Optimal Monetary Policy When Interest Rates Are Bounded at Zero

IMES DISCUSSION PAPER SERIES

Optimal Monetary Policy When Interest Rates are Bounded at Zero

Ryo KATO and Shin-Ichi NISHIYAMA

Discussion Paper No. 2003-E-11

INSTITUTE FOR MONETARY AND ECONOMIC STUDIES

BANK OF JAPAN

C.P.O BOX 203 TOKYO 100-8630 JAPAN

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Do not reprint or reproduce without permission. NOTE: IMES Discussion Paper Series is circulated in order to stimulate discussion and comments. Views expressed in Discussion Paper Series are those of authors and do not necessarily reflect those of the Bank of Japan or the Institute for Monetary and Economic Studies. IMES Discussion Paper Series 2003-E-11 October 2003

Optimal Monetary Policy When Interest Rates are Bounded at Zero

Ryo KATO* and Shin-Ichi NISHIYAMA**

Abstract

This paper characterizes the optimal monetary policy reaction function in the presence of a zero lower bound on the nominal interest rate. We analytically prove and numerically show that the function is highly nonlinear, more expansionary, and more aggressive than the Taylor rule. We then test its empirical validity taking the case of Japan in the 1990s. Qualitatively, we find some evidence of nonlinear monetary policy. Quantitatively, we find the actual monetary policy to be too contractionary during the first half of the decade, while the low interest policy during the latter half turns out to be fairly consistent with the simulated path.

Key words: Deflation, Liquidity trap, Pre-emptive monetary policy, Zero bound

JEL classification: E52, E58, C63

* Global Economic Research Division, International Department, Bank of Japan (E-mail: [email protected]) ** Research Division 1, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: [email protected])

This paper is a revised version of our earlier draft circulated as OSU Working Paper No.01- 12. We would like to thank Kosuke Aoki, Ken Brevoort, Steve Cecchetti, C.Y. Choi, Paul Evans, Bill Gavin, Takatoshi Ito, Andrew Levin, Nelson Mark, Satoshi Miyata, Masao Ogaki, Raphael Solomon, Dan Thornton, Takashi Ui, Nick Vriend, Tsutomu Watanabe, and four anonymous referees for their valuable comments. We thank Yasuo Hirose for providing us the data. We are especially grateful to Mario Miranda for his invaluable guide in building the numerical code. Any remaining errors are our own. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of Japan or the Institute for Monetary and Economic Studies. 4Lqwurgxfwlrq

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Htq +5, dqg htq +6, vwdqg iru wkh LV htxdwlrq dqg DV htxdwlrq/ uhvshfwlyho|/ zkhuh dqg % duh dvvxphg wr eh l=l=g= udqgrp glvwxuedqfhv1 Dowkrxjk htq +5, frqwdlqv d iruzdug0orrnlqj yduldeoh/ wklv fdq eh vxevwlwxwhg e| wkh iroorzlqj uhodwlrqvkls ehwzhhq wkh h{shfwhg lq dwlrq udwh dqg wkh fxuuhqw lq dwlrq udwh dqg wkh rxwsxw jds/

H||n @ | ||= +7,

Wkhq/ d fhqwudo edqn*v sureohp lv irupxodwhg dv dq lqwhuwhpsrudo plqlpl}dwlrq sureohp zlwk wkh remhfwlyh ixqfwlrq/ [" plq = H| O|n +8, | 'f vxemhfw wr wkh LV htxdwlrq ||n @+ ,|| +l| |, |n zlwk wkh }hur orzhu erxqg frqvwudlqw rq wkh qrplqdo lqwhuhvw udwh/

l| 3 dqg wkh DV htxdwlrq +6,1 Zh iroorz wkh wuhdwphqw ri wkh qrq0qhjdwlylw| frqvwudlqw dv lq Zdwdqdeh +5333, dqg dsso| Nxkq0Wxfnhu frqglwlrqv lq wklv g|qdplf rswlpl}dwlrq sureohp1 Vlqfh wklv sureohp fdq eh lqwhusuhwhg dv d frqyhqwlrqdo rswlpdo erxqghg frqwuro sureohp zlwk d olqhdu v|vwhp/ zh fdq vhw xs d Ehoopdq htxdwlrq: zlwk wkuhh Odjudqjh pxowlsolhuv dv iroorzv/ q r 4 2 W 2 Y +||>|,@plq^ || +| , H|!|ni+ ,|| l| | ||nj | 5 H||n+| || |n,

#|l|

H|Y +||n>|n,`= +9,

: Khuh zh dvvxph d fhqwudo edqn*v glvfrxqw idfwru q wr eh vx!flhqwo| vpdoo iru wkh Frqwudfwlrq Pdsslqj Wkhruhp wr krog1 Iru wkh olvwv ri uhjxodulw| frqglwlrqv uhjduglqj wkh Frqwudfwlrq Pdsslqj Wkhruhp/ vhh Vwrnh| dqg Oxfdv +4<;<,1 Wkurxjkrxw wklv sdshu/ zh vlpso| dvvxph wkdw uhjxodulw| frqglwlrqv duh vdwlv hg1

8 Zh pxvw eh yhu| fduhixo lq zulwlqj wkh vljqv ri Odjudqjh pxowlsolhuv1 Dv wklv lv d plq0 lpl}dwlrq sureohp zlwk d qrq0qhjdwlylw| frqvwudlqw/ hdfk vljq lq iurqw ri wkh pxowlsolhu pxvw eh vhw vr wkdw wkh pxowlsolhu kdv d srvlwlyh ydoxh zkhq wkh frqvwudlqw lv elqglqj1 Wkh uvw rughu frqglwlrqv +IRFv, ri wklv sureohp duh dv iroorzv/

H|!|n @ #| +:, 4 H @ H + W, H ! H +;, | |n | |n | |n2 | |n2 4 H ! @ H | + ,H ! H +<, | |n | |n | |n2 | |n2 zkhuh htq +:,/ htq +;,/ dqg htq +<, uhsuhvhqw wkh IRFv zlwk uhvshfw wr wkh qrplqdo lqwhuhvw udwh/ l/ wkh lq dwlrq udwh/ / dqg wkh rxwsxw jds/ |/ uhvshfwlyho|1 Wr jdlq vrph lqwxlwlrq uhjduglqj wkhvh IRFv/ vxssrvh wkhuh lv qr }hur orzhu erxqg rq wkh lqwhuhvw udwh/ vr wkdw IRF +:, ehfrphv H|!|n @ #| @3iru dq| shulrg w1

Wkhq wkh rqo| frqvwudlqw zklfk vxevwdqwldoo| pdwwhuv lv | wkh Odjudqjh pxowlsolhu dvvrfldwhg zlwk wkh DV htq +6,/ zklfk fdq eh lqwhusuhwhg dv wkh vkdgrz frvw ri DV vkrfn lq wklv fdvh1 Lq rwkhu zrugv/ lq wkh devhqfh ri wkh }hur orzhu erxqg frqvwudlqw/ d fhqwudo edqn fdq frpsohwho| qhxwudol}h wkh h{0dqwh frvw vwhpplqj iurp wkh LV vkrfn/ zkloh idflqj d wudgh0r ehwzhhq lq dwlrq dqg rxwsxw vwdelol}dwlrq lq uhvsrqglqj wr DV vkrfnv1 Lq wkh frqwh{w ri rxu prgho glvfxvvhg lq wklv sdshu/ xqghu rswlpdo prqhwdu| srolf| frqgxfw/ H|!|n +zklfk uhsuhvhqwv wkh vkdgrz frvw ri LV vkrfnv, zloo eh htxdo wr }hur/ zkloh H||n +zklfk uhsuhvhqwv wkh vkdgrz frvw ri DV vkrfnv, uhpdlqv vwulfwo| srvlwlyh1 Wkxv/ djjuhjdwh ghpdqg glvwxuedqfhv fdqqrw eh d uhvwudlqw rq wkh fhqwudo edqn*v prqhwdu| srolf| frqgxfw lq wkh devhqfh ri wkh }hur orzhu erxqg1 Lq frqwudvw/ vxssrvh wkdw wkhuh h{lvwv d }hur orzhu erxqg frqvwudlqw dqg lw lv elqglqj lq wkh fxuuhqw shulrg1 Wkhq zh kdyh H|!|n A 3 zklfk lpsolhv wkdw d vkdgrz frvw lv hphujlqj iurp wkh LV vkrfnv1 Lq wklv fdvh/ hyhq li wkh srolf| lv frqgxfwhg rswlpdoo|/ d fhqwudo edqn fdqqrw frpsohwho| rvhw LV vkrfnv1 Wkxv/ lq wkh suhvhqfh ri d }hur orzhuerxqgfrqvwudlqw/dfhqwudoedqnlvfrqiurqwhgzlwkwkhgl!fxowwdvnriedodqflqj wkh rssruwxqlw| frvwv dulvlqj iurp erwk LV dqg DV vkrfnv1 Qrwh wkdw lq rxu prgho/ prqhwdu| srolf| kdv d rqh shulrg odj ehiruh lw dhfwv wkh hfrqrp|/ dqg wkhuhiruh wkh }hur orzhu erxqg pdwwhuv iru wkh delolw| ri d fhqwudo edqn wr vwdelol}h wkh hfrqrp| lq wkh iroorzlqj shulrg1 Qh{w/ pxowlso|lqj rq erwk vlghv ri htq +;, dqg vxewudfwlqj htq +<,/ zh rewdlq wkh iroorzlqj htxdwlrq/

W H||n @ H|||n H|+|n , H|!|n2 H|!|n= +43,

E| xsgdwlqj htq +43, rqh shulrg dqg vxevwlwxwlqj edfn wr htq +<, iru H||n2/zhrewdlq wkh iroorzlqj uhodwlrqvkls ehwzhhq H|||n dqg H|||n21

9 4 H | H + W, H | @ H ! +4 ,H ! H ! | |n2 | |n2 | |n | |n | |n2 | |n +44,

Dowhuqdwlyho|/ e| xvlqj wkh IRF iru wkh qrplqdo lqwhuhvw udwh l1h1/ htq +:, / wkh deryh uhodwlrqvkls fdq dovr eh h{suhvvhg dv d ixqfwlrq ri wkh Odjudqjh pxowlsolhuv/ #/ dvvrfldwhg zlwk wkh Nxkq0Wxfnhu frqglwlrq/ +4 , 4 H | H + W, H | @ H # H # # = | |n2 | |n2 | |n | |n2 | |n | +45,

; Vlqfh wkh fkrlfh ri H|||n dqg l| lv whfkqlfdoo| htxlydohqw/ htq +45, fdq eh frqvlghuhg wr eh wkh Hxohu htxdwlrq ri wkh frqwuro yduldeoh1 Dowkrxjk lw lv whfkqlfdoo| srvvleoh wr h{suhvv wkh Hxohu htq +45, lq whupv ri l|/ iru wkh frqyhqlhqfh ri dojheudlf pdqlsxodwlrq/ zh zloo wdnh H|||n dv wkh sur{| ri wkh frqwuro yduldeoh iru d zkloh1 Qrz lw vkrxog 2 eh qrwhg wkdw wkh Hxohu htxdwlrq +45, frqwdlqv h{shfwhg ydoxhv ri i#|nj'f1Wklv lpsolhv wkdw hyhq li d }hur orzhu erxqg frqvwudlqw lv qrw elqglqj lq wkh fxuuhqw shulrg

H|#|n zklfk lv lq jhqhudo srvlwlyh gxh wr wkh qrq0}hur suredelolw| ri wkh hyhqw wkdw wkh frqvwudlqw lv elqglqj lq wkh iroorzlqj shulrg1 Ruskdqlghv dqg Zlhodqg +5333, suhvhqwv qxphulfdo hylghqfh wr fodlp wkdw hyhq li wkh qrq0qhjdwlylw| frqvwudlqw glg qrw elqg lq dq| sdvw shulrg/ rswlpdo prqhwdu| srolf| lv glhuhqw iurp wkh fdvh zkhuh wkhuh lv qr vxfk frqvwudlqw1 Htq +45, ghulyhg khuh surylghv wkh dqdo|wlfdo h{suhvvlrq zklfk lv frqvlvwhqw zlwk wkhlu fodlp1

515 Rswlpdo Prqhwdu| Srolf| Uhdfwlrq Ixqfwlrq

Rxu jrdo khuh lv wr ghulyh wkh dqdo|wlfdo h{suhvvlrq ri wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq zkhq wkh frqvwudlqw lv qrw elqglqj lq wkh fxuuhqw shulrg1 Vlqfh H|||n @ k +H||n2 H||n, dqg H|||n2 @ k +H||n H||n2, iurp wkh DV htq +6,/ vxevwlwxwlqj wkhvh lqwr wkh Hxohu htq +45, |lhogv wkh vhfrqg0rughu glhuhqfh htxdwlrq lq whupv ri H||n dv iroorzv/ W 2 W W H|+|n , 4 H|+|n2 ,H|+|n ,@H| | +46, zkhuh 4 # +4 ,# 3# = | |n2 |n |

; Lq rwkhu zrugv/ |+|n dqg | kdyh d rqh0wr0rqh uhodwlrqvkls jlyhq wkh vwdwh EZ|c+|1Qrwhwkdw e| dsso|lqj wkh frqglwlrqdo h{shfwdwlrq rshudwru | rq erwk vlghv ri wkh LV htxdwlrq/ lw iroorzv wkdw

|+|n 'E4 n kB+| n BZ| 3 B|

: 2 2 Ohw c2 eh wkh urrwv ri wkh fkdudfwhulvwlf htxdwlrq/ } 4 } @3= Wkh urrwv ri wkh fkdudfwhulvwlf htxdwlrq fdq eh h{suhvvhg dv/ s 4 2 +4 2,2 7 @ = c2 5 Qrz/ vlqfh +4 2,2 A 7> wklv lpsolhv wkdw erwk urrwv duh uhdo1 Ixuwkhu/ e| qrwlflqj wkdw 2 A 3/ zh fdq lqihu wkdw rqh urrw lv juhdwhu wkdq rqh dqg wkh rwkhu lv < ohvv wkdq rqh l1h1/ A 4 dqg 2 ? 4= Wkhq zh fdq ghulyh wkh xqltxh vroxwlrq wr wkh vhfrqg0rughu glhuhqfh htxdwlrq dv iroorzv/ "[ W W H|+|n2 ,@H|+|n , 2H| |n= +47, 'f

Uhfdoolqj wkdw H||n2 @ H||n H|||n iurp wkh DV htxdwlrq/ wkh vroxwlrq wr wkh vhfrqg0rughu glhuhqfh htxdwlrq fdq eh wudqviruphg dv 4 4 [" H | @ +H W, H > +48, | |n | |n 2 | |n 'f zklfk fdq eh uhjdughg dv wkh rswlpdo uhdfwlrq ixqfwlrq ri H|||n lq uhvsrqvh wr H||n " +wkhh{shfwhglq dwlrqudwhdwshulrgw, dqg wkh vwuhdpv ri h{shfwhg ydoxhv ri i#|nj' dw shulrg w= Vlqfh rxu jrdo khuh lv wr ghulyh wkh dqdo|wlfdo h{suhvvlrq ri wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq lq whupv ri wkh qrplqdo lqwhuhvw udwh/ zh vxevwlwxwh H|||n dqg

H||n xvlqj wkh LV htxdwlrq dqg DV htxdwlrq/ uhvshfwlyho|1 Wklv |lhogv wkh iroorzlqj rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq/ [" W 4 4 W 4 l +|>||,@| || +| , 2H| |n 'f~} X +49, zkhuh

s 2 4 +2 4,2 7 @ / A 4 5

s 2 4 +2 4,2 7 @ / 3 ? ? 4= +4:, 2 5 2 < Wklv fdq eh hdvlo| vhhq e| hydoxdwlqj wkh sro|qrpldo ixqfwlrq/ sE5'52 3 E n q n k2qb5 n q/dw 5 '1Vlqfhs E ' 3k2qb f dqg s E5 : f/ lw vkrxog eh wkh fdvh wkdw rqh ri wkh fkdudfwhulvwlf urrwv eh juhdwhu wkdq rqh dqg wkh rwkhu eh ohvv wkdq rqh1

; Wkh deryh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq +49, lv ydolg iru wkh vwdwh W +|>||, vxfk wkdw l| A 31 Iru dq| rwkhu vwdwh zkhuh wkh }hur orzhu erxqg frqvwudlqw lv W elqglqj/ wkh rswlpdo prqhwdu| srolf| lv wulyldoo| l| @31 Vrph uhpdunv duh lq rughu uhjduglqj wkh irxuwk whup ri htq +49,/ 1 Iluvw ri doo/ lw vkrxog eh qrwhg wkdw fdq eh h{suhvvhg dv d ixqfwlrq ri wkh fxuuhqw vwdwh | dqg

||1 Wklv uhvxow lqgluhfwo| iroorzv iurp wkh dvvxpswlrq wkdw wkh Frqwudfwlrq Pdsslqj Wkhruhp krogv iru wkh ydoxh ixqfwlrq lq htq +9,1 Vlqfh d fhqwudo edqn*v ydoxh ixqfwlrq lv d ixqfwlrq ri wkh fxuuhqw vwdwh +|>||, dqg wkh ixqfwlrqdo vkdsh lv wlph0lqyduldqw/ dv d frqvhtxhqfh/ wkh rswlpdo ihhgedfn uxoh lv dovr d ixqfwlrq ri wkh fxuuhqw vwdwh +|>||, dqg lv wlph0lqyduldqw dv zhoo l1h1/ wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq fdq W eh h{suhvvhg dv l +|>||, iru dq| shulrg w1 Qrz/ vlqfh wkh uvw whup wkurxjk wkh wklug whup lq htq +49, lv reylrxvo| d olqhdu +dqg wlph0lqyduldqw, ixqfwlrq ri +|>||,/wklv dxwrpdwlfdoo| uhtxluhv wkh whup wr eh d wlph0lqyduldqw ixqfwlrq ri wkh fxuuhqw vwdwh

| dqg ||1 Lq rughu wr vhh wklv uhvxow lq d pruh lqwxlwlyh zd|/ qrwlfh wkdw wkh whup " fdq eh h{suhvvhg lq whupv ri wkh vhtxhqfh ri iH|#|nj'f1 Ixuwkhu/ qrwlfh wkdw e| glhuhqwldwlqj htq +9, zlwk uhvshfw wr ||n dqg lqyrnlqj wkh hqyhorsh wkhruhp/ lw iroorzv wkdw 4 H Y + >| ,@ H ! 1 | + |n |n | |n

E| h{sorlwlqj IRF+:, dqg xvlqj wkh odz ri lwhudwhg h{shfwdwlrq/ zh fdq olqn H|#|n dqg H|Y++|n>||n, dv iroorzv 4 H Y + >| ,@ H # iru ;lA3= +4;, | + |n |n | |n

Qrz/ xvlqj edfnzdug0vxevwlwxwlrq/ |n dqg ||n frxog eh h{suhvvhg lq whupv ri wkh fxuuhqw vwdwh +|>||, dqg vwuhdpv ri udqgrp vkrfnv i |nj' dqg i%|nj' xqghu wkh rswlpdo srolf| frqgxfw1 Wkxv/ wkh h{shfwhg ydoxh ri Y++|n>||n, frqglwlrqhg xsrq wkh lqirupdwlrq vhw dydlodeoh dw shulrg w fdq eh/ lqghhg/ vkrzq wr eh d ixqfwlrq ri wkh fxuuhqw vwdwh | dqg || l1h1/ H|Y++|n>||n,@j+|>||,1 Lq wklv pdqqhu/ dw ohdvw lq sulqflsoh/ lw lv srvvleoh wr h{suhvv H|#|n iru dq| l dv d ixqfwlrq ri wkh fxuuhqw vwdwh | dqg ||/ zklfk lq wxuq lpsolhv wkdw wkh whup lv d ixqfwlrq ri wkh fxuuhqw vwdwh dv zhoo1 Krzhyhu/ gxh wr wkh qdwxuh ri wkh OT vwrfkdvwlf sureohp zlwk d erxqghg frqwuro yduldeoh/ wkh h{solflw ixqfwlrqdo irup ri lq whupv ri | dqg || grhv qrw h{lvw lq jhqhudo1 Wklv lv rqh ri wkh uhdvrqv zk| zh uho| rq wkh qxphulfdo phwkrg lq Vhfwlrq 61 Dv d pdwwhu ri idfw/ zh qxphulfdoo| ghprqvwudwh wr eh d ixqfwlrq ri wkh fxuuhqw vwdwh lq Vhfwlrq 61 Vhfrqg uhpdun uhjduglqj wkh whup lv wkh qrq0olqhdulw| zlwk uhvshfw wr wkh fxuuhqw vwdwh yduldeohv | dqg ||1 Lw vkrxog eh qrwhg wkdw wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq +49, lv olqhdu lq vwdwh yduldeohv | dqg || h{fhsw iru wkh irxuwk whup/ 1Vxssrvh

< wkhuh lv qr }hur orzhu erxqg frqvwudlqw/ vr wkdw |n @3iru dq| l1 Wkhq wkh rswlpdo uhdfwlrq ixqfwlrq lv olqhdu dqg lv h{dfwo| wkh vdph dv wkh idploldu uhvxow vkrzq lq Vyhqvvrq +4<<:d,/ zklfk fdq eh uhjdughg dv rqh w|sh ri wkh Wd|oru uxoh1 Krzhyhu/ rqfh wkh }hur orzhu erxqg lv lqwurgxfhg/ hyhq li wkh frqvwudlqw lv qrw elqglqj dw wkh fxuuhqw vwdwh/ wkhuh h{lvwv d qrq0}hur suredelolw| wkdw vxfk d frqvwudlqw pd| elqg lq wkh ixwxuh/ zklfk dowhuv wkh rswlpdo prqhwdu| srolf| frqgxfw iurp wkh fdvh zkhuh wkhuh lv qr }hur orzhu erxqg1 Lq rwkhu zrugv/ H|#|n*v +zklfk fdq eh h{suhvvhg dv d ixqfwlrq ri wkh fxuuhqw vwdwh | dqg || iru dq| l, zloo/ lq jhqhudo/ wdnh srvlwlyh ydoxhv wkdw wkh rswlpdo uhdfwlrq ixqfwlrq zloo ghyldwh iurp wkh vwdqgdug Wd|oru uxoh1 Lqghhg/ wklv yhu| ghyldwlrq iurp wkh Wd|oru uxoh lv fdswxuhg e| wkh whup lq htq +49,1 Dv vxfk/ e| uhfdoolqj wkdw wkh " whup lv d ixqfwlrq ri wkh vhtxhqfh ri iH|#|nj'f dqg dovr frqvlghulqj wkdw H|#|n*v zloo olnho| wdnh kljkhu +orzhu, ydoxhv zkhq wkh qrplqdo lqwhuhvw udwh lv forvh wr +dsduw iurp, wkh }hur orzhu erxqg frqvwudlqw/ wkhuh lv qr uhdvrq wr eholhyh wkdw wkh whup lv olqhdu lq wkh fxuuhqw vwdwh yduldeohv1 Dqdo|}lqj wkh whup ixuwkhu/ wkh iroorzlqj wzr sursrvlwlrqv fdq eh pdgh zlwk uhjdug wr wkh txdolwdwlyh surshuwlhv ri wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq lq wkh suhvhqfh ri wkh }hur orzhu erxqg frqvwudlqw1

A@+,Jo Sursrvlwlrq 4 +H{sdqvlrqdu| Srolf|, Ohw l +|>||, eh wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq zkhq wkhuh lv qr }hur erxqg rq wkh qrplqdo lqwhuhvw udwh1 Ohw W l +|>||, eh wkh rswlpdo prqhwdu| srolf| uhdfwlrq ixqfwlrq lq wkh suhvhqfh ri d }hur erxqg W rq wkh qrplqdo lqwhuhvw udwh1 Wkhq iru dq| vwdwh +|>||, zkhuh l lv vwulfwo| juhdwhu wkdq }hur/ wkh prqhwdu| srolf| lW zloo eh dw ohdvw dv h{sdqvlrqdu| dv wkh prqhwdu| srolf| lA@+,Jo/ l1h1/ lW lA@+,Jo1

Surri1 Vhh Dsshqgl{1

W Sursrvlwlrq 5 +Djjuhvvlyh Srolf|, Iru dq| vwdwh +|>||, zkhuh l lv vwulfwo| juhdwhu wkdq }hur/ wkh prqhwdu| srolf| lW zloo eh dw ohdvw dv djjuhvvlyh dv wkh prqhwdu| srolf| A@+,Jo W A@+,Jo W A@+,Jo l / l1h1/ Cl @C| Cl @C| dqg Cl @C|| Cl @C||1

Surri1 Vhh Dsshqgl{1

516 Glvfxvvlrq

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6: Figure 1: Optimal Monetary Policy Reaction Function with Zero Bound (Inflation Target = 2%, l = 1, s = 1.5)

Figure 2: Value Function with Zero Bound (Inflation Target = 2%, l = 1, s = 1.5) Figure 3: Cross Sectional View of the Optimal Policy Reaction Function (Inflation rate held constant at –1.77%)

Taylor Rule

Optimal Rule (s=0)

Optimal Rule (s=1.5)

Figure 4: Cross Sectional View of the Optimal Policy Reaction Function (Output gap held constant at 5.29%)

Taylor Rule

Optimal Rule (s=0)

Optimal Rule (s=1.5) Figure 5: Sensitivity Analysis of the Policy Reaction Function (Deterministic Environment)

p*=1 l=0.5 p*=3 l=0.5

10 16.1 22.6 10 24.9 28 9.67 18.7 8 3.22 25.8 8 12.4 0 6.22 6 6 21.8 4 4

2 19.3 2

0 0 15.6

Inflation Rate -2 12.9 Inflation Rate -2

-4 -4 9.33

-6 -6 0 3.11 6.44 -8 -8

-10 -10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 GDP Gap GDP Gap

p*=1 l=1 p*=3 l=1

10 0 6.67 13.3 30 10 23.3 20 26.7 8 8 26.7 16.7 13.3 23.3 6 6 0 6.67 20 4 4

2 2 16.7

0 0

Inflation Rate -2 Inflation Rate -2 10

-4 -4 10 3.33 -6 -6

-8 -8 3.33 -10 -10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 GDP Gap GDP Gap

p*=1 l=2 p*=3 l=2

Comparing the Contours of Two Policies 10 11 18.3 25.7 10 28.4 3.67 7.11 21.3 14.2 8 29.3 8 0 24.9 6 6

4 4 22 2 0 2 17.8

0 0 14.7

Inflation Rate -2 Inflation Rate -2 10.7

-4 -4

-6 7.33 -6 3.56

-8 -8

-10 -10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 GDP Gap GDP Gap Figure 6: Sensitivity Analysis of the Policy Reaction Function (Stochastic Environment)

p*=1 l=0.5 p*=3 l=0.5

10 10 28

24.9 8 25.8 8 21.8 22.6 6 19.3 6 18.7 16.1 15.6 4 12.9 4 9.33 12.4 2 9.67 2 3.22 6.44 3.11 0 0 0 6.22 0

Inflation Rate -2 Inflation Rate -2

-4 -4

-6 -6

-8 -8

-10 -10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 GDP Gap GDP Gap

p*=1 l=1 p*=3 l=1

10 26.7 30 10 20 26.7 6.67 13.3 8 8 23.3

6 6 20 23.3 16.7 4 4 13.3 10 2 2 0 3.33 6.67 16.7 0 0 0

Inflation Rate -2 Inflation Rate -2

-4 10 -4

-6 -6 3.33 -8 -8

-10 -10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 GDP Gap GDP Gap

p*=1 l=2 p*=3 l=2

10 10 3.56 21.3 28.4 14.2 29.3 8 25.7 8

6 18.3 22 6 24.9

4 11 14.7 4

2 3.67 2 17.8 0 7.33 0 0

Inflation Rate -2 Inflation Rate -2 10.7 -4 -4 7.11 -6 -6

-8 -8 0 -10 -10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 GDP Gap GDP Gap Figure 7: Inflation Rate, Output Gap, and Call Rate: 1983:Q2 - 2002:Q3

(%) 10 inflation rate 8 output gap call rate 6

-2

-4

-6 1983Q2 1984Q2 1985Q2 1986Q2 1987Q2 1988Q2 1989Q2 1990Q2 1991Q2 1992Q2 1993Q2 1994Q2 1995Q2 1996Q2 1997Q2 1998Q2 1999Q2 2000Q2 2001Q2 2002Q2

Sources: Bank of Japan, Financial and Economic Statistics Monthly; Ministry of Public Management, Home Affairs, Posts and Telecommunications, Consumer Price Index; Hirose and Kamada (2002).

Figure 8: Simulated Path, Estimated Taylor Rule, and Actual Call Rate

(%) 12

10 Actual Call Rate Estimated Taylor Rule 8 Simulated Path 6

-2

-4 1990Q1 1990Q4 1991Q3 1992Q2 1993Q1 1993Q4 1994Q3 1995Q2 1996Q1 1996Q4 1997Q3 1998Q2 1999Q1 1999Q4 2000Q3 2001Q2 2002Q1