MbBQM #2M2}i- Q` bQK2iBK2b i?2 #bB+ T2MbBQM Bib2H7X hQ pQB/ +QM7mbBQM- r2 rBHH QMHv mb2 i?2 #bB+ T2MbBQM UEBbQ L2MFBMV- r?B+? +QMbiBimi2b i?2 }`bi iB2` Q7 i?2 Tm#HB+ T2MbBQM bvbi2K M/ Bb TTHB+#H2 7Q` i?2 2MiB`2 TQTmHiBQMX

Rk

jXk G#Q` 7Q`+2 T`iB+BTiBQM M/ 2`MBM;b q2 mb2 i?2 G#Q` 6Q`+2 am`p2v Q7 kyR8 #v i?2 JBMBbi`v Q7 AMi2`MH zB`b M/ *QKKm@ MB+iBQMb iQ +QKTmi2 i?2 /Bbi`B#miBQM Q7 2KTHQvK2Mi ivT2b #v ;2M/2`X AM/BpB/mHb `2 BM QM2 Q7 7Qm` 2KTHQvK2Mi bii2bc `2;mH` DQ# U_V- +QMiBM;2Mi U*V- b2H7@2KTHQvK2Mi UaV M/ MQi rQ`FBM; UlVX h?2 Hbi bii2 BM+Hm/2b BM/BpB/mHb r?Q `2 2Bi?2` mM2KTHQv2/ Q` MQi BM i?2 H#Q` 7Q`+2X 6B;m`2 9 b?Qrb i?2 H#Q` 7Q`+2 T`iB+BTiBQM `i2b #v 2KTHQvK2Mi ivT2 M/ ;2M/2`X G#Q` 7Q`+2 T`iB+BTiBQM `i2b Q7 KH2b biv ?B;? i `QmM/ NyW 7`QK Hi2 kyb iQ 8ybX h?2 MmK#2` Q7 `2;mH` rQ`F2`b /2+HBM2 b?`THv BM eyb b KMv BM/BpB/mHb 7+2 `2iB`2K2Mi ;2b b2i #v 2KTHQv2`bX h?2 T`Q}H2 Q7 72KH2b 2t?B#Bib M J@b?T2 b  H`;2 MmK#2` Q7 rQK2M rBi?/`r 7`QK i?2 H#Q` 7Q`+2 BM Hi2 kyb M/ jyb M/ i +?BH/@ #2`BM; ;2bX S`iB+BTiBQM `i2b `Bb2 ;BM BM 9yb M/ 8yb b i?2v `2im`M iQ rQ`F- i?Qm;? i?2 MmK#2` Q7 `2;mH` DQ#b /Q2b MQi b?Qr  `Bb2 M/ KMv Q7 i?2K `2bmK2 rQ`FBM; i +QMiBM;2Mi DQ#bX

UV JH2

U#V 62KH2

6B;m`2 9, G#Q` 7Q`+2 T`iB+BTiBQM `i2 1`MBM;b T`Q}H2b Q7 2KTHQv2/ rQ`F2`b `2 +QKTmi2/ 7`QK i?2 "bB+ am`p2v QM q;2 ai`m+im`2 U"aqaV BM kyR8- #v i?2 JBMBbi`v Q7 >2Hi?- G#Q` M/ q2H7`2 UJ>GqVX h?2 "aqa /Q2b MQi +Qp2` b2H7@2KTHQv2/ rQ`F2`b M/ r2 mb2 i?2 LiBQMH am`p2v Q7 6KBHv AM+QK2 M/ 1tT2M/Bim`2 ULa6A1V BM kyRy@kyR8X q2 bbmK2 i?i i?2 b?T2 Q7 2`MBM;b T`Q}H2b Bb BMp`BMi Qp2` iBK2 M/ i?2 H2p2H Q7 2`MBM;b rBHH `Bb2 rBi? i?2 2+QMQKv@rB/2 r;2 ;`Qri?X

Rj

UV JH2

U#V 62KH2

6B;m`2 8, 1`MBM;b #v 2KTHQvK2Mi ivT2b AM b2+iBQM 9- r2 HbQ +QMbB/2` Hi2`MiBp2 b+2M`BQb #Qmi +QMp2`;2M+2 Q7 72KH2 2K@ THQvK2Mi M/ r;2b iQ i?Qb2 Q7 KH2 rQ`F2`bX

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R9

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PMHBM2 TT2M/Bt T`QpB/2b //BiBQMH `2bmHib M/ MHvbBb i?i `2 MQi BM+Hm/2/ BM i?2 TT2` /m2 iQ bT+2 +QMbi`BMi R3 h?`Qm;?Qmi i?2 TT2`- r2 #bi`+i 7`QK BM~iBQM M/ `2TQ`i `2H pHm2b Q7 p`B#H2bX

R3

6B;m`2 e, hQiH ;Qp2`MK2Mi QmiHvb M/ `2+2BTib UW Q7 :.SV h?2 THMM2/ BM+`2b2 BM i?2 +QMbmKTiBQM it `i2 7`QK 3W iQ RyW BM kyRN Bb BM+Q`TQ@ `i2/ BM i?2 bBKmHiBQM M/ b?Qrb b M mTiB+F BM `2+2BTib BM 6B;m`2 e M/  /QrMiB+F BM iQiH ;Qp2`MK2Mi #m/;2i /2}+Bi #2HQrX ++Q`/BM; iQ 6B;m`2 e- iQiH QmiHvb `2 T`QD2+i2/ iQ 2t+22/ `2+2BTib BMiQ i?2 7Q`2b22#H2 7mim`2 M/ iQ ;`Qr i M BM+`2bBM; T+2X 6B;m`2 d b?Qrb i?2 iBK2 Ti? Q7 i?2 M2i /2#i iQ :.S `iBQ- (Bt − Ft )/Yt - bi`iBM; 7`QK kyR8X qBi? i?2 Tm#HB+ T2MbBQM 7mM/ bm#i`+i2/ 7`QK i?2 QmibiM/BM;- +QMbQHB/i2/ ;Qp2`MK2Mi BM/2#i2/M2bb- i?Bb M2i /2#i iQ :.S `iBQ `Bb2b 7`QK RjRW BM kyky iQ kkNW #v ky9y M/ KQMQiQMB+HHv BM+`2b2b iQ ?2B;?ib i?i `2 Q#pBQmbHv mMT`2+2/2Mi2/X h?2 ++QmMiBM; KQ/2H mb2/ BM i?Bb TT2` TQ`i`vb  bQ#2`BM; TB+im`2 Q7 ?Qr `TB/Hv i?2 CTM2b2 }b+H QmiHQQF rQmH/ /2i2`BQ`i2 rBi?Qmi Mv +iBQMbX

RN

6B;m`2 d, L2i ;Qp2`MK2Mi /2#i iQ :.S `iBQ UM2i Q7 6- WV q?i *QMi`B#mi2b iQ L2i "Q``QrBM;\ AM Q`/2` iQ [mMiB7v mM/2`HvBM; 7+iQ`b i?i +QMi`B#mi2 iQ i?2 `TB/ `Bb2 BM i?2 /2#i iQ :.S `iBQ- +QMbB/2` i?2 7QHHQrBM; /2+QK@ TQbBiBQM Q7  +?M;2 BM M2i /2#i iQ :.S `iBQ UiQiH /2}+BiV BMiQ }p2 7+iQ`b,RN Dt (Bt+1 − Ft+1 ) − (Bt − Ft ) (Gt + T Rt − Tt − T Ct ) ≡ = Yt Yt Yt (Pt − P Rp,t ) (Mtg − P Rm,t ) (LCtg − P Rlc,t ) + + + Yt Yt Yt (rb,t Bt − rf,t Ft ) . + Yt h?2 iQiH #m/;2i /2}+Bi Ub W Q7 :.SV ?b }p2 +QKTQM2Mib, URV #bB+ T`BK`v /2}+Bi 2t+Hm/BM; Tm#HB+ T2MbBQM- ?2Hi? M/ HQM;@i2`K +`2 BMbm`M+2- UkV Tm#HB+ T2MbBQM /2}+BiRN AM+Hm/BM; i?2 TvK2Mi Qmi Q7 ;2M2`H it `2p2Mm2b iQ }MM+2 8yW Q7 i?2 iQiH #bB+ T2MbBQM #2M2}ibi?2 #Qp2 #`2F@/QrM Bb `2@r`Bii2M b 7QHHQrbX

(Bt+1 − Ft+1 ) − (Bt − Ft ) Yt

=

(Gt + T Rt + Xt − Tt − T Ct ) Yt (Pt − P Rp,t − Xt ) (Mtg − P Rm,t ) (LCtg − P Rlc,t ) + + + Yt Yt Yt (rb,t Bt − rf,t Ft ) . + Yt

ky

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PMHBM2 TT2M/Bt BM+Hm/2b  i#H2 i?i b?Qrb /2iBH2/ };m`2b Q7 i?2 /2+QKTQbBiBQMX

kR

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UV 1tT2M/Bim`2b- i`Mb72`b M/ it2b

U#V .2}+Bi UG + T r − T − T CV

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UV S2MbBQM #2M2}ib M/ T`2KBmK +QHH2+i2/

U#V S2MbBQM /2}+Bi U#2M2}ib@T`2KBmKV

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kj

UV >2Hi? BMbm`M+2 #2M2}ib M/ T`2KBmK

U#V >2Hi? T`2KBmKV

BMbm`M+2

/2}+Bi

U#2M2}ib@

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k9

UV Gh* BMbm`M+2 #2M2}ib M/ T`2KBmK

U#V Gh* BMbm`M+2 /2}+Bi U#2M2}ib@T`2KBmKV

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UV AMi2`2bi TvK2Mi M/ `2+2BTi

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A7 i?2 6_ Bb `Bb2/ 7`QK i?2 +m``2Mi e8 iQ  ?B;?2` ;2- BM/BpB/mHb bi`i `2+2BpBM; #2M2}ib Hi2` M/ ?p2  b?Q`i2` T2`BQ/ Q7 `2+2BpBM; #2M2}ibX h?2 `27Q`K rQmH/ BKT`Qp2 i?2 #m/;2i Q7 i?2 Tm#HB+ T2MbBQM bvbi2K M/ `2/m+2 i?2 T2MbBQM /2}+Bi 7`QK i?2 #b2HBM2 H2p2H Q7 8XkW BM kydy iQ 9XjW- jX9W M/ kX8W- r?2M i?2 6_ Bb `Bb2/ iQ ed- eN M/ dR- `2bT2+iBp2HvX GQr2` T2MbBQM /2}+Bi ?2HTb `2/m+2 iQiH /2}+Bi 7m`i?2` b Bi `2/m+2b i?2 ;Qp2`MK2Mi /2#i M/ BMi2`2bi TvK2MiX q2 MQi2- ?Qr2p2`- i?2 BM+`2b2 BM i?2 6_ HQM2 Bb ?`/Hv bm{+B2Mi iQ +?B2p2 7Q` }b+H bmbiBM#BHBivX LQi2 i?i r2 /Q MQi HHQr BM/BpB/mHb BM i?2 KQ/2H iQ QTiBKBx2 ;Bp2M i?2B` 2MpB`QM@ K2MibX AM  ivTB+H Qp2`HTTBM; ;2M2`iBQMb KQ/2H- r?2M BM/BpB/mHb 2tT2+i  `2/m+iBQM BM #2M2}ib- i?2v ivTB+HHv T`QpB/2 KQ`2 H#Q` M/ HbQ +?QQb2 iQ bp2 KQ`2 `i?2` i?M +QMbmK2 M/ BM+`2b2 i?2 +TBiH biQ+F Qp2` iBK2- H2/BM; iQ  H`;2` it #b2X h?Bb rQmH/ TQi2MiBHHv `2/m+2 i?2 #m/;2i /2}+Bi 7m`i?2` M/ T`QpB/2  KQ`2 bB;MB}+Mi `2HB27 BM i?2 }b+H Qmi+QK2b- r?B+? rQmH/ #2 //2/ iQ i?2 ;BMb i?i r2 `2TQ`i2/ #Qp2X h?2 BM+`2b2 BM i?2 6_ HHQrb i?2 Tm#HB+ T2MbBQM 7mM/ iQ bm`pBp2 //BiBQMH v2`bX qBi? 6_ i ed- i?2 T2MbBQM 7mM/ Bb MQr T`QD2+i2/ iQ #2 /2TH2i2/ BM kyd3 BMbi2/ Q7 i?2 #b2HBM2 v2` Q7 ky8dX qBi? M 6_ Q7 eN- i?2 7mM/ bm`pBp2b Tbi kRyy rBi?  /2+HBMBM; Ti? i 9dXkW BM kRyyX q?2M i?2 6_ Bb `Bb2/ iQ dR- i?2 Tm#HB+ T2MbBQM 7mM/ KQMQiQMB+HHv BM+`2b2b rBi?  pHm2 Q7 RkkXRW BM kRyyX

jy

_2/m+BM; S2MbBQM "2M2}ib q?2M T2MbBQM #2M2}ib `2 /B`2+iHv `2/m+2/- i?2 }b+H `2HB27 Bb BKK2/Bi2 M/ bB;MB}+MiX q2 bBKmHi2  `27Q`K iQ `2/m+2 #2M2}ib #v RyW- kyW M/ jyW Qp2`  T2`BQ/ Q7 jy v2`bX h#H2 e b?Qrb i?i 2p2M  KQ/2bi +mi Q7 RyW BM T2MbBQM #2M2}ib +M ;Q /22T BM +miiBM; i?2 #m/;2i /2}+BiX  `2bQM 7Q` i?Bb BKT`Qp2K2Mi BM i?2 }b+H QmiHQQF Bb i?2 7+i i?i i?2 T2MbBQM +mi z2+ib MQi QMHv i?2 7mim`2 `2iB`22b #mi KQ`2 BKTQ`iMiHv i?2 +m``2Mi T2MbBQM2`bX  H`;2` T2MbBQM #2M2}i +mi bm+? b  jyW `2/m+iBQM rQmH/ HQr2` i?2 /2}+Bi #v #Qmi dW Q7 :.S +QKT`2/ iQ i?2 #b2HBM2 +b2`2/m+BM; i?2 QmibiM/BM; M2i /2#i #v KQ`2 i?M R3yW Q7 :.S #v kydyX h?Bb }M/BM; bm;;2bib i?i  T2MbBQM `27Q`K BM i?2 7Q`K Q7  `2/m+iBQM BM #2M2}ib +QmH/ T`Q/m+2 bB;MB}+Mi ;BMb BM 2bi#HBb?BM; }b+H bmbiBM#BHBivX h#H2 e, _2/m+iBQM BM S2MbBQM "2M2}ib, .2}+Bib M/ .2#i iQ PmiTmi "b2HBM2 u2` /2}+Bi kyky kyjy ky9y ky8y kyey kydy

yXyjk yXy88 yXRyy yXRj3 yXRe8 yXR3k

RyW *mi

/2#i /2}+Bi RXjRy RXeky kXk3d jX9jj 9Xd8d eXk89

yXyjR yXy9N yXy3N yXRky yXR98 yXRek

kyW *mi

/2#i /2}+Bi RXjyR RX8NR kXR38 jXRyR 9Xjj3 8Xe8e

yXyjy yXy99 yXyd3 yXRyk yXRk9 yXRj3

jyW *mi

/2#i /2}+Bi RXjy9 RX8ek kXy39 kXN98 jXNR3 8Xyje

yXykN yXyjN yXyed yXy39 yXRyj yXRR9

/2#i RXjyR RX8jj RXN3k kXdye jX8yy 9X9Re

qBi? #2M2}i +mib b?QrM BM h#H2 e- i?2 Tm#HB+ T2MbBQM 7mM/ bm`pBp2b Tbi kydy BM HH i?2 Hi2`MiBp2 +b2bX A7 i?2 +mib `2 /22T 2MQm;?- MK2Hv kyW Q` jyW- i?2 7mM/ BM+`2b2b Tbi kydyX _BbBM; i?2 *QMbmKTiBQM ht AM Qm` KQ/2H- i?2 +QMbmKTiBQM it `i2 Bb bbmK2/ iQ BM+`2b2 7`QK 3W iQ RyW BM kyRN #b2/ QM i?2 +m``2Mi TQHB+v THMX AM Hi2`MiBp2 2tT2`BK2Mib- r2 +QMbB/2` ?B;?2` +QMbmKTiBQM it `i2b M/ H2i i?2K BM+`2b2 iQ R8WkyW- M/- k8W- i?2 H2p2Hb +QKT`#H2 iQ i?Qb2 BM KMv 1m`QT2M +QmMi`B2bX AM i?2 2tT2`BK2Mib- r2 H2i i?2 +QMbmKTiBQM it BM+`2b2 #v R T2`+2Mi;2 TQBMi 2+? v2` bi`iBM; BM kykyX

jR

h#H2 d, _BbBM; i?2 *QMbmKTiBQM ht, .2}+Bib M/ .2#i iQ PmiTmi "b2HBM2 u2` /2}+Bi kyky kyjy ky9y ky8y kyey kydy

yXyjk yXy88 yXRyy yXRj3 yXRe8 yXR3k

R8W

/2#i /2}+Bi RXjRy RXeky kXk3d jX9jj 9Xd8d eXk89

yXykd yXyk3 yXydk yXRyd yXRjR yXR9e

kyW /2#i /2}+Bi

RXjye RX9Rd RX3k9 kXedN jXdR8 9XNRj

yXyke yXyy9 yXy9e yXyd3 yXRyy yXRRj

k8W /2#i

/2}+Bi

/2#i

RXjyj RXj9y RX8yk kXyNy kX3eR jXd3e

yXyke −0.001 yXykR yXy8R yXydk yXy39

RXjyy RXjj8 RXjRR RXe8R kXRd8 kX38y

++Q`/BM; h#H2 d- `BbBM; i?2 +QMbmKTiBQM it `i2 iQ R8W +mib i?2 #m/;2i /2}+Bi BM kyjy `Qm;?Hv BM ?H7 +QKT`2/ iQ i?2 #b2HBM2 +b2X >B;?2` it `i2b rQmH/ #`BM; i?2 /2}+Bi +HQb2 iQ x2`Q Q` 2p2M  bm`THmb #v kyjyX *H2`Hv-  ?B;?2` +QMbmKTiBQM it Bb BKTQ`iMi BM ?2HTBM; CTM +?B2p2 }b+H bmbiBM#BHBivX >Qr2p2`- b i?2 ;BM;@`2Hi2/ T`ib Q7 i?2 #m/;2i +QMiBMm2 iQ `Bb2 i?2 }b+H #m`/2Mi?2 HQM;2` `mM ?2Hi? Q7 i?2 ;Qp2`MK2Mi #m/;2i /2i2`BQ`i2b M/ 2p2M  kyW +QMbmKT@ iBQM it H2/b iQ  #m/;2i /2}+Bi Q7 RyW Q7 :.S Q` ?B;?2` #v kyeyX h?Bb `2bmHib `;m2b i?i mbBM; i?2 +QMbmKTiBQM it b i?2 QMHv }b+H BMbi`mK2Mi +MMQi T`Q/m+2 }b+H bmb@ iBM#BHBivX _BbBM; *Q@Svb 7Q` >2Hi? M/ GQM;@h2`K *`2 AMbm`M+2 b /2b+`B#2/ BM i?2 +HB#`iBQM b2+iBQM- Tm#HB+ ?2Hi? BMbm`M+2 +Qp2`b 3yW Q7 ;`Qbb 2tT2M/Bim`2b 7Q` BM/BpB/mHb i ;2 y iQ 8- dyW 7Q` ;2 e@eN- 3yW 7Q` dy@d9 M/ NyW 7Q` i?Qb2 #Qp2 d9X h?2 HQM;@i2`K +`2 BMbm`M+2 +Qp2`b NyW Q7 ;`Qbb 2tT2M/Bim`2b Q7 HH i?2 BMbm`2/ i M/ #Qp2 ;2 9yX AM i?Bb bm#b2+iBQM r2 +QMbB/2` TQHB+B2b i?i `Bb2 i?2 +QTvb 7Q` Tm#HB+ ?2Hi? Q` Gh* 2tT2Mb2b- 2Bi?2` i kyW Q` jyW 7Q` i?2 QH/2` rQ`F2`bX

jk

h#H2 3, _BbBM; *Q@Svb 7Q` Sm#HB+ >2Hi? M/ GQM;@h2`K *`2 AMbm`M+2b, .2}+Bib M/ .2#i iQ PmiTmi

"b2HBM2 u2` /2}+Bi kyky kyjy ky9y ky8y kyey kydy

yXyjk yXy88 yXRyy yXRj3 yXRe8 yXR3k

>2Hi? BMbm`M+2 +QTv kyW 7Q` ≥ 70 jyW 7Q` ≥ 70

/2#i /2}+Bi RXjRy RXeky kXk3d jX9jj 9Xd8d eXk89

yXyk3 yXy93 yXyNj yXRkN yXR8j yXRdy

/2#i /2}+Bi RXjy8 RX8e8 kXRe3 jXkjj 9X9e9 8X3ey

yXykk yXy9R yXy39 yXRRd yXR9y yXR8e

GQM;@i2`K +`2 +QTv kyW 7Q` ≥ 40 jyW 7Q` ≥ 40

/2#i /2}+Bi RXjyR RX9N3 kXyk9 kXNNj 9XRRe 8XjN8

yXykN yXy9N yXyN9 yXRjy yXR88 yXRdR

/2#i /2}+Bi RXjy9 RX8d9 kXR3e jXkek 9X8yd 8XNRR

yXyk8 yXy99 yXy3d yXRkk yXR98 yXRey

/2#i RXkN3 RX8k3 kXy3e jXyNy 9Xk8d 8X8eN

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jX *QK#BMiBQM j, UV aK2 b *QK#BMiBQM R- THmb +QMbmKTiBQM it `Bb2/ 7`QK RyW iQ R8WX h#H2 N, aQ+BH AMbm`M+2 _27Q`Kb M/ 62KH2 1`MBM;b *?M;2b, .2}+Bib M/ L2i .2#i iQ PmiTmi "b2HBM2 u2` /2}+Bi kyky kyjy ky9y ky8y kyey kydy

yXyjk yXy88 yXRyy yXRj3 yXRe8 yXR3k

*QK#BMiBQM R

/2#i /2}+Bi RXjRy RXeky kXk3d jX9jj 9Xd8d eXk89

yXyR8 yXyyR yXyke yXy9N yXye9 yXydj

*QK#BMiBQM k

*QK#BMiBQM j

/2#i

/2}+Bi

/2#i

/2}+Bi

/2#i

RXkdR RXRNk RXk9d RXeRy kXyNj kXede

yXyy3 −0.033 −0.013 yXyy9 yXyR9 yXyR3

RXk9e yXNkN yXeje yX83N yXe8y yXd33

yXyyN −yXyk8 −yXyyk yXyR3 yXyjy yXyje

RXkee yXNNj yXdN9 yX3e3 RXyej RXj9e

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