EUROPEAN CENTRAL BANK WO R K I N G PA P E R S E R I E S WORKING PAPER NO. 206 EMPIRICAL ESTIMATES OF REACTION FUNCTIONS FOR THE EURO AREA BY DIETER GERDESMEIER AND BARBARA ROFFIA January 2003 EUROPEAN CENTRAL BANK WO R K I N G PA P E R S E R I E S WORKING PAPER NO. 206 EMPIRICAL ESTIMATES OF REACTION FUNCTIONS FOR THE EURO AREA1 BY DIETER GERDESMEIER2 AND BARBARA ROFFIA2 January 2003 1 We would like to thank Frank Smets for very useful suggestions and Frank Sedillot for his very useful help to apply the Chow and Lin procedure.We are also grateful to Vitor Gaspar, Hans-Joachim Klöckers, Klaus Masuch and Sergio Nicoletti Altimari and an anonymous referee for their comments. The opinions expressed herein are those of the authors and do not necessarily represent those of the European Central Bank. This paper can be downloaded without charge from http://www.ecb. int or from the Social Science Research Network electronic library at: http://papers.ssrn.com/abstract_id=xxxxxx 2 European Central Bank. Correspondence: European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany. Fax: +49-6913447604. E-mail addresses and telephone numbers: [email protected], +49-69-13447928; [email protected], +4969-13447432. © European Central Bank, 2003 Address Postal address Telephone Internet Fax Telex Kaiserstrasse 29 D-60311 Frankfurt am Main Germany Postfach 16 03 19 D-60066 Frankfurt am Main Germany +49 69 1344 0 http://www.ecb.int +49 69 1344 6000 411 144 ecb d All rights reserved. Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. The views expressed in this paper do not necessarily reflect those of the European Central Bank. ISSN 1561-0810 (print) ISSN 1725-2806 (online) Contents Abstract 4 Non-technical summary 5 1. Introduction 7 2. A brief review of the literature 8 3. Taylors original rule and related estimation issues 11 4. Estimates of reaction functions for the euro area 4.1 Reaction function specifications 4.2 The estimation technique and diagnostic tests 4.3 Estimation results 4.4 The equilibrium real interest rate 12 13 20 21 35 5. Conclusions 38 References 41 Annex A. Description of the data 43 Annex B. Calculation of potential output, monthly GDP, reference value for M3 growth and inflation objective 46 Annex C. Parameter constancy tests 51 Annex D. 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Specifications of the reaction functions 7KH IROORZLQJ UHDFWLRQ IXQFWLRQV ± ZKRVH UHVXOWV DUH FRQWDLQHG LQ WDEOHV EHORZ ± DUH HVWLPDWHG IRU WKH HXUR DUHD Table 1 D HT it = - r a + - r bp t + - r g yt - y + r it - + e t E HT it = - r a + - r bp t + - r g yt - y + r it - + e t Table 2 F HT it = - r a + - r bp t + - r g yt - y + - r d xt + r it - + e t Table 3 G HT it = - r a + - r bp t + + - r g yt - y + r it - + e t HT it = - r a + - r bp t - + - r g yt - y + r it - + e t HT it = - r a + - r b p t - p + - r g yt - y + r it - + e t HT it = - r a + - r bp t + + - r g yt - y + r it - + e t HT it = - r a + - r bp t - + - r g yt - y + r it - + e t HT it = a + bp t + g yt - y + e t HT it = - r a + - r bp t + - r g yt - y + r it - + e t HT it = - r a + - r bp t + - r g yt - y + r it - + e t Table 4 H HT it = - r a + - r bp t + - r g yt - y + r it - + e t Table 5 I HT it = - r a + - r bp t + - r g yt - y + r it - + e t Table 6 J HT it = - r a + - r bp t + - r g yt - y + r it - + e t HT it = a + bp t + g yt - y + e t HT it = - r a + - r bp t + - r g yt - y + - r d xt + r it - + e t HT it = a + bp t + g yt - y + d xt + e t HT it = - r a + - r bp t + - r g yt - y + r it - + e t 18 ECB Working Paper No 206 January 2003 Table 7 K HTEF it = - r a + - r b p t - p + - r g yt - y + - r d xt + r it - + e t Table 8 L HT it = a + bp t + g yt - y + d xt + e t HT it = - r a + - r bp t + - r g yt - y + - r d xt + - r l zt + r it - + e t Note: the ”*” next to the explanatory variables in some of the formulas in Table 1,Table 3 and Table 6 denotes an alternative measure of the correspondent variable with respect to the measure used in the baseline specification. 7KH GDWD VHW XVHG IRU WKH HVWLPDWLRQV LQFOXGHV PRQWKO\ GDWD JHQHUDOO\ FRYHULQJ WKH SHULRG 7KH YDOXHV RI WKH FRHIILFLHQWV WRJHWKHU ZLWK WKH VWDQGDUG HUURUV RI a r b DQG g DQGLQDGGLWLRQ d l ZKHQHYHULWDSSOLHVDUHUHSRUWHGLQWKHWDEOHVLQ6HFWLRQ:KHQWKHnSHULRGDKHDGLQIODWLRQLVXVHGDVH[SODQDWRU\YDULDEOHWKHHQGLQJSRLQWLVn PRQWKVSULRUWRWKHODWHVW 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8VLQJWKH1HZH\:HVW+$&FRQVLVWHQWFRYDULDQFHHVWLPDWHVGRHVQRWFKDQJHWKHSRLQWHVWLPDWHVRIWKHSDUDPHWHUVEXW RQO\WKHHVWLPDWHGVWDQGDUGHUURUV 7KH NH\ DGYDQWDJH RI *00 LV WKDW LW UHTXLUHV VSHFLILFDWLRQ RQO\ RI FHUWDLQ PRPHQW FRQGLWLRQV UDWKHU WKDQ WKH IXOO GHQVLW\VHH+DPLOWRQS )RUIXUWKHUGHWDLOVHH-RKQVWRQDQG'L1DUGRSDQGff 6HH%URZQ'XUELQDQG(YDQV )RUWKHFDOFXODWLRQRIWKHFULWLFDOYDOXHVVHH-RKQVWRQDQG'L1DUGRS ECB Working Paper No 206 January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igure 4 Actual and fitted interest rate for the euro area Percentage points 14 12 10 8 6 4 2 86 88 90 92 Actual interest rate 22 94 96 98 00 Fitted interest rate ECB Working Paper No 206 January 2003 Table 1 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a (1) r (2) b g (3) (4) d (5) r (6) R J-test (7) Wald Test 1 0.99 0.024 1.93 (0.15) Baseline specification 1 GMM Simple Taylor rule 1.80 (0.67) 0.87 (0.05) 1.93 (0.25) 0.28 (0.13) (-) 3.20 Alternative measurements of the output gap 2 GMM 3 GMM 4 GMM 5 GMM 6 GMM HP-filter on ind. prod. 2 1.21 (0.53) 0.82 (0.07) 2.17 (0.19) 0.28 (0.21) (-) 2.97 0.98 0.015 12.4 (0.00) Linear trend of ind. prod. 1.31 (0.59) 0.85 (0.06) 2.13 (0.22) 0.13 (0.10) (-) 3.01 0.98 0.018 14.5 (0.00) Quadratic trend on real GDP 1.50 (0.56) 0.84 (0.06) 2.07 (0.23) 0.21 (0.14) (-) 3.11 0.98 0.037 3.58 (0.03) HP-filter on real GDP 1.18 (0.54) 0.84 (0.06) 2.16 (0.20) 0.53 (0.64) (-) 2.92 0.98 0.019 11.1 (0.00) Linear trend on real GDP 1.89 (0.71) 0.86 (0.05) 1.89 (0.28) 0.38 (0.23) (-) 3.23 0.99 0.025 2.34 (0.31) Notes to Table 1: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. In the baseline case, a quadratic trend is used to calculate potential output (and, therefore, the output gap). 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 2 When potential output is computed using the Hodrick-Prescott filter, the smoothing parameter is set equal to 14400 for monthly data and 1600 for quarterly data. ECB Working Paper No 206 January 2003 23 2. Sensitivity of the results to the addition of other explanatory variables 7KHEDVHOLQHVSHFLILFDWLRQLVDPHQGHGWRLQFOXGHVRPHDGGLWLRQDOYDULDEOHVZKLFKPLJKWKDYHSOD\HG DWOHDVWLQFHUWDLQSHULRGVDQLPSRUWDQWUROHLQWKHLQWHUHVWUDWHVHWWLQJRIDFHQWUDOEDQNVHH7DEOH 7KHIROORZLQJLQWHUHVWLQJUHVXOWVKDYHEHHQIRXQG )LUVWO\ZKHQLQFOXGLQJWKHeuro effective exchange rateDQGWKH euro exchange rate vis-à-vis the US dollar±ERWKLQQRPLQDODQGUHDOWHUPVVHHHTHT±LWWXUQVRXWWKDWDVH[SHFWHGWKH VKRUWWHUPLQWHUHVWUDWHKDVSRVLWLYHO\UHVSRQGHGWRDGHSUHFLDWLRQRIWKHVHPHDVXUHVRIWKHH[FKDQJH UDWH+RZHYHUWKHFRHIILFLHQWVRIWKHVHYDULDEOHVDUHQRWIRXQGWREHVLJQLILFDQWRQDVWDWLVWLFDOEDVLVD UHVXOWZKLFKLVFRQVLVWHQWZLWKWKHHDUOLHUILQGLQJVE\*HUODFKDQG6FKQDEHO$ORQJWKHVDPH OLQHVDOVRWKHworldcommodity pricesDQGWKH86PRQHWDU\SROLF\WKHODWWHUPHDVXUHGE\WKHUS Federal Funds rateDUHQRWIRXQGWRKDYHDQ\DGGLWLRQDOVLJQLILFDQWLQIOXHQFHRQWKHOHYHORIWKHHXUR DUHDLQWHUHVWUDWHV 6HFRQGO\DYHU\LQWHUHVWLQJUHVXOWLVUHSUHVHQWHGE\WKHVLJQLILFDQFHRIWKHFRHIILFLHQWRIWKHGHYLDWLRQ RI 0 JURZWK IURP LWV UHIHUHQFH YDOXH ZKLFK LV GHQRWHG DV money growth gap indicator 7KLV YDULDEOHWXUQVRXWWRKDYHDSRVLWLYHLPSDFWRQWKHHXURDUHDLQWHUHVWUDWH7KLVUHVXOWLVYDOLGQRWRQO\ ZKHQWKHUHIHUHQFHYDOXHIRUPRQHWDU\JURZWKLVVHWWREHHTXDOWRòRYHUWKHZKROHVDPSOHSHULRG cfPRQH\JURZWKJDSDLQHTEXWDOVRZKHQWKHUHIHUHQFHYDOXHSULRUWRLVFDOFXODWHGDV WLPHYDU\LQJDQGGHULYHGDVWKHVXPRIWKHHVWLPDWHGDQQXDOLQIODWLRQREMHFWLYHDQGSRWHQWLDORXWSXW JURZWK PLQXV WKH PHGLXPWHUP YHORFLW\ WUHQG cf PRQH\ JURZWK JDS ELQ HT 7KLV ILQGLQJ ZRXOGLPSO\WKDWSULRUWRDILFWLWLRXVFHQWUDOEDQNLQWKHHXURDUHDFDQEHSRUWUD\HGDVKDYLQJ UHVSRQGHGWRDQH[FHVVPRQHWDU\JURZWKE\LQFUHDVLQJWKHLQWHUHVWUDWH 7KLUGO\ZHFRQVLGHUZKHWKHUVRPHPHDVXUHVRIVWRFNSULFHVPLJKWKDYHLQIOXHQFHGWKHUHVSRQVHRIWKH PRQHWDU\DXWKRULW\)RUWKLVSXUSRVHZHXVHWKH DJ Euro Stoxx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orking Paper No 206 January 2003 Table 2 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a (1) r (2) b g (3) (4) d (5) r (6) R J-test (7) Wald Test 1 Additional explanatory variables Nom. euro eff. exchange rate 2 0.88 (0.81) 0.95 (0.02) 1.59 (0.37) 0.72 (0.28) -0.17 (0.11) 1.78 0.99 0.091 0.86 (0.42) Real euro eff. exchange rate 0.80 (0.80) 0.95 (0.02) 1.70 (0.37) 0.68 (0.25) -0.18 (0.10) 1.85 0.99 0.092 0.77 (0.46) Nominal euro exchange rate visà-vis US $ 2.13 (1.29) 0.95 (0.03) 1.57 (0.61) 0.87 (0.59) -0.02 (0.04) 2.99 0.99 0.096 1.09 (0.34) Real euro exchange rate visà-vis US $ 2.13 (1.29) 0.95 (0.03) 1.55 (0.59) 0.87 (0.58) -0.02 (0.04) 2.96 0.99 0.096 GMM 0.95 (0.39) 11 Commodity prices 1.58 (2.16) 0.98 (0.03) 1.31 (1.43) 1.24 (1.54) 0.22 (0.30) 2.05 0.99 0.056 0.29 (0.75) Money growth gap (a) 3 2.05 (0.59) 0.87 (0.04) 1.50 (0.27) 0.24 (0.10) 0.49 (0.16) 2.80 0.99 0.035 3.45 (0.03) Money growth gap (b) 4 1.51 (0.69) 0.92 (0.03) 1.86 (0.30) 0.26 (0.18) 0.41 (0.17) 2.80 0.99 0.050 1.21 (0.30) Federal Funds rate 1.54 (1.41) 0.92 (0.02) 1.81 (0.28) 0.41 (0.18) 0.04 (0.20) 2.78 0.99 0.056 0.59 (0.55) DJ Euro Stoxx 50 5 -1.71 (1.04) 0.95 (0.02) 2.39 (0.32) 0.53 (0.28) 0.06 (0.03) 0.38 0.99 0.065 4.65 (0.01) DJ Euro Stoxx 50 corrected for ind. prod. growth -1.29 (0.93) 0.95 (0.02) 2.30 (0.34) 0.54 (0.28) 0.06 (0.03) 0.67 0.99 0.068 3.89 (0.02) DJ Euro Stoxx 50 corrected for real GDP growth 0.07 (0.70) 0.91 (0.02) 2.31 (0.25) 1.34 (0.67) 0.01 (0.01) 1.90 0.99 0.050 12.06 (0.00) Real DJ Euro Stoxx 50 corrected for ind. prod. growth -1.29 (0.93) 0.95 (0.02) 2.36 (0.33) 0.54 (0.28) 0.06 (0.03) 0.76 0.99 0.068 4.27 (0.02) Real DJ Euro Stoxx 50 corrected for real GDP growth 0.07 (0.70) 0.91 (0.02) 2.31 (0.26) 1.84 (0.67) 0.01 (0.01) 2.03 0.99 0.050 11.40 (0.00) 7 GMM 8 GMM 9 GMM 10 GMM 12 GMM 13 GMM 14 GMM 15 GMM 16 GMM 17 GMM 18 GMM 19 GMM Notes to Table 2: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. ECB Working Paper No 206 January 2003 25 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 2 All exchange rate variables used in the estimations are measured in terms of annual changes. In all the equations which include the exchange rate as an additional right-hand variable, the list of instruments is expanded by adding lagged values of M3 growth and the commodity prices. 3 The money growth gap (a) indicator is measured by the deviation of annual M3 growth from the ECB’s reference value for monetary growth (4½% per annum). 4 The money growth gap (b) indicator is measured by the deviation of the annual M3 growth from a timevarying reference value based on the ECB’s definition of price stability, the growth rate of potential output and the medium-term velocity trend based on the Calza-Gerdesmeier-Levy (CGL) money demand model (see Annex B for further detail). 5 The DJ Euro Stoxx 50 in eq.(15) is measured as annual growth rates in nominal terms. In eq.(16) and eq.(17) the additional indicators are derived as the differences between the annual changes in the DJ Euro Stoxx 50 and in industrial production, while eq.(18) and eq.(19) refer to the differences between annual changes in the DJ Euro Stoxx 50 and real GDP growth. Sensitivity of the results to a different modelling of the inflation term ,Q7DEOHZHDOORZIRUDGLIIHUHQWPRGHOOLQJRIWKHLQIODWLRQWHUPE\K\SRWKHVLVLQJWKDWWKHFHQWUDO EDQNPD\UHDFWDHLWKHUWRSDVWLQIODWLRQLHLWLVEDFNZDUGORRNLQJVHHHTRUEWKDWFHQWUDO EDQNV FDQ RQO\ DIIHFW LQIODWLRQ ZLWK VRPH ODJV LH DGRSWLQJ D IRUZDUGORRNLQJ 7D\ORU UXOH VHH HT,QERWKWKHVHFDVHVWKHFRHIILFLHQWRQWKHLQIODWLRQWHUPWXUQVRXWWREHVLJQLILFDQWO\GLIIHUHQW IURP]HURDQGQRWVWDWLVWLFDOO\GLIIHUHQWIURP0RUHRYHUWKHVHUHVXOWVDUHUREXVWWRWKHFKRLFHRI PRGHOOLQJ WKH LQIODWLRQ WHUP DV WKH GLIIHUHQFH EHWZHHQ WKH HXUR DUHD LQIODWLRQ UDWH DQG WKH FHQWUDO EDQN¶VDYHUDJHLPSOLFLW³LQIODWLRQREMHFWLYH´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a - p +RZHYHULWPXVWEHQRWHGWKDWWKHUHJUHVVLRQVIRULQIODWLRQPHDVXUHGLQWHUPVRIWKH+,&3LQGH[H[FOXGLQJXQSURFHVVHG IRRGDQGHQHUJ\SULFHVDUHUXQRQDVKRUWHUVDPSOHSHULRGVWDUWLQJLQ-DQXDU\GXHWRWKHODFNRIGDWDIRUWKHHXUR DUHD7KLVPLJKWKDYHLQIOXHQFHGWKHILQDOHVWLPDWHV )RU WKH *'3 GHIODWRU RQO\ D EDFNZDUGORRNLQJ HTXDWLRQ LV IRXQG WR SHUIRUP VDWLVIDFWRULO\ ,Q WKH FDVH RI D IRUZDUG ORRNLQJVSHFLILFDWLRQFRQYHUJHQFHSUREOHPVDULVH 26 ECB Working Paper No 206 January 2003 4. Sensitivity of the results to the exclusion of the smoothing term and a change in the frequency :H DOVR LQYHVWLJDWH WKH SHUIRUPDQFH RI WKH RULJLQDO 7D\ORU UXOH ZKLFK RPLWV WKH VPRRWKLQJ RI WKH LQWHUHVWUDWH,QWKLVFDVHWKHFRHIILFLHQWRILQIODWLRQLVDSSUR[LPDWHO\DQGVLJQLILFDQWO\GLIIHUHQWIURP ZKLOHWKHUHVSRQVHWRRXWSXWLVDOPRVWQHJOLJLEOHVHHHT 7KHUHVXOWVRIWKHEDVHOLQHVSHFLILFDWLRQDUHQRWVLJQLILFDQWO\DIIHFWHGZKHQTXDUWHUO\GDWDDUHXVHGVHH HT DQG HT ,Q WKLV FDVH WKH FRHIILFLHQW RQ LQIODWLRQ RXWSXW JDS LV VOLJKWO\ KLJKHU ORZHU ZKHQXVLQJLQGXVWULDOSURGXFWLRQFRPSDUHGWRUHDO*'3 $VDJHQHUDOREVHUYDWLRQWKHH[SODQDWRU\SRZHURIDOOWKHPRGHOVLVUDWKHUKLJK,QWKHOLWHUDWXUHWKLVLV XVXDOO\ DWWULEXWHG WR WKH LQFOXVLRQ RI WKH VPRRWKLQJ LQ LQWHUHVW UDWHV 2XU UHVXOWV FRQILUP WKLV YLHZ ,QGHHGLWFDQEHQRWHGWKDWLUUHVSHFWLYHO\RIWKHHVWLPDWLRQPHWKRGHPSOR\HGVHHDOVRWKHUHVXOWVLQ 7DEOHWKHH[SODQDWRU\SRZHURIWKHHTXDWLRQGHFUHDVHVVXEVWDQWLDOO\ZKHQWKHODJJHGLQWHUHVWUDWHLV RPLWWHG ECB Working Paper No 206 January 2003 27 Table 3 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a r (1) (2) b g d (3) (4) (5) r (6) R J-test (7) Wald Test 1 Alternative specifications 20 GMM 21 GMM 22 GMM 23 GMM 24 GMM 25 GMM 26 GMM 1 GMM 27 GMM 28 GMM Forward-looking inflation (t+6) 1.73 (2.34) 0.97 (0.01) 1.82 (0.99) 0.77 (0.55) (-) 2.95 0.99 0.051 0.55 (0.58) Backward-looking inflation (t-12) 1.79 (2.57) 0.98 (0.02) 1.53 (1.08) 1.39 (1.10) (-) 2.59 0.99 0.042 0.67 (0.51) Deviation of infl. from its target 5.50 (0.48) 0.93 (0.04) 1.91 (0.45) 0.38 (0.24) (-) 4.00 0.99 0.029 0.41 (0.66) HICP (excl. unpr. food & energy prices) forwardlook. infl. (t+12) 0.04 (0.52) 0.90 (0.02) 2.57 (0.20) 0.13 (0.13) (-) 2.40 0.99 0.027 29.7 (0.00) HICP (excl. unpr. food & energy prices) backwardlook. infl. (t-12) 0.64 (0.58) 0.93 (0.01) 2.05 (0.29) 0.90 (0.15) (-) 2.22 0.99 0.039 3.73 (0.03) GDP deflator backward-look. infl. (t-12) 0.58 (0.42) 0.86 (0.03) 2.09 (0.14) 0.51 (0.07) (-) 2.22 0.99 0.036 9.17 (0.00) No lagged interest rate 1.61 (0.55) (-) 2.08 (0.18) 0.06 (0.05) (-) 3.23 0.67 0.031 66.2 (0.00) Simple Taylor rule (monthly) 1.80 (0.67) 0.87 (0.05) 1.93 (0.25) 0.28 (0.13) (-) 3.20 0.99 0.024 1.93 (0.15) Baseline spec. (quarterly data) – ind. prod. 1.33 (0.94) 0.71 (0.18) 2.11 (0.34) 0.30 (0.34) (-) 3.00 0.95 0.001 3.23 (0.20) Baseline spec. (quarterly data) – real GDP 1.99 (1.02) 0.75 (0.16) 1.79 (0.42) 0.77 (0.91) (-) 3.18 0.96 0.014 1.26 (0.53) Notes to Table 3: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 28 ECB Working Paper No 206 January 2003 5. Sensitivity of the results to different sample periods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orking Paper No 206 January 2003 29 Table 4 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a r (1) (2) b g d (3) (4) (5) r 36 (6) R J-test (7) Wald Test 1 Eq.(1) estimated over different sample periods 1 1985:01– GMM 2002:02 29 1988:01– GMM 2002:02 30 1990:01– GMM 2002:02 31 1992:01– GMM 2002:02 32 1995:01– GMM 2002:02 2 33 1999:01– GMM 2002:02 1.80 (0.67) 0.87 (0.05) 1.93 (0.25) 0.28 (0.13) (-) 3.20 (3.7) 0.99 0.024 1.93 (0.15) 0.75 (0.59) 0.91 (0.04) 2.20 (0.25) 0.33 (0.17) (-) 2.55 0.99 0.046 4.43 (0.01) 0.17 (1.10) 0.96 (0.02) 1.89 (0.54) 0.57 (0.31) (-) 1.51 0.99 0.059 0.83 (0.44) 0.89 (1.06) 0.95 (0.02) 1.59 (0.58) 0.55 (0.36) (-) 1.78 (2.1) 0.99 0.074 0.03 (0.97) 2.19 (0.38) 0.90 (0.01) 1.02 (0.21) 0.01 (0.06) (-) 2.22 0.97 0.152 46.70 (0.00) 2.60 (0.20) 0.72 (0.04) 0.45 (0.10) 0.30 (0.03) (-) 1.78 0.97 0.148 145.5 (0.00) Notes to Table 4: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 2 The instrument list includes: lagged values (1 up to 6 lags) of the monthly annualised inflation rate and the output gap; lagged values rate (2 up to 3) of the short-term interest rate, the monthly annualised changes in nominal M3 and the annual changes in commodity prices. 7KHYDOXHVRIWKHHTXLOLEULXPUHDOLQWHUHVWUDWHUHSRUWHGLQEUDFNHWVUHIHUWRDQLQIODWLRQREMHFWLYHHTXDOWR 30 ECB Working Paper No 206 January 2003 6. Sensitivity of the results using different sets of Instrumental Variables $VDOUHDG\PHQWLRQHGLQ6HFWLRQWKHFKRLFHRIWKH,QVWUXPHQWV9DULDEOHV,9VHWWKDWZHXVHLQ RXUPDLQHVWLPDWLRQVDSDUWIURPEHLQJFRQVLVWHQWZLWKZKDWLVFRPPRQO\XVHGLQWKHOLWHUDWXUHFDQ DOVREHMXVWLILHGIRUUHDVRQVRISDUVLPRQ\,QIDFWDVWKHHVWLPDWHVLQ7DEOHEHORZVKRZDGGLWLRQDO LQVWUXPHQWV HDVLO\ WHQG WR ZLGHQ WKH VWDQGDUG HUURUV RI WKH FRHIILFLHQWV WKXV PDNLQJ WKH WHVWV PRUH LPSUHFLVH Table 5 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a r (1) (2) b g d (3) (4) (5) r (6) R J-test (7) Wald Test 1 Different instrumental variables (IV) 1 GMM 34 GMM 35 GMM 36 GMM Simple Taylor 1.80 (0.67) 0.87 (0.05) 1.93 (0.25) 0.28 (0.13) (-) 3.20 0.99 0.024 1.93 (0.15) 0.96 (1.82) 0.98 (0.01) 1.97 (0.76) 1.00 (0.68) (-) 2.42 0.99 0.098 0.94 (0.39) 0.60 (0.98) 0.96 (0.01) 1.97 (0.43) 0.47 (0.19) (-) 2.10 0.99 0.106 0.73 (0.48) 0.33 (0.55) 0.94 (0.01) 2.16 (0.22) 0.37 (0.09) (-) 2.07 0.99 0.143 4.51 (0.01) rule Simple Taylor rule 2 Simple Taylor rule 3 Simple Taylor rule 4 Notes to Table 5: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 2 The instrument set includes: lagged values (1 up to 6, 9 and 12 lags) of the monthly annualised inflation rate and the output gap; lagged values (2 up to 6, 9 and 12 lags) of the short-term interest rate and a constant. 3 The instrument set includes: lagged values (1 up to 6, 9 and 12 lags) of the monthly annualised inflation rate, the output gap and monthly annualised changes in nominal M3; lagged values (2 up to 6, 9 and 12 lags) of the short-term interest rate and a constant. 4 The instrument set includes: lagged values (1 up to 6, 9 and 12 lags) of the monthly annualised inflation rate, the output gap, monthly annualised changes in nominal M3 and in the nominal euro effective exchange rate; lagged values (2 up to 6, 9 and 12 lags) of the short-term interest rate, lagged values (2 up to 6) of the monthly annualised changes in commodity prices and a constant. ECB Working Paper No 206 January 2003 31 7. Sensitivity of the estimates to different estimation techniques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orking Paper No 206 January 2003 Table 6 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a r (1) (2) b g d (3) (4) (5) r (6) R J-test (7) Wald Test 1 GMM, OLS and TSLS estimations 1a 1.80 (0.67) 0.87 (0.05) 1.93 (0.25) 0.28 (0.13) (-) 3.20 0.99 0.024 1.93 (0.15) “ 2.41 (3.10) 0.98 (0.01) 1.03 (1.25) 1.78 (1.27) (-) 2.46 0.99 (-) 0.54 (0.58) “ 1.77 (0.59) 0.88 (0.04) 1.94 (0.23) 0.26 (0.12) (-) 3.18 0.99 (-) 2.28 (0.10) 1.61 (0.55) (-) 2.08 (0.18) 0.06 (0.05) (-) 3.23 0.67 0.031 66.2 (0.00) “ 1.88 (0.31) (-) 1.97 (0.11) 0.06 (0.03) (-) 3.34 0.66 (-) 82.5 (0.00) “ 1.25 (0.34) (-) 2.24 (0.12) 0.01 (0.04) (-) 3.11 0.68 (-) 86.47 (0.00) 1.51 (0.69) 0.92 (0.03) 1.86 (030) 0.26 (0.18) 0.41 (0.17) 2.80 0.99 0.050 1.21 (0.30) “ 4.39 (5.31) 0.99 (0.01) -0.01 (2.71) 2.18 (2.35) 0.28 (0.85) 2.92 0.99 (-) 0.25 (0.78) “ 2.843 (2.16) 0.96 (0.03) 1.18 (1.05) 0.71 (0.73) 0.36 (0.29) 3.11 0.99 (-) 0.05 (0.95) 2.18 (0.53) (-) 1.77 (0.21) -0.02 (0.05) 0.40 (0.11) 3.34 0.74 0.068 52.90 (0.00) “ 1.34 (0.31) (-) 2.04 (0.13) -0.10 (0.03) 0.42 (0.06) 2.90 0.75 (-) 149.90 (0.00) “ 1.07 (0.33) (-) 2.15 (0.13) -0.10 (0.04) 0.40 (0.06) 2.80 0.76 (-) 132.49 (0.00) 1.18 (0.54) 0.84 (0.06) 2.16 (0.20) 0.53 (0.64) (-) 2.92 0.98 0.019 11.1 (0.00) “ 0.48 (4.61) 0.99 (0.01) 1.54 (1.60) 7.89 (8.99) (-) 1.29 0.99 (-) 0.40 (0.67) “ 1.40 (0.58) 0.89 (0.04) 2.11 (0.21) 0.73 (0.64) (-) 3.07 0.99 (-) 5.70 (0.00) Simple Taylor rule GMM 1b OLS 1c TSLS 26a GMM No lagged interest rate 26b OLS 26c TSLS 13a GMM 13b Money growth gap (b) OLS 13c TSLS 37a GMM 37b No lagged interest rate & money growth gap (b) OLS 37c TSLS 5a GMM 5b HP-filter on real GDP 2 OLS 5c TSLS Notes to Table 6: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 2 When potential output is computed using the Hodrick-Prescott filter, the smoothing parameter is set equal to 14400 for monthly data and 1600 for quarterly data. ECB Working Paper No 206 January 2003 33 8. Sensitivity of the results to selected Taylor rule variants 7DEOH FRQWDLQV D FRPSDULVRQ RI VRPH YDULDQWV RI WKH 7D\ORU UXOH %HVLGHV WKH LQFOXVLRQ RI WKH GHYLDWLRQ RI LQIODWLRQ IURP LWV HVWLPDWHG REMHFWLYH VHH HTD WKHVH YDULDQWV DOVR LQFOXGH DV DGGLWLRQDOH[SODQDWRU\YDULDEOHVHLWKHUDWKHPRQH\JURZWKJDSELQGLFDWRUVHHHTERUEWKH FKDQJHV LQ UHDO DVVHW SULFHV FRUUHFWHG IRU HFRQRPLF DFWLYLW\ JURZWK VHH HTF %RWK DGGLWLRQDO H[SODQDWRU\YDULDEOHVWXUQRXWWRH[KLELWWKHH[SHFWHGVLJQDQGWREHVWDWLVWLFDOO\GLIIHUHQWIURP]HUR +RZHYHULQWKHODVWVSHFLILFDWLRQDOOFRHIILFLHQWHVWLPDWHVYDU\VXEVWDQWLDOO\ZLWKUHVSHFWWRWKRVHRI WKHEDVHOLQHHTXDWLRQVHHHT Table 7 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a r (1) (2) b g d (3) (4) (5) (6) r R J-test (7) Wald Test 1 Variants of eq.(22) 22a GMM 22b GMM 22c GMM Deviation of infl. from its target 5.50 (0.48) 0.93 (0.04) 1.91 (0.45) 0.38 (0.24) (-) 4.00 0.99 0.029 0.41 (0.66) Deviation of infl. from its target & money growth gap (b) 4.91 (0.44) 0.94 (0.03) 1.56 (0.50) 0.30 (0.23) 0.75 (0.23) 3.41 0.99 0.049 0.40 (0.67) Deviation of infl. from its target & DJ real Euro Stoxx 50 corrected for ind. prod. growth 2.21 (1.20) 0.97 (0.02) 2.65 (0.56) 0.72 (0.45) 0.08 (0.04) 0.71 0.99 0.065 3.21 (0.04) Notes to Table 7: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 7DEOH SUHVHQWV WKH UHVXOWV GHULYHG IURP D VLPLODU W\SH RI H[HUFLVH XVLQJ WKH VSHFLILFDWLRQ RI WKH 7D\ORU UXOH ZKLFK LQFOXGHV WKH PRQH\ JURZWK JDS E LQGLFDWRU VHH HTD ,Q WKLV UHVSHFW ZH FRQVLGHU WZR YDULDQWV WKH ILUVW RQH RPLWV WKH VPRRWKLQJ WHUP ZKHUHDV WKH VHFRQG RQH FRQWDLQV WKH DGGLWLRQDO H[SODQDWRU\ YDULDEOH UHSUHVHQWHG E\ WKH UHDO '- (XUR 6WR[[ FRUUHFWHG IRU HFRQRPLF JURZWK ,QGHSHQGHQWO\ RI WKH LQFOXVLRQ RI WKH VPRRWKLQJ RI WKH LQWHUHVW UDWH WKH FRHIILFLHQW RI WKH RXWSXW JDS LV QRW VWDWLVWLFDOO\ GLIIHUHQW IURP ]HUR 7KH RSSRVLWH UHVXOW KROGV IRU WKH VSHFLILFDWLRQ LQ 34 ECB Working Paper No 206 January 2003 HTZKHUHWKHRXWSXWJDSDQGDVVHWSULFHVHQWHUVLJQLILFDQWO\LQWRWKHHTXDWLRQZKHUHDVWKHPRQH\ JURZWKJDSLQGLFDWRULVQRWIRXQGWREHRIUHOHYDQFHDQ\ORQJHU Table 8 Estimates of Taylor rules in the euro area – sample period 1985:01-2002:02 No. of eq. Specification a r (1) (2) b g d (3) (4) (5) l r (6) R J-test (7) Wald Test 1 Variants of eq.(13) 13a GMM 37 GMM 38 GMM Money growth gap (b) 1.51 (0.69) 0.92 (0.03) 1.86 (0.30) 0.26 (0.18) 0.41 (0.17) (-) 2.80 0.99 0.050 1.21 (0.30) No lagged interest rate & money growth gap (b) 2.18 (0.53) (-) 1.77 (0.21) -0.02 (0.05) 0.40 (0.11) (-) 3.342 0.74 0.068 53.00 (0.00) Money growth gap (b) & real DJ Euro Stoxx 50 corrected for ind. prod. growth -1.24 (0.97) 0.95 (0.02) 2.36 (0.40) 0.55 (0.25) -0.07 (0.24) 0.06 (0.03) 0.80 0.99 0.072 2.77 (0.07) Notes to Table 8: The equations are estimated using the Generalised Method of Moments. When not specified otherwise, the instrument set includes lagged values (up to 6 lags) of inflation and the output gap. Industrial production is used to capture output developments on a monthly frequency, apart from the cases when the use of real GDP is explicitly mentioned. 1 p-value, null hypothesis that the coefficients on the output gap and the inflation term are jointly not statistically different from 0.5 and 1.5, respectively. 4.4 The equilibrium real interest rate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orking Paper No 206 January 2003 35 ,Q WKH ILUVW DSSURDFK ZH GHULYH WKH YDOXH RI WKLV YDULDEOH UHFXUVLYHO\ XVLQJ WKH WLPHYDU\LQJ HXUR DUHD LQIODWLRQ REMHFWLYH GHVFULEHG LQ $QQH[ % DVVXPLQJ WKDW GXULQJ WKH FRQYHUJHQFH SURFHVV WKLV LQIODWLRQREMHFWLYHLQHDFKUHFXUVLYHO\VHOHFWHGVDPSOHSHULRGFRLQFLGHGZLWKLWVODWHVWREVHUYDWLRQLQ WKHVDPHVHOHFWHGVDPSOHSHULRG)LJXUHEHORZVKRZVWKDWVRPHORFDOSHDNVZHUHSUHVHQWDURXQG WKHHDUO\VEXWVXEVHTXHQWO\WKHLPSOLFLWHTXLOLEULXPUHDOLQWHUHVWUDWHH[KLELWVDVWHHSGHFOLQHIURP RQZDUGV Figure 5 Recursive estimates of the equilibrium real interest rate in the euro area Percentage points per annum 8 7 6 5 4 3 1992 1994 1996 1998 2000 Equilibrium real interest rate ,QRXUVHFRQGDSSURDFKZHGHULYHWKHHTXLOLEULXPUHDOLQWHUHVWUDWHXVLQJD.DOPDQILOWHUIUDPHZRUN VHH$QQH['IRUIXUWKHUGHWDLO,QSDUWLFXODULWLVDVVXPHGWKDWLQWKHEDVHOLQHVSHFLILFDWLRQRIWKH 7D\ORUUXOHVHHHTWKHFRQVWDQWRXWRIZKLFKWKHHTXLOLEULXPUHDOLQWHUHVWUDWHLVGHULYHGIROORZV DQ DXWRUHJUHVVLYH SURFHVV RI RUGHU RQH LH LW LV DQ $5 SURFHVV ZKLOH WKH RWKHU FRHIILFLHQWV DUH DVVXPHGWREHFRQVWDQW,QRUGHUWRGHULYHWKHHTXLOLEULXPUHDOLQWHUHVWUDWHWKHWLPHYDU\LQJLQIODWLRQ REMHFWLYHLVXVHG,QWKLVFDVHWKHHTXLOLEULXPUHDOLQWHUHVWUDWHORRNVDELWPRUHYRODWLOH1HYHUWKHOHVV IURPRQZDUGVWKLVSURFHGXUHDOVRVKRZVDSURQRXQFHGGHFOLQH LQ WKH HTXLOLEULXP UHDO LQWHUHVW UDWHZKLFKUHDFKHGDYDOXHRIDURXQGDWWKHHQGRIWKHVDPSOH ,QWKLVH[HUFLVHZHXVHWKHEDVHOLQHVSHFLILFDWLRQVHH7DEOHHT 7KHUHDUHJRRGUHDVRQVWRDVVXPHWKDWWKHEHKDYLRXURIWKHUHDOLQWHUHVWUDWHIROORZVDUDQGRPZDON,QWKLVUHVSHFWRXU VSHFLILFDWLRQLVPRUHHQFRPSDVVLQJLQWKDWLWDOORZVIRUSDUDPHWHUYDOXHVGLIIHUHQWIURPRQH7KHUHVXOWLQJ FRHIILFLHQW KRZHYHULVZLWKDVWDQGDUGHUURURIWKXVEDVLFDOO\FRQILUPLQJWKHUDQGRPZDONK\SRWKHVLV 36 ECB Working Paper No 206 January 2003 Figure 6 Time-varying estimate of the euro area equilibrium real interest rate Percentage points per annum 10 8 6 4 2 0 -2 86 88 90 92 94 96 98 00 Equilibrium real interest rate ,WWXUQVRXWWKDWWKHWDUJHWLQWHUHVWUDWHGHULYHGIURPWKH7D\ORUUXOHVSHFLILFDWLRQHVWLPDWHGXVLQJWKH .DOPDQILOWHUVHHPVWRWUDFNTXLWHZHOOWKHSDWWHUQRIWKHVKRUWWHUPLQWHUHVWUDWHVHHILJXUHEHORZ 7KLVUHVXOWKROGVDOVRZKHQDEDFNZDUGORRNLQJVSHFLILFDWLRQLVDGRSWHG ECB Working Paper No 206 January 2003 37 Figure 7 Actual and target interest rates implied by the Taylor rule (baseline specification, eq.(1)) Percentage points per annum 14 12 10 8 6 4 2 0 86 88 90 92 Target interest rate 5. 94 96 98 00 Actual interest rate Conclusions 7KLVSDSHUKDVLQYHVWLJDWHGWKHLPSDFWRIDQXPEHURIYDULDEOHVRQWKHGHFLVLRQVRIDILFWLWLRXVFHQWUDO EDQNLQWKHHXURDUHDLQLWV VHWWLQJRIWKHSROLF\LQWHUHVWUDWHRYHUWKHODVWWZRGHFDGHV7KHH[HUFLVH KDV DOVR FRQVLGHUHG D 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PARAMETER CONSTANCY TESTS 7KLVDQQH[SURYLGHVWKHUHVXOWVRIVRPHVWDELOLW\DQGVSHFLILFDWLRQWHVWVIRUVHOHFWHGPRQHWDU\SROLF\ UHDFWLRQIXQFWLRQV,QWKLVUHVSHFWZHIRFXVRQWKHZLGHO\NQRZQCusumDQGCusum of Squares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igure 12 Specification and diagnostics tests - baseline specification, eq.(1) Cusum Cusum of Squares 40 1.2 30 1.0 20 0.8 10 0.6 0 0.4 -10 0.2 -20 0.0 -30 -0.2 -40 1992 1994 Upper band 1996 1998 Lower band ECB Working Paper No 206 January 2003 2000 Cusum 1990 1992 1994 1996 1998 2000 Cusum of Squares Lower band Upper band 51 Figure 13 Specification and diagnostics tests - baseline specification without lagged interest rate, eq.(26) Cusum Cusum of Squares 40 1.2 30 1.0 20 0.8 10 0.6 0 0.4 -10 0.2 -20 0.0 -30 -0.2 -40 1992 1994 Upper band 1996 1998 Lower band 1992 2000 1994 1996 1998 2000 Cusum of Squares Lower band Upper band Cusum Figure 14 Specification and diagnostics tests - baseline specification with the money growth gap (b) indicator and no lagged interest rate, eq.(37a) Cusum Cusum of Squares 40 1.2 30 1.0 20 0.8 10 0.6 0 0.4 -10 0.2 -20 0.0 -30 -0.2 -40 1992 1994 Upper band 52 1996 1998 Lower band 2000 Cusum 1992 1994 1996 1998 2000 Cusum of Squares Lower band Upper band ECB Working Paper No 206 January 2003 ANNEX D. 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