Regime-dependent impulse response functions in a Markov-switching vector autoregression model

BANK OF FINLAND

DISCUSSION PAPERS

11

•

2001

Michael Ehrmann – Martin Ellison –

Natacha Valla

Research Department

3.8.2001

Regime-dependent impulse

response functions

in a Markov-switching vector

autoregression model

Suomen Pankin keskustelualoitteita Finlands Banks diskussionsunderlag

KWWSZZZERIIL 6XRPHQ3DQNNL %DQNRI)LQODQG

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BANK OF FINLAND

DISCUSSION PAPERS

11

•

2001

Michael Ehrmann* – Martin Ellison** – Natacha Valla***

Research Department

3.8.2001

Regime-dependent impulse response

functions in a Markov-switching vector

autoregression model

The views expressed are those of the authors and do not necessarily reflect the views of the Bank of Finland.

The paper was finalized while Martin Ellison visited the Bank of Finland. We would like to thank Mike Artis, Stephen Cecchetti, Roger Farmer, Soren Johansen and Frank Smets for helpful comments.

* European Central Bank, [email protected]. This paper has been written before the author joined the ECB.

** European University Institute, [email protected]. *** European University Institute, [email protected].

Suomen Pankin keskustelualoitteita Finlands Banks diskussionsunderlag

http://www.bof.fi ISBN 951-686-723-5 ISSN 0785-3572 (print) ISBN 951-686-724-3 ISSN 1456-6184 (online)

Suomen Pankin monistuskeskus Helsinki 2001

3

Regime-dependent impulse response functions

in a Markov-switching vector autoregression model

Bank of Finland Discussion Papers 11/2001

Michael Ehrmann – Martin Ellison – Natacha Valla Research Department

Abstract

In this paper we introduce identifying restrictions into a Markov-switching vector autoregression model. We define a separate set of impulse responses for each Markov regime to show how fundamental disturbances affect the variables in the model GHSHQGHQW on the regime. We go to illustrate the use of these regime-dependent impulse response functions in a model of the U.S. economy. The regimes we identify come close to the “old” and “new economy” regimes found in recent research. We provide evidence that oil price shocks are much less contractionary and inflationary than they used to be. We show furthermore that the decoupling of the US economic performance from oil price shocks cannot be explained by “good luck” alone, but that structural changes within the US economy have taken place.

4

Tilasidonnaiset impulssivasteet markovilaisessa

kahden regiimin autoregressiomallissa

Suomen Pankin keskustelualoitteita 11/2001

Michael Ehrmann – Martin Ellison – Natacha Valla Tutkimusosasto

Tiivistelmä

Tutkimuksessa kehitetään talouden toimintaa kuvaavia aikasarjamalleja siten, että niillä voidaan käsitellä talouden rakenteiden tilamuutoksia. Tämä tehdään liittä-mällä identifioivia rajoitteita markovilaiseen usean tilan vektoriautoregressiomal-liin. Kullekin talouden tilalle määritellään omat impulssivasteensa, niin että talou-den reaktiot häiriöihin riippuvat tilasta, jossa talous on. Näitä tilasidonnaisia im-pulssivasteita havainnollistetaan Yhdysvaltain taloutta kuvaavalla mallilla. Tutki-muksessa tunnistettavat talouden tilat vastaavat läheisesti ”vanhan talouden” ja ”uuden talouden” regiimejä, jotka ovat tulleet esiin viimeaikaisissa tutkimuksissa. Tulosten mukaan öljyn hintasokkien vaikutukset eivät nykyisin ole yhtä kontrak-tiivisia ja inflatorisia kuin aiemmin. Tutkimuksessa osoitetaan myös, että Yhdys-valtain talouden aiempaa vähäisempi herkkyys öljyn hintojen vaikutuksille ei rii-pu pelkästään sattumasta, vaan johtuu taloudessa tapahtuneista rakennemuutoksis-ta.

5

Contents

2.1 A Markov-switching vector autoregression model ... 8

2.2 Estimation... 9

2.3 Identification... 10

2.4 Regime-dependent impulse response functions ... 10

2.5 Bootstrapping ... 12

3 An illustrative example ... 13

4 Conclusions... 19

References... 21

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Rlo sulfhv wkhpvhoyhv vkrz d glhuhqw sdwwhuq lq wkhlu uhwxuq wr edvholqh1 Lq uhjlph 4/ wkh| duh pxfk pruh shuvlvwhqw wkdq lq uhjlph 51 Wklv pljkw eh dq h{sodqdwlrq zk| wkh rxwsxw uhvsrqvh lv pruh surwudfwhg lq wklv uhjlph1

Lq rughu wr hydoxdwh zkhwkhu wkh uhjlph0ghshqghqfh ri rxu lpsxovh uh0 vsrqvhv frqyh|v dgglwlrqdo lqirupdwlrq/ lw lv khosixo wr frpsduh wkh uhvxowv wr wkrvh ri d frqyhqwlrqdo YDU1 Iljxuh 6 uhsruwv wkh lpsxovh uhvsrqvhv wr dq rlo sulfh vkrfn/ zklfk kdyh ehhq fdofxodwhg lq h{dfwo| wkh vdph zd| dv ehiruh/ exw zlwkrxw doorzlqj iru Pdunry vzlwfklqj uhjlphv1 Reylrxvo|/ wkh uhvsrqvhv duh dq dyhudjh ri wkrvh iru wkh wzr vhsdudwh uhjlphv lq jxuh 51 Vhyhudo srlqwv duh zruwk phqwlrqlqj khuh1 Iluvwo|/ lq rughu wr jdxjh wkh hhfwv ri wkh 4<<<25333 rlo sulfh vkrfn rq wkh XV hfrqrp|/ d frqyhqwlrqdo YDU dqdo|vlv zrxog kdyh ehhq plvohdglqj1 Qrw dffrxqwlqj iru wkh glhuhqfhv dfurvv uhjlphv uhvxowv lq lpsxovh uhvsrqvhv zklfk xqghuhvwlpdwh wkh hhfwv lq uhjlph 4/ zkhuhdv wkh| ryhuhvwlpdwh wkh frqvhtxhqfhv ri dq rlo sulfh vkrfn lq uhjlph 5/ wkh fxuuhqw 49

uhjlph1 Lq d frqyhqwlrqdo YDU hvwlpdwh/ Ghudyl dqg Khjml +4<<5/ s1 4, irxqg wkdw d qhjoljleoh shufhqwdjh ri lq dwlrq*v iruhfdvw huuru yduldqfh fdq eh dw0 wulexwdeoh wr lqfuhdvhv lq wkh sulfh ri rlo  zklfk fdq eh gxh wr pl{hg hylghqfh ryhu wkhlu vdpsoh shulrg 4<:3 wr 4<<31

0 10 20 30 40 50 60 70 80 90 100 -.1 0 Capacity Utilisation 0 10 20 30 40 50 60 70 80 90 100 0 .0005 .001

CPI excl. energy

0 10 20 30 40 50 60 70 80 90 100

0 .5 1

Oil Price

Iljxuh 6= Uhvsrqvhv wr dq rlo sulfh vkrfn lq d frqyhqwlrqdo YDU Dqrwkhu lqwhuhvwlqj dvshfw ri wklv jxuh lv wkdw wkh errwvwudsshg huuru edqgv duh qrw rqo| kljko| dv|pphwulf/ exw vrphwlphv gr qrw hyhq zuds wkh srlqw hvwlpdwh1 Wklv lv d vljq iru vhulrxvo| qrq0qrupdo uhvlgxdov lq wkh hvwlpdwlrq/ d vxvslflrq zklfk fdq eh vxevwdqwldwhg e| orrnlqj dw wkh uhvlgxdov lq jxuh D6 lq wkh dsshqgl{1 Wkh uhvlgxdov lq wkh frqyhqwlrqdo YDU vxhu iurp DUFK hhfwv dqg duh e| qr phdqv qrupdoo| glvwulexwhg1 Rq wkh rwkhu kdqg/ wkh Pdunry vzlwfklqj uhvlgxdov duh pxfk ehwwhu ehkdyhg/ dv fdq eh vhhq e| wkh pxfk pruh v|pphwulfdoo| errwvwudsshg huuru edqgv dqg e| orrnlqj dw d sorw ri wkh uhvlgxdov dqg dffruglqj whvw vwdwlvwlfv lq jxuhv D4 dqg D51

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ehhq dujxhg wkdw jrrg pdfurhfrqrplf srolflhv kdyh uhgxfhg wkh exvlqhvv f|foh yrodwlolw|145

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45_{Vhh Fodulgd/ Jdol dqg Jhuwohu +5333,1}

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hfrqrp| wrgd|/ lq uhjlph 5B Iljxuh 8 dqvzhuv wklv txhvwlrq1 Qdwxudoo|/ wkh uhvsrqvh ri rxwsxw dqg sulfhv zrxog eh pruh surwudfwhg wkdq wkh| duh rwkhu0 zlvh lq uhjlph 51 Krzhyhu/ wkh pdjqlwxgh ri uhvsrqvhv vwloo grhv qrw frpsduh wr wkrvh irxqg lq uhjlph 41 Zh fdq wkhuhiruh frqfoxgh wkdw wkh vhyhuh rxwsxw frqwudfwlrqv dqg sulfh lqfuhdvhv wkdw iroorz rlo sulfh vkrfnv lq uhjlph 4 duh qrw rqo| d frqvhtxhqfh ri wkh shuvlvwhqf| ri wkh vkrfnv> vkrfnv zlwk wkh vdph sdwwhuq lq uhjlph 5 gr vwloo fdxvh pxfk ohvv glvuxswlrq lq rxwsxw dqg sulfhv1

0 10 20 30 40 50 60 70 80 90 100 -.03 -.02 -.01 0 Capacity Utilisation 0 10 20 30 40 50 60 70 80 90 100 .0005 .001

CPI excl. energy

0 10 20 30 40 50 60 70 80 90 100

.5 1

Oil Price

Iljxuh 8= Hhfwv ri d uhjlph 40w|sh rlo vkrfn klwwlqj lq uhjlph 5

7 Frqfoxvlrqv

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46_{Wklv pljkw eh d uhdvrqdeoh dvvxpswlrq iru rlo sulfh vkrfnv/ zklfk prvw suredeo| ghshqg}

pxfk pruh rq RSHF*v ehkdylrxu1

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Uhihuhqfhv

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CPI excl. energy

1975 1980 1985 1990 1995 2000

-5 0 5

Oil Price

Iljxuh D4= Uhvlgxdov lq wkh Pdunry Vzlwfklqj YDU

1975 1980 1985 1990 1995 2000 -2.5 0 2.5 capacity utilisation 1975 1980 1985 1990 1995 2000 -2.5 0 2.5 5

CPI excl. energy

1975 1980 1985 1990 1995 2000

-5 0 5

Oil Price

Iljxuh D4= Uhvlgxdov lq wkh Pdunry Vzlwfklqj YDU

1975 1980 1985 1990 1995 2000 0

5 CPI excluding energy

1975 1980 1985 1990 1995 2000 -2.5 0 2.5 5 capacity utilisation 1975 1980 1985 1990 1995 2000 -5 0 5 Oil price

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%$1.2)),1/$1'',6&866,213$3(56

ISSN 0785-3572, print; ISSN 1456-6184, online

1/2001 Risto Herrala $QDVVHVVPHQWRIDOWHUQDWLYHOHQGHURIODVWUHVRUWVFKHPHV 2001. 28 p. ISBN 951-686-701-4, print; ISBN 951-686-702-2, online. (TU) 2/2001 Esa Jokivuolle – Karlo Kauko 7KHQHZEDVHODFFRUGVRPHSRWHQWLDO

LPSOLFDWLRQVRIWKHQHZVWDQGDUGVIRUFUHGLWULVN 2001. 23 p.

ISBN 951-686-703-0, print; ISBN 951-686-704-9, online. (RM)

3/2001 Mika Kortelainen $FWXDODQGSHUFHLYHGPRQHWDU\SROLF\UXOHVLQDG\QDPLF

JHQHUDOHTXLOLEULXPPRGHORIWKHHXURDUHD 2001. 76 p.

ISBN 951-686-705-7, print; ISBN 951-686-706-5, online. (TU)

4/2001 Martin Ellison 6WDELOLVDWLRQELDVLQPRQHWDU\SROLF\XQGHUHQGRJHQRXV

SULFHVWLFNLQHVV 2001. 20 p. ISBN 951-686-707-3, print; ISBN 951-686-708-1,

online. (TU)

5/2001 Erkki Koskela – Rune Stenbacka (TXLOLEULXPXQHPSOR\PHQWZLWKFUHGLW

DQGODERXUPDUNHWLPSHUIHFWLRQV 2001. 35 p. ISBN 951-686-709-X, print;

ISBN 951-686-710-3, online. (TU)

6/2001 Jarmo Pesola 7KHUROHRIPDFURHFRQRPLFVKRFNVLQEDQNLQJFULVHV 2001. 61 p. ISBN 951-686.713-8, print; ISBN 951-686-714-6, online. (TU)

7/2001 Anssi Rantala 'RHVPRQHWDU\XQLRQUHGXFHHPSOR\PHQW" 2001. 36 p. ISBN 951-686-715-4, print; ISBN 951-686-716-2, online. (TU)

8/2001 Tuomas Välimäki )L[HGUDWHWHQGHUVDQGWKHRYHUQLJKWPRQH\PDUNHW

HTXLOLEULXP 2001. 72 p. ISBN 951-686-717-0, print; ISBN 951-686-718-9,

online (TU)

9/2001 Morten L. Bech – Kimmo Soramäki *ULGORFNUHVROXWLRQLQLQWHUEDQN

SD\PHQWV\VWHPV 2001. 34 p. ISBN 951-686-719-7, print;

ISBN 951-686-720-0, online (RM)

10/2001 Antti Ripatti – Jouko Vilmunen 'HFOLQLQJODERXUVKDUH±(YLGHQFHRID

FKDQJHLQWKHXQGHUO\LQJSURGXFWLRQWHFKQRORJ\" 2001. 43 p.

ISBN 951-686-721-9, print; ISBN 951-686-722-7, online (TU)

11/2001 Michael Ehrmann – Martin Ellison – Natacha Valla 5HJLPHGHSHQGHQW

LPSXOVHUHVSRQVHIXQFWLRQVLQD0DUNRYVZLWFKLQJYHFWRUDXWRUHJUHVVLRQ PRGHO 2001. 24 p. ISBN 951-686-723-5, print; ISBN 951-686-724-3, online