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Iurp wkhvh jxuhv/ lw lv whpswlqj wr pdnh wkh frqfoxvlrq wkdw sulfh0ohyho wdujhwlqj
jhqhudwhv kljkhu rxwsxw0jds yduldelolw| wkdq grhv lq dwlrq wdujhwlqj1 Wklv frqfoxvlrq
lv uhdfkhg e| {lqj b dqg yhuwlfdoo| h{dplqlqj jxuh 71 Wklv ohdgv Nloh| ^<` wr wkh
frqfoxvlrq wkdw d sulfh0ohyho wdujhw lv zruvh wkdq dq lq dwlrq wdujhw/ vlqfh lw jhqhudwhv d
kljkhu yduldelolw| ri wkh rxwsxw jds +kh pdnhv d frpsdulvrq zlwk Vyhqvvrq ^4:` zkr qgv
4:
Variance of the output-gap,
4
κ=0.33333, ρ=0.5
3.5
3
Var(y)
2.5
2
PTD
1.5
1
ITC
0.5
0
ITD
0
0.5
1
1.5
λ
2
2.5
Iljxuh 7=
wkdw +jlyhq vrph frqglwlrqv, d sulfh0ohyho wdujhw jlyhv wkh vdph yduldelolw| ri wkh rxwsxw
jds dv grhv dq lq dwlrq wdujhw/ exw d orzhu yduldelolw| ri lq dwlrq dqg wkxv frqfoxghv d
sulfh0ohyho wdujhw wr eh suhihudeoh,1 Krzhyhu/ wkh vdph h{shulphqw lq jxuh 6 uhyhdov wkdw
wkh yduldqfh ri lq dwlrq lv orzhu zlwk d sulfh0ohyho wdujhw wkdw zlwk dq lq dwlrq wdujhw1 Lw
wkxv vhhpv lqfrqfoxvlyh zklfk lv wkh ehwwhu1
Wklv sdshu vxjjhvwv/ krzhyhu/ wkdw lw lv pruh lqvwuxfwlyh wr uhdg wkh jxuh krul}rq0
wdoo|1 D jlyhq yduldqfh ri lq dwlrq uhvxowlqj iurp d sduwlfxodu ydoxh ri b fdq dozd|v eh
xqghu d sulfh0ohyho wdujhw1 Lw lv qrw re0
lpsohphqwhg e| dvvljqlqj d glhuhqw ydoxh ri b
ylrxv wkdw erwk wkh yduldqfh ri lq dwlrq dqg wkh rxwsxw jds xqghu sulfh0ohyho wdujhwlqj
fdq eh uhgxfhg frpsduhg wr lq dwlrq wdujhwlqj +erwk xqghu glvfuhwlrq, vlpxowdqhrxvo| e|
lqvshfwlqj wkh jxuhv1 Wr hydoxdwh wklv/ wkh qh{w vhfwlrq sorwv h!flhqf| iurqwlhuv1
717
H!flhqf| iurqwlhuv
D iurqwlhu sorwv doo frpelqdwlrqv ri rxwsxw jds yduldqfh dqg lq dwlrq yduldqfh dwwdlqdeoh
iru glhuhqw ydoxhv ri wkh suhihuhqfh sdudphwhu b1 Vlqfh wkhuh lv d whqvlrq ehwzhhq wkhvh
4;
Policy frontier, κ=0.33333, ρ=0.5
12
Variance of outputgap
10
8
6
4
PTD
ITD
2
ITC
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Variance of inflation
Iljxuh 8=
yduldqfhv/ wkhuh zloo dozd|v eh d wudgh0r ri lqfuhdvhg lq dwlrq yduldelolw| lq rughu wr
uhgxfh rxwsxw jds yduldelolw|1 Whfkqlfdoo|/ wkh iurqwlhuv duh frqvwuxfwhg e| {lqj V dqg
wkhq sorwwlqj lq dwlrq yduldqfh dqg rxwsxw0jds yduldqfh iru glhuhqw ydoxhv ri b1 Zlwk
q $ / wkh vorsh ri wkh h!flhqf| iurqwlhu lv htxdo wr b1
Sursrvlwlrq 5 Sulfh0ohyho wdujhwlqj jlyhv d ehwwhu lq dwlrq0 rxwsxw0jds yduldqfh wudgh0r
wkdq lq dwlrq wdujhwlqj1
Iljxuh 8 uhyhdov wkdw sulfh0ohyho wdujhwlqj grplqdwhv lq dwlrq wdujhwlqj +zkhq wkh
fhqwudo edqn dfwv xqghu glvfuhwlrq, vlqfh wkh iurqwlhuv qhyhu furvv1 Wkxv/ xvlqj d sulfh0
ohyho wdujhw lv suhihudeoh lq wkh devhqfh ri frpplwphqw1 Qrwh wkdw wkh yduldqfh iurqwlhuv
iru lq dwlrq wdujhwlqj dqg sulfh0ohyho wdujhwlqj doprvw frlqflgh1 Li shuvlvwhqfh lv lqfuhdvhg
wr doprvw rqh/ wkhuh lv d pruh surqrxqfhg glhuhqfh lq wkh wzr fdvhv/ exw wkh sulfh0ohyho
wdujhw vwloo grplqdwhv wkh lq dwlrq wdujhw144 Iurp dq hfrqrplf srlqw ri ylhz/ d sulfh0ohyho
wdujhw dggv fuhglelolw| lq wkh iroorzlqj vhqvh= zlwk dq lq dwlrq wdujhw/ d whpsrudu| lqfuhdvh
44
Iru yhu| kljk ydoxhv ri / wkhuh zloo eh d glvfuhsdqf| ehwzhhq wkh frpplwphqw fdvh dqg wkh sulfh ohyho
wdujhwlqj fdvh1 Krzhyhu/ wkh sulfh ohyho wdujhw zloo vwloo grplqdwh wkh lq dwlrq wdujhw xqghu glvfuhwlrq1
4<
lq lq dwlrq lv glvuhjdughg lq wkh qh{w shulrg1 Zlwk d sulfh0ohyho wdujhw/ wklv lv qr orqjhu
wuxh1 Lqvwhdg/ d whpsrudu| lqfuhdvh lq lq dwlrq pxvw vrrqhu ru odwhu eh frxqwhudfwhg e|
d uhgxfwlrq lq lq dwlrq ehorz wdujhw1 Wklv kdv ehhq xvhg dv dq dujxphqw djdlqvw xvlqj
sulfh0ohyho wdujhwv/ dqg wkh fodlp lv wkdw lw zrxog lqfuhdvh yrodwlolw| ri lq dwlrq1 Krzhyhu/
zlwk iruzdug0orrnlqj djhqwv/ wkh dqwlflsdwhg uhgxfwlrq wkdw pxvw wdnh sodfh lq wkh ixwxuh
uhgxfhv lq dwlrqdu| h{shfwdwlrqv dqg wkxv khosv wkh fhqwudo edqn jkw lq dwlrq1 Wkhvh
uhvxowv duh uhodwhg wr rqh ri wkh qglqjv lq Vphwv ^48`/ zkr vkrzv wkdw lw riwhq sd|v wr jlyh
wkh fhqwudo edqn d sulfh ohyho remhfwlyh hyhq li vrflhw| fduhv derxw lq dwlrq vwdelol}dwlrq1
718
Fhqwudo edqn frqvhuydwlvp dqg wkh lqwhusuhwdwlrq ri b
Qrz/ zh zloo uhwxuq wr wkh fodlp wkdw wkhuh lv d uroh iru d frqvhuydwlyh fhqwudo edqnhu zlwk
glvfuhwlrq dqg lq dwlrq wdujhwlqj1 Qrwh wkdw wkh irup ri wkh orvv0ixqfwlrq +7, phdqv wkdw
zh fdq ghvfuleh vrfldo suhihuhqfhv lq whupv ri olqhdu lqglhuhqfh fxuyhv/ zlwk vorsh 0 b 1
Wkxv/ jlyhq wkdw zh dvvxph wkh vdph lqvwlwxwlrqdo vhwxs iru wkh lq dwlrq wdujhwlqj fdvh
+wkdw lw lv srvvleoh wr dvvljq d b glhuhqw iurp wkh wuxh ydoxh, dv zh glg iru wkh sulfh0ohyho
wdujhwlqj fdvh/ wkh rswlpdo vroxwlrq uhtxluhv qglqj wkh srlqw zkhuh wkh lqglhuhqfh fxuyh
lv wdqjhqw wr wkh srolf| iurqwlhu +uhphpehu wkdw orvv lv jurzlqj lq qruwk0hdvw gluhfwlrq lq
jxuh 8,1 Uhphpehu wkdw wkh wzr htxdwlrqv +4<, dqg +4;, ghqhv wkh yduldqfhv1 Qh{w/
ohw +4;, lpsolflwo| ghqh bEV@h
EZ | 1 Wkhq zh fdq zulwh
_V@h E%| '
_V@h EZ| _V@hE%| _b
_V@hEZ| _b
' ' 2E3q4V2
2
V nbE3q4
E
2
2bV
2
V
n
b
E3
q4
E
E q4
b
Wr qg wkh srlqw ri wdqjhqf|/ zh vhw
E q4
' b
b
' E q4 b
b
53
+58,
b dqg wkxv wkdw jryhuqphqw vkrxog dssrlqw d pruh
Zlwk 4 : f zh frqfoxgh wkdw b
frqvhuydwlyh fhqwudo edqnhu145 Wklv uhvxow fdq eh lqwhusuhwhg vrphzkdw vlplodu wr wkh
sulfh0ohyho wdujhwlqj fdvh1 Qrwh wkdw lw lv wkh shuvlvwhqfh wkdw gulyhv grzq wkh rswlpdo
Wkh uhdvrq lv wkdw d pruh frqvhuydwlyh fhqwudo edqnhu zloo jxdudqwhh wkdw
ydoxh iru b1
lq dwlrqdu| vkrfnv duh frxqwhuhg kdughu1 Wkxv lq dwlrqdu| h{shfwdwlrqv duh uhgxfhg
+vlqfh ixwxuh ydoxhv |n fdq eh iruhfdvwhg/ wr vrph h{whqw,/ zklfk khosv wkh fhqwudo edqn
wr vwdelol}h fxuuhqw lq dwlrq1
Iru wkh fdvh ri sulfh0ohyho wdujhwlqj/ wklqjv duh voljkwo| pruh frpsolfdwhg/ gxh wr wzr
uhdvrqv1 Iluvw/ lw lv kdug wr qg dq dqdo|wlfdo vroxwlrq iru wkh vorsh ri wkh yduldqfh iurqwlhu1
dqg b1
Vhfrqg/ wkhuh lv dq lqwhusuhwdwlrq sureohp zlwk uhvshfw wr frpsdulqj b
Lq sulqflsoh/ zh frxog glhuhqwldwh +57, dqg +56, wr jhw wkh vorsh ri wkh iurqwlhu iru
wkh sulfh0ohyho wdujhwlqj fdvh1 Krzhyhu/ vlqfh e dqg s duh qrqwulyldo ixqfwlrqv ri @ dqg K/
wklv lv qrw dq hdv| wdvn1 Dq dowhuqdwlyh dssurdfk lv
zklfk wkhpvhoyhv duh ixqfwlrqv ri b/
iru vrph uhdvrqdeoh sdudphwhu ydoxhv1
wr h{dplqh wkh rswlpdo ydoxhv ri b
Iru frqvlvwhqf|/ zh uhwdlq wkh dvvxpswlrq wkdw V '
dqg 4 ' 2 1 Iljxuh 9 sorwv wklv iru
glhuhqw ydoxhv ri wkh wuxh b1 Iru h{dpsoh/ wkh orzhvw olqh fruuhvsrqgv wr d wuxh ydoxh ri
f21 Wzr slhfhv ri lqirupdwlrq fdq eh h{wudfwhg iurp wklv jxuh1 Iluvw/ wkhuh lv d xqltxh
wkdw plqlpl}hv orvv iru hdfk wuxh ydoxh ri b +iru h{dpsoh/ zkhq
ydoxh ri wkh dvvljqhg b
lv f2b,1 Vhfrqg/ wkh vkdsh ri wkh orvv0ixqfwlrq lv dwwhqlqj zlwk
b ' f2/ wkh rswlpdo b
wkh vl}h ri b1 Iru d odujh b/ wklv phdqv wkdw lw lv wkh sulfh0ohyho wdujhw shu vh/ dqg qrw vr
wkdw pdwwhuv1 Xvlqj wkh rswlpdo ydoxhv lq jxuh 9 +ri frxuvh/
pxfk wkh suhflvh ohyho ri b/
ru vlpso| bEb1
zlwk d orw pruh ydoxhv iru wkh wuxh b/ lw srvvleoh wr pds b lqwr b/
Wklv
wkdw vkrxog eh xvhg dv d ixqfwlrq ri wkh wuxh b1
jxuh zrxog wkhq uhyhdo zklfk ydoxh ri b
Krzhyhu/ ehiruh grlqj wklv zh pxvw h{dplqh dq lvvxh ri lpsruwdqfh iru lqwhusuhwlqj wkh
uhvxow1
Urjr irxqg wkdw dvvljqlqj d b ohvv wkdq wkh wuxh ydoxh uhgxfhg wkh lq dwlrq eldv1
Kh lqwhusuhwhg wklv dv dssrlqwlqj d frqvhuydwlyh fhqwudo edqnhu1 Wkhuhiruh/ lw lv whpswlqj
45
Wklv frqupv Uhvxow :/ s1 49;3 lq Fodulgd/ Jdol dqg Jhuwohu ^6`/ zklfk wkh| ghulyh e| h{dplqlqj d
uhvwulfwhg irup ri frpplwphqw dqg qrwlflqj wkdw wklv vroxwlrq orrnv lghqwlfdo wr wkh fdvh ri glvfuhwlrq/
exw zlwk d orzhu ydoxh ri 1
54
Loss, L = Var(πt )+λ Var(xt ), price-level target
3
Loss
2.5
2
1.5
1
0
1
2
3
4
5
assigned λ
Iljxuh 9=
55
6
7
8
9
: b phdqv wkdw d ohvv frqvhuydwlyh fhqwudo edqnhu
wr gudz wkh frqfoxvlrq wkdw qglqj b
vkrxog eh dssrlqwhg1 Wklv lv d suhpdwxuh frqfoxvlrq/ krzhyhu1 Wkh uhdvrq lv wkdw b dqg
kdyh glhuhqw lqwhusuhwdwlrqv dv fdq eh vhhq iurp frpsdulqj wkh wzr orvv0ixqfwlrqv/ iru
b
frqyhqlhqfh uhsurgxfhg lq whupv ri yduldqfhv1
, du| o ' V@h EZ | n bV@h E+| , du| o ' V@h ER| n bV@h
E+| Lq wkh uvw orvv0ixqfwlrq/ b fdq eh lqwhusuhwhg dv wkh uhodwlyh zhljkw sodfhg rq wkh yduldelo0
lw| ri wkh rxwsxw jds/ frpsduhg wr wkh yduldelolw| ri lq dwlrq1 Lq wkh fdvh ri sulfh0ohyho
phdvxuhv wkh uhodwlyh zhljkw sodfhg rq rxwsxw0jds yduldelolw|/ frpsduhg wr
wdujhwlqj/ b
wkh yduldelolw| ri wkh sulfh ohyho1 Vlqfh wkh wzr zhljkwv kdyh glhuhqw ehqfkpdunv/ qrw
pxfk lv jdlqhg iurp frpsdulqj wkhlu devroxwh ydoxhv1 Krzhyhu/ vlqfh wkh lq dwlrq udwh
lv wljkwo| olqnhg wr wkh sulfh ohyho/ lw lv srvvleoh wr lqwhusuhw wkh uhodwlyh vl}h ri wkh wzr
zhljkwv1 Wr uhfdslwxodwh/ wkh sulfh ohyho/ lw*v yduldqfh dqg wkh yduldqfh ri lq dwlrq duh
jlyhq e|
R|3 n K| R| ' @
V@h ER| '
E n @
4 K2
j2
E @2 E @4 V@h EZ| '
2 E 4 K2
j2 E @4 E n @ Wkxv/ e| wdnlqj wkh udwlr zh jhw
V@h EZ| 2 E 4 E @
'
c
V@h ER| n@
4
ru/
V@h ER| '
n@
4
V@h EZ | 2 E 4 E @
56
Central bank conservatism
1
0.9
0.8
IT
assignedλ
0.7
PT
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
True λ
1.2
1.4
1.6
1.8
2
Iljxuh :=
Lq rughu wr jhw d frpsdudeoh zhljkw +l1h1 wr kdyh wkh vdph qrupdol}dwlrq lq erwk
orvv0ixqfwlrqv, wkh iroorzlqj htxdwlrq pxvw eh vdwlvhg=
2 E 4 @ b
b'
b
n@
b 4
Wkdw lv/ b :
2E34E3
@Eb b
n
@Eb4
+59,
lpsolhv wkdw wkh fhqwudo edqn vkrxog eh pruh zhljkw0
frqvhuydwlyh1 Wr xqghuvwdqg wklv uhvxow/ zh wdnh wkh qxphulfdo ydoxhv iurp jxuh 9/ dqg
ydoxhv frqyhuwhg wr
pxowlso| wkhp zlwk wkh dssulsuldwh vfdoh idfwru lq +59,1 Wklv jlyh xv b
kdyh wkh vdph qrupdol}dwlrq +yduldqfh ri lq dwlrq, dv wkh lq dwlrq wdujhwlqj fdvh1 Dovr/ zh
xvh +58, wr jhw wkh rswlpdo ydoxhv iru wkh lq dwlrq wdujhwlqj fdvh1 Iljxuh +:, suhvhqwv erwk
wkhvh judskv lq rughu wr ghflgh rq wkh frqvhuydwlvp pdwwhu1Wkh lq dwlrq wdujhwlqj fdvh/
uhsuhvhqwhg e| wkh vwudljkw olqh +vlqfh wkh frh!flhqw lq +58, lv mxvw d frqvwdqw, lqwhuvhfw
wkh sulfh0ohyho wdujhwlqj fdvh1 Wkxv/ iru wkh sdudphwhu ydoxhv xvhg lq wkh h{dpsoh/ iru
b : fDD/ wkh sulfh0ohyho wdujhw lv dffrpsdqlhg e| d voljkwo| pruh frqvhuydwlyh fhqwudo0
edqnhu/ zkloh d b fDD lpsolhv d voljkwo| ohvv1 Krzhyhu/ wkh glhuhqfh lv vpdoo +d uhvxow
urexvw iru rwkhu sdudphwhu ydoxhv,/ hvshfldoo| lq oljkw ri wkh deryh glvfxvvlrq wkdw wkh
57
orvv0ixqfwlrq lv dw iru odujh ydoxhv ri b Wkh frqfoxvlrq lv wkdw frqvhuydwlvp lv htxdoo|
lpsruwdqw iru sulfh0ohyho wdujhwlqj dv lw lv iru lq dwlrq wdujhwlqj1
8
Frqfoxvlrqv
Wkh pdlq uhvxow ri wkh sdshu lv wkdw zkhq iruzdug0orrnlqj sulfh vhwwlqj lv lpsruwdqw dqg
wkh fhqwudo edqn dfwv xqghu glvfuhwlrq/ d sulfh0ohyho wdujhw pd| grplqdwh dq lq dwlrq wdu0
jhw1 Wkh uhvxow fdq eh lqwhusuhwhg lq olqh zlwk Urjr*v fodvvlf uhvxow wkdw e| vwudwhjlfdoo|
ghohjdwlqj d orvv0ixqfwlrq glhuhqw iurp vrflhw|*v +lq Urjr*v fdvh/ d pruh frqvhuydwlyh
fhqwudo edqnhu lq wkh vhqvh wkdw bedqnhu bvrflhw| ,/ d ehwwhu rxwfrph fdq rffxu1 Lq wklv
fdvh/ wkhuh lv d wzr0glphqvlrqdo dvvljqphqw1 Iluvw/ wkh lq dwlrq wdujhw lv uhsodfhg e| d
sulfh0ohyho wdujhw1 Vhfrqg/ d glhuhqw ydoxh ri b lv dvvljqhg1
Lq wkh suhylrxv olwhudwxuh wkh hhfwv ri d sulfh0ohyho wdujhw kdyh ehhq vxemhfw wr d
plvlqwhusuhwdwlrq1 Lw kdv ehhq uhfrjql}hg wkdw iru d jlyhq ydoxh ri b/ d sulfh0ohyho wdujhw
jhqhudwhv pruh yduldelolw| ri wkh rxwsxw jds wkdq grhv dq lq dwlrq wdujhw1 Lw kdv dovr
ehhq uhfrjql}hg/ krzhyhu/ wkdw lq dwlrq yduldelolw| lv orzhu xqghu wkh sulfh0ohyho wdujhw1
Frqyhqwlrqdo zlvgrp h{sodlqhg wklv uhvxow e| fodlplqj wkdw lq wkh sulfh0ohyho wdujhwlqj
fdvh/ d srvlwlyh vkrfn pxvw eh frxqwhuhg e| d prqhwdu| wljkwhqlqj dw d odwhu vwdjh/ zklfk
zloo lqgxfh pruh yrodwlolw| ri wkh rxwsxw jds wkdq lq wkh lq dwlrq wdujhwlqj fdvh/ zkhuh
e|jrqhv duh wuhdwhg dv e|jrqhv1 Wkh srlqw ri wklv sdshu lv wkdw wklv lv qrw wkh prvw
lqwhuhvwlqj frpsdulvrq1 Li zh lqvwhdg h{dplqh wkh srolf| iurqwlhuv/ lw ehfrphv fohdu wkdw
wkh sulfh0ohyho wdujhw grplqdwhv wkh lq dwlrq wdujhw/ vlqfh d ehwwhu rxwfrph fdq dozd|v eh
lpsohphqwhg e| dvvljqlqj d glhuhqw b lq wkh sulfh0ohyho wdujhwlqj fdvh1 Dovr/ wkh sdshu
vkrzv wkdw d surshu lqwhusuhwdwlrq ri wkh rswlpdo dvvljqhg ydoxhv ri b uhyhdov wkdw wkh
fhqwudo edqnhu vkrxog eh derxw dv frqvhuydwlyh zlwk d sulfh0ohyho wdujhw dv kh vkrxog eh
zlwk dq lq dwlrq wdujhw1 Wklv phdqv wkdw wkh uhvxow grhv qrw klqjh xsrq wkh srvvlelolw|
wr vhohfw b/ lw lv udwkhu wkh srvvlelolw| wr ghohjdwh d sulfh0ohyho wdujhw wkdw lv lpsruwdqw1
Wkh lqvwlwxwlrqdo vhwxs dvvxphg lq wklv sdshu lv wkdw wkh jryhuqphqw lv deoh wr ghohjdwh
d wdujhw glhuhqw iurp vrflhw|*v wr dq rwkhuzlvh lqghshqghqw fhqwudo edqn1 Lw pljkw eh
dujxhg wkdw vrph rwkhu wdujhw fdq jlyh dq hyhq ehwwhu rxwfrph wkdq d sulfh0ohyho wdujhw1
58
Lw pljkw dovr eh dujxhg wkdw wkh lqvwlwxwlrqdo vhwxs ehfrphv pruh lpsodxvleoh wkh pruh
wkh dvvljqhg wdujhw ghyldwhv iurp wkdw ri vrflhw|1 Wkh srlqw ri wklv sdshu lv wr sursrvh
d wdujhw wkdw lv idluo| forvh wr wkh wdujhwv suhvhqwo| xvhg e| fhqwudo edqnv/ dqg rqh wkdw
zrxog eh hdv| wr frppxqlfdwh wr wkh sxeolf1
Zlwk qr shuvlvwhqfh/ wkh frpplwphqw vroxwlrq ri wkh lq dwlrq wdujhwlqj fdvh fdq eh
lpsohphqwhg1 Zlwk shuvlvwhqfh/ wklv lv qrw wuxh1 Krzhyhu/ lw lv vwloo dozd|v wkh fdvh +lq
wkh prgho h{dplqhg/ wkdw lv, wkdw d sulfh0ohyho wdujhw jhqhudwhv d ehwwhu rxwfrph wkdq
wkh lq dwlrq wdujhw/ dqg lv doprvw dv jrrg dv wkh frpplwphqw vroxwlrq1 Zlwk sulfh0ohyho
wdujhwlqj/ wkh sulydwh vhfwru h{shfwv wkh fhqwudo edqn wr frxqwhu dq deryh dyhudjh lq dwlrq
+qrupdol}hg wr }hur lq wklv sdshu, zlwk d ehorz dyhudjh lq dwlrq vrphzkhuh lq wkh ixwxuh1
Lq rwkhu zrugv/ d srvlwlyh vkrfn wr lq dwlrq uhgxfhv wkh h{shfwhg ixwxuh lq dwlrq dqg wkxv
orzhuv wkh fxuuhqw dprxqw ri lqwhuyhqwlrq1
59
Uhihuhqfhv
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