DOES MONEY MATTER IN THE EURO AREA? EVIDENCE FROM A NEW DIVISIA INDEX

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1 BRUEGEL WORKING PAPER / DOES MONEY MATTER IN THE EURO AREA? EVIDENCE FROM A NEW DIVISIA INDEX ZSOLT DARVAS Highlighs Sandard simple-sum moneary aggregaes, like M, sum up moneary asses ha are imperfec subsiues and provide differen ransacion and invesmen services. Divisia moneary aggregaes, originaed from Barne (9), are derived from economic aggregaion and index number heory and aim o aggregae he money componens by considering heir ransacion service. No Divisia moneary aggregaes are published for he euro area, in conras o he Unied Kingdom and Unied Saes. We derive and make available a daase on euro-area Divisia money aggregaes for January February using monhly daa. We plan o updae he daase in he fuure. Using srucural vecor-auoregressions, we find ha Divisia aggregaes have significan impacs on euro-area oupu and prices. Following a shor-erm liquidiy effec, Divisia-money shocks end o increase ineres raes, suggesing ha he European Cenral Bank reacs o developmens in moneary aggregaes. Divisia-money declines afer a shock o user cos, consisenly wih a money-demand funcion, while an ineres rae shock increases user cos and decreases Divisiamoney, suggesing ha he ECB can influence moneary developmens. Mos of hese resuls are no significan when we use simple-sum measures of money. Our findings complemen he evidence from US daa ha Divisia moneary aggregaes are useful in assessing he impacs of moneary policy and ha hey work beer in SVAR models han simple-sum measures of money. NOVEMBER (UPDATED APRIL ) Zsol Darvas (zsol.darvas@bruegel.org) is a Senior Fellow a Bruegel. The auhor is graeful o Barry E. Jones for a discussion on Divisia calculaions and for suggesing he use of ECB ransacions daa, o an anonymous reviewer, Bruegel colleagues and paricipans a he rd European Conference on Banking and he Economy (ECOBATE ) for commens and suggesion, and o Pia Hül and Thomas Walsh for research assisance.

2 . Inroducion Money has a minor role in moneary policy and macroeconomic modelling. One imporan cause for his disregard is empirical: esimaed money demand funcions have been found o be unsable and money has proved o be less effecive in predicing economic oucomes. However, such empirical failures are challenged by he lieraure on aggregaion-heoreic measuremen of money. The mos widely used measures of money, like M and M, are simple-sum measures. Simple-sum aggregaion implies ha all componens of he money sock are perfec subsiues, which is a very resricive and improbable assumpion. Correc aggregaion can be obained by using eiher aggregaion heory or index number heory, as firs underlined by Barne (9), who suggesed he discree-ime Törnquis-Theil approximaion of he Divisia index. Recen sudies using US daa also underlined he usefulness of Divisia money indicaors for moneary analysis. Wihin a coinegraed vecor-auoregressive model, Hendrickson () idenified a sable money demand equaion using Divisia indicaors and demonsraed ha hey Granger-cause he growh and level of oupu and he level of prices. The same analyses wih simple-sum money indicaors led o weaker resuls. Keaing e al () showed ha a srucural vecor-auoregressive (SVAR) model wih Divisia money worked as well as he model wih he Federal funds rae before he crisis. I worked equally well in he sample period ha includes he zero lower bound when he Federal funds rae model could no be used. Using a differen SVAR model, Belongia and Ireland () found suppor for he inclusion of Divisia money in he US moneary policy rule and also idenified reasonable money demand and moneary sysem shocks. Our paper creaes a new daase on euro-area Divisia money aggregaes and examines he impacs of shocks o money, money user cos and ineres rae on oupu, prices and moneary variables in he euro area, using SVAR models.. A new euro-area Divisia money daase No Divisia moneary aggregaes are available for he euro area, in conras o he US and UK. We creae and make available a daase on euro-area Divisia aggregaes corresponding o he simple-sum aggregaes published by he European Cenral Bank (ECB), ie M, M and M, for January February. We plan o updae he daase in he fuure. Earlier academic works on he euro-area Divisia aggregaes include Wesche (997), Reimers (), Sracca (), Barne (7), Binner e al (9), Jones and Sracca () and Barne and Gaekwad-Babulal (). In conras o mos of hese papers, we base our calculaions on euro-area daa as opposed o aggregaing counry-specific daa a he euro-area level. Furhermore, insead of relying on an ad-hoc spread Oher reasons were policy shifs by cenral banks o focus on ineres raes and he developmen of heories suggesing ha money is redundan, see Leeper and Roush (), Belongia and Ireland (), Keaing e al (). Divisia indices are published by he Cener of Financial Sabiliy (CFS) and he Federal Reserve Bank of S. Louis for he US and he Bank of England for he UK. Our daase is downloadable from: hp://

3 assumpion o approximae he benchmark rae (he reurn on a moneary asse ha does no provide ransacion services), as generally done in he lieraure, we derive i by considering longer mauriy bank debs. The ECB indicaors of euro-area ousanding money socks are subjec o wo major shorcomings. Firs, hey relae o he changing counry-composiion euro-area and hence here was a level shif in hese indicaors whenever a new member joined he euro area. Second, hey are subjec o reclassificaion changes, such as halving he ousanding sock of he measure of repurchase agreemens in June. For economic analysis, such level shifs should be eliminaed. We creae a Divisia index for he firs welve euro-area members based on ransacions daa, which does no suffer from level shif problems. Deails are provided in he online Appendix.. Models and daa We esimae impulse response funcions wih SVAR models including five variables: GDP, GDP deflaor, money, he user cos of money and ineres rae. The sample period is quarerly beween Q and Q, which is shorer han sample periods available for he US, so we are obliged o use relaively small-scale models and canno sudy sub-sample sabiliy. Oupu, prices and money ener he model in log-levels, while he ineres rae and user cos are included in percen. Such a specificaion leads o consisen esimaion, irrespecive of wheher or no here is a co-inegraion relaionship beween he variables. For GDP and GDP deflaor we use he seasonally adjused euro-area welve (i.e. consan counry composiion) aggregaes published by Eurosa. For money, we use seasonally adjused end-of-quarer M daa from our new daase (resuls wih M are very similar). We compare he resuls obained wih Divisia and simple-sum measures. To faciliae he comparison, we calculae he simple-sum measure for he firs welve euro-members using ransacions daa o exclude level shifs, similarly o he Divisia-index. The user cos of a moneary asse is he funcion of he ineres forgone by holding ha asse raher han he benchmark asse. Thereby, a higher user cos reduces he demand for ha asse. Noe ha he impac of a higher ineres rae on he demand for moneary asses (oher han he zero-yielding cash) is ambiguous, because, for example, a higher cenral bank ineres rae may increase he ineres rae paid on deposis, which in iself makes deposis more aracive. For he ineres rae we use he -year mauriy German governmen bond yield, because he ECB policy rae or a measure of shor-erm ineres rae canno be used due o reaching zero lower bound in he laer par of our sample period. The expecaion hypohesis of he erm srucure of ineres raes defines he relaionship beween curren and expeced shor-erm ineres raes and he long-erm ineres rae. Thereby, he long-erm rae can be informaive abou moneary policy acions, including when various unconvenional measures, such We allow four lags in he VARs, which reduces our effecive sample period by o. We need o esimae parameers per equaion (four lags of each of he five variables plus an inercep), which leaves reasonable degrees of freedom.

4 as large-scale asse purchases, are implemened. We use he German rae and no he euro-area average, because he average was influenced by redenominaion risk during he euro-area sovereign deb crisis, while he German rae is he closes o a euro-area risk-free asse. Our relaively shor sample period does no allow a rich idenificaion of srucural shocks. We herefore use he generalised impulse response funcion derived by Pesaran and Shin (99), which does no depend on he variable ordering, in conras o he Cholesky-decomposiion. Thereby we canno inerpre any of our shock as a moneary policy shock, ye shocks o he ineres rae may capure mos of such shocks. A shock o user cos is no a pure money demand shocks, bu may approximae i, while a shock o money may comprise money supply shocks.. Resuls Figure shows ha he response of oupu o a Divisia-money shock is posiive and saisically significan abou -9 quarers afer he shock, which corresponds o he horizon a which moneary policy is hough o have an effec on he economy. The oupu level response is emporary as he impulse-response funcion reurns o zero, which is sensible and in line wih he long-run neuraliy hypohesis. While he shape of he response o a simple-sum money shock is similar, i is significan for a shorer period (- quarers). The price response is marginally significan for he Divisia aggregae, bu no significan for he simple-sum aggregae. The poin esimaes sugges ha prices increase afer a money shock, which is sensible. The price response o he ineres rae is negaive, as expeced, and is significan in he Divisia- model, bu no in he simple-sum model. The ineres rae decreases significanly in he shor-erm afer a Divisia money shock and hereby no liquidiy puzzle arises. When simple-sum money is used, he shor-erm impac is no significan. Saring from abou a year afer he money shock, he ineres rae response urns o posiive, which is significan for boh measures of money. To he exen ha he long-erm ineres rae reflecs ECB moneary acions, his finding suggess ha he ECB reaced o moneary developmens, e.g. by cuing is policy rae or by adoping unconvenional moneary measures following a negaive money shock. A shock o user cos reduces money, which is consisen wih a money-demand funcion. This effec is significan for up o hree years afer he shock in he Divisia-model and for less han wo years in he simplesum model. Finally, in he Divisia-model an ineres rae shock increases he user cos of money, which may explain why he reacion of money is negaive o an ineres rae shock. These findings imply ha he ECB can influence money growh by impacing long-erm ineres raes. However, hese findings do no hold in he simple-sum model, as

5 he impacs of an ineres rae shock on user cos and money are no significan and even he poin esimaes are virually zero. Figure : Impulse responses o ineres rae and money shocks A: Using M Divisia Shock o money Shock o user cos Response of oupu Shock o ineres rae... Response of prices Response of money Response of user cos Response of ineres rae All resuls repored are robus o he exclusion of eiher he user cos, or he ineres rae, or boh, form he model: he remaining impulse responses are virually unchanged compared o Figure.

6 Response of oupu B: Using M simple sum Shock o money Shock o user cos Shock o ineres rae Response of prices Response of money Response of user cos Response of ineres rae Noe. Solid line: esimaed impulse response funcion; dashed lines: 9 percen confidence band. The horizonal axis indicaes he number of quarers afer he shock (wih he shock occurring in quarer ).

7 . Conclusions We have creaed and made available a new daase on euro-area Divisia moneary aggregaes and used srucural vecor-auoregressions o analyse he impacs of shocks o money, money user cos and ineres rae in he euro area. We find ha a Divisia-shock had significan impacs on oupu and prices. Following a shorerm liquidiy effec, ineres raes increase afer a money shock, suggesing ha he European Cenral Bank reaced o developmens in money aggregaes. We also find ha a user-cos shock reduces money growh, which is consisen wih a money demand funcion, and ha money growh can be amed by measures which increase long-erm ineres raes. Mos of hese resuls are no significan when we use simple-sum measures of money. Therefore, our findings for he euro area complemen he evidence from US daa ha Divisia moneary aggregaes are useful in assessing he impacs of moneary policy and ha hey work beer in SVAR models han simple-sum measures of money. 7

8 References Barne, W.A. (9) Economic moneary aggregaes: an applicaion of index number and aggregaion heory, Journal of Economerics, Barne, W.A. (7) Mulilaeral aggregaion-heoreic moneary aggregaion over heerogeneous counries, Journal of Economerics, 7 Barne, W.A., Gaekwad-Babulal, N. () Divisia Moneary Aggregaes for he European Moneary Union, presened a he Sociey for Economic Measuremen conference, Chicago, - Augus Belongia, M.T., Ireland, P.N. () Ineres Raes and Money in he Measuremen of Moneary Policy, NBER Working Paper Binner, J.M., Bissoondeeal, R.K., Elger, C.T., Jones, B.E., Mullineux, A.W. (9) Admissible moneary aggregaes for he euro area, Journal of Inernaional Money and Finance, 99- Hendrickson, J.R. () Redundancy or Mismeasuremen: A Reappraisal of Money, Macroeconomic Dynamics, 7 Jones, B.E., Sracca, L. () Does Money Ener ino he Euro Area IS Curve?, unpublished manuscrip Keaing, J.W., Kelly, L.J., Valcarcel, V.J. () Solving he Price Puzzle wih an Alernaive Indicaor of Moneary Policy, Economics Leers, 9 Leeper, E.M., Roush, J. () Puing M Back in Moneary Policy, Journal of Money, Credi and Banking (), 7 Pesaran, H.H., Shin, Y. (99) Generalized Impulse Response Analysis in Linear Mulivariae Models, Economics Leers, 7 9. Reimers, H.E. () Analysing Divisia Aggregaes for he Euro Area, Discussion Paper /, Deusche Bundesbank Sracca, L. () Does Liquidiy Maer? Properies of a Divisia Moneary Aggregae in he Euro Area, Oxford Bullein of Economics and Saisics (), 9 Wesche, K. (997) The Demand for Divisia Money in a Core Moneary Union, Federal Reserve Bank of S. Louis Review,

9 Appendix: Consrucion of he new euro-area Divisia daase. Inroducion Sandard simple-sum moneary aggregaes, like M, sum up moneary asses ha are imperfec subsiues and provide differen ransacion and invesmen services. Divisia moneary aggregaes, originaed from Barne (9), are derived from economic aggregaion and index number heory and aim o aggregae he money componens by considering heir ransacion service. As noed by Barne and Chauve (), he name Divisia is from François Divisia, who firs proposed a formula for aggregaing quaniies of perishable consumer goods (see Divisia, 9). No official Divisia moneary aggregaes are published for he euro area, in conras o he UK and US. Esimaes for he euro area by academic researchers are scarce and we could no find any publicly available daase. Earlier works on he euro area include Wesche (997), Reimers (), Sracca (), Barne (7), Binner e al (9), Jones and Sracca () and Barne and Gaekwad-Babulal (). Mos of hese papers aggregaed counry-specific daa o obain an aggregae for he euro area. In our paper we derive and make available a daase on euro-area Divisia moneary aggregaes corresponding o he sandard (simple sum) moneary aggregaes published by he European Cenral Bank (ECB), ie M, M and M. Our sample period covers monhly daa beween January and February and we plan o updae he daase in he fuure. Our daase is downloadable from: hp:// During our sample period, he euro area exised and daa on (changing composiion of) euro-area aggregaes is also available. We herefore base our calculaions on euro-area daa insead of using counry-specific daa and aggregaing hem a he euro-area level. For calculaing Divisia indices, daa on he componens of he money sock and heir ineres raes are needed. Daa on he sock of ousanding quaniies of he componens of M, he broades moneary aggregae published by he ECB, is available from Sepember 997 (on a changing counry-composiion basis). Ineres rae daa on all of hese componens is available from January onwards (for a few indicaors, earlier daa is available from oher sources), implying ha from his dae, high-qualiy Divisia aggregaes can be calculaed for he euro area. Using counry-specific daa, we approximae he missing euro-area ineres raes for January - wih a good level of confidence. The use of changing composiion euro-area ousanding socks for economeric analysis is inappropriae, because here is a level shif in he daa when a new member joins. Furhermore, reclassificaion changes, such as halving he ousanding sock of he measure of repurchase agreemens which is included in he ECB s M aggregae in June, also lead o level shifs in he daa which should be eliminaed. We herefore derive four versions of he Divisia index, of which hree versions do no suffer from (some or all) level shifs: one considers only he firs welve members of he euro area and is based on ousanding sock of he componens, he oher is based on ransacions daa also published by he ECB for he changing-composiion euro area, while he hird version is based on approximaed ransacions daa of he firs welve members. We will describe he meris and drawbacks of hese versions. This appendix deails our mehodology, daa sources and adjusmens made, and presens he resuling indicaors. 9

10 . The heory and mehodology of calculaing Divisia moneary aggregaes The simple-sum moneary aggregaes published by many cenral banks simply add up he differen componens of money: N () S = M i where i=,, S is he simple-sum moneary aggregae (like M), M i, is he level of he i-h money holding (like demand deposis) and N denoes he number of componens considered (e.g. 7 for he ECB s M aggregae). We denoe by v i, he share of each componen in he moneary aggregae, which is: () v i, i, = N. M j = M j, As Barne, Fisher and Serleis (99) noed, he simple sum aggregaion in equaion () implies ha all componens are perfec subsiues, since all indifference curves and isoquans over hose componens mus be linear wih slopes of minus one, if his aggregae is o represen he acual quaniy seleced by economic agens. They also noe ha Irving Fisher found he simple-sum index o be he leas useful of he hundreds of possible indices he sudied. The perfec subsiuabiliy condiion is very problemaic, because eg cash differs so much from shor mauriy bank bills and bonds, which are par of he ECB s M indicaor. Beer aggregaion can be obained by using eiher aggregaion heory or saisical index number heory, as firs underlined by Barne (9). In aggregaion heory, aggregaor funcions are uiliy funcions for consumers and producion funcions for firms. While aggregaion heory is imporan in heory and in hypohesis esing, derived aggregaors depend on unknown parameers, making hem impracical for use by cenral banks and governmen agencies for calculaing and publishing daa. For his reason, Barne (9) proposed he use of index number heory, which does no depend on unknown parameers, bu can depend on he prices of componens (beyond he quaniy of componens). He also noes ha he definiion of exac saisical index numbers does depend upon he maximising behaviour of economic agens and ha Hulen (97) has proved ha in coninuous ime he Divisia index is always exac for any consisen (blockwise homoheically weakly separable) aggregaor funcion. In discree ime he Divisia index has o be approximaed, for which differen choices can be made. Barne (9) proposed he Törnquis-Theil Divisia index, which is: () D D = N M M i, i= i, ( )( s, +, ) i si, An index number is called exac if i exacly equals he aggregaor funcion whenever he daa is consisen wih microeconomic maximising behaviour. See Diewer (97), who also defined a quaniy (price) index as superlaive if i is exac for a flexible aggregaor (uni cos) funcion. An aggregaor (uni cos) funcion is flexible if i can provide a secondorder approximaion o an arbirary wice differeniable linearly homogeneous aggregaor (uni cos) funcion. See Hill () on he difficulies in selecing which superlaive index should be used.

11 () s i, = N π M j = i, π j, i, M j,, where D is he quaniy of he Divisia index, s i, is he share of he i-h componen, user cos) for good in period. The (nominal) user cos of money was derived by Barne (97): π i, is he renal price (or () * rb, ri, π = i, p, + rb, where * p is he cos of living index, r, is he rae of reurn on he benchmark asse (which provides no B liquidiy or oher moneary services and is solely used o ransfer wealh ineremporally) and rae of reurn on asse i. The real user cos ( ρ ) is obained by aking away i, * p from (): r, is he own i () r B, ri, ρ = i,. + rb, By aking logs of (), i is easy o see ha for he Divisia index he growh rae (log change) of he aggregae is he share-weighed average of he growh raes of componen quaniies, as highlighed by Barne, Fisher and Serleis (99): N * (7) ( D ) log( D ) = si, ( log( M i, ) log( M i, ) ) log, * where ( )( s s ) s. i, = i, i, i = The Bank of England wries he expression in a differen form (see Hancock, ) 7 : ΔD D N () = ( wi, + wi, ) ΔM i, i = M i, where he weighs, w,, are defined as: (9) w i, = N i ( r B, ri, ) ( r B, r j, ) j = M i, M j,, However, he only difference beween (7) and () is ha (7) uses log-changes while () uses percen changes. * This is because in fac s i, = wi,, since he p ( + r B, ) componen of π i, cancels ou in (). Log-changes are almos idenical o percen changes for small changes and money componens used no o change much 7 According o Hancock (), he Bank of England uses a moving average of Δ M i, on he righ hand side of equaion (), i.e. insead of Δ M i,, hey use ( ΔM i, + ΔM i, ), bu we could no confirm his smoohing from oher sources. In our calculaion we use Δ and no is moving average. M i,

12 from one monh o he oher, so (7) and () should lead o virually idenical resuls. We calculae our Divisia indices according o (). In pracice, calculaions in he lieraure also used o differ wheher he nominal socks of money componens ( M i, ) or heir real socks or per capia socks are used in he aggregaion. Some researches use break-adjused ransacion daa for measuring he change in money componens in (7) and (). We use he simple nominal sock of money componens and eiher is acual change or is break-adjused change. Finally, we calculae he real user cos of moneary aggregaes M, M and M as he weighed average of real user coss of heir componens, using he same weighs which are used o calculae he Divisia aggregaes: ρ ρi,, N () = ( wi, + wi, ) i= The nominal user cos can be obained by muliplying ρ wih he cos of living index.. The ECB s moneary aggregaes Using harmonised definiions of he money-issuing secor, he money-holding secor and moneary financial insiuions (MFI) liabiliies caegories, he ECB calculaes and publishes hree moneary aggregaes for he euro area (on a changing counry-composiion basis): a narrow aggregae (M), an "inermediae" aggregae (M) and a broad aggregae (M). Table, aken from he ECB websie, presens he componens of he moneary aggregaes. These aggregaes are calculaed by simply adding he euro value of he componens (ie hese are simple sum measures). Table : ECB s definiions of euro-area moneary aggregaes M M M. Currency in circulaion X X X. Overnigh deposis X X X. Deposis wih an agreed mauriy up o years X X. Deposis redeemable a a period of noice up o monhs X X. Repurchase agreemens X. Money marke fund (MMF) shares/unis X 7. Deb securiies up o years X Noe. Liabiliies of he money-issuing secor and cenral governmen liabiliies wih a moneary characer held by he money-holding secor. Source: hp:// Figure shows he imporance of he seven componens of M, he broades moneary aggregae (using he daa sources o be deailed in he nex secion). Overnigh deposis have he larges share in he simple sum M, followed by deposis redeemable a noice.

13 Figure : Componens of euro-area (changing composiion) M, seasonally adjused, rillions, Sepember 997 February GR SI CY, MT SK EE LV LT M M M 9 Currency in circulaion Overnigh deposis Deposis wih an agreed mauriy up o years Deposis redeemable a a period of noice Repurchase agreemens Money marke fund shares/unis Deb securiies up o years Noe: he verical lines wih he counry-codes above indicae he daes when hese counries joined he euro area. GR: Greece, SI: Slovenia, CY: Cyprus, MT: Mala, SK: Slovakia, EE: Esonia, LV: Lavia, LT: Lihuania.. Daa sources and adjusmens Our aim is o calculae Divisia moneary aggregaes corresponding o he hree moneary aggregaes published by he ECB, boh for he changing composiion euro area and for he firs welve member saes ha joined he euro (consan composiion). We also aim o calculae he user cos of he hree aggregaes.. Daa sources Mos of our daa is from he ECB s Saisical Daa Warehouse. In addiion, Daa on currency issued was downloaded from he Inernaional Moneary Fund s Inernaional Financial Saisics (IFS); Some German deposi raes were colleced form he websie of he Bundesbank; The reurn on deb securiies up o wo years is approximaed by he Bank of America Merrill Lynch - Year Euro Financial Index. Table on he nex page presens a summary of he daa availabiliy.

14 Table : Summary of daa availabiliy (firs available observaion unless oherwise noed) A: Moneary aggregaes Euro area (changing composiion) Counry-specific daa. Currency in circulaion SA: January 9, NSA: Sepember 997 No, bu currency issued is available from he IMF IFS. Overnigh deposis SA: January 9, NSA: Sepember 997 For a differen reference secor*: Sepember 997, NSA, for he firs counries of he euro area; March 99 for Greece; oher seven members: from abou wo years before heir euro enry. Deposis wih an Sepember 997, boh NSA and SA same as for overnigh deposis agreed mauriy up o wo years. Deposis redeemable a a period of noice Sepember 997, boh NSA and SA same as for overnigh deposis. Repurchase agreemens Sepember 997, boh NSA and SA Only for oal repos** and for a differen reference secor: same as for overnigh deposis; for some counries here are only zero values. Money marke funds Sepember 997, boh NSA and SA same as for overnigh deposis; for some counries here are only zero values 7. Deb securiies up o wo years Sepember 997, boh NSA and SA No*** Source: All daa excep currency issued by member saes is from he ECB s Saisical Daa Warehouse. Noe: NSA: Neiher seasonally nor working day adjused; SA: Working day and seasonally adjused. * The reference secor used by he ECB for calculaing he hree moneary aggregaes is MFIs, cenral governmen and pos office giro insiuions. Unforunaely, counry-specific daa is no available for his reference secor, bu available for he reference secor MFIs excluding ESCB. ECSB = European Sysem of Cenral Banks. The difference beween he daa for he wo reference secors of he euroarea aggregaes is generally small or even zero, see Secion. in which we plo he differences. ** The exac definiion of repurchase agreemens included in he ECB s moneary aggregaes is: Repurchase agreemens excluding repos wih cenral counerparies. Unforunaely, counry-specific daa is no available for his componen, bu only for oal repurchase agreemens, and for he reference secor described in * above. As we highligh in Secion., cenral counerparies are excluded only from June onwards, causing a break in his componen and also in M. *** Daa on shor erm deb securiies issued by MFIs is available, bu i has a very differen level and dynamics compared o he componen included in M.

15 B: Ineres raes Euro area (changing composiion) Counry-specific daa. Currency in circulaion assumed o be zero assumed o be zero. Overnigh deposis January Harmonised daa: January for he firs members; from he dae of euro enry (or a few monhs earlier) for he newer members. Nonharmonised daa*: December 99- June/Sepember for six counries (Ausria, Finland, Greece, Ialy, Neherlands and Spain); German daa from Bundesbank for January -December. Deposis wih an agreed mauriy up o wo years. Deposis redeemable a a period of noice. Repurchase agreemens January Harmonised daa: same as for overnigh deposis. Non-harmonised daa*: December 99-June/Sepember for en counries (firs welve euro members excep Ireland and Luxembourg), bu for somewha differen mauriies January Harmonised daa:january for five counries (Germany, Spain, Finland, France, Ireland); from laer daes for oher counries, bu here are many gaps in he daa; in Sepember daa was available for 9 counries. Non-harmonised daa*: December 99-June/Sepember for four counries (Belgium, Germany, Greece and Ireland) January. Money marke funds We use he Eonia rae; available from January 99** 7. Deb securiies up o wo years We use he Bank of America Merrill Lynch - Year Euro Financial Index; available from January 99*** Harmonised daa: January for he four counries (Spain, France, Greece, Ialy), bu he Greek daa end in Source: All daa excep German overnigh deposi rae in - and he Bank of America Merrill Lynch - Year Euro Financial Index are from he ECB s Saisical Daa Warehouse. Noe: * Some of he non-harmonised ineres rae daa mus have very differen definiions from he harmonised daa and herefore canno be used o proxy euro-area daa for earlier years, as we discuss in he nex secion. ** Eonia, euro overnigh index average, is a measure of he effecive ineres rae prevailing in he euro inerbank overnigh marke. I is calculaed as a weighed average of he ineres raes on unsecured overnigh lending ransacions denominaed in euro, as repored by a panel of conribuing banks. See hps:// ***The BofA Merrill Lynch Euro Financial Index racks he performance of EUR denominaed invesmen grade deb publicly issued by financial insiuions in he eurobond or euro member domesic markes. The BofA Merrill Lynch - Year Euro Financial Index is a subse of The BofA Merrill Lynch Euro Financial Index including all securiies wih a remaining erm o final mauriy less han years. Qualifying securiies mus have a leas one year remaining erm o final mauriy, a leas monhs o final mauriy a poin of issuance, a fixed coupon schedule and a minimum amoun ousanding of EUR million See: hp:// No No In order o check he consisency of he money componens wih he simple sum aggregaes M, M and M published by he ECB, we calculaed he sum of he componens: he sums calculaed by us were idenical o he moneary aggregaes published by he ECB, boh for he unadjused and he seasonally adjused daa.

16 In addiion o moneary aggregaes, he ECB publishes daa on monhly ransacions and he percen changes in a co-called index of noional socks. Transacions daa are derived by adjusing he change in socks wih reclassificaion, revaluaion and exchange rae adjusmen of he componens. Such changes and breaks in he series should be disregarded when growh raes of money socks are calculaed or when a ime series is used for economeric analysis. The index of noional socks is calculaed as a chain-index, by muliplying he previous period value of noional sock wih he percen increased derived from ransacion daa, where he percen change is calculaed by dividing he ransacion in a given monh wih he ousanding amouns of he asse a he end of he period. See equaion.. and secions. and. of ECB (a) for deails.. Approximaing non-available euro-area average ineres raes for - Panel B of Table shows ha ineres raes for four componens of M are available for he euro area (changing composiion) saring in January. We approximae hese four ineres rae series for - using counry-specific daa and explain he daa limiaions ha do no allow a proper approximaion of wo of hese four ineres rae series pre- wih a sufficien coverage. Approximaing for would be possible, bu we decided o sar our sample in January because Greece joined he euro area in his monh and our focus is on a consan composiion euro-area aggregae for he firs welve members. Saring our sample period in January implied ha no aggregaion is needed for counries wih differen currencies. Also, in Greek ineres raes behave very differenly from hose of euro-area members ha joined in 999, which would make i more difficul o inerpre heir aggregae in. Overnigh deposi rae The ECB publishes counry-specific ineres raes on overnigh deposis saring in January for all he euroarea counries a ha ime (daa for newer euro-area members is available from laer daes). The series are regularly updaed (he laes daa is for February ). For seven of he firs welve members, separae series are available from he ECB for December 99 June or Sepember. We could find pre- daa only a he Bundesbank websie for Germany, bu no a he cenral bank websies of he oher larger euro-area counries. The firs seven panels of Figure plo he new and he old ECB series for he seven counries for which he ECB publishes pre- daa, along wih he euro-area average overnigh deposi rae and he -week EURIBOR. For Finland, Ialy and Greece he old and new daa mach quie well. For Ausria and he Neherlands he old series are very differen from he new series and he old series are almos consan a a ime when all oher ineres rae series (of hese wo counries and of oher euro-area counries) exhibied an increasing rend in lae 999 and hen a falling rend in mid-. Because of hese discrepancies, we do no use he pre- Ausrian and Duch ime series. The old Spanish series are also differen in levels from he new Spanish series, bu is dynamics are quie plausible given he dynamics in oher counries. Therefore, for Finland, Ialy, Greece and Spain we make use of he old ECB series and chain hem backwards o he new ECB series, by adding o he old series he average spread beween he new and he old series in he period when boh are available (ie in he firs seven or nine monhs of ; see he hick green lines on he chars). For Germany, he Bundesbank publishes effecive overnigh ineres raes separaely for German households and non-financial corporaions, for wo sample periods: a new one saring in January, which is regularly updaed, while he old one is available for January December. We used he volume of

17 households and non-financial corporaions overnigh deposi ousanding quaniies (available from January ) o calculae he average overnigh deposi rae. The weighed average overnigh deposi rae of he new series calculaed by us was idenical o he German overnigh deposi rae published by he ECB in each monh during January -February. Lacking pre- quaniies on deposis, we used he January volume of deposis o weigh he ineres raes for he wo secors pre-. Since he shares of households and nonfinancial corporaions in overnigh deposis were relaively sable afer, using he January values for calculaing a weighed average for - likely does no inroduce any major disorion. As he las panel of Figure shows, he old and new series are nicely conneced and herefore we use he old series for -. Figure : Overnigh deposi raes for seven euro-area counries wih available daa before, January 99 February Ausria Finland 7 Greece Ausria: Old ECB daa Ausria: New ECB daa Ausria: difference beween old and new ECB daa Euro area: ECB daa Euro area: week EURIBOR Finland: Old ECB daa Finland: New ECB daa Finland: difference beween old and new ECB daa Euro area: ECB daa Euro area: week EURIBOR Greece: Old ECB daa Greece: New ECB daa Greece: difference beween old and new ECB daa Euro area: ECB daa Euro area: week EURIBOR Ialy Neherlands Spain Ialy: Old ECB daa Ialy: New ECB daa Ialy: difference beween old and new ECB daa Euro area: ECB daa Euro area: week EURIBOR Neherlands: Old ECB daa Neherlands: New ECB daa Neherlands: difference beween old and new ECB daa Euro area: ECB daa Euro area: week EURIBOR Spain: Old ECB daa Spain: New ECB daa Spain: difference beween old and new ECB daa Euro area: ECB daa Euro area: week EURIBOR Germany Germany: Old Bundesbank daa Germany: New Bundesbank daa Euro area: ECB daa Euro area: -week EURIBOR - Afer hese amendmens, we have pre- daa on overnigh deposis for five counries: Germany (from January ) and Finland, Ialy, Greece and Spain (from December 99). The group of he laer four counries is far from being sufficien o approximae a euro-area average before. Greece, which joined he euro area in January, exhibied very differen ineres rae developmens relaive o he oher euro-area counries before joining he euro, and herefore mixing Greek daa wih he daa of he oher eleven members 7

18 before Greece s enry o he euro area migh lead o an aggregae ha is difficul o inerpre. We herefore approximae he missing daa for he euro-area average for only -. While he five counries ogeher accoun for abou half of he euro area, calculaing a weighed average of he daa of he five counries (eg using weighs from heir shares in moneary aggregaes) would be appropriae only if hey are represenaive of he average. However, as Figure shows, Germany, he euro area s larges counry, used o have persisenly higher overnigh deposi raes han he euro-area average, while Finland and Spain used o have lower raes. Ialian and Greek raes were he closes o he euro-area average. The drop in he euro-area average is mosly visible in Spain (see he righ panel of Figure ). Figure shows ha here was a non-consan and sizeable spread beween he average of hese five counries and he euro-area average. Figure : Overnigh deposi raes: euro area versus he average of he five counries, January February Euro-area (changing composiion) Five euro-area counries.. Noe: he five counries are Finland, Germany, Greece, Ialy and Spain. We weighed he deposi raes of hese five counries wih he shares of hese counries in he aggregae ousanding volume of overnigh deposi of he five counries. We herefore decided no o weigh he counry-specific raes of he five counries using heir shares in aggregae volume of he five counries, bu we esimaed a regression o deermine he weighs. Specifically, we regressed he euro-area average rae on he ineres raes of he five counries as explanaory variables in he period - (a period ha may have similariies o he - period for which we aim o approximae he euro-area average). We do no include an inercep in he regression and consrain he parameers o sum up o one. Table shows he regression resuls. Ialy has he larges esimaed weigh ( percen), perhaps because Ialian ineres raes were he mos similar o he ineres raes of hose euro-area counries which are omied from he regression due o missing daa. The lef panel of Figure shows he fied values for - and he prediced values for -. The righ panel of Figure compares he euro-area average o he daa of he five counies.

19 Table : OLS regression of euro-area overnigh deposi rae on he overnigh deposi raes of five counries Coefficien Sd. Error -Saisic Germany... Finland.. 7. Ialy... Spain Greece. r, = β r + β r + β r + β r + β β β β β r, + u Noe: esimaed regression: EA DE, FI, IT, ES, ( ) GR. Since he parameer of he Greek ineres rae is consrained, is sandard error is no esimaed. The sample period includes monhly daa beween January and December. The coefficien of deerminaion (R) is.99. Figure : Overnigh deposi raes for he euro area and is approximaion for -, January February. Predicion period Esimaion period Euro-area overnigh deposi rae (ECB daa) Regression fi for - and esimae for - Euro area Finland Germany Greece Ialy Spain Deposis wih an agreed mauriy up o years Similarly o oher deposi raes, he ECB publishes euro-area average (changing composiion) and counryspecific ineres raes from January on deposis wih an agreed mauriy of up o years. For he following en counries, he ECB publishes separae imes series from December 99 o eiher June or Sepember : Deposis wih agreed mauriy, up o year: Ausria, Belgium, Germany, Greece and Porugal; Deposis wih agreed mauriy, over and up o years: France, Ialy, he Neherlands and Spain; Deposis wih agreed mauriy, oal: Finland. Presumably, deposi raes for hese mauriies should no differ much from he raes on deposis wih mauriy up o years. 9

20 Figure on he nex page shows ha he difference beween he old and he new series are indeed ypically small wih perhaps he excepion of Belgium. Ye for Belgium he dynamics of he old and new series are very similar in he period when boh raes are available. Therefore, we chain he old series o he new series similarly as we did wih he overnigh deposi raes, ie by adding o he old series he average spread beween he new and old series in. Figure also shows ha he differences compared o he euro-area average ineres rae (which is available from ) are ypically smaller (a leas up o he crisis) han in he cases of overnigh deposis raes. For example, he German erm deposi rae was pracically idenical o he euro-area average in -, while Figure showed ha he overnigh German deposi rae was higher han he euro-area average. Also, Figure repors ha Greek ineres raes developed very differenly from he raes in oher euro-area counries before Greece joined he moneary union in.

21 Figure : Raes on deposis wih an agreed mauriy up o years* for en euro-area counries wih available daa before, January 99 February Ausria Belgium Finland Ausria: Old ECB daa Ausria: New ECB daa Ausria: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Belgium: Old ECB daa Belgium: New ECB daa Belgium: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Finland: Old ECB daa Finland: New ECB daa Finland: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR France Germany Greece France: Old ECB daa France: New ECB daa France: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Germany: Old ECB daa Germany: New ECB daa Germany: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Greece: Old ECB daa Greece: New ECB daa Greece: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Ialy Neherlands 7 Spain Ialy: Old ECB daa Ialy: New ECB daa Ialy: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Neherlands: Old ECB daa Neherlands: New ECB daa Neherlands: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Spain: Old ECB daa Spain: New ECB daa Spain: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR 9 Porugal Porugal: Old ECB daa Porugal: New ECB daa Porugal: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR * The new counry-specific daa (available from January onwards) and he euro-area average (also available from January onwards) refer o deposis wih an agreed mauriy up o years. The old series available for December 99-June/Sepember refer o deposis wih differen mauriies: up o year (Ausria, Belgium, Germany, Greece and Porugal), over and up o years (France, Ialy, he Neherlands and Spain) and oal (Finland).

22 The group of en counries for which we have pre- ineres rae daa is likely represenaive for he euro area as a whole, which had members ha ime. Since he ousanding sock of deposis is available, we weighed he ineres raes of he counries wih weighs derived from heir combined sock of deposis. As Figure shows, he gap beween he changing composiion euro-area average and he average for hese member saes is very narrow indeed. In order o approximae he euro-area average in -, we calculaed he average spread beween he wo indicaors in - and subraced i from he euro-area rae in - (his approximaion is also indicaed on Figure ). Figure : The approximaion of euro area (changing composiion) ineres raes on deposis wih an agreed mauriy up o years using he weighed average ineres rae of en euro-area counries, January February Approximaion period Euro area (changing composiion) Ten euro-area counries (consan composiion) Noe: he euro area (changing composiion) daa is available from he ECB from January onwards; he - values of his ineres rae are our approximaion. Deposis redeemable a noice Pre- ineres raes on deposis redeemable a noice are available from he ECB for only four counries: Belgium, Germany, Greece and Ireland. There is no new daa for Belgium saring in, while for Greece he new ime series is available only for June April and herefore here is no overlapping period beween he old and new daa o check heir consisency, so we will no use he old daa of hese wo counries o approximae he euro-area average before. Moreover, he old and new German and Irish daa should have very differen definiions, as revealed by Figure 7. We herefore canno use counry-specific pre- ineres raes o approximae he euro-area average. Insead, we approximaed pre- euro-area average raes a differen way. The spread beween he ineres raes on deposis redeemable a noice and he raes on overnigh deposis was broadly sable (Figure ), so we link he former o he laer by using he approximaed value of he laer in -.

23 Figure 7: Ineres raes on deposis redeemable a noice for he wo euro-area counries wih available daa boh before and afer, January 99 February Germany Ireland Germany: Old ECB daa Germany: New ECB daa Germany: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Ireland: Old ECB daa Ireland: New ECB daa Ireland: difference beween old and new ECB daa Euro area: ECB daa Euro area: -monh EURIBOR Figure : The spread beween euro-area average ineres raes on deposis redeemable a noice and overnigh deposi rae, January February Consan spread assumpion Euro area: Ineres rae on deposis redeemable a noice Euro area: Ineres rae on overnigh deposis Spread beween he wo Repurchase agreemens Pre- daa on repurchase agreemens is available only for Spain, which is no sufficien o approximae he euro-area average. We approximae he euro-area repo rae for - by observing ha he spread beween he repo rae and he EURIBOR was raher sable in - (Figure 9). We herefore subrac basis poins (he average difference beween he -monh EURIBOR and he repo rae in -) from he - monh EURIBOR o approximae he pre- average euro-area repo rae.

24 Figure 9: Ineres raes on repurchase agreemens and he EURIBOR, January February Euro area: Ineres rae on repurchase agreemens Euro area: -week EURIBOR Euro area: -monh EURIBOR Euro area: -monh EURIBOR. The benchmark rae The so-called benchmark rae is he rae of reurn on an asse ha does no provide moneary service, only invesmen income. As Barne (97, 9) proved, he benchmark rae is needed o derive he weighs of he componens for he Divisia moneary indices and o calculae he user cos of money. Such a benchmark asse is hardly observable and herefore researchers/insiuions adoped differen approaches o approximae he benchmark rae. The mos widely used assumpion is o add a spread o he maximum reurn of some observed asses. The selecion of he maximum reurn (a each poin in ime) is called he upper envelope approach and in mos cases he componens of he money sock are considered. The spread which is added o he maximum reurn o ge he benchmark rae is called he liquidiy services premium. For example, Sracca () proxies he benchmark rae by adding basis poins o he rae on markeable insrumens (ha he defined as he sum of hree componens ha differeniae ECB s M and M: repurchase agreemens, money marke funds and deb securiies up o years). Jones and Sracca () adoped he same approach. El-Shagi and Kelly () adoped wo proxies: () adding basis poins o he reurn on he maximum reurn of he componens of he money sock, () adding a variable premium o he maximum reurn of he componens amouning o he spread beween he en-year and one-year governmen bond yields. Up o, he Bank of England proxied he benchmark rae as he ineres rae on hree-monh Local Governmen (LG) bills plus a basis poin spread, bu hen swiched o an envelope approach, whereby he benchmark asse is he M componen ha pays he highes ineres rae (see Hancock, ). The Cener for Financial Sabiliy (CFS) uses an envelope approach applied o all componens of he money sock plus a loan rae from 997, he dae from when his loan rae is available. For earlier years, basis poins are added o he yield on he highes yielding asse of M (see Barne e al, ). We find he fixed-spread assumpion o be ad hoc and herefore we sough an alernaive. Since only bank deb up o years mauriy is included in euro-area M, we also considered he yield on bank deb for longer The loan rae considered is he Weighed average effecive loan rae, low risk, o days, all commercial banks. The reason for he use of his rae is ha i acs as an upper limi o he ineres rae a bank will offer on any deposi caegory, because a bank will no pay ou o is deposiors more han i earns in ineres on he shor-erm loans i makes.

25 mauriies. BofA Merrill Lynch Year Euro Bond Indices are also calculaed for mauriies - years, -7 years, - years and over years. Bank deb wih such a long mauriy may have characerisics similar o he heoreical benchmark asse. Longer mauriy bank deb had higher reurns han he reurns on he componens of M. The lef panel of Figure plos he benchmark rae and he own rae of seven money componens. The righ panel of Figure shows he difference beween he benchmark rae and he maximum rae among he M componens. This spread, which can be regarded as an esimae of he liquidiy services premium, was quie variable boh before and afer he oubreak of he global financial and economic crisis. Figure : The benchmark rae, raes on he componens of M and he liquidiy premium (percen per year), January February Raes of reurn on M componens and he benchmark rae Liquidiy services premium Overnigh deposis Deposis up o years Deposis redeemable wih noice Repurchasemen agreemens Money marke funds Deb securiies up o wo years Benchmark rae Benchmark rae minus max rae of money componens Noe: The own rae on currency is zero and is no shown on he lef panel. The benchmark rae is he maximum of he rae on bank deb wih he following mauriies: -7 years, - years and over years. A drawback of our selecion of he benchmark asse is ha i should be risk-free in principle, while he longermauriy bank debs we consider are no risk free. However, mos componens of he money sock involve risk, including he -year mauriy bank deb and bank deposis 9. The rae on any risk-free benchmark asse would likely be lower han he reurn on many componens of he moneary aggregaes. For example, he reurn on - year German governmen bonds, which is probably a safe asse, is only. percen per year a he ime of wriing his paper, which is below all bu wo ineres raes indicaed on he lef panel of Figure. While Barne, Liu and Jensen (997) developed an aggregaion formula for he case of risk by using he consumpion capial asse pricing model (CCAPM), ha model is no wihou problems and he available Divisia moneary aggregaes for he EU and US are also no risk-adjused. We herefore do no adjus our aggregaion mehod o risk bu leave his issue for furher research. 9 Noe ha in Denmark (a non-euro area EU counry) and in Cyprus (a euro-area counry) deposiors having deposis over he, guaraneed amoun suffered losses during he resrucuring of some banks. Moreover, deposis were wihdrawn o a significan level from several euro-area periphery counries and ransferred o oher (safer) euro-area counries. This suggess ha even in he cases when deposiors did no suffer any acual loss, many of hem regarded heir deposis as unsafe in euro-area periphery counries.