The Relativity Theory Revisited: Is Publishing Interest Rate Forecasts Really so Valuable?

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The Relativity Theory Revisited: Is Publishing

Interest Rate Forecasts Really so Valuable?

0LFKDï%U]R]D%U]H]LQD

Adam Kot

NATIONAL BANK OF POLAND

WORKING PAPER

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Design: Oliwka s.c.

Layout and print:

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Contents

5 Conclusions . . . 17

References . . . 18

Appendix 1 . . . 21

Appendix 2 . . . 23

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Table 1

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Table 2

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Table 3

Average central bank loss and gains in the baseline scenario . . .

Table 4

7D\ORUUXOHFRHIILFLHQWVLQWKHEDVHOLQHVFHQDULR . . .

Figure 1

$YHUDJHFHQWUDOEDQNORVVIRUGLIIHUHQWYDOXHVRIhbea under various

monetary policy rules . . .

Figure 2

$YHUDJHFHQWUDOEDQNORVVIRUGLIIHUHQWYDOXHVRIe under various

monetary policy rules . . .

Figure 3

$YHUDJHFHQWUDOEDQNORVVIRUGLIIHUHQWYDOXHVRISZ^ under various

monetary policy rules . . . .

(5)

Abstract

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(6)

Introduction

1

Introduction

The last two decades have witnessed a substantial increase in transparency about

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(7)

Introduction

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publishing the interest rate path may be minor.

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widely analysed in the literature. The literature on the relationship between central bank

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(8)

Introduction

1

New Keynesian model with learning to show that publishing the interest rate path lowers the

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On technical grounds our paper is directly linked to an increasing literature on

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The Model

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we set its standard deviation to SE^

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The Model

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the output gap we use the unemployment gap. Taking into account that the variability

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For our model we assume Lj=4 and L^ ZKLFKLVHTXLYDOHQWWRDVWDQGDUGORVV IXQFWLRQZLWKWKHZHLJKWRQLQIODWLRQDQGRXWSXWJDSYDULDELOLW\EHLQJHTXDODQGIRXUWLPHV

higher than the weight on interest rate variability.

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omitting these elements we are likely erring on the upside when assessing the relative gains

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(11)

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is assumed to be conditional on what the central bank reveals.

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$

A

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1

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FRYHUVODVWREVHUYDWLRQVLHIURPiŞWLOOiŞWKHHDUOLHUGDWDLVVLPSO\IRUJRWWHQE\

agents. 7KLV9$5LVQH[WDSSOLHGWRFRPSXWHH[SHFWDWLRQV^Z ijiZ and PiZ$WZRSHULRG DKHDGG\QDPLFIRUHFDVWVLVFRPSXWHGDFFRUGLQJWR

$

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$

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and

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A

$

6KRFNVEPiEji and E^i at periods i and iDUHDVVXPHGWREHXQNQRZQWRWKH DJHQWV7KHH[SHFWDWLRQV^Z

ijZijiZ and PiZDUHWKHQSOXJJHGLQWRWKHWUXHPRGHORIWKH

HFRQRP\FRQVLVWLQJRIDQGWRREWDLQWKHDFWXDOODZRIPRWLRQ$/0:KHQ

shocks EPiEji and E^i arrive this can be used to generate ^iji and Pi.

The second variant K'GLIIHUVIURPK& in that economic agents are assumed to

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(12)

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we consider two alternative solutions:

ľWKH SURMHFWLRQ FDQ EH FRQVLGHUHG DV DQ DGGLWLRQDO GDWDVHW GHULYHG IURP WKH

FHQWUDOEDQNĳVHFRQRPHWULFPRGHOZKLFKE\DVVXPSWLRQUHIOHFWVWKH$/0RIWKH HFRQRP\7KLVGDWDVHWPD\EHHVSHFLDOO\YDOXDEOHIRUDJHQWVVLQFHLWLVOHVVQRLV\WKDQ PDFURHFRQRPLFGDWDļWKHRQO\VRXUFHRIYDULDELOLW\LVWKHH[RJHQRXVLQWHUHVWUDWH SDWKZKLOHDOOVKRFNVDUHVHWWR]HUR$FFRUGLQJO\ZHDVVXPHWKDWDJHQWVDSSHQGWKH SURMHFWLRQGDWDWRWKHGDWDVHWWKH\DOUHDG\SRVVHVVZKHQHVWLPDWLQJWKHILUVWWZR

HTXDWLRQVRIWKH9$5LHZLWKji and PiRQWKHOHIWKDQGVLGH$JHQWVGRQRW

LQFUHDVHWKHLUGDWDVHWZKHQHVWLPDWLQJWKHSROLF\UXOHVLQFHWKH\NQRZWKDWWKHGDWD IRULWZDVJHQHUDWHGH[RJHQRXVO\+HQFHDJHQWVDFWDVLQK&ZLWKWKHRQO\GLIIHUHQFH WKDWWKH\KDYHDODUJHUGDWDVHW([SHFWDWLRQV^Z ijiZjiZ and PZiDUHWKHQIRUPHG DFFRUGLQJWRDQG ľLQFHQWUDOEDQNLQJSUDFWLFHDQLQKHUHQWSDUWRIVKRZLQJPDFURHFRQRPLFSURMHFWLRQV LVWKHSXEOLFDWLRQRIWKHXQGHUO\LQJHFRQRPHWULFPRGHO6LQFHWKHVHSXEOLVKHGPRGHOV XVXDOO\GRQRWFRQWDLQPRQHWDU\SROLF\UXOHVWKLVLVHTXLYDOHQWWRVKRZLQJHTXDWLRQV DQGWRWKHDJHQWVDWOHDVWWRWKRVHZKRUHDGFHQWUDOEDQNZRUNLQJSDSHUV 6LQFHDJHQWVNQRZWKHPRGHOGULYLQJWKHHFRQRP\DOOWKH\QHHGLQDGGLWLRQWREXLOG H[SHFWDWLRQVIRUi and iLVWKHSROLF\UXOH6LPLODUO\WRK&WKH\OHDUQLWIURPSDVW GDWDZKLFKLVXVHGWRHVWLPDWHWKHSROLF\UXOH

1

$

1

%

(VWLPDWLRQLVSHUIRUPHGE\2/6RQDQSHULRGPRYLQJVDPSOHLQWKHEDVHOLQH FDVH1H[WDJHQWVDGGWKHHVWLPDWHGSROLF\UXOHWRWKHPRGHORIWKHHFRQRP\SXEOLVKHGE\ WKHFHQWUDOEDQNDQG7KHUHIRUHWKHPRGHO3/0WKH\XVHWRFRPSXWHH[SHFWDWLRQV IRUi and iEHFRPHV

1

+1

$

1

$

+1

;

1

;

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1

ZKHUHHVWLPDWHVRISDUDPHWHUVREWDLQHGWKURXJKOHDUQLQJDUHGHQRWHGZLWKKDWVFÜP and

FÜj7KHPRGHOLVVROYHGXQGHUUDWLRQDOH[SHFWDWLRQVDQGJLYHQWKHGDWDIRUSHULRGiŞWKH

solution is used to obtain ^Z

ijZijZi and PZi. 2EYLRXVO\IROORZLQJWKHVHWZRDSSURDFKHVOHDYHVWKHDJHQWVZLWKGLIIHUHQWIRUHFDVWV DQGUHVXOWVLQGLIIHUHQW$/0V,QWXLWLYHO\SXEOLFDWLRQRIWKHPRGHOLVPRUHYDOXDEOHWKDQ RQO\LQFUHDVLQJWKHGDWDVHWVRWKHFKRLFHRIWKHDSSURDFKPXVWPDWWHUIRURXUUHVXOWV,W VHHPVXQOLNHO\WKDWDOODJHQWVUHDGWKHFHQWUDOEDQNĳVSXEOLFDWLRQEXWFHUWDLQO\VRPHGR 0RUHRYHUWKHLUUHDGLQJLVRIWHQVKDUHGZLWKWKHUHVWRIWKHSRSXODWLRQLQIRUPRISULYDWH IRUHFDVWVHJSXEOLVKHGE\FRPPHUFLDOEDQNV$FFRUGLQJO\ZHGHFLGHGWRFRQVWUXFW WKHDJJUHJDWHDJHQWVĳIRUHFDVWDVDZHLJKWHGDYHUDJHRIIRUHFDWVWIURPWKHWZRDERYH DSSURDFKHVDVLQ0XWR

&

where mZ

iLVWKHDJJUHJDWHSULYDWHVHFWRUIRUHFDVWRIWKHYDULDEOHmimeZiVWDQGVIRUWKHIRUHFDVW EDVHGRQDGGLWLRQDOSURMHFWLRQGDWDDQGmZ

(13)

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3

PRGHOLHDQG+DYLQJQRGLUHFWPHDVXUHRISZHGHFLGHGWRWDNHDFRQVHUYDWLYH DSSURDFKDQGDVVXPHGIRURXUEHQFKPDUNVSHFLILFDWLRQWKDWRQO\RIDJHQWVNQRZWKH PRGHOZKLOHXVHWKHSURMHFWLRQWRDXJPHQWWKHLUGDWDVHWLHe :HFKHFNWKH UREXVWQHVVRIRXUUHVXOWVIRUGLIIHUHQWYDOXHVRIe.

The third variant K(DVVXPHVIXOONQRZOHGJHRQWKHVLGHRIHFRQRPLFDJHQWV7KLV

VHWXSZLWKQRDV\PPHWULFLQIRUPDWLRQPD\EHUHJDUGHGDVUHIHUULQJWRDFHQWUDOEDQN SXEOLVKLQJLWVIRUHFDVWHGSDWKRIIXWXUHSROLF\UDWHVWRJHWKHUZLWKDPDFURHFRQRPLF IRUHFDVWFRQGLWLRQDORQWKLVSDWK7KHSXEOLFFDQWKHQXVHGLUHFWO\WKHFHQWUDOEDQNIRUHFDVW DVLWVRZQ7HFKQLFDOO\DQGDUHVROYHGXQGHUUDWLRQDOH[SHFWDWLRQVZLWKWKHVDPH

timing assumptions as in K& and K'. As in K'LWLVDVVXPHGWKDWWKHFHQWUDOEDQNKDVIXOO DQGFRUUHFWNQRZOHGJHRIWKHHFRQRP\DQGWKHPRGHOLWXVHVDQGSXEOLVKHVFRQVLVWLQJRI HTXDWLRQVDQGLQGHHGGHSLFWVWKHDFWXDOODZRIPRWLRQRIWKHHFRQRP\

7KH LQIRUPDWLRQ VWUXFWXUH RI WKH YDULDQWV GHVFULEHG DERYH LV VXPPDULVHG LQ 7DEOH:HLQWHUSUHWWKHJDLQVIURPJRLQJIURPK& to K' as corresponding to publishing

DPDFURHFRQRPLFSURMHFWLRQDQGWKHJDLQVIURPJRLQJIURPK' to K( as corresponding to additionally showing an interest rate path.

Table 1

Information structure applied in the model

K& K' K(

central bank knows: IS equation Philips curve policy rule

IS equation Philips curve policy rule

public knows: –

)UDFWLRQŘe): IS equation, Philips curve Fraction e: projection

(additional data for estimation)

IS equation Philips curve policy rule

(14)

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4.1 Simulations

:HUXQVWRFKDVWLFVLPXODWLRQVLQRUGHUWRFRPSDUHFHQWUDOEDQNORVVHVXQGHUGLIIHUHQW VWDJHVRIWUDQVSDUHQF\GLVFXVVHGDERYH(DFKVLPXODWLRQUXQVSDQVRYHUIh^bSHULRGVIRU

ZKLFKWKHYDOXHVRIPj and ^DUHFRPSXWHG:HWDNHIh^b DQGEXUQWKHILUVW

W LQLWLDOIRUZHFRQVLGHUWKHPEHLQJWRRPXFKGHSHQGHQWRQLQLWLDOFRQGLWLRQV:H

DQDO\VHWKUHHVLPXODWLRQFDVHVHDFKZLWKGLIIHUHQWSROLF\UXOHFRHIILFLHQWVDFFRUGLQJWRWKH FODVVLILFDWLRQSUHVHQWHGLQVHFWLRQ,QDWKHRUHWLFDOVHWXSDFFRUGLQJWRFHQWUDOEDQN

ORVVLVFRPSXWHGRYHUWKHLQILQLWHKRUL]RQ,QVLPXODWLRQVZHUHVWULFWWKHKRUL]RQWR]

periods ahead since B]_{LVLQVLJQLILFDQWO\GLIIHUHQWIURP]HUR}8_{IRUKLJKHUYDOXHVRI}_]_6RWKH

central bank loss in period i is computed as:

=1

2₊

$

2+

+

+1

2

0LQLPL]DWLRQRIWKHDYHUDJHFHQWUDOEDQNORVV$/WRSLFNWKHSROLF\UXOHFRHIILFLHQWV IROORZV

HDI

=+1

7KHPLQLPL]DWLRQLVSHUIRUPHGQXPHULFDOO\7KHLQLWLDOYHFWRUIRUK( is [FjFP]= >@7KHLQLWLDOYHFWRUIRUK& and K' is the argminUHDFKHGIRUK(.

$JHQWVFDQFKRRVHGLIIHUHQWVDPSOHOHQJWKVRISDVWGDWDIRUWKHSXUSRVHRIOHDUQLQJ,Q

the baseline scenario it is assumed that the learning sample smplVWUHWFKHVRYHUSHULRGV

\HDUVZKLFKFRUUHVSRQGV to the perpetual learning gain K 2USKDQLGHVDQG:LOOLDPV

ILQGWKDWKSHUIRUPEHVWLQPRGHOOLQJ63)H[SHFWDWLRQV7KH\DOVRUHSRUWWKDW WKLVYDOXHLVLQOLQHZLWK6KHULGDQĳVDQDO\VLVRIH[SHFWDWLRQVIURPWKH/LYLQJVWRQ6XUYH\GDWD )RUWKHVDNHRIUREXVWQHVVZHDOVRDQDO\VHGLIIHUHQWYDOXHVRIsmpl,QWKHSURFHVVRIOHDUQLQJ WKHUHJUHVVLRQVUXQE\DJHQWVDUHWHVWHGIRUVWDWLRQDULW\6KRXOGWKLVWHVWEHEUHDFKHGWKHPRGHOVĳ FRHIILFLHQWVXVHGWRSURGXFHH[SHFWDWLRQVDUHVHWHTXDOWRWKHDYHUDJHRISDUDPHWHUVDSSOLHGLQ WKHSUHYLRXVSHULRGV,QSUDFWLVHZHIRXQGWKLVUHVWULFWLRQELQGLQJRQO\ZLWKQHJOLJLEOHIUHTXHQF\ 7KHPDLQSDUDPHWHUVDSSOLHGLQWKHEDVHOLQHVFHQDULRDUHVXPPDUL]HGLQ7DEOHEHORZ

4.2 Results

7KHUHVXOWVIRUWKHEDVHOLQHVFHQDULRDUHVXPPDULVHGLQ7DEOHVDQG,QRUGHUWR HDVLO\FRPSDUHWKHJDLQVIURPSXEOLVKLQJWKHPDFURHFRQRPLFPRGHODQGIURPSXEOLVKLQJ WKHSROLF\UXOHZHFDOFXODWHJDLQVGHILQHGDV

8 _:HWDNH_B_7KHQ_B_y _K₌_ļ iXQGHUOHDVWVTXDUHVOHDUQLQJZLWKLQILQLWHPHPRU\

(15)

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4

Table 2

Baseline scenario parametrization

hbea=80 e=0.8 G

K D S

SP Sj S^

B W Ih^bh

] L_j=4 L_^

where <^_VWDQGVIRUJDLQLQYDULDQW^ versus variant _DQG6A^ denotes average central bank ORVVLQYDULDQWL7KHIROORZLQJILQGLQJVVWHPIURPWKHEDVHOLQHVFHQDULRVLPXODWLRQV

ľ&HQWUDOEDQNORVVGHFUHDVHVZKLOHPRYLQJIURP:HVWWR(DVWLQWKH7DEOHIRUDQ\

SROLF\UXOH7KLVLQGLFDWHVWKDWDGRSWLQJIXUWKHUWUDQVSDUHQF\VWDJHVSD\VRII ľ,QDOOFDVHVJDLQVIRUK' vs. K&DUHPXFKKLJKHUWKDQIRUK( vs. K'. This points to

EHQHILWVIURPSXEOLVKLQJPDFURHFRQRPLFSURMHFWLRQVEHLQJVXEVWDQWLDOO\KLJKHUWKDQ JDLQVIURPDGGLWLRQDOO\VKRZLQJWKHIXWXUHLQWHUHVWUDWHSDWK)RULQVWDQFHXQGHUWKH RSWLPL]HGSROLF\UXOH275SXEOLFDWLRQRIFRQGLWLRQDOIRUHFDVWLPSURYHVFHQWUDOEDQN ORVVE\SHUFHQWFRPSDUHGWRLPSURYHPHQWRIRQO\SHUFHQWIROORZLQJWKH SXEOLFDWLRQRIDQXQFRQGLWLRQDOSDWKRIIXWXUHLQWHUHVWUDWHV ľ&RPSDULVRQRIFHQWUDOEDQNORVVHVXQGHUWKHUXOHRSWLPL]HGIRUUDWLRQDOH[SHFWDWLRQV 5(75DQGWKHRSWLPL]HGUXOH275FRQILUPVWKDWWKHFHQWUDOEDQNFDQEHQHILWIURP RSWLPL]LQJWKHSROLF\UXOHFRHIILFLHQWVVXEMHFWWRWKHDJHQWVĳDFWXDOLQIRUPDWLRQ)RU H[DPSOHFRPSDUHWKHORVVIRUK&XQGHU5(756A DQG2756A ļDSSO\LQJWKHUXOHRSWLPL]HGXQGHUWKHDVVXPSWLRQRIDJHQWVIROORZLQJUDWLRQDO H[SHFWDWLRQVIRUWKHDV\PPHWULFLQIRUPDWLRQFDVHK& can end up with disappointing

UHVXOWV,QGHHGHYHQWKHVWDQGDUG7D\ORUUXOH675SHUIRUPVEHWWHULQWKLVFDVH

6A 7KXVFHQWUDOEDQNVVKRXOGFRQVLGHUUHGHILQLQJSROLF\UXOHVWKH\IROORZ

ZKHQPRYLQJDORQJWKHODGGHURIWUDQVSDUHQF\VWDJHV

ľ7KHFRHIILFLHQWVRQLQIODWLRQDQGXQHPSOR\PHQWLQSROLF\UXOHGHFUHDVH_{along the}

:(GLUHFWLRQIRUWKHFDVHRIRSWLPL]HGSROLF\2757DEOH7KLVFDQEHLQWHUSUHWHG DVDQHHGWROLPLWWKHQHFHVVDU\GHJUHHRIFHQWUDOEDQNUHVSRQVLYHQHVVRQFHDJHQWV JHWPRUHLQIRUPDWLRQRQWKHHFRQRP\DQGFHQWUDOEDQNSUHIHUHQFHVLHZKHQ WUDQVSDUHQF\LQFUHDVHV6XFKDUHVXOWLVFRQVLVWHQWZLWKWKHFRQFHSWRIXVLQJWKH

central bank communication channel as support to other transmission channels.

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

GLIIHUHQWOHQJWKVRIWKHSDVWGDWDVSDQhbeaWKDWDJHQWVXVHIRUOHDUQLQJIRUGLIIHUHQW

IUDFWLRQVeRIDJHQWVXVLQJPDFURHFRQRPLFSURMHFWLRQVSXEOLVKHGE\WKHFHQWUDOEDQNWR

HVWLPDWHWKHPRGHODQGDOVRIRUGLIIHUHQWYDULDQFHVRIVKRFNVWRWKHLQWHUHVWUDWHUXOHSZ^. To HQDEOHFRPSDULVRQVDOOWKHUHPDLQLQJSDUDPHWHUVZHUHOHIWXQFKDQJHGDWWKHEHQFKPDUN VFHQDULRYDOXHVLHGXULQJHDFKVLPXODWLRQRQO\WKHYDOXHRIhbeae or SZ^ was altered. The

UDQJHRIhbeaXQGHUDQDO\VLVVSDQQHGIURPWRZLWKDVWHSRI,QFDVHRIeWKH

GRPDLQVWUHWFKHGIURPWRZLWKDVWHSDQGIRUSZ^ZHXVHGWKHYDOXHVRI EHQFKPDUNDQG _{:LWKWKHH[FHSWLRQRIFRHIILFLHQWRQXQHPSOR\PHQWLQ}_K'_vs._K(_{%XWWKHGLIIHUHQFHEHWZHHQWKHWZR} LVWLQ\DQGPD\VWHPIURPUDQGRPIOXFWXDWLRQVLQQXPHULFDOVLPXODWLRQVZHSHUIRUP

(16)

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4

Table 3

Average central bank loss and gains in the baseline scenario

Case nick Loss Gain (in per cent)

K& K' K( K' vs. K& K( vs. K'

Standard Taylor rule STR 95.85 82.83 80.92 13.59 2.30 rule optimized for RE

(variant V3) RETR 121.62 78.83 76.77 35.18 2.62 optimized rule OTR 95.81 78.83 76.77 17.72 2.61

Table 4

Taylor rule coefficients in the baseline scenario

Case nick Loss

K& K' K(

Standard Taylor rule STR FP=1.5

F_j Ř

FP=1.5

F_j Ř

FP=1.5

F_j Ř

rule optimized for RE (variant V3) RETR F_P=1.16 F_j Ř F_P=1.16 F_j Ř F_P=1.16 F_j Ř

optimized rule OTR FP

Fj Ř

F_P=1.17

Fj Ř

F_P=1.16

Fj Ř

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used by agents rises the central bank loss tends to be lower. This is in line with the intuition

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the remaining gains that can be achieved by additionally showing the interest rate path.

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(17)

Conclusions

5

Conclusions

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to start publishing interest rate paths. Although we strongly believe that most banks will

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Figure 1

Average central bank loss for different values of hbea under various monetary policy rules

Figure 2

Average central bank loss for different values of e under various monetary policy rules

40 60 80 100 120 140 160 80 85 90 95 100 105 110

average central bank loss

STR 40 60 80 100 120 140 160 75 85 95 105 115 125

average central bank loss

RETR 40 60 80 100 120 140 160 75 80 85 90 95 100 105 110 smpl smpl smpl

OTR V1 V2 V3 40 60 80 100 120 140 160 80 85 90 95 100 105 110

STR 40 60 80 100 120 140 160 75 85 95 105 115 125

RETR 40 60 80 100 120 140 160 75 80 85 90 95 100 105 110 smpl smpl smpl

OTR V1 V2 V3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 85 90 95 100 105 110

STR p 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 85 90 95 100 105 110

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Figure 3

Average central bank loss for different values of SZ^ under various monetary policy rules

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 60 80 100 120 140 160

RETR 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 70 80 90 100 110 120 130 p p

OTR V1 V2 V3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 60 80 100 120 140 160

RETR 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 70 80 90 100 110 120 130 p p

OTR V1 V2 V3 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 80 85 90 95 100 105 110 _i _i i

average central bank loss

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RETR 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 70 80 90 100 110 120

OTR 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 80 85 90 95 100 105 110 _i _i i

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The Relativity Theory Revisited: Is Publishing Interest Rate Forecasts Really so Valuable?