The Science of Monetary Policy: A New Keynesian Perspective

TL;DR: In this article, a review of the recent literature on monetary policy rules is presented, and the authors exposit the monetary policy design problem within a simple baseline theoretical framework and consider the implications of adding various real word complications.

Abstract: This paper reviews the recent literature on monetary policy rules. To organize the discussion, we exposit the monetary policy design problem within a simple baseline theoretical framework. We then consider the implications of adding various real word complications. We concentrate on developing results that are robust across a reasonable variety of competing macroeconomic frameworks. Among other things, we show that the optimal policy implicitly incorporates inflation targeting. We also characterize the gains from making credible commitments to fight inflation and consider the implications of frictions such as imperfect information and model uncertainty. Finally, we assess how proposed simple rules, such as the Taylor rule, square with the principles for optimal policy that we describe. We use this same metric to evaluate the recent course of U.S. monetary policy.

Summary

Introduction

• Wklv sdshu uhylhzv wkh uhfhqw olwhudwxuh rq prqhwdu| srolf| uxohv1.
• Zh dovr fkdudfwhul}h wkh jdlqv iurp pdnlqj fuhgleoh frpplwphqwv wr jkw lq dwlrq1.
• Kdylqj orrnhg dw prqhwdu| srolf| iurp erwk vlghv qrz/ L fdq whvwli| wkdw fhq0 wudo edqnlqj lq sudfwlfh lv dv pxfk duw dv vflhqfh1 Qrqhwkhohvv/ zkloh sudfwlflqj wklv gdun duw/ L kdyh dozd|v irxqg wkh vflhqfh txlwh xvhixo 14 Dodq V1 Eolqghu.

41 Lqwurgxfwlrq

• Wr rujdql}h wkh glvfxvvlrq/ zh h{srvlw wkh prqhwdu| srolf| ghvljq sureohp lq d vlpsoh wkhruhwlfdo prgho1.
• Iru dq dqdo|vlv ri prqh0 wdu| srolf| uxohv lq wkhvh nlqgv ri prghov 0 nqrz dv olplwhg sduwlflsdwlrq iudphzrunv 0 vhh Fkulvwldqr dqg Jxvw +4<<<,1 6 Dq lpsruwdqw frpsolfdwlrq lv wkdw sulydwh vhfwru ehkdylru ghshqgv rq wkh h{0 shfwhg frxuvh ri prqhwdu| srolf|/ dv zhoo dv rq fxuuhqw srolf|.
• Wkh rssruwxqlvwlf dssurdfk erlov grzq wr wu|lqj wr nhhs lq dwlrq iurp ulvlqj exw doorzlqj lw wr udwfkhw grzq lq wkh hyhqw ri idyrudeoh vxsso| vkrfnv1.
• Wkh ghjuhh ri lq dwlrq shuvlvwhqfh lv fulwlfdo vlqfh wklv idfwru jryhuqv wkh rxwsxw2lq dwlrq wudgh0r wkdw wkh srolf|0pdnhu idfhv1 Lq rxu edvholqh prgho/ shuvlvwhqfh lq lq dwlrq dqg rxwsxw lv gxh hqwluho| wr vhul0 doo| fruuhodwhg h{rjhqrxv vkrfnv1.

51 D Edvholqh Iudphzrun iru Dqdo|vlv ri Prqhwdu| Srolf|

• Wklv vhfwlrq fkdudfwhul}hv wkh irupdo prqhwdu| srolf| ghvljq sureohp1.
• Lw uvw suhvhqwv d vlpsoh edvholqh pdfurhfrqrplf iudphzrun/ dqg wkhq ghvfulehv wkh sro0 lf| remhfwlyh ixqfwlrq1.
• Wkh lvvxh ri fuhglelolw| lv wdnhq xs qh{w1 Lq wklv uhjdug/ zh ghvfuleh wkh glvwlqfwlrq ehwzhhq rswlpdo srolflhv zlwk dqg zlwkrxw fuhgleoh frp0 plwphqw 0 zkdw wkh olwhudwxuh uhihuv wr dv wkh fdvhv ri uxohv yhuvxv glvfuhwlrq1.

5141 D Vlpsoh Pdfurhfrqrplf Iudphzrun

• Rxu edvholqh iudphzrun lv d g|qdplf jhqhudo htxloleulxp prgho zlwk prqh| dqg whpsrudu| qrplqdo sulfh uljlglwlhv1.
• Lq uhfhqw |hduv wklv sdudgljp kdv ehfrph : zlgho| xvhg iru wkhruhwlfdo dqdo|vlv ri prqhwdu| srolf |1: Lw kdv pxfk ri wkh hp0 slulfdo dsshdo ri wkh wudglwlrqdo LV2OP prgho/ |hw lv jurxqghg lq g|qdplf jhq0 hudo htxloleulxp wkhru|/ lq nhhslqj zlwk wkh phwkrgrorjlfdo dgydqfhv lq prghuq pdfurhfrqrplfv1.
• Zlwklq wkh prgho/ prqhwdu| srolf| d hfwv wkh uhdo hfrqrp| lq wkh vkruw uxq/ pxfk dv lq wkh wudglwlrqdo Nh|qhvldq LV2OP iudphzrun1.
• Iru frqyhqlhqfh/ zh devwudfw iurp lqyhvwphqw dqg fdslwdo dffxpxodwlrq1.

5151 Wkh Srolf| Remhfwlyh

• Wkh fhqwudo edqn remhfwlyh ixqfwlrq wudqvodwhv wkh ehkdylru ri wkh wdujhw yduldeohv lqwr d zhoiduh phdvxuh wr jxlgh wkh srolf| fkrlfh1.
• Wkhvh dxwkruv vkrz wkdw dq remhfwlyh ixqfwlrq orrnlqj vrphwklqj olnh htxdwlrq +51:, pd| eh rewdlqhg dv d txdgudwlf dssur{lpdwlrq ri wkh xwlolw|0edvhg zhoiduh ixqfwlrq1.
• Lw lv fohdu wkdw wkh h{shulhqfh ri 4<:3v dzdnhqhg srolf|0pdnhuv wr wkh frvwv ri kljk lq dwlrq +GhOrqj/ 4<<:,1 Rwkhuzlvh/ wkhuh lv qr gluhfwo| revhuydeoh lqglfdwru ri wkh uhodwlyh zhljkwv dvvljqhg wr rxwsxw dqg lq dwlrq remhfwlyhv1 Qru/ dujxhv Eolqghu +4<<:,/ lv wkhuh dq| reylrxv frqvhqvxv dprqj srolf|0pdnhuv derxw zkdw wkhvh zhljkwv uhdoo| duh lq sudfwlfh1.
• Rq wkh rwkhu kdqg/ Ihogvwhlq +4<<:, dujxhv wkdw wkh wd{ glvwruwlrqv wkdw dulvh ehfdxvh frusrudwh dqg shuvrqdo lqfrph wd{hv duh qrw lqgh{hg wr lq dwlrq mxvwli| prylqj iurp wkuhh shufhqw wr }hur lq dwlrq1 4:.

5161 Wkh Srolf| Sureohp dqg Glvfuhwlrq yhuvxv Uxohv

• Wkh srolf| sureohp lv wr fkrrvh d wlph sdwk iru wkh lqvwuxphqw | wr hqjlqhhu wlph sdwkv ri wkh wdujhw yduldeohv %| dqg Z| wkdw pd{lpl}h wkh remhfwlyh ixqfwlrq +51:,/ vxemhfw wr wkh frqvwudlqwv rq ehkdylru lpsolhg e| +514, dqg +515,1.
• Wklv irupxodwlrq lv lq pdq| zd|v lq wkh wudglwlrq ri wkh fodvvlf Mdq Wlqehujhq +4<85,2 Khqul Wkhlo +4<94, +WW, wdujhwv dqg lqvwuxphqwv sureohp1.
• Wkhuh lv/ krzhyhu/ dq lpsruwdqw gl huhqfh iurp wkh fodvvlf sureohp=.
• Wkh rxwsxw jds ghshqgv rq wkh ixwxuh sdwk ri wkh lqwhuhvw udwh +htxdwlrq 518,> dqg/ lq wxuq/ lq dwlrq ghshqgv rq wkh fxuuhqw dqg h{shfwhg ixwxuh ehkdylru ri wkh rxwsxw jds +htxdwlrq 519,1 Dv Ilqq N|godqg dqg Hgzdug Suhvfrww +4<::, ruljlqdoo| hpskdvl}hg/ lq wklv nlqg ri hqylurqphqw/ fuhglelolw| ri ixwxuh srolf| lqwhqwlrqv ehfrphv d fulwlfdo lvvxh1.
• Wkh wzr dssurdfkhv gl hu/ krzhyhu/ lq wkhlu lpsolfdwlrqv iru wkh olqn ehwzhhq srolf| lqwhqwlrqv dqg sulydwh vhfwru eholhiv1 Xqghu glvfuhwlrq/ d shufhswlyh sulydwh vhfwru irupv lwv h{shfwdwlrqv wdnlqj lqwr dffrxqw krz wkh fhq0 wudo edqn dgmxvwv srolf|/ jlyhq wkdw wkh fhqwudo edqn lv iuhh wr uh0rswlpl}h hyhu| shulrg1.

61 Rswlpdo Prqhwdu| Srolf| zlwkrxw Frpplwphqw

• Zh ehjlq zlwk wkh fdvh zlwkrxw frpplwphqw + glvfuhwlrq , iru wzr uhdvrqv1.
• Lw lv lq wklv vhqvh wkdw rxu dqdo|vlv lv txlwh urexvw1 58Zh duh ljqrulqj wkh srvvlelolw| ri uhsxwdwlrqdo htxloleuld wkdw frxog vxssruw d pruh h!flhqw rxwfrph1.
• Wklv frqvlghudwlrq ohdgv wr wkh qh{w uhvxow=.
• Wkh gl huhqfh vwhpv iurp wkh wuhdw0 phqw ri frvw sxvk lq dwlrq=.

71 Fuhglelolw| dqg wkh Jdlqv iurp Frpplwphqw

• Vlqfh wkh slrqhhulqj zrun ri N|godqg dqg Suhvfrww +4<::,/ Urehuw Eduur dqg Gdylg Jrugrq +4<;6,/ dqg Urjr +4<;8,/ d yroxplqrxv olwhudwxuh kdv ghyhorshg rq wkh lvvxh ri fuhglelolw| ri prqhwdu| srolf|166 Iurp wkh vwdqgsrlqw ri rewdlqlqj sudfwlfdo lqvljkwv iru srolf|/ zh qg lw xvhixo wr glylgh wkh sdshuv lqwr wzr vwudqgv1.
• Wkh xowlpdwh vrxufh ri wklv lq dwlrqdu| eldv lv d fhqwudo edqn wkdw ghvluhv wr sxvk rxwsxw deryh lwv qdwxudo ohyho1 Wkh vhfrqg lv hpskdvl}hg pruh lq dssolhg glvfxvvlrqv ri srolf|.
• Exw wkh vrxufh ri wkh sureohp lq hdfk fdvh lv gl huhqw lq vxewoh exw lpsruwdqw zd|v1.
• Lq wklv uhvshfw/ zh 68D qxpehu ri sdshuv kdyh vkrzq wkdw d glvlq dwlrq zloo eh ohvv sdlqixo li wkh sulydwh vhfwru shufhlyhv wkdw wkh fhqwudo edqn zloo fduu| lw rxw1.
• Exw wkh| gr qrw vkrz irupdoo| wkdw/ xqghu glvfuhwlrq/ wkh fhqwudo edqn zloo eh ohvv lqfolqhg wr gr vr +vhh1/ h1j1 Edoo/ 4<<8/ dqg Erq p dqg Uxghexvfk/ 4<<:,1 69Zlwk lq dwlrqdu| eldv suhvhqw/ lw lv dovr srvvleoh wr lpsuryh zhoiduh e| dvvljqlqj d kljkhu frvw wr lq dwlrq/ dv Urjr +4<;8, ruljlqdoo| hpskdvl}hg1.

715151 Prqhwdu| Srolf| Xqghu Frpplwphqw= Wkh Xqfrqvwudlqhg Rswl0

• Zh qrz surylgh d eulhi ghvfulswlrq ri wkh jhqhudo vroxwlrq iru wkh rswlpdo srolf| xqghu frpplwphqw176.
• Lq rwkhu zrugv/ frpplwphqw fkdqjhv wkh ohyho uxoh iru %| xqghu glvfuhwlrq lqwr d gl huhqfh uxoh iru %|/ dv d frpsdulvrq ri htxdwlrqv +616, dqg +714;, lqglfdwh781.
• Wkh joredoo| rswlpdo srolf| uxoh xqghu frpplwphqw kdv wkh fhq0 wudo edqn sduwldoo| dgmxvw ghpdqg lq uhvsrqvh wr lq dwlrqdu| suhvvxuhv1.
• Wr wkh h{whqw wkdw vxfk frh!flhqw lv qrw wrr odujh/ lpsohphqwdwlrq ri vxfk d uxoh zloo uhvxow lq d xqltxh htxloleulxp +vhh wkh glvfxvvlrq lq vhfwlrq : dqg dovr lq Fodulgd/ Jdol dqg Jhuwohu +4<<;,,1 77.

8141 Lpshuihfw Lqirupdwlrq

• Wkxv idu zh kdyh dvvxphg wkdw wkh fhqwudo edqn lv deoh wr frqwuro shuihfwo| wkh sdwkv ri wkh nh| wdujhw yduldeohv1 Lq sudfwlfh/ ri frxuvh/ wklv lv qrw wkh fdvh1 Rqh lpsruwdqw uhdvrq lv lpshuihfw revhuydelolw|.
• Dw wkh wlph lw vhwv lqwhuhvw udwhv/ d fhqwudo edqn pd| qrw kdyh doo wkh uhohydqw lqirupdwlrq dydlodeoh derxw wkh vwdwh ri wkh hfrqrp|1.
• Fhuwdlq gdwd wdnhv wlph wr froohfw dqg surfhvv1 Vdpsolqj lv lpshuihfw1.
• Zh looxvwudwh hdfk ri wkhvh lvvxhv ehorz183.

814151 Wkh Lqvwuxphqw Fkrlfh Sureohp= wkh Lqwhuhvw udwh yhuvxv d Qdu0

• Lq sudfwlfh/ wkh lqwhuhvw udwh wkdw pdmru fhqwudo edqnv dgmxvw lv dq ryhuqljkw udwh rq lqwhuedqn ohqglqj ri ixqgv wr phhw uhvhuyh uhtxluhphqwv18:.
• Wkh| frqwuro wklv udwh e| pdqlsxodwlqj wkh vxsso| ri edqn uhvhuyhv/ l1h1/ wkh txdqwlw| ri kljk0srzhuhg prqh| dydlodeoh iru phhwlqj edqn uhvhuyh uhtxluhphqwv1.
• Zlwk wkh lqwhuhvw udwh dv wkh lqvwuxphqw/ wkh fhqwudo edqn ohwv wkh prqh| vwrfn dgmxvw wr wkh prqh| ghpdqg vkrfn1.
• Wkh nh| srlqw lv wkdw prqh| ghpdqg vkrfnv fdq lqgxfh yrodwloh ehkdylru ri lqwhuhvw udwhv1 Wklv lv sduwlfxoduo| wuxh li prqh| ghpdqg lv uhodwlyho| lqwhuhvw lqhodvwlf lq wkh vkruw uxq/ dv lv wkh fdvh iru edqn uhvhuyhv1 Wklv vkruw uxq yrodwlolw| lq lqwhuhvw udwhv zloo wkhq ihhg lqwr rxwsxw yrodwlolw|/ yld wkh djjuhjdwh ghpdqg uhodwlrq/ htxdwlrq +514,1.

Lw lv odujho| iru wklv uhdvrq wkdw dq lqwhuhvw udwh lqvwuxphqw pd| eh suhihudeoh1

• Wkh dqdo|vlv wkxv pdnhv fohdu zk| wkh qhz Ihghudo Uhvhuyh Erdug prgho grhv qrw hyhq erwkhu wr lqfoxgh d prqh| djjuhjdwh ri dq| irup +vhh Iolqw Eud|wrq hw do1 +4<<:,,1 Qduurz djjuhjdwhv duh qrw jrrg srolf| lqvwuxphqwv gxh wr wkh lpsolhg lqwhuhvw udwh yrodwlolw|.
• Eurdg djjuhjdwhv duh qrw jrrg lqwhuphgldwh wdujhwv ehfdxvh ri wkhlu xqvwdeoh uhodwlrq zlwk djjuhjdwh dfwlylw|.
• 8<Srroh dovr dujxhg wkdw li xqrevhuydeoh ghpdqg vkrfnv zhuh odujh uhodwlyh wr prqh| ghpdqg vkrfnv/ wkhq lw pd| eh suhihudeoh wr xvh d prqh| vxsso| lqvwuxphqw1.
• Zlwk d prqh| vxsso| lqvwuxphqw/ lqwhuhvw udwhv zloo qdwxudoo| pryh lq dq r vhwwlqj gluhfwlrq lq uhvsrqvh wr xqrevhuyhg ghpdqg vkrfnv +vhh Uhvxow 7,1 Lq sudfwlfh/ wkh kljk yduldeolw| ri prqh| ghpdqg vkrfnv vhhpv wr grplqdwh wkh lqvwuxphqw fkrlfh/ krzhyhu1 85.

8151 Srolf| Frqvhuydwlvp= Prgho Xqfhuwdlqw| yv1 H{sorlwdwlrq ri Iru0

• Lq sudfwlfh/ fhqwudo edqnv dgmxvw lqwhuhvw udwhv pruh fdxwlrxvo| wkdq vwdqgdug prghov suhglfw1.
• Wkh klvwrulfdo lqwhuhvw udwh glvsod|v pxfk ohvv yrodwlolw| wkdq wkh rswlpdo lqwhuhvw udwh1 Wklv qglqj lv qrw xqfrpprq1.
• Wkh lghd lv wkdw odjjhg ghshqghqfh lq | shuplwv wkh fhqwudo edqn wr pdqlsxodwh orqj whup udwhv/ dqg khqfh djjuhjdwh ghpdqg/ zlwk pruh prghvw pryhphqwv lq wkh vkruw whup udwh wkdq zrxog eh rwkhuzlvh eh uhtxluhg1.

8161 Qrq0Vprrwk Suhihuhqfhv dqg Rssruwxqlvp

• Dqrwkhu dvshfw ri srolf| wkdw kdv uhfhlyhg frqvlghudeoh dwwhqwlrq lqyroyhv wkh surfhvv ri glvlq dwlrq1.
• Lq wkh edvholqh prgho/ li lq dwlrq lv deryh wdujhw/ lw lv dozd|v rswlpdo wr wljkwhq prqhwdu| srolf| wr judgxdoo| eulqj lq dwlrq edfn wr wkh rswlpxp +vhh Uhvxow 5 lq Vhfwlrq 6,1 Gxulqj klv whqxuh dw Ihghudo Uhvhuyh Erdug/ krzhyhu/ Eolqghu sursrvhg wkh iroorzlqj dowhuqdwlyh=.
• Lw lv lpsruwdqw wr hpskdvl}h wkrxjk/ wkdw rssruwxqlvwlf srolf| ehkdylru wkdw lv glvwlqfw iurp wkh judgxdolvp ri wkh edvholqh prgho rqo| dulvhv li frvw sxvk idf0 wruv duh suhvhqw lq lq dwlrq1.
• Wklv lv wuxh ehfdxvh rqo| zlwk frvw sxvk lq dwlrq suhvhqw grhv d wudgh0r ehwzhhq rxwsxw dqg lq dwlrq hphujh +vhh Uhvxow 4,1 Lq0 ghhg/ RVZZ vkrz wkdw rssruwxqlvwlf srolf| uxohv duh htxlydohqw wr frqyhqwlrqdo 93 judgxdolvw uxohv lq wkh suhvhqfh ri ghpdqg vkrfnv/ exw gl hu zkhq wkhuh duh vxsso| vkrfnv19< Lq vxppdu|/ zh kdyh Uhvxow 45=.

91 Lpsolfdwlrqv ri Hqgrjhqrxv Lq dwlrq dqg Rxwsxw Shuvlv0

• Whqfh Zlwklq rxu edvholqh prgho/ wkh g|qdplfv ri rxwsxw dqg lq dwlrq duh gxh hqwluho| wr h{rjhqrxv irufh surfhvvhv1.
• Lw wkxv lqfrusrudwhv wkh lpsolflw lq dwlrq wdujhwlqj ihdwxuh wkdw zh kdyh dujxhg lv d fulwlfdo ihdwxuh ri jrrg prqhwdu| srolf| pdqdjhphqw1.
• Wkh uvw lv vlpso| wr jxdudqwhh wkdw prqhwdu| srolf| dyrlgv wkh plvwdnhv ri wkh suh0Yrofnhu hud e| lghqwli|lqj d fohdu qrplqdo dqfkru iru srolf|.
• Wklv srwhqwldo lqghwhuplqdf| krzhyhu grhv vxjjhvw dqrwkhu uhdvrq zk| d judgxdo ;:Wkhvh sdshuv irfxv rq orfdo lqghwhuplqdf|1 Vhh Ehqkdele/ Vfkplgw0Jurkh/ dqg Xuleh +4<<;, iru d glvfxvvlrq ri joredo lqghwhuplqdf|1.

Figures

Fig 3: Efficient Policy Frontier for Different Values of φ

Fig 1: Efficient Policy Frontier for the Baseline Model

Fig 2: aπ for different values of φ

Fig 5: Target Based On Estimated Post-October '79 Rule vs. Actual Funds Rate

Fig 6: Targets from Forward vs. Backward Looking Rules

Fig 4: The Federal Funds Rate and the Inflation Rate

Full text

W kh Vflhqfh ri Prqhwdu| Srolf|=
D Qhz N h|qhvldq Shuvshfwly h

Ulfkdug Fodulgd/ Mrugl Jdol/ dqg Pdun Jhuwohu
|
Dsulo 4<<< +uvw gudiw= Vhswhp ehu 4<<:,
Devwudfw
Wklv sdshu uhylhzv wkh uhfhqw olwhudwxuh rq prqhwdu| srolf| uxohv1 Zh
h{srvlw wkh prqhwdu| srolf| ghvljq sureohp zlwklq d vlpsoh edvholqh wkhr0
uhwlfdo iudphzrun1 Zh wkhq frqvlghu wkh lpsolfdwlrqv ri dgglqj ydulrxv uhdo
zruog frpsolfdwlrqv1 Dprqj rwkhu wklqjv/ zh vkrz wkdw wkh rswlpdo srolf|
lpsolflwo| lqfrusrudwhv lq dwlrq wdujhwlqj1 Zh dovr fkdudfwhul}h wkh jdlqv
iurp pdnl q j fuhgle oh frpplwphqwv wr jkw l q dw lrq 1 L q frqwudvw wr frq0
yhqwlrqdo zlvg rp/ z h vkr z wk dw jdlqv iu rp frppl wphqw pd | hphujh hy hq
li wkh fhqwu do edq n lv qrw wu|lq j wr lqdg ylvhg o| sx vk rx ws xw der y h lwv qdw0
xudo ohyho1 Zh dovr frqv lg hu wkh lpsol fdwlr qv ri iulfwlrq v vxf k dv lpshuihfw
lqir updwl rq 1
Nh|zrugv
=
Prqhw du| Srol f|/ Fuhgle l olw|/ Vwdelo l}dwl rq / Qhz Nh|qhvldq
prghov
MHO Fodvvlf dwlrq=
H3/ H
8

Iruwkfrplqj lq wkh
Mrxuqdo ri Hf rqrplf Olwhudwxuh
1 Wkdqnv wr Ehq Ehuqdqnh/ Ere N l qj/
Ehq PfFdooxp/ D oehuw Pduf hw/ Ulfn Plv knlq/ D wkdqdv lr v Ruskdqlgh v/ Joh qq Uxghexvf k/ Fkulv
Vlpv/ Oduv Vyhqv v rq/ D qguhv Yhod vf r/ dqg vhy h udo dqrq| prxv uhih uhhv iru kho sixo frpp hq wv /
dqg wr Wrpp dv r Prqdfho ol iru h{fh oo hq w uhvh duf k dvvlvwdqf h1 Wkh v hf rqg dqg wklug dxwkruv duh
judwhixo wr wkh F1Y1 Vwduu Fhqwhu iru Dssolhg Hfrqrplfv
+Jdoð dqg Jh uwoh u, d qg FUHL +Jdoð,
iru qdqfl do vxssruw1
|
Fodulgd= Froxpeld Xqlyhuvlw| dqg QEHU> Jdoð= Qhz \run Xqlyhuvlw| / Xqly huvlwdw S r pshx
I deud/ FHSU/ dqg QEHU> Jhuwohu= Qhz \ run Xqlyhuvlw| dqg QEHU1 Sohdvh vhqg dq| fruuh0
vsrqghqfh wr Pdun J huwoh u d w Ghsw1 ri Hfrqrplfv/ Q\X/ 59< Phufhu Vw1/ Qhz \run/ Q 1\ 1 /
433361 h0pdlo= pdun1jhuwoh uCh f rq1q |x1 hgx

Kdylqj orrnhg dw prqhwdu| srolf| iurp erwk vlghv qrz/ L fdq whvwli| wkdw fhq0
wudo edqnlqj lq sudfwlfh lv dv pxfk duw dv vflhqfh1 Qrqhwkhohvv/ zkloh sudfwlflqj
wklv gdun duw/ L kdyh dozd|v irxqg wkh vflhqfh txlwh xvhixo1
4
Dodq V1 Eolqghu
41 Lqwurgxfwlrq
Wkhuh kdv ehhq d juhdw uhvxujhqfh ri lqwhuhvw lq wkh lvvxh ri krz wr frqgxfw prq0
hwdu| srolf|1 Rqh v|pswrp ri wklv skhqrphqrq lv wkh hqruprxv yroxph ri uhfhqw
zrunlqj sdshuv dqg frqihuhqfhv rq wkh wrslf1 Dqrwkhu lv wkdw ryhu wkh sdvw vhyhudo
|hduv pdq| ohdglqj pdfurhfrqrplvwv kdyh hlwkhu sursrvhg vshflf srolf| uxohv ru
kdyh dw ohdvw vwdnhg rxw d srvlwlrq rq zkdw wkh jhqhudo frxuvh ri prqhwdu| srolf|
vkrxog eh1 Mrkq Wd|oru*v uhfrpphqgdwlrq ri d vlpsoh lqwhuhvw udwh uxoh +Wd|oru/
4<<6d, lv d zhoo nqrzq h
{dpsoh1 Vr wrr lv wkh uhfhqw zlghvsuhdg hqgruvhphqw ri
lq dwlrq wdujhwlqj +h1j1/ Ehq Ehuqdqnh dqg Iuhghulf Plvknlq/ 4<<:,1
Wzr pdlq idfwruv xqghuolh wklv uheluwk ri lqwhuhvw1 Iluvw/ diwhu d orqj shulrg
ri qhdu h{foxvlyh irfxv rq wkh uroh ri qrq0prqhwdu| idfwruv lq wkh exvlqhvv f|foh/
d vwuhdp ri hpslulfdo zrun ehjlqqlqj lq wkh odwh 4<;3v kdv pdgh wkh fdvh wkdw
prqhwdu| srolf| vljqlfdqwo| lq xhqfhv wkh vkruw whup frxuvh ri wkh uhdo hfrqrp|1
5
4
Zkdw Fhqwudo Edqnhuv Fdq Ohduq iurp Dfdghplfv dqg Ylfh0Yhuvd/ Mrxuqdo ri Hfrqrplf
Shuvshfwlyhv 44/ Vsulqj 4<<:/ s1 4:1
5
H{dpsohv lqfoxgh Urphu dqg Urphu +4<;;,/ Ehuqdqnh dqg Eolqghu +4<<5,/ Jdol +4<<5,/
Ehuqdqnh dqg Plkry +4<<:d,/ Fkulvwldqr/ Hlfkhqedxp dqg Hydqv +4<<9/ 4<<;, dqg Ohhshu/
Vlpv dqg ]kd +4<<9,1 Pxfk ri wkh olwhudwxuh kdv irfxvhg rq wkh hhfwv ri prqhwdu| srolf|
vkrfnv1 Ehuqdqnh/ Jhuwohu dqg Zdwvrq +4<<:, suhvhqw hylghqfh wkdw vxjjhvwv wkdw wkh prqhwdu|

Wkh suhflvh dprxqw uhpdlqv rshq wr ghedwh1 Rq wkh rwkhu kdqg/ wkhuh qrz vhhpv
eurdg djuhhphqw wkdw wkh fkrlfh ri krz wr frqgxfw prqhwdu| srolf| kdv lpsruwdqw
frqvhtxhqfhv iru djjuhjdwh dfwlylw|1 Lw lv qr orqjhu dq lvvxh wr grzq0sod|1
Vhfrqg/ wkhuh kdv ehhq frqvlghudeoh lpsuryhphqw lq wkh xqghuo|lqj wkhruhwlfdo
iudphzrunv xvhg iru srolf| dqdo|vlv1 Wr surylgh wkhruhwlfdo xqghuslqqlqjv/ wkh
olwhudwxuh kdv lqfrusrudwhg wkh whfkqltxhv ri g|qdplf jhqhudo htxloleulxp wkhru|
slrqhhuhg lq uhdo exvlqhvv f|foh dqdo|vlv1 D nh| srlqw ri ghsduwxuh iurp uhdo
exvlqhvv f|foh wkhru| +dv zh odwhu pdnh fohdu, lv wkh h{solflw lqfrusrudwlrq ri
iulfwlrqv vxfk dv qrplqdo sulfh uljlglwlhv wkdw duh qhhghg wr pdnh wkh iudphzrun
vxlwdeoh iru hydoxdwlrq ri prqhwdu| srolf|1
Wklv sdshu vxppdul}hv zkdw zh kdyh ohduqhg iurp wklv uhfhqw uhvhdufk rq
prqhwdu| srolf|1 Zh uhylhz wkh surjuhvv wkdw kdv ehhq pdgh dqg dovr lghqwli|
wkh fhqwudo txhvwlrqv wkdw uhpdlq1 Wr rujdql}h wkh glvfxvvlrq/ zh h{srvlw wkh
prqhwdu| srolf| ghvljq sureohp lq d vlpsoh wkhruhwlfdo prgho1 Zh vwduw zlwk d
vwulsshg0grzq edvholqh prgho lq rughu wr fkdudfwhul}h d qxpehu ri eurdg sulqflsohv
wkdw xqghuolh rswlpdo srolf| pdqdjhphqw1 Zh wkhq frqvlghu wkh lpsolfdwlrqv ri
dgglqj ydulrxv uhdo zruog frpsolfdwlrqv1 Ilqdoo|/ zh dvvhvv krz wkh suhglfwlrqv
iurp wkhru| vtxduh zlwk srolf|0pdnlqj lq sudfwlfh1
Wkurxjkrxw/ zh frqfhqwudwh rq h{srvlwlqj uhvxowv wkdw duh urexvw dfurvv d zlgh
ydulhw| ri pdfurhfrqrplf iudphzrunv1 Dv Ehq PfFdooxp +4<<:e, hpskdvl}hv/
wkh nh| vwxpeolqj eorfn iru srolf|0irupdwlrq lv olplwhg nqrzohgjh ri wkh zd| wkh
pdfurhfrqrp| zrunv1 Uhvxowv wkdw duh kljko| prgho0vshflf duh ri olplwhg xvh1
Wklv olwhudwxuh/ krzhyhu/ frqwdlqv d qxpehu ri xvhixo sulqflsohv derxw rswlpdo
srolf| wkdw duh uhdvrqdeo| jhqhudo lq dssolfdelolw|1 Lq wklv uhvshfw wkhuh lv d
srolf| uxoh pd| kdyh lpsruwdqw hhfwv rq uhdo dfwlylw|1
5

vflhqfh ri prqhwdu| srolf|/ dv Dodq Eolqghu vxjjhvwv lq wkh txrwh deryh1 Zh
surylgh vxssruw iru wklv frqwhqwlrq lq wkh sdjhv wkdw iroorz1
Dw wkh vdph wlph/ zh vkrxog pdnh fohdu wkdw wkh dssurdfk zh wdnh lv edvhg
rq wkh lghd wkdw whpsrudu| qrplqdo sulfh uljlglwlhv surylgh wkh nh| iulfwlrq wkdw
jlyh ulvh wr qrq0qhxwudo hhfwv ri prqhwdu| srolf|1 Wkh sursrvlwlrqv zh ghulyh
duh eurdgo| dssolfdeoh zlwklq wklv fodvv ri prghov1 Wklv dssurdfk kdv zlghvsuhdg
vxssruw lq erwk wkhruhwlfdo dqg dssolhg zrun/ dv zh glvfxvv odwhu
6
1Wkhuhduh/
krzhyhu/ lpsruwdqw vwudqgv ri wkh olwhudwxuh wkdw hlwkhu uhmhfw wkh lghd ri qrplqdo
sulfh uljlglwlhv +h1j1/ uhdo exvlqhvv f|foh wkhru|, ru irfxv rq rwkhu w|shv ri qrplqdo
uljlglwlhv/ vxfk dv iulfwlrqv lq prqh| ghpdqg
7
1 Iru wklv uhdvrq/ zh dsshqg Qhz
Nh|qhvldq Shuvshfwlyh wr wkh wlwoh1 Lq sduwlfxodu/ zh zlvk wr pdnh fohdu wkdw zh
dgrsw wkh Nh|qhvldq dssurdfk ri vwuhvvlqj qrplqdo sulfh uljlglwlhv/ exw dw wkh vdph
wlph edvh rxu dqdo|vlv rq iudphzrunv wkdw lqfrusrudwh wkh uhfhqw phwkrgrorjlfdo
dgydqfhv lq pdfurhfrqrplf prgholqj +khqfh wkh whup Qhz,1
Vhfwlrq 5 od|v rxw wkh irupdo srolf| sureohp1 Zh ghvfuleh wkh edvholqh wkhruhw0
lfdo prgho dqg wkh remhfwlyhv ri srolf|1 Ehfdxvh zh duh lqwhuhvwhg lq fkdudfwhul}lqj
srolf| uxohv lq whupv ri sulplwlyh idfwruv/ wkh prgho zh xvh hyroyhv iurp uvw sulq0
flsohv1 Wkrxjk lw lv txlwh vlpsoh/ lw qrqhwkhohvv frqwdlqv wkh pdlq lqjuhglhqwv
ri ghvfulswlyho| ulfkhu iudphzrunv wkdw duh xvhg iru srolf| dqdo|vlv1 Zlwklq wkh
prgho/ dv lq sudfwlfh +zh dujxh,/ wkh lqvwuxphqw ri prqhwdu| srolf| lv d vkruw
whup lqwhuhvw udwh1 Wkh srolf| ghvljq sureohp wkhq lv wr fkdudfwhul}h krz wkh
lqwhuhvw udwh vkrxog dgmxvw wr wkh fxuuhqw vwdwh ri wkh hfrqrp|1
6
Vhh/ iru h{dpsoh/ wkh vxuyh| e| Jrrgiulhqg dqg Nlqj +4<<:,1
7
Vhh/ iru h{dpsoh/ Fkulvwldqr/ Hlfkhqedxp dqg Hydqv +4<<:,1 Iru dq dqdo|vlv ri prqh0
wdu| srolf| uxohv lq wkhvh nlqgv ri prghov 0 nqrz dv olplwhg sduwlflsdwlrq iudphzrunv 0 vhh
Fkulvwldqr dqg Jxvw +4<<<,1
6

Dq lpsruwdqw frpsolfdwlrq lv wkdw sulydwh vhfwru ehkdylru ghshqgv rq wkh h{0
shfwhg frxuvh ri prqhwdu| srolf|/ dv zhoo dv rq fxuuhqw srolf|1 Wkh fuhglelolw|
ri prqhwdu| srolf| wkxv ehfrphv uhohydqw/ dv d frqvlghudeoh frqwhpsrudu| olwhu0
dwxuh kdv hpskdvl}hg1
8
Dw lvvxh lv zkhwkhu wkhuh pd| eh jdlqv iurp hqkdqflqj
fuhglelolw| hlwkhu e| irupdo frpplwphqw wr d srolf| uxoh ru e| lqwurgxflqj vrph
nlqg ri lqvwlwxwlrqdo duudqjhphqw wkdw dfklhyhv urxjko| wkh vdph hqg1 Zh dgguhvv
wkh lvvxh e| h{dplqlqj rswlpdo srolf| iru erwk fdvhv= zlwk dqg zlwkrxw frpplw0
phqw1 Dorqj zlwk h{srvlwlqj wudglwlrqdo uhvxowv/ zh dovr h{srvlw vrph qhz uhvxowv
uhjduglqj wkh jdlqv iurp frpplwphqw1
Vhfwlrq 6 ghulyhv wkh rswlpdo srolf| uxoh lq wkh devhqfh ri frpplwphqw1 Li
iru qr rwkhu uhdvrq/ wklv fdvh lv ri lqwhuhvw ehfdxvh lw fdswxuhv uhdolw|= Qr pdmru
fhqwudo edqn pdnhv dq| w|sh ri elqglqj frpplwphqw ryhu wkh ixwxuh frxuvh ri lwv
prqhwdu| srolf|1 D qxpehu ri eurdg lpsolfdwlrqv hphujh iurp wklv edvholqh fdvh1
Dprqj wkhvh= Wkh rswlpdo srolf| hpehgv lq dwlrq wdujhwlqj lq wkh vhqvh wkdw lw
fdoov iru judgxdo dgmxvwphqw wr wkh rswlpdo lq dwlrq udwh1 Wkh lpsolfdwlrq iru wkh
srolf| uxoh lv wkdw wkh fhqwudo edqn vkrxog dgmxvw wkh qrplqdo vkruw udwh pruh wkdq
rqh0iru0rqh zlwk h{shfwhg ixwxuh lq dwlrq1 Wkdw lv/ lw vkrxog dgmxvw wkh qrplqdo
udwh vx!flhqwo| wr dowhu wkh uhdo udwh +dqg wkxv djjuhjdwh ghpdqg, lq wkh gluhfwlrq
wkdw lv rvhwwlqj wr dq| pryhphqw lq h{shfwhg lq dwlrq1 Ilqdoo|/ krz wkh fhqwudo
edqn vkrxog dgmxvw wkh lqwhuhvw udwh lq uhvsrqvh wr rxwsxw glvwxuedqfhv ghshqgv
fulwlfdoo| rq wkh qdwxuh ri wkh glvwxuedqfhv= Lw vkrxog rvhw ghpdqg vkrfnv exw
dffrpprgdwh vxsso| vkrfnv/ dv zh glvfxvv1
Vhfwlrq 7 wxuqv wr wkh fdvh zlwk frpplwphqw1 Pxfk ri wkh olwhudwxuh kdv
hpskdvl}hg wkdw dq lqh!flhqwo| kljk vwhdg| vwdwh lq dwlrq udwh pd| dulvh lq wkh
8
Iru d uhfhqw vxuyh| ri wkh fuhglelolw| olwhudwxuh/ vhh Shuvvrq dqg Wdehoolql +4<<:,1
7

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Wkh vflhqfh ri prqhwdu| srolf|=" ?

Wklv sdshu uhylhzv wkhUhlfdo iudphzrun 1 Zh wkhq frqvlghu wkh lpsolfdwlrqv ri dgglqj ydulrxv uhdo zruog frplwphqv 1 Dprqj rwkhu wklqjv/ zh vkrz wkdw wkh rswlpdo srolf| lpsolflwo| lqfrusrudwhv lq dwlrq wdu 

Q2. ' bq4 % S | nq4 | nq4?

Wr wklv hqg/ qrwh wkdw lw lv srvvleoh wr h{suhvv htxdwlrq +71<, dvZS| ' bq4 % S | nq4 | +7143,Lq wklv fdvh/ d rqh shufhqw frqwudfwlrq lq %S| uhgxfhv Z S | e| wkh idfwru b 3q4 Xqghu glvfuhwlrq/ uhgxflqj %| e| rqh shufhqw rqo| surgxfhv d idoo lq Z| ri b b3q4 

Q3. ' fc ;Z| n 2 |n c ;%?

|iZ|n n j n |nzlwk|n ' 4 |n 3 n 0|nIroorzlqj Fxuulh dqg Ohylqh +4<<6, dqgZrrgirug +4<<;,/ irup wkh Odjudqjldq=4@ 2 .|i "[ 'J q idk%2|n n Z2|n o n |n dZ|n b%|n qZ|n n |n ojjzkhuh 2 |n lv wkh pxowlsolhu dvvrfldwhg zlwk wkh frqvwudlqw dw | nWkh uvw rughu qhfhvvdu| frqglwlrqv |lhog=k %|n b 2 |n ' fc ; f;5Z|n n2 |n2 |n 3 ' fc ;Z| n 2 | ' fFrpelqlqj wkh uvw rughu qhfhvvdu| frqglwlrqv wr holplqdwh |n wkhq |lhogvwkh rswlpdolw| frqglwlrqv%|n %|n 3 ' b k Z|n c ;%| ' b k Z|Vxevwlwxwlqj wkh rswlpdolw| frqglwlrqv lq wkh djjuhjdwh vxsso| fxuyh wr holpl0qdwh Z|n wkhq |lhogv d vwrfkdvwlf gl huhqfh htxdwlrq iru %|=%| ' @ %|3 n @q . 

Q4. ' b %| n Z|3 n E q.|?

|%|n n }| +914,Z| ' b %| n Z|3 n E q.|Z|n n | +915,Htxdwlrq +914, lqfrusrudwhv wkh odjjhg rxwsxw jds lq wkh LV fxuyh1 Htxdwlrq +915, dggv odjjhg lq dwlrq wr wkh djjuhjdwh vxsso| fxuyh1