Uncertain potential output: implications for monetary policy

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E U R O P E A N C E N T R A L B A N K

W O R K I N G PA P E R S E R I E S

WORKING PAPER NO. 59

UNCERTAIN POTENTIAL

OUTPUT: IMPLICATIONS FOR

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E U R O P E A N C E N T R A L B A N K

W O R K I N G PA P E R S E R I E S

WORKING PAPER NO. 59

UNCERTAIN POTENTIAL

OUTPUT: IMPLICATIONS FOR

MONETARY POLICY

BY MICHAEL EHRMANN

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© European Central Bank, 2001

Address Kaiserstrasse 29

D-60311 Frankfurt am Main Germany

Postal address Postfach 16 03 19

D-60066 Frankfurt am Main Germany Telephone +49 69 1344 0 Internet http://www.ecb.int Fax +49 69 1344 6000 Telex 411 144 ecb d

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2 A simple backward/forward-looking model for policy analysis 9 2.1 A backward/forward-looking model 9 2.2 Estimation and calibration 11 3 Optimal policy under commitment and discretion 12 3.1 The optimal instrument rule under commitment and discretion 13 3.2 The Kalman gain matrix and the information value

of various indicators 14

3.3 Economic stabilisation and the value of information 15 4 Potential output uncertainty and simple instrument rules 18 4.1 Taylor rules and nominal income growth rules 19 4.2 Simple inflation-forecast-based rules 21 5 Output gap uncertainty and optimal delegation 21 5.1 The optimal degree of “conservativeness” 21 5.2 The optimal weight on price level stability 23 6 Some sensitivity analysis 23

6.1 Changing the relative variance of the potential output

and cost-push shocks 23

6.2 The case of asymmetric information 24

7 Conclusions 26

A Appendix 29

Tables and figures 34

References 47

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(21)

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(22)

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(23)

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(24)

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(25)

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(26)

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(27)

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(28)

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f|n*|' EM n af|*| +4;,

Lq dgglwlrq/ wkh odz ri prwlrq ri wkh dfwxdo dqg shufhlyhg iruzdug0orrnlqj yduldeohv dqg wkh srolf| lqvwuxphqw duh jlyhq e|=

t-1 t-1 t-1 t-1 t-1 t/t-1 t/t-1 t-1

(33)

%|' Cf|n C2f|*| +4<,

%|*|' Cf|*| +53,

o|' 8f|*| +54,

zkhuh wkh pdwulfhv M/ a/ g/ u/ C_{/ C}2_{/ C dqg 8 duh ghqhg lq VZ +4<<<,1}

D1515 Vlpsoh uxohv

D vlplodu vhw ri g|qdplf htxdwlrqv fdq eh ghulyhg zkhq wkh fhqwudo edqn frpplwv wr d vlpsoh lqvwuxphqw uxoh ri wkh iroorzlqj irup/

o|' 8f|*|n 82%|*| +55, Xvlqj +D147, dqg +, wkh g|qdplfv ri wkh shufhlyhg vwdwh yduldeohv fdq eh ghvfulehg e|= f|n*| %|n*| ' E _n2_{n d8}_{n 8}2_o f|*| %|*| +56, Xvlqj/ iru h{dpsoh/ Nohlq*v dojrulwkp iru vroylqj olqhdu udwlrqdo h{shfwdwlrqv prghov/ wklv |lhogv wkh iroorzlqj h{suhvvlrq iru wkh iruzdug0orrnlqj yduldeohv= %|*|' Cf|*| +57,

o| ' E8n 82Cf|*|' 8 f|*| +58,

Wdnlqj lqwr dffrxqw wkh qhz h{suhvvlrq iru C dqg 8 / htxdwlrqv lghqwlfdo wr wkrvh deryh fdq eh ghulyhg1

D1516 Frpplwphqw

Ilqdoo|/ zkhq wkh fhqwudo edqn rswlplvhv xqghu frpplwphqw/ wkh fruuhvsrqg0 lqj vhw ri g|qdplf htxdwlrqv fdq eh ghulyhg=

(34)

f|*|' f|*|3n guEf| f|*|3 n | +5:,

f|n*|' EM n af|*|n [s|3 +5;,

s|' 7f|*|n Ps|3 +5<,

zkhuh s| lv wkh yhfwru ri Odjudqjh pxowlsolhuv dvvrfldwhg zlwk wkh htxdwlrqv

iru wkh iruzdug0orrnlqj yduldeohv1 Wkh iruzdug0orrnlqj yduldeohv dqg wkh srolf| lqvwuxphqw duh ghqhg e|=

%|' Cf|n C2f|*|n Ks|3 +63,

%|*| ' Cf|*|n Ks|3 +64,

o|' 8 f|*|n xs|3 +65,

Djdlq wkh pdwulfhv duh ghqhg lq VZ +4<<<,1 Rqh ri wkh pdlq glhuhqfhv ehwzhhq wkh rxwfrph xqghu glvfuhwlrq yhuvxv wkh rxwfrph xqghu frpplw0 phqw lv wkdw doo wkh yduldeohv qrz dovr ghshqg rq wkh Odjudqjh pxowlsolhuv dvvrfldwhg zlwk wkh htxdwlrqv iru wkh iruzdug0orrnlqj yduldeohv1 Dv glvfxvvhg lq VZ+4<<<, wklv ohdgv wr klvwru|0ghshqghqfh dv wkh Odjudqjh pxowlsolhuv duh wkhpvhoyhv ixqfwlrqv ri sdvw suhghwhuplqhg yduldeohv1

D16 Wkh ydoxh ri wkh orvv ixqfwlrq=

Lq wklv Vhfwlrq zh ghulyh dq h{suhvvlrq iru wkh ydoxh ri wkh orvv ixqfwlrq lq wkh fdvh ri d glvfuhwlrqdu| fhqwudo edqn ru zlwk vlpsoh uxohv1 D vlplodu h{suhvvlrq fdq eh ghulyhg iru wkh fdvh ri frpplwphqw1

Wkh ydoxh ri wkh orvv ixqfwlrq lv jlyhq e|= a| ' .| " [ 'f q_u |n +66, Wklv fdq eh uhzulwwhq dv= a| ' u|*|n qa|n*| +67, t/t-1 t-1 t-1 t-1 t-1 t-1

(35)

Ehfdxvh wkh sureohp lv olqhdu0txdgudwlf/ wkh orvv0ixqfwlrq fdq eh zulwwhq dv d txdgudwlf irup lq wkh shufhlyhg suhghwhuplqhg vwdwh yduldeohv=

a|' f|*|A T f|*|n +68, Vxevwlwxwlqj +D146, lqwr +D147, |lhogv= fA |*|T f|*|n ' u|*|n q.|if|n*|nA T f|n*|nn j +69, Xvlqj htxdwlrqv +D1709, lq htxdwlrq +, |lhogv= t|' f|*|n 2Ef| f|*| +6:, zkhuh _' n 2C n 8 dqg 2 ' n 2C1

Wkhuhiruh/ wkh uvw whup rq wkh uljkw0kdqg0vlgh ri htxdwlrq +D147, fdq eh zulwwhq dv=

u|*|' f|*|A A` f|*|n .|iEf| f|*|A2A`2Ef| f|*|j

+6;, Xvlqj htxdwlrqv +D1406, |lhogv wkh iroorzlqj h{suhvvlrq=

f|n*|n ' EM n af|*|n guMEf| f|*| n gu|nn g|n +6<,

Ehfdxvh hdfk ri wkh whupv lq +D14:, duh lqghshqghqw ri hdfk rwkhu/ wkh vhfrqg whup lq htxdwlrq +D147, fdq eh zulwwhq dv=

fA

|*|EM n aAT EM n af|*|n .|iEf| f|*|AEguMAT EguMEf| f|*|j

n.|iA|nEugAT gu|nj n .|i|nA gAT g|nj +73,

Vxevwlwxwlqj htxdwlrqv +D149, dqg +D4;, lq +D147, dqg froohfwlqj whupv/ wkh iroorzlqj h{suhvvlrqv iru T dqg fdq eh ghulyhg=

T ' A_`_{n qEM n a}A_{T EM n a} _+74,

' _q i|o@SeE

|*| n q|o@SeE2|*| n q|o@SeEP n q|o@SeEePj

+75, zkhuh _'2A_`2_/2 _{' EguM}A_{T EguM/} _{' g}A_uA_{T gu dqg}

e _{' g}A_{T g dqg}

|*|lv wkh fryduldqfh pdwul{ ri wkh zlwklq0shulrg suhglfwlrq

(36)

Sdudphwhu ydoxhv xvhg lq wkh fdoleudwlrq B V k j j2

0 j2 j2 j2c+ q

3177 314; 317; 03139 3196 3175 3146 3139 31<9

Table 1

(37)

Vwdqgdug Vwdqgdug Vwdqgdug Frpplwphqw fdvh Orvv ghyldwlrq ri ghyldwlrq ri ghyldwlrq ri

rxwsxw jds lq dwlrq lqwhuhvw udwh fkdqjhv b ' fc b' ff U 5:137 3198 31;9 4<15: UU 79174 4144 31;6 4;1:3 b ' fc b' f U 8:188 413: 31<: 5136 UU :9158 416: 31<: 5136 b ' fc b' f2D U 9:133 4149 4136 4176 UU ;81:7 4176 4137 4176 b ' ffc b' f U 57164 4173 31<3 4196 UU 58166 4194 31<5 419: b ' fDc b' f U 5;194 4167 31<3 4196 UU 85197 4178 31<6 41;4 b ' fc b' f U 8:188 413: 31<: 5136 UU :9158 416: 31<: 5136 b ' 2fc b' f U ;3165 31<6 4138 5183 UU 44;165 415; 4137 5179

Vwdqgdug Vwdqgdug Vwdqgdug

Glvfuhwlrqdu| fdvh Orvv ghyldwlrq ri ghyldwlrq ri ghyldwlrq ri rxwsxw jds lq dwlrq lqwhuhvw udwh fkdqjhv b ' fc b' ff U 6816< 3186 4144 53166 UU 87154 4138 413: 5316; b ' fc b' f U :4137 4134 414< 5174 UU <3174 4164 4154 5178 b ' fc b' f2D U ;:16: 4144 4164 41:: UU 43:15: 416< 4166 41;3 b ' ffc b' f U 68169 4154 413: 41;< UU 6:139 4178 4143 41<7 b ' fDc b' f U 871<: 413< 4146 5148 UU 9815: 416: 4148 5153 b ' fc b' f U :4137 4134 414< 5174 UU <3174 4164 4154 5178 b ' 2fc b' f U <:16: 31<3 4163 51;< UU 468187 4158 4164 51<3 Table 2

(38)

W|sh ri uxoh Orvv o|3 Z| }@R|*| Fdvh 4= U Zlwkrxw vprrwklqj <71<7 06133 31;4 Zlwk vprrwklqj 9316< 31<; 417; 4166 Fdvh 5= UU Zlwkrxw vprrwklqj 44615 06138 3174 Zlwk vprrwklqj :;19: 31<< 4179 415< Plvvshflhg uxoh zlwkrxw vprrwklqj 44619 06146 314; Plvvshflhg uxoh zlwk vprrwklqj ;418: 4136 41;8 31;; Table 3a

Taylor rule, with varying information

Table 3b

Income growth rule, with varying information

Table 3c

Simple inflation-forecast based rules, with varying information W|sh ri uxoh Orvv o|3 Z| {+|*| Fdvh 4= U Zlwkrxw vprrwklqj <:18; 06143 03136 Zlwk vprrwklqj :41<: 31<8 41<: 413: Fdvh 5= UU Zlwkrxw vprrwklqj 4461; 06146 3137 Zlwk vprrwklqj ;9137 31<; 5136 4154 W|sh ri uxoh Orvv o|3 Z| ru Z|n*| Fdvh 4= U Z| :8148 31:9 41<< Z|n*| 9819; 4147 7178 ZS |n*| 96159 4164 7158 Fdvh 5= UU Z| ;<1<4 31:: 41<; Z|n*| ;519< 4149 7178 ZS _;31;< ₄₁₆₅ _714:

(39)

vrolg olqhv= dfwxdo> gdvkhg olqhv= shufhlyhg> odvw froxpq= vrolg olqhv= lqwhuhvw udwh> gdvkhg= dfwxdo lq dwlrq

Figure 1a

(40)

vrolg olqhv= dfwxdo> gdvkhg olqhv= shufhlyhg> odvw froxpq= vrolg olqhv= lqwhuhvw udwh> gdvkhg= dfwxdo lq dwlrq

Figure 1b

(41)

vrolg olqhv= lqfrpsohwh lqirupdwlrq> gdvkhg= frpsohwh lqirupdwlrq Figure 2a

(42)

vrolg olqhv= lqfrpsohwh lqirupdwlrq> gdvkhg= frpsohwh lqirupdwlrq Figure 2b

(43)

vrolg olqhv= frpplwphqw> gdvkhg= glvfuhwlrq Figure 3

(44)

gdvkhg +grwwhg, krul}rqwdo olqh= glvfuhwlrqdu| htxloleulxp zlwkb ' fD/ frpsohwh +lqfrpsohwh, lqirupdwlrq> vrolg +gdvkhg, olqh= orvv iru ydu|lqjb/

frpsohwh +lqfrpsohwh, lqirupdwlrq Figure 4

(45)

gdvkhg +grwwhg, krul}rqwdo olqh= glvfuhwlrqdu| htxloleulxp zlwkb ' fD/ b2 ' ff/ frpsohwh +lqfrpsohwh, lqirupdwlrq> vrolg +gdvkhg, olqh= orvv iru ydu|lqj

b2/ frpsohwh +lqfrpsohwh, lqirupdwlrq Figure 5

(46)

Figure 6

Perception errors in the output gap and the relative variance of cost-push and potential output shocks

(47)

Vrolg olqhv= VLL> gdvkhg olqhv= FL> grwwhg olqhv= DLL

Figure 7

(48)

Vrolg olqhv= DLL> gdvkhg olqhv= VLL1

Figure 8

(49)

Uhihuhqfhv

sudfwlfh= Vrph lqwhuqdwlrqdo hylghqfh/ Hxurshdq Hfrqrplf Uhylhz 75+9,/ 43660439:1

^7` Fodulgd/ U1/ M1 Jdol dqg P1 Jhuwohu +4<<<,/ Wkh vflhqfh ri prqhwdu| srolf|= D qhz0Nh|qhvldq shuvshfwlyh/ Mrxuqdo ri Hfrqrplf Olwhudwxuh 6:+7,/ 499404:3:1

^8` Frhqhq/ J1/ D1 Ohylq dqg Y1 Zlhodqg +5334,/ Prqh| dqg prqhwdu| srolf| xqghu gdwd xqfhuwdlqw|/ plphr/ Hxurshdq Fhqwudo Edqn1

^9` Grwvh|/ P1 dqg D1 Kruqvwhlq +5333,/ Lv wkh ehkdylrxu ri prqh| xvh0 ixo wr d glvfuhwlrqdu| srolf| pdnhuB/ plphr/ Ihghudo Uhvhuyh Edqn ri Ulfkprqg1

^:` Guhz/ D1 dqg E1 Kxqw +5333,/ H!flhqw srolf| uxohv dqg wkh lpsolfdwlrqv ri srwhqwldo rxwsxw xqfhuwdlqw|/ Mrxuqdo ri Hfrqrplfv dqg Exvlqhvv/ 85=425/ Mdqxdu|2Dsulo 5333/ 47604941

^;` Hvwuhood/ D1 dqg M1 Ixkuhu +4<<;,/ G|qdplf lqfrqvlvwhqflhv= frxqwhu0 idfwxdo lpsolfdwlrqv ri d fodvv ri udwlrqdo h{shfwdwlrqv prghov/ Ihghudo Uhvhuyh Edqn ri Ervwrq Zrunlqj Sdshu Qr1<;081

^43` Jdlgxfk/ Y1 dqg E1 Kxqw +5333,/ Lq dwlrq wdujhwlqj xqghu srwhqwldo rxwsxw xqfhuwdlqw|/ LPI Zrunlqj Sdshu1

^44` Jdvsdu/ Y1 dqg I1 Vphwv +5333,/ Sulfh ohyho vwdelolw|= vrph lvvxhv/ Qdwlrqdo Lqvwlwxwh Hfrqrplf Uhylhz Qr14:7/ Rfwrehu 5333/ 9;0:<1

(50)

^45` Jhuodfk/ V1 dqg J1 Vfkqdeho +5333,/ Wkh Wd|oru uxoh dqg lqwhuhvw udwhv lq wkh HPX duhd/ Hfrqrplfv0Ohwwhuv 9:+5,/ 49804:41

^46` Jhuodfk/ V1 dqg I1 Vphwv +4<<<,/ Rxwsxw jdsv dqg prqhwdu| srolf| lq wkh HPX duhd/ Hxurshdq Hfrqrplf Uhylhz 76/ ;340;451

^47` Jrrgiulhqg/ P1 dqg U1 Nlqj +4<<:,/ Wkh qhz qhrfodvvlfdo v|qwkhvlv dqg wkh uroh ri prqhwdu| srolf|/ QEHU Pdfurhfrqrplfv Dqqxdo 45= 56405;61

^48` Odqvlqj/ N1 +5333,/ Ohduqlqj derxw d vkliw lq wuhqg rxwsxw= Lpsolfd0 wlrqv iru prqhwdu| srolf| dqg lq dwlrq/ Ihghudo Uhvhuyh Edqn ri Vdq Iudqflvfr Zrunlqj Sdshu1

^49` Od{wrq/ G1/ S1 Lvdug/ D1 Hooldvrq +5333,/ Lq dwlrq wdujhwlqj zlwk QDLUX xqfhuwdlqw| dqg hqgrjhqrxv srolf| fuhglelolw|/ Mrxuqdo ri Hfr0 qrplf G|qdplfv dqg Frqwuro/ 58/ 448047;1

srolf|/ Fduqhjlh Urfkhvwhu Frqihuhqfh Vhulhv rq Sxeolf Srolf| 5</ 4:60 5371

^4<` PfFdooxp/ E1 +4<<:,/ Lvvxhv lq wkh ghvljq ri prqhwdu| srolf| uxohv/ QEHU Zrunlqj Sdshu Qr1 9349

^53` PfFdooxp/ E1 +5333,/ Frpphqwv rq Hulf Vzdqvrq*v sdshu cRq vljqdo h{wudfwlrq dqg qrq0fhuwdlqw| htxlydohqfh lq rswlpdo prqhwdu| srolf| uxohv*/ Pdufk 53331

^54` PfFdooxp/ E1 dqg H1 Qhovrq +5333,/ Wlphohvv shuvshfwlyh yhuvxv glv0 fuhwlrqdu| prqhwdu| srolf| lq iruzdug0orrnlqj prghov/ plphr/ Edqn ri Hqjodqg1

^55` Ruskdqlghv/ D1 +4<<;,/ Prqhwdu| srolf| hydoxdwlrq zlwk qrlv| lqiru0 pdwlrq/ Ilqdqfh dqg Hfrqrplfv Glvfxvvlrq Vhulhv Zrunlqj Sdshu Qr1 4<<;0831 Erdug ri Jryhuqruv ri kh Ihghudo Uhvhuyh V|vwhp1

^56` Ruskdqlghv/ D1 +5333,/ Wkh txhvw iru survshulw| zlwkrxw lq dwlrq/ HFE Zrunlqj Sdshu Qr1481

Uncertain potential output: implications for monetary policy

WORKING PAPER NO. 59

UNCERTAIN POTENTIAL

OUTPUT: IMPLICATIONS FOR

WORKING PAPER NO. 59

UNCERTAIN POTENTIAL

OUTPUT: IMPLICATIONS FOR

MONETARY POLICY

BY MICHAEL EHRMANN

Contents

4 Lqwurgxfwlrq

5 D vlpsoh edfnzdug2iruzdug0orrnlqj prgho

iru srolf| dqdo|vlv

514 D edfnzdug2iruzdug0orrnlqj prgho

515 Hvwlpdwlrq dqg fdoleudwlrq

6 Rswlpdo srolf| xqghu frpplwphqw dqg glv0

fuhwlrq

614 Wkh rswlpdo lqvwuxphqw uxoh xqghu frpplwphqw

dqg glvfuhwlrq

615 Wkh Ndopdq jdlq pdwul{ dqg wkh lqirupdwlrq ydoxh

ri ydulrxv lqglfdwruv

616 Hfrqrplf vwdelolvdwlrq dqg wkh ydoxh ri lqirupd0

wlrq

7 Srwhqwldo rxwsxw xqfhuwdlqw| dqg vlpsoh lq0

vwuxphqw uxohv

714 Wd|oru uxohv dqg qrplqdo lqfrph jurzwkuxohv

715 Vlpsoh lq dwlrq0iruhfdvw0edvhg uxohv

8 Rxwsxw jds xqfhuwdlqw| dqg rswlpdo ghoh0

jdwlrq

814 Wkh rswlpdo ghjuhh ri frqvhuydwlyhqhvv

815 Wkh rswlpdo zhljkw rq sulfh ohyho vwdelolw|

9 Vrph vhqvlwlylw| dqdo|vlv

914 Fk dqjlqj wk h uhodwlyh yduldqfh ri wk h srwhqwldo rxw0

sxw dqg frvw0sxvkvkrfnv

915 Wkh fdvh ri dv|pphwulf lqirupdwlrq

: Frqfoxvlrqv

D Dsshqgl{

D14 Wkh prgho lq vwdwh vsdfh irup

D15 Rswlpdo prqhwdu| srolf|

D16 Wkh ydoxh ri wkh orvv ixqfwlrq=

Uhihuhqfhv

814 Wkh rswlpdo ghjuhh ri frqvhuydwlyhqhvv