Identifying the monetary transmission mechanism using structural breaks

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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 P A P E R S E R I E S E C B E Z B E K T B C E E K P

WORKING PAPER NO. 275

IDENTIFYING THE MONETARY

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WORKING PAPER NO. 275

IDENTIFYING THE MONETARY

TRANSMISSION MECHANISM USING

STRUCTURAL BREAKS

1

ANDREAS BEYER

2

_,

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

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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

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Table of Contents

Abstract 4

Non technical summary 5

1 Introduction 7

2 Related research 8

3 Identification through exclusion restrictions 9

4 A three equation model 12

5 The recoverable structure 15

6 A model with rational expectations 19

7 The recoverable structure with expectations 22

8 A description of the data 25

9 Estimation method 26

10 Non identification of the policy role 28

11 Two methods for identifying the recoverable structure 29

12 The results of our estimation procedure 30

13 Determinacy of equilibrium 32

14 Conclusions 34

Appendix 36

References 41

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(13)

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(14)

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(16)

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(17)

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(18)

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(19)

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(20)

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(29)

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43 Qrq Lghqwlfdwlrq ri wkh Srolf| Uxoh

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(30)

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(31)

soxv wkh frlqwhjudwhg yduldeohv

iCI2t3; CIt3; CIet3j;

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dqg YS

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45 Wkh Uhvxowv ri Rxu Hvwlpdwlrq Surfhgxuh

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88% Chi-squared with 12 degrees of freedom J = (.06) x 118 = 6.61 (2) GMM with cointegrating vectors 97% Chi-squared with 12 degrees of freedom J = (.04) x 118 = 4.72 (1) GMM with unrestricted levels P-value Distribution Test statistic Estimation method 88% Chi-squared with 12 degrees of freedom J = (.06) x 118 = 6.61 (2) GMM with cointegrating vectors 97% Chi-squared with 12 degrees of freedom J = (.04) x 118 = 4.72 (1) GMM with unrestricted levels P-value Distribution Test statistic Estimation method

Wdeoh 4= M0Vwdwlvwlfv iru wkh Uhfryhudeoh Vwuxfwxuh

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(33)

vdpsohv1 Zh frqfoxgh wkdw wkh uhvwulfwlrq ri d vwdeoh uhfryhudeoh vwuxfwxuh lv qrw uhmhfwhg e| wkh gdwd1

46 Ghwhuplqdf| ri Htxloleulxp

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(34)

5331zpi 89% 599 672 Volcker-Greenspan 80% 478 598 Burns-Miller Uniqueness conditional on existence Uniqueness Existence # Determinate equilibria in 1000 draws 89% 599 672 Volcker-Greenspan 80% 478 598 Burns-Miller Uniqueness conditional on existence Uniqueness Existence # Determinate equilibria in 1000 draws Wdeoh 5= Iuhtxhqf| ri H{lvwhqfh dqg Xqltxhqhvv lq 4333 Vlpxodwlrqv

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<_{Wkhvh uhvxowv zhuh rewdlqhg zlwk dq lpsohphqwdwlrq ri Vlpv dojrulwkp e| Oxeln dqg} Vfkruikhlgh/ dqg dq lpsohphqwdwlrq ri wkh T] ghfrpsrvlwlrq lq Jdxvv gxh wr Sdxo Vrghu0 olqg1 Vfkruikhlgh*v frgh lv dydlodeoh dw kwws=22zzz1hfrq1xshqq1hgx2vfkrui21 Vrghuolqg*v frgh lv dydlodeoh dw kwws=22zzz1kkv1vh2shuvrqdo2Svrghuolqg21 Zh duh lqghewhg wr Iudqn Vfkruikhlgh iru txlfno| fruuhfwlqj d exj lq dq hduolhu yhuvlrq klv surjudp1

(35)

47 Frqfoxvlrqv

Wkh pdlq lghd lq wklv sdshu lv wkdw rqh fdq xvh vwuxfwxudo fkdqjh lq rqh sduw ri wkh hfrqrp| wr ohduq vrphwklqj derxw sduwv ri wkh hfrqrp| wkdw gr qrw fkdqjh1 Zh surylghg dq h{dpsoh ri rxu dssurdfk e| vwxg|lqj XV prqhwdu| srolf| iurp 4<:3wkurxjk 4<<<1 Zh dujxhg wkdw wkhuh zdv d vljqlfdqw euhdn lq 4<:<=T6 zkhq Fkdlupdq Yrofnhu wrrn ryhu wkh khop iurp J1 Zlooldp Ploohu1 Wkh uhjlphv ri Duwkxu Exuqv dqg wkdw ri Zlooldp Ploohu fdq eh prghohg dv d vlqjoh vwdeoh sdudphwhu uxoh1 Vr fdq wkh uhjlphv ri Sdxo D1 Yrofnhu dqg wkdw ri Dodq Juhhqvsdq1 Exw wkh Exuqv0Ploohu dqg Yrofnhu0 Juhhqvsdq uhjlphv duh yhu| glhuhqw iurp hdfk rwkhu1 Jlyhq wkh idfw wkdw wkhuh zdv d fkdqjh lq wkh zd| wkdw wkh Ihg frqgxfwhg srolf| zh vkrzhg krz wr xvh wklv lqirupdwlrq wr lghqwli| vrph ri wkh sdudphwhuv ri d vwuxfwxudo udwlrqdo h{shfwdwlrqv prgho1 Zh uhihu wr wkh vhw ri sdudphwhuv wkdw fdq eh lghqwlhg dv wkh uhfryhudeoh vwuxfwxuh1

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(36)

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(37)

Dsshqgl{ D

Frqvlghu wkh prgho Yt' k [ i' iYt3i6EtdYtno nxCnUt: +D4,

Wkh frpsdqlrq irup uhihuuhg wr lq wkh wh{w lv ghqhg dv iroorzv/

W 5 9 9 9 9 9 7 6 t3kn2 t3kn f I f f 111 111 111 111 111 f f I f f f f I 6 : : : : : 8 XW t 5 9 9 9 9 9 7 EtEYtn Yt 111 Yt3kn2 Yt3kn 6 : : : : : 8' n W 5 9 9 9 9 9 7 f f f t3k I f f f 111 111 111 111 111 f f 111 f f f f I f 6 : : : : : 8 XW t3 5 9 9 9 9 9 7 Et3EYt Yt3 111 Yt3kn Yt3k 6 : : : : : 8 xW 5 9 9 9 9 7 x f f f f 6 : : : : 8Cn [W u 5 9 9 9 9 7 I f f f f 6 : : : : 8Utn [W 5 9 9 9 9 7 f I f f f 6 : : : : 8t; +D5, Qrwlfh wkdw t lv ghqhg lq urz 5 ri wklv v|vwhp wr eh YtEt3dYto:

(38)

Dsshqgl{ E

Wkh frpsohwh vwuxfwxudo prgho lq glhuhqfhv lv jlyhq e| Htxdwlrq +E4,/

DYt'

k3

[

i'

iDYt3i6EtdDYtno nY t3nxCnUt: +E4,

Frqvlghu wkh iroorzlqj htxlydohqw ohyhov uhsuhvhqwdwlrq/

Yt' k [ i' iYt3i6EtdYtno nxC nUt: +E5,

Wkh sdudphwhuv ri +E4, duh uhodwhg wr wkrvh ri +E5, e| wkh lghqwlwlhv/

n6; i k3 [ i'2 i; i' ; ::k; +E6, k [ i' in6:

Wklv wudqvirupdwlrq lv vlplodu/ exw qrw lghqwlfdo/ wr wkdw zklfk wxuqv d yhfwru dxwruhjuhvvlrq lqwr d yhfwru htxloleulxp fruuhfwlrq prgho1 Li wkh gdwd lv vwdwlrqdu|/ hvwlpdwlqj wkh prgho lq ohyhov lv htxlydohqw wr hvwlpdwlqj +E4,1 Li wkh gdwd lv qrq0vwdwlrqdu|/ exw frlqwhjudwhg/ wkh pdwul{ zloo kdyh uhgxfhg udqn zlwk d uhsuhvhqwdwlrq

fS'fe T efS;

zkhuh wkhT _{uhsuhvhqw +lqyduldqw, frlqwhjudwlqj yhfwruv1 E| irupxodwlqj wkh}

prgho lq glhuhqfhv/ zh duh deoh wr whvw k|srwkhvhv derxw wkh zd| wkdw wkh frlqwhjudwlqj yhfwruv hqwhu wkh vwuxfwxudo htxdwlrqv1

(39)

Dsshqgl{ F

Wklv Dsshqgl{ uhsruwv wkh xquhvwulfwhg sdudphwhu hvwlpdwhv iru wkh wzr dowhuqdwlyh hvwlpdwlrq vwudwhjlhv uhsruwhg lq Vhfwlrq <1

(0.81) 0.02 NA NA CI1 NA NA (2.27) 0.02 i lag 1 (0.56) -0.03 (0.63) 0.02 Di lag 1 NA NA (0.81) -0.17 πlag 1 (0.65) 1.98 (1.76) 0.57 Dπlag 1 NA NA (0.01) -0.005 u lag 1 (1.01) 0.15 (2.68) 0.39 Du lag 1 (0.77) 0.03 (0.06) 0.002 Di lag 2 (0.10) -0.14 (1.51) 0.12 Di lead 1 (0.33) -0.14 (2.15) -0.53 Dπlag 2 (1.39) 2.54 (1.17) 0.73 Dπlead 1 (0.72) 0.08 (1.17) 0.12 Du lag 2 (4.98) 0.98 (3.60) 0.47 Du lead 1 (0.01) 0.084 (0.36) 0.04 Di (0.55) 0.002 (0.84) 0.054 Constant t-stat Coef. t-stat Coef. t-stat Coef. t-stat Coef. (2) GMM CI (1) GMM LEVELS (2) GMM CI (1) GMM LEVELS Unemployment Equation (0.81) 0.02 NA NA CI1 NA NA (2.27) 0.02 i lag 1 (0.56) -0.03 (0.63) 0.02 Di lag 1 NA NA (0.81) -0.17 πlag 1 (0.65) 1.98 (1.76) 0.57 Dπlag 1 NA NA (0.01) -0.005 u lag 1 (1.01) 0.15 (2.68) 0.39 Du lag 1 (0.77) 0.03 (0.06) 0.002 Di lag 2 (0.10) -0.14 (1.51) 0.12 Di lead 1 (0.33) -0.14 (2.15) -0.53 Dπlag 2 (1.39) 2.54 (1.17) 0.73 Dπlead 1 (0.72) 0.08 (1.17) 0.12 Du lag 2 (4.98) 0.98 (3.60) 0.47 Du lead 1 (0.01) 0.084 (0.36) 0.04 Di (0.55) 0.002 (0.84) 0.054 Constant t-stat Coef. t-stat Coef. t-stat Coef. t-stat Coef. (2) GMM CI (1) GMM LEVELS (2) GMM CI (1) GMM LEVELS Unemployment Equation

(40)

2.27 0.02 NA NA Ci1 NA NA (1.76) -0.02 i lag 1 (1.70) -0.03 (0.82) -0.28 Di lag 1 NA NA (0.17) 0.033 πlag 1 (0.47) 0.12 (0.87) 0.26 Dπlag 1 NA NA (0.64) 0.009 U lag 1 (0.58) -0.03 (0.84) -0.12 DU lag 1 (1.46) 0.03 (0.70) -0.015 Di lag 2 (3.94) -0.13 (2.36) -0.16 Di lead 1 (0.43) -0.06 (0.38) -0.07 Dπlag 2 (0.58) -0.24 (0.94) 0.53 Dπlead 1 (1.26) -0.05 (0.46) -0.03 DU lag 2 (2.11) 0.17 (1.69) 0.18 DU lead 1 (2.49) 0.07 (0.62) 0.04 Di (1.67) -0.002 (0.045) -0.02 Constant t-stat Coef. t-stat Coef. t-stat Coef. t-stat Coef. (2) GMM CI (1) GMM LEVELS (2) GMM CI (1) GMM LEVELS Inflation Equation 2.27 0.02 NA NA Ci1 NA NA (1.76) -0.02 i lag 1 (1.70) -0.03 (0.82) -0.28 Di lag 1 NA NA (0.17) 0.033 πlag 1 (0.47) 0.12 (0.87) 0.26 Dπlag 1 NA NA (0.64) 0.009 U lag 1 (0.58) -0.03 (0.84) -0.12 DU lag 1 (1.46) 0.03 (0.70) -0.015 Di lag 2 (3.94) -0.13 (2.36) -0.16 Di lead 1 (0.43) -0.06 (0.38) -0.07 Dπlag 2 (0.58) -0.24 (0.94) 0.53 Dπlead 1 (1.26) -0.05 (0.46) -0.03 DU lag 2 (2.11) 0.17 (1.69) 0.18 DU lead 1 (2.49) 0.07 (0.62) 0.04 Di (1.67) -0.002 (0.045) -0.02 Constant t-stat Coef. t-stat Coef. t-stat Coef. t-stat Coef. (2) GMM CI (1) GMM LEVELS (2) GMM CI (1) GMM LEVELS Inflation Equation

Wdeoh F5= Hvwlpdwhv ri wkh Uhfryhudeoh Vwuxfwxuh 0 HT51

(0.95) -0.08 NA NA CI2 (2.15) -0.24 NA NA CI1 NA NA (3.27) -0.35 i lag 1 (2.65) 1.38 (2.10) 0.22 Di lag 1 NA NA (3.53) 6.73 π lag 1 (1.88) -0.47 (3.08) -5.94 Dπ lag 1 NA NA (5.68) -0.61 u lag 1 (0.33) 0.19 (2.41) -0.78 Du lag 1 (3.16) -2.50 (2.32) -0.31 Di lag 2 NA NA NA NA Di lead 1 (4.11) 15.18 (1.04) -2.48 Dπ lag 2 NA NA NA NA Dπ lead 1 (2.17) -1.66 (2.14) -0.69 DU lag 2 NA NA NA NA Du lead 1 NA NA NA NA Di (0.01) -0.00 (4.47) -3.00 Constant S.E. Coef. S.E. Coef. S.E. Coef. t-stat Coef. (2) FIML CI (1) GMM LEVELS (2) GMM CI (1) GMM LEVELS

Burns-Miller Reduced-Form Interest Rate Equation