WORKING PAPER SERIES STOCKS, BONDS, MONEY MARKETS AND EXCHANGE RATES MEASURING INTERNATIONAL FINANCIAL TRANSMISSION NO.

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1 WORKING PAPER SERIES NO. 452 / MARCH 25 STOCKS, BONDS, MONEY MARKETS AND EXCHANGE RATES MSURING INTERNATIONAL FINANCIAL TRANSMISSION by Michael Ehrmann, Marcel Frazscher and Robero Rigobon

2 WORKING PAPER SERIES NO. 452 / MARCH 25 STOCKS, BONDS, MONEY MARKETS AND EXCHANGE RATES MSURING INTERNATIONAL FINANCIAL TRANSMISSION by Michael Ehrmann 2, Marcel Frazscher 3 and Robero Rigobon 4 In 25 all publicaions will feaure a moif aken from he 5 banknoe. This paper can be downloaded wihou charge from hp:// or from he Social Science Research Nework elecronic library a hp://ssrn.com/absrac_id= We are graeful o Terhi Jokipii for excellen research assisance.we also would like o hank an anonymous referee for he Working Paper series, as well as Jon Faus, Dimirios Malliaropulos, Mark Spiegel, Cedric Tille and he paricipans of he -IMF conference on Global financial inegraion, sabiliy and business cycles, of he New York Fed conference on Financial globalizaion and seminars a Triniy College Dublin and a Frankfur Universiy for commens and suggesions.this paper presens he auhors personal views and does no necessarily reflec he views of he European Cenral Bank. 2 European Cenral Bank, Kaisersrasse 29, D 63 Frankfur, Germany; 3 European Cenral Bank, Kaisersrasse 29, D 63 Frankfur, Germany; 4 Massachuses Insiue of Technology, Cambridge MA , A;

3 European Cenral Bank, 25 Address Kaisersrasse Frankfur am Main, Germany Posal address Posfach Frankfur am Main, Germany Telephone Inerne hp:// Fax Telex 4 44 ecb d All righs reserved. Reproducion for educaional and noncommercial purposes is permied provided ha he source is acknowledged. The views expressed in his paper do no necessarily reflec hose of he European Cenral Bank. The saemen of purpose for he Working Paper Series is available from he websie, hp:// ISSN 56-8 (prin) ISSN (online)

4 CONTENTS Absrac 4 Non-echnical summary 5. Inroducion 7 2. Relaed lieraure 9 3. Measuring domesic and inernaional financial Inegraion 3. The srucural-form and he reduced-form models 3.2 Idenificaion hrough heeroskedasiciy Idenificaion resricions Conrolling for common shocks and idenified macro shocks 8 4. Resuls 9 4. Domesic ransmission Inernaional ransmission Response of he exchange rae Variance decomposiion Robusness 3 6. Conclusions 32 References 34 Tables 38 Figures 44 European Cenral Bank working paper series 46 March 25 3

5 Absrac The paper presens a framework for analyzing he degree of financial ransmission beween money, bond and equiy markes and exchange raes wihin and beween he Unied Saes and he euro area. We find ha asse prices reac sronges o oher domesic asse price shocks, and ha here are also subsanial inernaional spillovers, boh wihin and across asse classes. The resuls underline he dominance of markes as he main driver of global financial markes: financial markes explain, on average, more han 25% of movemens in euro area financial markes, whereas euro area markes accoun only for abou 8% of asse price changes. The inernaional propagaion of shocks is srenghened in imes of recession, and has mos likely changed in recen years: prior o EMU, he paper finds smaller inernaional spillovers. JEL classificaion number: E44, F3, C5 Keywords: inernaional financial markes; inegraion; ransmission; financial marke linkages; idenificaion; heeroskedasiciy; asse pricing; Unied Saes; euro area. 4 March 25

6 Non-echnical summary Financial markes have become increasingly inegraed, boh domesically and inernaionally. The naure of his inegraion and he ransmission channels hrough which shocks dissipae are, however, sill no well undersood. One srand of he lieraure focuses exclusively on spillovers across differen domesic asse prices, whereas anoher srand concenraes on inernaional spillovers only for individual asse prices. However, undersanding he increasingly close domesic and inernaional linkages of asse prices requires a complee and comprehensive modeling of all ransmission channels ha are a play. In his paper we measure he inensiy of he ransmission mechanisms among differen asse markes wihin a counry, and across counries. The main limiaion he lieraure has faced in measuring hese propagaion channels has been he endogeneiy of asse prices. In his paper, we esimae he propagaion of shocks by modeling each asse price wih a mulifacor model, and hen using he heeroskedasiciy ha exiss in he daa o esimae he conemporaneous financial ransmission coefficiens. More precisely, we make idenifying assumpions in order o solve he model. These assumpions are well in line wih VAR and moneary policy models now sandard in he lieraure. For insance, we inerpre innovaions o he shor rae as moneary policy shocks, o he long rae as inflaionary expecaions, o he sock marke as produciviy or supply shocks, and o he exchange rae as relaive demand shocks. Under hese inerpreaions, we can resric he signs of several coefficiens ha allow us o esimae he model. We use his approach o analyze he naure of financial inegraion and he ransmission channels wihin as well as beween he wo larges economies in he world he Unied Saes and he euro area. The empirical model concenraes on daily reurns over a 6-year period of for seven asse prices: shor-erm ineres raes, bond yields and equiy marke reurns in boh economies, as well as he exchange rae. The resuls of he paper underline he imporance of inernaional spillovers, boh wihin asse classes as well as across financial markes. Alhough he sronges inernaional ransmission of shocks akes place wihin asse classes, we find evidence ha inernaional cross-marke spillovers are significan, boh saisically as well as economically. For insance, shocks o shor-erm ineres raes exer a subsanial influence on euro area bond yields and equiy markes, and in fac explain as much as % of overall euro area bond marke movemens. Bu he ransmission of shocks also runs in he opposie direcion as in paricular shor-erm ineres raes of he euro area have a significan impac on bond and equiy markes. Overall, financial markes explain on average more han 25% of euro area financial marke movemens in he period , whereas euro area markes accoun for 8% of he variance of asse prices. March 25 5

7 A second key resul of he paper is ha in almos all cases he direc ransmission of financial shocks wihin asse classes is magnified subsanially, mosly by more han 5%, hrough indirec spillovers hrough oher asse prices. These wo resuls underline ha a beer undersanding of financial linkages requires he modeling of inernaional cross-marke financial linkages, which so far has been missing in he lieraure. We also confirm some familiar resuls of he lieraure as, in paricular, we find ha financial markes are mosly driven by counry-specific and marke-specific facors. However, we deec a rich ineracion beween asse prices domesically and our mehodology allows us o quanify domesic financial marke ransmissions much more accuraely by conrolling for foreign and oher ypes of shocks. A highly revealing finding is he difference in he asse price ineracion wihin markes versus wihin euro area markes. For he, we find ha shor-erm ineres raes reac significanly o changes in domesic equiy markes, whereas euro area shor-erm raes are no affeced by sock markes. By conras, euro area shor raes and equiy markes are more responsive o shocks in bond yields and exchange raes han markes. These findings hus also idenify some imporan differences in he financial ransmission processes wihin he wo economies, which may reflec differences in economic srucure, in he degree of openness as well as differen policy objecives. Finally, we conduc several sensiiviy ess and show ha he resuls are broadly robus, alhough we find some suggesive indicaion ha he inernaional ransmission channel has inensified over ime, and in paricular since EMU. Furhermore, we find ha he inernaional propagaion of shocks is srenghened in imes of recession. 6 March 25

8 I. Inroducion Financial markes have become increasingly inegraed, boh domesically and inernaionally. The naure of his inegraion and he ransmission channels hrough which shocks dissipae are, however, sill no well undersood. One srand of he lieraure focuses exclusively on spillovers across differen domesic asse prices, whereas anoher srand concenraes on inernaional spillovers only for individual asse prices. However, undersanding he increasingly close domesic and inernaional linkages of asse prices requires a complee and comprehensive modeling of all ransmission channels ha are a play. Policy makers and praciioners are well aware of he exisence of hese linkages, bu very lile is known abou heir srengh and scope. The main limiaion he lieraure has faced in measuring hese propagaion channels has been he endogeneiy of asse prices, even a daily frequencies. Clearly, macroeconomic shocks such as shocks o produciviy, moneary policy, inflaion expecaions, risk premia, ec. have an effec on all asse prices; and herefore, esimaing he impac of one innovaion on he ohers requires idenifying shocks ha are unobservable a hese frequencies. In his paper, we esimae he propagaion of shocks by modeling each asse price wih a mulifacor model, and hen using he heeroskedasiciy ha exiss in he daa o esimae he conemporaneous financial ransmission coefficiens. In order o solve he problem of idenificaion we need o make simplifying or idenifying assumpions. The mos imporan ones are relaed o he inerpreaion of he mulifacor models. We assume ha each asse price is given by a srucural equaion, alhough we undersand ha hey are linearized versions of more complex equaions describing he economy. These assumpions are well in line wih VAR and moneary policy models now sandard in he lieraure. For insance, we inerpre innovaions o he shor rae as moneary policy shocks, o he long rae as inflaionary expecaions, o he sock marke as produciviy or supply shocks, and o he exchange rae as relaive demand shocks. Under hese inerpreaions, we can resric he signs of several coefficiens ha allow us o esimae he model. In paricular, we employ an empirical mehodology ha explois he heeroskedasiciy of asse prices as a ool for idenificaion of financial shocks. 2 This means ha we can deermine differen regimes based on he heeroskedasiciy of he underlying asse prices o pin down he direcion of financial ransmission process. I also implies ha all The wo possible excepions are Andersen e. al. (24), which sudies he ransmission among sock markes for each counry, and hen across counries for each ype of asse marke separaely; as well as Dungey and Marin (2) who also sudy he propagaion of shocks across counries and markes. We discuss below in which dimensions our approach differs from hese wo papers. 2 See Wrigh (928), Senana and Fiorenini (2), Rigobon (23), and Rigobon and Sack (23a) for he heory and some applicaions of he mehodology. March 25 7

9 of he resricions imposed are over-idenifying resricions ha can be verified empirically. We hen use his approach o analyze he naure of financial inegraion and he ransmission channels wihin as well as beween he wo larges economies in he world he Unied Saes and he euro area. The empirical model concenraes on daily reurns over a 6-year period of for seven asse prices: shor-erm ineres raes, bond yields and equiy marke reurns in boh economies, as well as he exchange rae. The resuls of he paper underline he imporance of inernaional spillovers, boh wihin asse classes as well as across financial markes. Alhough he sronges inernaional ransmission of shocks akes place wihin asse classes, we find evidence ha inernaional cross-marke spillovers are significan, boh saisically as well as economically. For insance, shocks o shor-erm ineres raes exer a subsanial influence on euro area bond yields and equiy markes, and in fac explain as much as % of overall euro area bond marke movemens. Bu he ransmission of shocks also runs in he opposie direcion as in paricular shor-erm ineres raes of he euro area have a significan impac on bond and equiy markes. Overall, financial markes explain on average more han 25% of euro area financial marke movemens in he period , whereas euro area markes accoun for 8% of he variance of asse prices. A second key resul of he paper is ha in almos all cases he direc ransmission of financial shocks wihin asse classes is magnified subsanially, mosly by more han 5%, hrough indirec spillovers hrough oher asse prices. For insance, he coefficien for he direc effec of shocks o bond yields on euro area bond markes is.3, bu i rises o.48 when allowing for indirec spillovers of hese shocks via oher and euro area asse prices where he indirec effec measures how he shocks affec oher asse prices and he exchange rae, and how hose asse prices ulimaely aler he euro bond rae. These wo resuls underline ha a beer undersanding of financial linkages requires he modeling of inernaional cross-marke financial linkages, which so far has been mosly missing in he lieraure. We confirm some familiar resuls of he lieraure as, in paricular, we find ha financial markes are mosly driven by counry-specific and marke-specific facors. However, we deec a rich ineracion beween asse prices domesically and our mehodology allows us o quanify domesic financial marke ransmissions much more accuraely by conrolling for foreign and oher ypes of shocks. A highly revealing finding is he difference in he asse price ineracion wihin markes versus wihin euro area markes. For he, we find ha shor-erm ineres raes reac significanly o changes in domesic equiy markes, whereas euro area shor-erm raes are no affeced by sock markes. By conras, euro area shor raes and equiy markes are more responsive o shocks in bond yields and exchange raes han markes. These findings hus also idenify some 8 March 25

10 imporan differences in he financial ransmission processes wihin he wo economies, which may reflec differences in economic srucure, in he degree of openness as well as differen policy objecives. Finally, we conduc several sensiiviy ess and show ha he resuls are broadly robus, alhough we find some suggesive indicaion ha he inernaional ransmission channel has inensified significanly over ime, and in paricular since EMU. Furhermore, we find ha he inernaional propagaion of shocks is srenghened in imes of recession. The paper is organized in he following way. Secion II. briefly reviews he lieraure on domesic and on inernaional financial linkages and inegraion. The mehodology based on idenificaion hrough heeroskedasiciy is summarized in Secion III. Secion IV. oulines he daa and he empirical findings for domesic and inernaional asse marke spillovers beween he Unied Saes and he euro area. Secion V. discusses caveas and robusness resuls and Secion VI. summarizes and concludes wih some policy implicaions arising from he findings. II. Relaed lieraure The lieraure on financial linkages has evolved along wo separae srands in recen years. One of hese srands has been focusing on he domesic ransmission of asse price shocks and is deerminans. Anoher direcion of he lieraure has been o analyze inernaional linkages, whereby he focus, however, has been mosly on individual asse prices in isolaion usually equiy markes or foreign exchange markes. Linkages across domesic financial markes are increasingly well-undersood. Earlier work on he spillovers across differen domesic asse prices ofen finds a posiive correlaion beween sock reurns and bond yields, such as Shiller and Belrai (992) and o some exen Barsky (989) and Campbell and Ammer (993) for he Unied Saes, hough he analysis of hose sudies is mosly based on low-frequency daa. More recen work finds ha equiy prices reac srongly o moneary policy shocks in he Unied Saes (Bernanke and Kuner 24, Ehrmann and Frazscher 24a) A he same ime, moneary policy has been shown o respond o equiy markes (Rigobon and Sack 23a). In a simulaneous analysis of bond prices, shor-erm ineres raes and equiy markes, Rigobon and Sack (23b) find ha he causaliy of he ransmission process may run in several direcions, as for insance he correlaion beween shor-erm ineres raes and equiy prices may change from posiive o negaive depending on which of he asse prices is dominan in paricular periods. A closely relaed lieraure focuses on explaining he price discovery process in domesic asse prices hrough economic fundamenals. Several papers concenrae hereby on March 25 9

11 he imporance of announcemens and news of seleced macroeconomic variables. Fleming and Remolona (997, 999), Balduzzi, Elon and Green (2), and Bollerslev, Cai and Song (2) show ha macroeconomic news in he are an imporan driving force behind bond markes. Fleming and Remolona (999) find a hump-shaped effec of macroeconomic news along he yield curve in ha he larges effec of such news usually occurs a inermediae mauriies. For equiy markes, Flannery and Proopapadakis (22) and Boyd, Jagannahan and Hu (2) also reveal a srong response of equiy markes o macroeconomic news, while he laer paper as well as David and Veronesi (24) show ha he relaionship beween economic fundamenals and equiy reurns may in some cases be dependen on economic condiions or he ype of news. There have also been various aemps o analyze inernaional spillovers, hough he focus in his lieraure has so far concenraed only on individual asse prices in isolaion, mosly on equiy markes. For insance, he empirical work by Hamao, Masulis and Ng (99), King, Senana and Wadhwani (994) and Lin, Engle and Io (994), based on reduced-form GARCH models, deecs some spillovers from he o he Japanese and UK equiy markes, boh for reurns and in paricular for condiional volailiy. Also Becker, Finnery and Friedman (995) find spillovers beween he and UK sock markes and show ha his is in par due o news and informaion, alhough more recen work by Connolly and Wang (23) argues ha such macroeconomic news can explain only a small share of he equiy marke spillovers beween maure economies. For foreign exchange markes, he seminal papers by Engle, Io and Lin (99) and Andersen and Bollerslev (998) find srong spillovers in foreign exchange markes, boh in condiional firs and second momens. Finally, a relaed paper sudying conagion across differen counries and financial markes is Dungey and Marin (2). They sudy mainly he ransmission of volailiy beween shor ineres rae markes and sock markes across counries. A relaed lieraure focuses on he effecs of macroeconomic announcemens on various asse prices. Andersen, Bollerslev, Diebold and Vega (23) and Ehrmann and Frazscher (24c) show ha in paricular macroeconomic news have a significan effec on he dollar euro exchange rae. For bond markes Goldberg and Leonard (23) and Ehrmann and Frazscher (24b) find ha no only macroeconomic news are an imporan driving force behind changes in bond yields, bu ha here are significan inernaional bond marke linkages beween he Unied Saes and he euro area. The resuls of Ehrmann and Frazscher (24b) indicae ha spillovers are sronger from he o he euro area marke, bu ha spillovers in he opposie direcion are presen since he inroducion of he euro in 999. Finally, Andersen, Bollerslev, Diebold and Vega (24), Fair (23) and Faus, Rogers, Wang and Wrigh (23) look a he effec of macro announcemens on high-frequency asse March 25

12 reurns across several asse prices, such as exchange raes and he yield curve, confirming he imporance of news and in some cases finding a significan response of risk premia or an overshooing of exchange raes in he shor run. Anoher srand on inernaional financial co-movemens aemps o explain he evoluion of financial spillovers hrough real and financial linkages of he underlying economies. Heson and Rouwenhors (994), Griffin and Karolyi (998) and Brooks and del Negro (22) argue ha mainly counry-specific shocks, and o a lesser exen indusryspecific and global shocks, can explain inernaional equiy reurns. In addiion, several papers emphasize he imporance of linkages hrough rade and capial flows for explaining financial marke spillovers. One direcion of he lieraure has been o focus on conagion in inernaional markes, marked by he seminal work by Bae, Karolyi and Sulz (23) and Forbes and Rigobon (22). Harmann, Sraemans and de Vries (23) show ha exchange rae linkages srenghen during financial crises for a broad se of emerging markes. Eichengreen and Rose (999) and Glick and Rose (999) find ha he degree of bilaeral rade raher han counry-specific fundamenals alone play an imporan role for undersanding financial co-movemens during crisis episodes. Focusing on maure economies, Forbes and Chinn (23) find ha he counry-specific facors have become somewha less imporan and bilaeral rade and financial linkages significanly are nowadays more imporan facors for explaining inernaional spillovers across equiy and bond markes. A key characerisic of his lieraure on financial ransmission is ha i has evolved along disinc pahs, one focusing exclusively on domesic cross-marke linkages and ohers on he inernaional ransmission wihin individual asse markes. Few sysemaic aemps have been made o link hese srands in order o gain a beer undersanding of he underlying naure of he ransmission channels of financial shocks. The objecive of his paper is o provide a framework for analyzing he ineracion of he domesic and inernaional ransmission of financial marke shocks. III. Measuring Domesic and Inernaional Financial Inegraion III. The srucural-form and he reduced-form models Our behavioral model implies he following srucural form: A y = ϑ + Π ( L) y + Ψ ( L) z + µ () March 25

13 where y is a vecor y r, b, s, r, b, s, e ) of he seven endogenous asse ( prices, namely he change in shor- erm ineres raes (r ), he change in long-erm bond yields (b ) and sock marke reurns (s ), for each of he wo economies, and he change in he exchange rae (e ). Π(L) capures he lagged effecs of he endogenous variables y and Ψ(L) he lagged and conemporaneous effecs of a se of exogenous variables and common shocks z. We will reurn below o explaining in more deail how z is consruced and wha i includes. The 7x7 marix A is of main ineres o us as is off-diagonal elemens capure he conemporaneous ineracions across asse markes. Finally, µ is he vecor of srucural-form innovaions µ i, of he behavioral model, which reflecs shocks o he underlying asse prices. For µ i, o ruly represen srucural-form innovaions, i needs o hold ha hey have zero mean, and are orhogonal o one anoher, boh conemporaneously and across ime: E E ( µ i, µ j, ) = i j ( µ µ ) = i j, ' i, j, ' The saring poin for idenificaion is o esimae he reduced-form or facor model of equaion () via OLS: y y = = A ϑ + A C + B Π ( L) y ( L) y + A + B Ψ ( L) z ( L) z + ε + ε (2) wih he reduced-form residuals ε as ε = { ε r,, ε b,, ε s,, ε r,, ε b,, ε s,, ε e, }' = A { µ r,, µ b,, µ s,, µ r,, µ b,, µ s,, µ e, }' The nex quesion, hen, is o deermine if he srucural coefficiens can be idenified from he reduced-form esimaes. The coefficiens ha can be esimaed from he daa are C, B, B and he covariance marix of he reduced-form residuals. If A was known, hen C, B, B are sufficien o recover he srucural coefficiens ϑ,π, Ψ. The covariance marix of he reduced-form residuals has 28 elemens (he diagonal 7, and he covariances). This covariance marix has o be used o explain he covariance marix of he srucural-form residuals (which only has 7 unknowns given our assumpion abou zero correlaion across srucural shocks), and he marix A (which has ones on he diagonal and herefore has 42 coefficiens ha need esimaing). This is he sandard problem of idenificaion: We have 28 equaions (from he reduced-form residuals) and 49 (7+42) unknowns. Hence, here are more unknowns han 2 March 25

14 equaions, which means ha a coninuum of soluions exiss and ha some mehod of idenificaion is required. One sandard economeric echnique ha has frequenly been employed o sudy problems of his kind resors o srucural vecor auoregression (SVARs), which goes back o he work by Sims (98). The idea is o impose resricions on some parameers of he empirical model, which are ideally derived from economic heory, ye remain unesable, as hey are required for idenificaion. A frequenly used mehodology consiss in a Cholesky decomposiion, which mainains ha he marix A is riangular. In his fashion, he model is exacly idenified, as 2 zero-resricions are imposed. As an alernaive, sign resricions on he parameers of A have been used, which canno uniquely pin down he parameers, ye are able o idenify he space in which he parameers can lie. We will show in secion IV. ha boh approaches are inappropriae for our purposes, as he sandard Cholesky decomposiion fails o achieve he proper idenificaion, and sign resricions lead o an exremely large admissible parameer space. Therefore, we will employ an alernaive approach o idenificaion, which we discuss in he nex sub-secion. III.2 Idenificaion hrough heeroskedasiciy In his paper, we use an alernaive mehodology for idenificaion, known as idenificaion hrough heeroskedasiciy (IH). This mehodology uses he fac ha financial variables are generally found o be heeroskedasic. The form of such heeroskedasiciy is of no paricular ineres o us. I could be described as a GARCH model (Rigobon and Sack 23b), or a regime swiching model. As is shown in Rigobon (23), he esimaes of he conemporaneous coefficiens are consisen, regardless of how he heeroskedasiciy is modeled. Therefore, for simpliciy, we assume ha here are N regimes. Under his assumpion, we obain one addiional covariance marix in he srucural model for each heeroskedasic regime s (which adds 7 unknowns), bu in each regime we can esimae a new reduced-form covariance marix (which provides 28 new equaions). Accordingly, here are enough equaions o solve he sysem of equaions if S * 28 S *7 + 42, which is saisfied for S 2 heeroskedasiciy regimes. Noe ha his mehodology of idenificaion is based on wo crucial assumpions. Firs, he srucural shocks are uncorrelaed. This means ha each addiional heeroskedasic regime adds more equaions han unknowns. Second, we assume ha he marix A is sable across heeroskedasic regimes. Alhough he sysem is idenified by he number of regimes, March 25 3

15 his is only rue up o a roaion of he marix A. We herefore need o impose some addiional resricions o ensure ha we pick he correc roaion, which represens he underlying economic relaionships. However, as hese are overidenifying resricions, i is possible o es wheher hey are binding or no. To illusrae his wih an example le s sudy he sandard supply and demand equaion se up: p q = αq = βp where he firs is he demand equaion and he second one is he supply equaion. This sysem of equaions has he exac same reduced-form variance-covariance marix as he following, alernaive sysem: p q = q β = p α In fac, boh have he exac same reduced-form p q = αβ = αβ + ε + η η β ε α ( ε + αη ) ( βε + η ) Bu, as should be obvious, he firs and second sysems of equaions are he same excep ha in he demand equaion we solve once for quaniies insead of prices, and he opposie for he supply equaion. Because boh sysems produce he exac same reduced-form, he quesion is which of he wo soluions we should pick. Here is where he sign resricions come ino play. If we impose ha he demand equaion is downward sloping and he supply equaion is upward sloping, hen we know ha α is negaive and β is posiive. Noe ha his can only occur in he firs sysem of equaions, given ha he second one implies exacly he opposie signs. The signs only help in he idenificaion because hey allow us o deermine which of he soluions is he one ha is economically meaningful, and i should be sressed again ha he validiy of he over-idenifying resricions can be esed explicily. III.3 Idenificaion resricions In order o impose sensible resricions, we sar by discussing he meaning of each of he equaions in he sysem. For he purpose of illusraion, we can wrie he A marix of he srucural-form model as follows 4 March 25

16 r b s r b s e A = α α β β β γ α 2 α β β β γ α α β β β γ β β β α α γ β β β α α γ β β β α α γ γ 7 γ 27 γ 37 γ 47 γ 57 γ 67 so ha he α parameers indicae he spillovers across domesic asse prices wihin he Unied Saes and wihin he Euro Area, he β parameers he inernaional spillovers, and γ he spillovers from and o he D-EUR exchange rae. Turning o he inerpreaion of he equaions, he equaions for he shor-erm ineres rae can essenially be inerpreed as a high-frequency moneary policy reacion funcion. Of course, moneary policy auhoriies do no adjus policy raes a a daily frequency, bu he reacion of shor-erm raes reflecs o a significan exen he marke s expecaions abou he course of moneary policy in he shor- o medium erm. The equaion of long-erm ineres raes may be undersood as reflecing inflaion expecaions over he medium- o long-run. Hence a fall a he long end of he yield curve may a leas in par indicae ha markes anicipae lower inflaion raes, condiional on he curren shor rae. The sock marke equaion may be inerpreed as a proxy of domesic demand in ha a posiive demand shock a home raises domesic equiy prices. Alernaively, changes in equiy prices may also be explained by supply shocks, such as produciviy changes. Finally, he exchange rae movemens may be undersood as reflecing changes in he relaive demand across he wo economies (see Pavlova and Rigobon 24). Of course, hese inerpreaions are in no way clear-cu, and may no exclude alernaive inerpreaions and explanaions. When discussing he empirical resuls, we will go in more deail abou he inerpreaion of each of he equaions and possible caveas. We impose a firs se of idenificaion resricions on domesic asse price spillovers, as we can use exising priors abou heir signs from he lieraure. Mos resricions are acually imposed on moneary policy, as his is probably he bes undersood subsysem in our model. Noe ha, since he marix A pre-muliplies he vecor of endogenous variables on he lef- March 25 5

17 hand side of equaion (), he sign of he resricion is opposie o he expeced reacion of asse prices. The assumpions are he following:. We would expec ha an inflaionary shock should rigger marke expecaions of a moneary ighening and hus a rise in shor-erm raes (due o he opposie sign we need o impose on A, his implies α 2, α 45 < ). 2. Similarly, one would expec ha a posiive shock o sock markes raises shor-erm ineres raes (α 3, α 46 < ) if moneary policy were expeced o respond o equiy price shocks. 3. As o he effecs of moneary policy, an increase in shor-erm ineres raes raises he discoun value and lowers he demand for goods and services and hence should lead o a decline in equiy prices (α 3, α 64 > ). 4. Moreover, also a rise in long-erm ineres raes should lower equiy prices (α 32, α 65 > ). Since we believe ha hese lines of reasoning should apply boh o he direc effecs of shocks on asse prices (as measured by he marix A) as well as he overall effecs, including indirec spillovers (as measured by A - ), we impose he equivalen se of resricions on A -. Turning o he inernaional linkages, our heoreical priors for some of he spillovers are fairly clear-cu bu less so for ohers. 5. A posiive shock o domesic equiy prices should induce a posiive spillover and lead o a rise in foreign equiy markes as firms and demand are linked inernaionally (β 36, β 63 < ). Mos of he lieraure on conagion has shown ha hese spillovers are indeed posiive. For a heoreical jusificaion see Zapaero (995), Cass and Pavlova (24) and Pavlova and Rigobon (24). 6. Similarly, domesic and foreign money markes and bond markes should exhibi posiive spillovers (β 4, β 4 < ; β 25, β 52 < ). This has indeed been found o hold empirically beween he Unied Saes and he euro area in Ehrmann and Frazscher (24b), based on a reduced-form GARCH-ype of model. However, various channels may explain his posiive relaionship. On he one hand, he openness of financial markes and arbirage may mean ha ineres rae shocks are ransmied across economies. On he oher hand, a close real inegraion of wo economies may imply ha a moneary policy shock or an inflaionary shock in one economy may lead invesors o expec similar developmens in he oher, hus inducing a significan ransmission of shocks in money and bond markes. Whaever he precise direc channel of ransmission, we can es wheher hese linkages are empirically relevan. 6 March 25

18 7. We normalize all variables and herefore we impose he resricions ha he inernaional spillovers wihin markes wihin equiy markes, wihin money markes and bond markes are posiive and less han one. This assumpion boils down o assume ha a domesic shock should no have an amplified and more han proporional effec on foreign markes (- < β 4, β 4, β 25, β 52, β 36, β 63 < ). This assumpion is reasonable for developed economies, whereas i may be incorrec for emerging markes. Moreover, we add a resricion ha reflecs our prior ha he overall spillovers from he money and equiy markes o he equivalen euro area markes should be larger han hose emanaing from he euro area. These resricions have been imposed on he srucural coefficiens. In fac, we find in he empirical resuls ha hese resricions are no binding, bu hey help us furher in he process of idenificaion. The nex issue relaes o he inernaional cross-marke spillovers. Recall ha he parameers in he srucural-form or behavioral model should be inerpreed as indicaing only he direc linkages beween markes, whereas he parameers of he reducedform model capure boh direc as well as indirec linkages across asse prices. By indirec linkages we mean spillovers of shocks ha occur via oher asse prices. For inernaional cross-marke spillovers i is hard o see how, for insance, a rise in shor-erm ineres raes in he Unies Saes should have a direc impac on euro area equiy prices (β 6). Of course, a rise in ineres raes is likely o affec also euro area equiy prices, bu his effec should be an indirec one in he sense ha i is ransmied hrough oher asse prices such as euro area ineres raes. In his case, a rise in ineres raes induces an increase in euro area raes, which hen in urn raises he discoun facor for and causes a drop in euro area equiy prices. 8. Hence, in addiion o he overall sign, we also impose zero resricions on all inernaional cross-marke spillovers in he srucural-form model. This assumes ha he cross-marke cross-counry spillover are zero, bu remember ha we sill allow for indirec spillovers in he reduced-form model indicaed by he marix A -. Moreover, in he sensiiviy analysis we relax hese resricions one by one o es for he robusness of he esimaes. 9. Finally, we resric some γ parameers for he spillovers from and o he D-EUR exchange rae. We presume ha an increase in long raes in he leads o a porfolio shif ino asses, leading o an appreciaion of he dollar and vice versa (γ 72 >, γ 75 < ).. We apply he same reasoning o shocks o he respecive sock markes (γ 73 >, γ 76 < ) in he srucural-form model, alhough we allow for unresriced effecs in he reduced-form model. March 25 7

19 Overall, our benchmark idenificaion of he marix A looks as follows: α 2 α 3 > A = < β 4 < γ 7 α 2 α > 32 < β < γ > < α 3 < β γ α 73 < > < < β α α 64 γ 54 > 74 4 < < β α < 45 α > γ < < < β α 46 α < γ < < γ 7 γ 27 γ 37 γ 47 γ 57 γ 67 This marix A is used for he esimaion of our benchmark model. Recall again ha mos of hese assumpions are used merely o help us idenify he correc roaion of he marix A, which represens he underlying economic relaionships. Indeed, as will become eviden below, mos of hem are no binding, so hey are only helping us deermine which roaion is he one ha is meaningful and consisen wih he heory. III.4 Conrolling for common shocks and idenified macro shocks Recall ha one of he cenral condiions o achieve idenificaion is ha he srucural-form shocks are orhogonal o one anoher, i.e. E ( µ ) µ. In realiy, his condiion may no i, j, = be fulfilled, in paricular if asse price shocks are driven by common shocks, as indicaed by he vecor z in equaion (). Common shocks for asse prices wihin a counry may be news abou economic fundamenals in he respecive counry, such as announcemens of releases of relevan macroeconomic daa. As discussed in secion II., he lieraure has analyzed and esed for he role of macroeconomic news exensively and found srong evidence for he imporance of such news for asse prices. Moreover, here may be common shocks for inernaional asse prices, such as oil price shocks. We address he issue of common shocks in hree separae ways in order o ensure he orhogonaliy of he srucural-form shocks. Firs, we include in our empirical model a se of macroeconomic news in he Unied Saes and he euro area. Money Marke Services (MMS) Inernaional conducs a weekly survey in which i asks marke paricipans abou heir expecaions abou upcoming macroeconomic daa releases. Based on hese expecaions daa, we obain he news componen of each release, which is he difference beween he acual announcemen and is expecaions. Our daa includes a broad se of he mos imporan macroeconomic news for he Unied Saes: he NAPM / ISM index of purchasing managers and consumer confidence; non-farm payroll employmen and unemploymen figures; average workweek, GDP, and indusrial producion; reail sales, rade balance and housing sar 8 March 25

20 figures; as well as PPI and CPI releases. For he euro area, our se of news includes hose for he euro area since 999 as well as for Germany going back o he early 99s: The Ifo business climae, business and consumer confidence indices; GDP, indusrial producion and manufacuring orders; unemploymen, reail sales and rade balance figures; and news abou M3, PPI and CPI numbers. A deailed analysis and background of he included daa is provided in Ehrmann and Frazscher (24b). In addiion o hese macroeconomic news, we include oil price changes in order o conrol for such shocks which are likely o influence mos if no all of he asse prices included. However, a key difficuly for addressing he issue of common shocks is ha such shocks are parly unobservable. Our second way of dealing wih common shocks is herefore o include a common facor in he srucural-form model (). The hird way is mainly o es direcly wheher or no common shocks are imporan. To do so, we need o define more han 2 heeroskedasic regimes which implies an over-idenificaion of he model, as discussed above. In fac, in our empirical applicaion we were able o uncover 5 separae regimes. If here are common shocks in he daa ha have no been modeled, he es for he overidenifying resricions should be rejeced. The inuiion is he following: he procedure o idenify he coefficiens is based on a roaion of he disribuion of he residuals ha is explained enirely by changes in he variances of he shocks and no by changes in he endogenous coefficiens (marix A). When he model is misspecified in he sense ha here are more common shocks han he ones modeled, hen here are roaions of he residuals ha canno be explained by he coefficiens and he shocks in he model. In oher words, here are roaions ha canno be mached wih he srucure imposed. In hese circumsances, he overidenifying resricions are rejeced. 3 IV. Resuls The empirical analysis focuses on financial linkages beween he and he euro area money markes, bonds markes, equiy markes and foreign exchange markes in he period For he Unied Saes, we include he hree-monh Treasury-bill rae for he shor rae, he en-year Treasury-bond rae for he long rae, and he S&P 5 index for he sock marke. For he euro area, we use he hree-monh inerbank rae he FIBOR rae before 999 and he EURIBOR afer 999 for he shor rae, he German en-year governmen bond for he long rae, and he S&P Euro index for he equiy marke. 4 The exchange rae included is he dollar Deusche mark before 999 and he dollar euro since We use he 3 See Rigobon and Sack (23) for a discussion on he imporance of common shocks in he conex of moneary policy and he sock marke. 4 The resuls presened below are robus o using oher variables, such as one-monh ineres raes and using German equiy indices insead of he euro area index. 5 The dollar Deusche mark exchange prior o 999 is muliplied wih he Deusche mark euro conversion rae. March 25 9

21 annualized reurn series of each asse price in our empirical model. Looking a he daily reurn series confirms ha all of hem exhibi he ypical characerisics of heeroskedasiciy, skewness and excess kurosis. A furher imporan issue is ha of he daa frequency and iming. Trading in he European markes akes place earlier han in he Unied Saes, which implies ha shocks emanaing from he European markes are always incorporaed ino asse prices on he same day. By conras, since here is only a limied overlap in rading imes beween he and he euro area markes (especially for he shor raes, as he closing quoes for he German and euro area markes are deermined a : Cenral European Time), some of he shocks only affec European asse prices on he subsequen business day. To reduce his problem of only parial overlap of rading imes, we change he frequency of he analysis and use wo-day reurns for all of he asse reurn series. 6 As discussed in secion III., we argue ha sandard idenificaion echniques are no adequae o solve he problem a hand. Table shows he resuls ha are obained wih he sandard Cholesky decomposiions and, alernaively, a VAR approach using sign resricions. For simpliciy, we decided o model only he domesic subsysems separaely; as we see from he resuls, even hese smaller subsysems canno be properly idenified in his fashion. For he Cholesky decomposiions, i is necessary o impose hree zero-resricions on he sysem. Given he endogeneiy of asse prices, however, i is no a all obvious which parameers can be reasonably resriced o zero. We have ried all combinaions, and repor how he nonresriced parameers change as a resul. I urns ou ha he hree zero-resricions are in mos cases able o pin down he oher, non-resriced, parameers reasonably well, alhough his is no rue for, e.g., α 3, α 23 or α 46. Furhermore, each of hese resuls is, in our view, implausible, as i is based on he assumpion ha hree oher parameers are equal o zero. Table here We have also esed wheher sign resricions alone could be employed insead, by imposing he same sign resricions ha we inroduced in secion III.3, as well as α α 2, 54 < and α α. These assumpions idenify a parameer space, he borders of which are 23, 56 > repored in he second se of columns in Table. I is obvious ha he range of parameers ha is admissible under hese resricions is exremely large, and in many cases exends all he way o zero, where he sign resricions become binding, such ha i is no possible o idenify 6 This canno eliminae he problem enirely, bu i reduces is imporance, as he relaive share of he non-overlapping ime periods is smaller in a wo-day window. As we will show below, he resuls are robus o using lower frequencies, such as weekly daa. 2 March 25

22 he parameers of ineres wih his mehodology eiher. In he following subsecions, we will herefore repor he resuls obained wih our alernaive idenificaion scheme. IV. Domesic ransmission We sar by presening he esimaes for he domesic asse price spillovers firs, before moving on o he inernaional linkages in he subsequen sub-secion. We highligh parameers ha are significan a he 95% level hrough bold fon. A more formal analysis of he significance is given in Tables 2 and 3 as well as Figures and 2, which synhesize he resuls of 5 boosrap replicaions. The significance is esed hrough he share of parameer values in he disribuions depiced in Figures and 2 ha are beyond zero, or he share of replicaions in which he parameer resricions are binding. 7 The boosrap is performed as follows: for each of he heeroskedasiciy regimes, we have esimaed he corresponding covariance marices. We use hese o creae new daa in each boosrap replicaion ha have he same covariance srucure. For each draw, we esimae he coefficiens by minimizing he momens given he resricions. If he resricions are binding, he esimaed parameers will be close o he consrain in several replicaions, and will hus show up in he parameer disribuion over all draws as a large mass in he viciniy of he consrain. 8 Tables 2-3 and Figures -2 around here Direc effecs: The following se of equaions presens he resuls for he conemporaneous spillovers for he hree asse reurns in he srucural-form model (): r =.74 b +.3 s +... (3) b =.65 r.46 s +... (4) s =.7575 r.469 b +... (5) For he euro area, he resuls for he hree asse prices are as follows: r =.474 b +. s +... (6) 7 Ineresingly, none of our no magnificaion resricions which se he parameers of inernaional marke-spillovers o be below one are ever binding. March 25 2

23 b =.277 r +. s +... (7) s = r.5328 b +... (8) Recall ha he esimaes of hese srucural-form equaions can be inerpreed as he direc effecs of he various shocks, hus no incorporaing possible indirec effecs via oher asse prices. The overall conclusion is ha all here are significan conemporaneous linkages across asse prices and across euro area asse prices, all hese relaions have he expeced sign, and mos of hese are saisically significan. The quesion is wheher he parameer esimaes and relaionships can be inerpreed in a meaningful way. Equaions (3) and (6) can be undersood as high-frequency moneary policy reacion funcions ha reflec marke expecaions abou he implicaions of oher asse prices movemens for fuure moneary policy. The esimae for he Unied Saes indicaes a response of shor-erm ineres raes by 7 basis poins (bp) o a bp shock o he bond yield (equaion (3)). As bond yields o some exen capure inflaionary expecaions and o some exen expecaions of changes in real ineres raes, as riggered, e.g., by anicipaions of higher economic growh his effec seems raher small, bu neverheless highly significan. For he euro area, we find a response of similar magniude wih 5 bp. Turning o he second par of he equaions, a % rise in equiy prices in he Unied Saes induces a rise of shor raes by bp. Given he large magniude of equiy movemens in paricular over he las few years, his resul suggess ha moneary policy indeed responds significanly o equiy markes. By conras, for he euro area he shor rae is esimaed o rise by only. bp o a % increase in equiy prices, a resul ha is subsanially smaller han ha for he equaion, and also no saisically significan. This finding consiues an ineresing and arguably quie inuiive resul as i suggess ha moneary policy is more responsive o equiy markes han he moneary auhoriies in he euro area. Equaions (4) and (7) show he bond marke equaions. The esimaes for he Unied Saes imply ha yields rise by abou 6 bp due o a bp change in shor raes, which is subsanially larger han for he euro area, where a bp increase in shor raes raises bond yields by only 28 bp. These responses migh seem small, alhough one would expec ha changes of shor raes are ofen undersood as emporary and hus only a modes fracion of such changes are ransmied o bond yields. Moreover, i has been argued in he lieraure ha he response of long raes o moneary policy very much depends on he marke percepion of moneary policy. I has been found ha in an environmen where a ighening in moneary policy is perceived as credible and effecive in lowering inflaion, long raes may acually fall 8 For example, a consrain ha is someimes binding is ha a coefficien is resriced o be posiive or negaive. When his consrain is binding, he esimaes are smaller han ^-5. Hence, in he 22 March 25

24 (Thornon 998). Hence, he relaively small sensiiviy of bond yields o changes in shorerm ineres raes may be convincing and underlines he credibiliy of moneary policy in he Unied Saes and in he euro area in conaining inflaionary pressures. The oher esimaes of equaions (4) and (7) indicae ha bond yields fall by bp due o a % increase in sock prices, whereas here is basically no response of bond yields in he euro area. Again, he relaively large movemens in equiy markes in recen years make his esimae appear plausible. As o he sign of he parameer esimaes, i appears ha bond yields drop in response o equiy markes srenghening because of a porfolio rebalancing. Equaions (5) and (8) presen he sock marke equaions and heir responses o shocks in domesic shor-erm and in long-erm ineres raes. Sock prices in he Unied Saes are esimaed o fall by.76% in response o a bp rise in shor-erm raes, and do no respond significanly o an increase in long raes. These effecs are larger for he euro area, where sock markes decline by 2.9% and.53% in response o a bp rise in shor raes and in long raes, respecively. Asse price models usually model equiy prices as he discouned sum of fuure dividends, and herefore a rise in ineres raes implies an increase in he discoun rae and a drop in equiy prices. I should be noed ha hese esimaes are smaller han hose found in he lieraure for he Unied Saes (e.g. Rigobon and Sack 22, Bernanke and Kuner 24, Ehrmann and Frazscher 24a), alhough hese papers use differen mehodologies and analyze differen ime periods. An ineresing poin o noe is ha long raes have a subsanially, almos hree imes smaller effec on sock markes han shor-erm ineres raes in he Unied Saes and only abou half he effec in he euro area. The raionale for his finding is quie inuiive as changes in equiy prices are no only caused by changes in he discoun facor bu also by changes in cash flows and/or risk preferences. Andersen, Bollerslev, Diebold and Vega (24) argue ha cash flow effecs on equiy markes are significan and dominae in recessionary periods over discoun rae effecs. A rise in shorerm ineres raes is likely o have lile effec on cash flows over he long-run whereas an increase in bond yields may a leas in par reflec an improved oulook for growh and hence expecaions of higher cash flows. Therefore in he case of bond yields, he negaive effec of a rise in he discoun facor is parly offse by he posiive effec of improved earnings expecaions, hus resuling in a smaller direc effec of bonds on sock reurns. Overall effecs: disribuion i shows as a large mass around zero. March 25 23

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