Working Paper No. 425 International transmission of shocks: a time-varying factor-augmented VAR approach to the open economy

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1 Working Paper No. 5 Inernaional ransmission of shocks: a ime-varying facor-augmened VAR approach o he open economy Philip Liu, Haroon Mumaz and Angeliki Theophilopoulou May

2 Working Paper No. 5 Inernaional ransmission of shocks: a ime-varying facor-augmened VAR approach o he open economy Philip Liu, () Haroon Mumaz () and Angeliki Theophilopoulou (3) Absrac A growing lieraure has documened changes o he dynamics of key macroeconomic variables in indusrialised counries and highlighed he possibiliy ha hese variables may reac differenly o srucural shocks over ime. However, exising empirical work on he inernaional ransmission of shocks largely absracs from he possibiliy of changes o he inernaional ransmission mechanism across ime. In addiion, he lieraure has largely employed small-scale models wih limied number of variables. This paper inroduces an empirical model which allows he esimaion of ime-varying response of a large se of domesic variables o foreign money supply, demand and supply shocks. The key resuls show ha a foreign moneary policy ighening resembles he classic beggar-hy-neighbour scenario for he Unied Kingdom in he period 9. In more recen periods, he response is negaive bu largely insignifican. Key words: Facor-augmened VAR, ime-variaion, Gibbs sampling. () Inernaional Moneary Fund. pliu@imf.org () Bank of England, Cenre for Cenral Banking Sudies. haroon.mumaz@bankofengland.co.uk (3) Universiy of Wesminiser. a.heophilopoulou@wesminser.ac.uk The views expressed in his paper are hose of he auhors, and no necessarily hose of he Bank of England. The auhors wish o hank Simon Price and Paule Sadler for useful commens. Emelie Jenser provided excellen research assisance. This paper was finalised on 3 December. The Bank of England s working paper series is exernally refereed. Informaion on he Bank s working paper series can be found a Publicaions Group, Bank of England, Threadneedle Sree, London, ECR 8AH Telephone + () 7 3 Fax + () mapublicaions@bankofengland.co.uk Bank of England ISSN (on-line)

3 Conens Summary 3 Inroducion 5 An open economy FAVAR model wih ime-varying coefficiens 7. Esimaion. Idenificaion of srucural shocks.3 Daa descripion 3 Empirical resuls 3 3. Inernaional comovemens 3 3. An unanicipaed increase in world ineres raes Inernaional demand and supply shocks 3. Forecas error variance decomposiion 3 Conclusions 8 Appendix 9 The empirical model 9 Idenificaion 3 Esimaion: muli-sep Gibbs sampling 33 Imposing he sign resricions 37 Generalised impulse response funcions 37 Descripion of he daa 38 MCMC convergence diagnosics References Working Paper No. 5 May

4 Summary Undersanding and quanifying he inernaional ransmission mechanism whereby economic shocks are propagaed around economies is imporan for formulaing possible policy responses o developmens in he world economy. This is one of he reasons why a subsanial empirical lieraure has focused on his issue. Bu he exising work on his issue shares wo shorcomings. Firs, analyses do no allow for he possibiliy of ime-variaion in he parameers of he model. This feaure is surprising as changing dynamics of variables such as inflaion and oupu have been highlighed by many sudies of macroeconomies. Second, mos empirical sudies on he inernaional ransmission of shocks are based on small-scale vecor auoregressions (VARs) (models ha relae each variable in he sysem o pas values of all included variables). Arguably, cenral banks across he world monior (and possibly respond o) a far wider informaion se han is ypically assumed in hese small VARs, leaving hem open o he possibiliy of misspecificaion. Moreover, from a pracical perspecive small VARs are unable o provide inference on a large number of variables ha may be of ineres o policy makers. The aim of his paper is o fill hese gaps in he empirical lieraure on inernaional ransmission. We aemp o do his by devising an empirical model ha: allows for ime-variaion in he inernaional ransmission mechanism; and allows he simulaneous esimaion of he response of a large se of UK variables o foreign moneary policy, demand and supply shocks. In paricular, his paper proposes an open economy facor-augmened VAR (a FAVAR) which incorporaes ime-varying coefficiens. This capures he widely acceped idea ha mos macroeconomic variables can be hough of as being largely driven by a small number of common facors. Those included in our proposed FAVAR can be hough of as weighed averages of a large panel of inernaional and UK daa. Consequenly he proposed model conains significanly more informaion han he small-scale VARs used in he exising lieraure. The empirical resuls, using quarerly daa from 97 o 5, indicae ha here have been imporan changes across ime in he response of UK variables o inernaional shocks. For example, while real aciviy responded srongly o foreign money expansion during he 97s, his response was mued during he period These resuls are consisen wih a fall in he degree of exchange rae pass-hrough o impor prices. Foreign aggregae demand shocks had Working Paper No. 5 May 3

5 a large posiive impac on UK GDP during he years However, he impac over he subsequen period was subsanially smaller. Foreign supply shocks had a persisen impac on UK inflaion and wages during he mid-97s, bu wih a smaller impac esimaed during he period Working Paper No. 5 May

6 Inroducion Undersanding he inernaional ransmission mechanism of economic shocks is an imporan sep owards idenifying he bes policy response in an individual economy o inernaional developmens. In a world economy, which has experienced a seady increase in inegraion across goods, capial and financial markes, he inernaional aspec of he ransmission mechanism has become an essenial ingredien in policy discussions. A large empirical lieraure has invesigaed he inernaional ransmission of moneary and non-moneary shocks using small-scale srucural vecor auo-regression (VAR) models. The idenificaion resricions in hese models are ofen a conroversial opic, where differen assumpions can lead o quie differen conclusions. Several recen papers have proposed alernaive idenificaion srucures including, among ohers, he recursive schemes in Grilli and Roubini (995), Eichenbaum and Evans (995) and Faus and Rogers (3), he non-recursive schemes in Cushman and Zha (997), Dungey and Pagan (), Kim and Roubini (), and Kim (), and he sign resricions in Canova (5), Scholl and Uhlig () and Liu (8). Despie he differen approaches o idenificaion, hese papers share wo imporan feaures. Firs, hese papers do no allow for he possibiliy of ime-variaion in he coefficiens and variances of he model. This feaure is surprising especially as an imporan empirical regulariy observed since he mid-98s is he change in macroeconomic dynamics. Kim and Nelson (999), McConnell and Perez-Quiros (), and Cogley and Sargen (5) show ha he volailiy of US oupu and he volailiy and persisence of US inflaion has fallen significanly over he las hree decades. Benai () presens similar resuls for he Unied Kingdom. In addiion, Cogley and Sargen () and Clarida, Galí and Gerler () show ha changing macroeconomic dynamics in he Unied Saes were accompanied by a change in he moneary policy rule adoped by he Federal Reserve, wih a higher weigh given o inflaion in he pos-98 period. A relaed srand of his lieraure has focused on he possibiliy of changes in he domesic ransmission of moneary policy. Boivin and Giannoni () esimae he response of oupu and inflaion o a moneary policy shock in he Unied Saes using a VAR based on wo subsamples: and 98-. Their resuls sugges ha he response of oupu and inflaion is smaller in he laer period. The recen work by Campa and Goldberg (5) provides some evidence of decline in he pass-hrough of exchange rae shocks o impor prices for OECD Working Paper No. 5 May 5

7 counries. Taken ogeher, his growing lieraure provides srong evidence ha srucural changes have occurred in prominen indusrialised counries over he las 3 years. The implicaions of hese changes for he inernaional ransmission mechanism remains largely unexplored. Second, mos empirical sudies on he inernaional ransmission of shocks are based on VAR models ha include only a few seleced variables. Arguably, cenral banks across he world monior (and possibly respond o) a far wider informaion se han ypically assumed in hese small-scale VARs leaving hem open o he possibiliy of misspecificaion. Moreover, from a pracical perspecive small-scale VARs are unable o provide inference on large number of variables ha may be of ineres. For example, lile or no evidence exiss on he ransmission of foreign shocks o domesic asse prices such as house prices and equiy prices. The aim of his paper is o fill hese gaps in he empirical lieraure on inernaional ransmission. In paricular, his paper aims o provide a comprehensive analysis of how he impac of foreign shocks on key macroeconomic variables of a small open economy like he Unied Kingdom has evolved over ime. We aemp o do his by devising an empirical model ha: (a) allows for ime-variaion in he inernaional ransmission mechanism, and (b) allows he simulaneous esimaion of he response of a large se of UK variables o foreign moneary policy, demand and supply shocks. In paricular, his paper proposes an open economy facor-augmened VAR (FAVAR) which incorporaes ime-varying coefficiens and sochasic volailiy in he shocks. The proposed model capures he changing comovemens among macroeconomic ime series by allowing heir dependence on common facors o evolve over ime. The main conribuion of he paper is o assess possible changes o he ransmission of exernal moneary policy, demand and supply shocks, a feaure ha, o he bes of our knowledge, has been ignored in he lieraure on inernaional ransmission and he Grea Moderaion. A furher advanage of our approach is ha i allows us o simulaneously derive he (ime-varying) dynamic responses for a wider range of economic indicaors wihou placing overly resricive prior resricions on he model s parameers. The main resuls of he paper are as follows. A foreign moneary policy conracion has Working Paper No. 5 May

8 subsanially differen effecs on he Unied Kingdom in he period afer 99 compared o he period -9. In paricular, he response of he domesic economy in he period before 99 resembles a classic beggar-hy-neighbour scenario, wih decreases in foreign money supply resuling in an increase in UK real aciviy. In conras, he pos-99 period is characerised wih negaive bu insignifican response of UK real aciviy o a fall in foreign money supply. Our esimaes are consisen wih a fall in he degree of exchange rae pass-hrough o impor prices. A foreign aggregae demand shock has a large posiive impac on UK GDP during he years Is impac over he more recen period has been subsanially smaller. Foreign supply shocks have a persisen impac on UK inflaion and wages during he mid-97s wih a smaller impac esimaed during he curren period. The paper is organised as follows. Secion oulines he empirical model and discusses he idenificaion assumpions. Secion 3 repors he comovemen of he inernaional facors, dynamic effecs of an unexpeced fall in world ineres raes, an unexpeced increase in world aciviies and an unanicipaed negaive world supply shock on a seleced subse of UK macroeconomic indicaors. Secion conains concluding remarks and direcions for fuure research. An open economy FAVAR model wih ime-varying coefficiens We aemp o formulae an empirical model ha allows us o efficienly model he relaionship beween a large se of UK and foreign variables, while simulaneously allowing his relaionship o be ime-varying. The saring poin is he following resriced VAR model F B (L) F F U K = B (L) B (L) B 3 (L) F U K + u () B 3 (L) B 3 (L) B 33 (L) R R The VAR in equaion () consiss of wo blocks, one for he Unied Kingdom and oher for he res of he world, which is ordered firs. The informaion abou he Unied Kingdom and he res of he world is summarised by he unobserved facors, F = [F F U K ], where denoes he foreign economies and U K denoes he domesic economy. The UK shor-erm ineres rae, R, See he appendix for a full echnical descripion of he model. The erms foreign and world are used inerchangeably in his paper. The erm home refers o he Unied Kingdom. Working Paper No. 5 May 7

9 is included o accoun for domesic moneary policy. The zero resricions in equaion () reflec our assumpion ha being a small open economy, he Unied Kingdom is unable o influence he res of he world. 3 There are hree foreign facors F facor, F π = F Y, F π is a foreign inflaion facor, F R and F R, where F Y is a foreign real aciviy is a foreign ineres rae facor. F U K denoe k = facors for he Unied Kingdom. The seven facors ogeher summarise he variaion in an underlying panel daa se of foreign and UK variables. They are linked o he panel daa se via he following equaion where X Y X Y X π X R X U K R = Y π R U K R denoes daa on foreign real aciviy, X π denoes daa on foreign ineres raes and X U K F Y F π F R F U K R + v () denoes daa on foreign inflaion, X R denoes a panel daa se for he Unied Kingdom ha includes indicaors on real aciviy, inflaion, money supply and asse prices. Y R, π and are he facor loadings on foreign real aciviy daa, foreign inflaion daa and foreign ineres rae daa. U K is N U K k marix of facor loadings ha link he k domesic unobserved facors o UK daa and R, N U K, capures he conemporaneous relaionship beween some of he fas-moving UK variables (eg asse prices) and he shor-erm ineres rae. We assume wo sources of ime-variaion in equaions () and (). Firsly, we allow he VAR covariance marix Var(u ) o evolve over ime as a random walk. Secondly, following Del Negro and Orok (8), he facor loadings Y, π, R, U K and R are also assumed o evolve over ime as random walks. This assumed srucure is an efficien way of inroducing ime-varying dynamics wihin our model. In paricular, he ime-varying facor loadings allow he relaionship beween he foreign variables (X Y, X π and X π ) and domesic variables X U K o be ime-varying. This can easily be seen by subsiuing he equaion for F U K from () o he equaion for X U K in (). This gives [ X U K = U K B (L)F + B (L)F U K + B ] 3(L)R + u + R R + v U K where he produc 3 We expand on his in our discussion of he VAR idenificaion scheme below. Working Paper No. 5 May 8

10 of U K B (L) is ime varying. Similarly, allowing o be ime varying implies ime-varying conemporaneous relaionship beween foreign and domesic variables. Equaions () and () capure he ime-varying dynamic relaionship beween macroeconomic condiions in he res of he world (as summarised by F Y, F π and F R ) and he UK economy (as summarised by F U K ). By using he VAR in equaion () i is possible o esimae he impulse response of F U K o an innovaion in F. Moreover, by using equaion (), i is possible o recover he response of any of he variables in he UK panel X U K o his foreign shock. Therefore, alhough he srucure of our VAR model is similar o ha in Cushman and Zha (997) and Kim (), (as in Mumaz and Surico (9)) our specificaion offers he disinc advanage ha he response of a wide range of UK variables o foreign shocks can easily be derived. Noe also ha as he facor loadings are ime-varying, he impulse response of X U K a each poin in ime over he sample period. can be esimaed This model is closely relaed o wo recen conribuions in he ime-varying VAR lieraure. Bianchi, Mumaz and Surico (9) esimae a ime-varying (closed economy) FAVAR model where ime-variaion is inroduced via ime-varying coefficiens in he VAR (ie equaion () in our conex). This approach is paricularly difficul o implemen wihin our framework because he large number of endogenous variables in () makes i compuaionally difficul o impose sabiliy on he VAR a each poin in ime. Anoher specificaion possibly suied o our problem is he elegan muli-counry VAR inroduced by Canova and Ciccarelli (). The auhors inroduce a VAR model of he following form Y i, j, = BY i, j, + e (3) where i indexes he counry and j denoes he variable. The dimensions of he VAR coefficien marix B can be subsanial if a large number of series/counries are included in Y. To deal wih his problem, Canova and Ciccarelli () sugges facorising he coefficiens B ino B = K + d () where K is a se of facors or linear combinaions of B (deermined by he srucure of he loading marix ) ha represen counry-specific or variable-specific feaures and d is an i.i.d disurbance. In his framework, ime-variaion can be inroduced by specifying some dynamic srucure for K. Working Paper No. 5 May 9

11 To see he link beween his specificaion and our model, subsiue equaion () ino (3) such ha Y i, j, = K Y i, j, + d Y i, j, + e. Noe ha Y i, j, represen linear combinaions of he daa analogous o he facors in a FAVAR (see equaion ()). The model in (3) has he advanage ha i reains daa for each counry (in he panel individually) and allows he invesigaion of links beween specific counries. However, is applicabiliy is less clear in our conex where ineres cenres on he influence of foreign shocks (wihou necessarily specifying he source of he shock as coming from a paricular counry). Also coefficien facorisaion in equaion () makes i difficul o direcly impose resricions implied by he small open economy assumpion.. Esimaion The model in equaions () o () is esimaed using Bayesian mehods described in Kim and Nelson (998), Primiceri (5) and Del Negro and Orok (8) o approximae he poserior disribuion. Essenially, his amouns o reducing a complex problem of sampling from he join poserior disribuion ino a sequence of racable ones by sampling from he condiional disribuion of a subse of parameers condiional on all oher parameers of he model. The muli-sep Gibbs sampling procedure can be broken down ino four main seps (see he appendix for full deails on he condiional poserior disribuions). Sep Condiional on all oher parameers, he VAR coefficiens have a normal poserior disribuion where he mean and variance of his disribuion can be derived via he Kalman filer (his is needed as he VAR covariance is ime-varying). We impose he small open economy resricions as a igh prior cenred on zero on he appropriae elemens of he VAR coefficien marix. Sep The unobserved facors can be sampled using he mehods described in Carer and Kohn (99). Sep 3 Similarly he mehods for sae-space models in Carer and Kohn (99) are used o sample he ime-varying facor loadings. Sep We use he mehods described in Primiceri (5) and Jacquier, Polson and Rossi (99) o sample he ime-varying VAR covariance marix. Working Paper No. 5 May

12 Our algorihm cycles hrough hese seps 5, imes using he las, draws for inference. The recursive means of he reained draws show lile variaion hus providing evidence in favour of convergence (see supplemenary maerial in he appendix).. Idenificaion of srucural shocks We are ineresed in sudying he dynamic effecs of hree shocks on he UK economy: an unanicipaed fall in he ineres raes in he res of he world, an unanicipaed expansion in inernaional aciviy and a negaive world supply shock. Noe ha he analysis of hese shocks is imporan from a heoreical and policy poin of view. For example, a key quesion in inernaional macroeconomics is he impac of exernal moneary shocks o a small open economy wih differen assumpions abou pricing behaviour implying a poenially differen impac on domesic variables. Using our model one can approach his quesion in a framework ha is flexible (ie allows he impac of he shock o be ime-varying) and poenially robus o misspecificaion due o he daa-rich naure of he model (see Mumaz and Surico (9)). Second he impac of hese shocks is policy relevan. The recen recession has been characerised by a reducion in ineres raes by a large group of counries (in paricular by mos of he counries included in he foreign block of our model). Similarly, several previous economic evens can be characerised as common demand or supply shocks abroad. In our model, hese foreign shocks are idenified using wo schemes based on a mixure of sign and zero resricions and a recursive scheme. The ordering of he FAVAR is [F Y, F π, F R, Fj, U K, R ] wih j =,..., k and he leers denoe inernaional real aciviy growh, inflaion and ineres raes, domesic facors and domesic shor-erm ineres rae, respecively. In our benchmark idenificaion scheme, we impose a mixure of sign and zero resricions: u Y + + e AD u + e AS u R = + + e R (5) u F,uk e F,uk u R e R Working Paper No. 5 May

13 where e are he srucural shocks and he sign resricions are imposed as described in he appendix. In he foreign block, a shock o aggregae demand is associaed, on impac, wih an increase in foreign aciviy, inflaion and ineres raes; a posiive supply shock implies a fall in inflaion and a rise in real aciviy, he ineres rae response is lef unresriced; a posiive shock o he shor-erm ineres raes comes wih a decline in real aciviy and inflaion. Noice ha he impac of inernaional shocks on he domesic economy is lef unresriced. We check our resuls using an alernaive idenificaion scheme based on a Choleski decomposiion. This implies he following conemporaneous resricions: u Y e Y u e u R = e R u F,uk e F,uk u R e R () Noe ha by placing he UK shor-erm ineres rae las, we implicily idenify a UK moneary policy shock under boh schemes. Also, he zero resricions in boh idenificaion schemes combined wih he block-zero srucure for he lag polynomial marix B(L) implies ha he res of he world does no reac o UK domesic condiions conemporaneously or wih lags..3 Daa descripion We use quarerly daa from 97 Q o 5 Q. 5 The daa se spans 7 counries and 5 series. We refer o he Unied Kingdom as he domesic economy. The foreign counries are Ausralia, Belgium, Canada, Finland, France, Germany, Ialy, Japan, Luxembourg, Neherlands, New Zealand, Norway, Porugal, Spain, Sweden and Unied Saes. The foreign block includes mos of he Unied Kingdom s main rading parners and he major indusrialised economies across he world. For each foreign counry, we collec daa on real aciviy, inflaion and ineres raes. For real aciviy, we consider daa on oupu growh, employmen, consumpion and invesmen. Inflaion A mixure of sign and zero resricions is also used by Faus and Rogers (3). 5 The laes period is excluded as real aciviy daa for some counries included in our panel was unavailable during hese years. To balance he panel we resric aenion o he period 97 Q o 5 Q. Working Paper No. 5 May

14 is measured on he basis of a variey of domesic price indices, wage growh and impor prices. Shor-erm ineres raes are colleced for each counry. The daa se for he Unied Kingdom is very similar in composiion o ha of he foreign block. In paricular, we have many differen real aciviy indicaors, inflaion series including componens of he reail price index, narrow and broad money and a se of asse prices ha include house prices and he effecive exchange rae. A more deailed descripion of he daa series is available upon reques (see supplemenary maerial in he appendix). 3 Empirical resuls This secion describes he empirical resuls of he ime-varying open economy FAVAR developed in Secion. We repor esimaes of he unobserved foreign facors and compue he dynamic effecs of an unanicipaed increase in world ineres raes, an unanicipaed expansion of inernaional aciviy and an unanicipaed negaive world supply shock using he generalised impulse response funcions described in he appendix. We also compue he forecas variance decomposiion of key UK variables in response o he hree foreign shocks. I is ineresing o noe ha wih a large informaion se, he Choleski and he sign resricion idenificaion schemes no longer produce significanly differen resuls. Here, we focus he discussion of he resuls based on he sign-resricion scheme. 3. Inernaional comovemens We exrac hree common componens from he foreign block of he panel using he idenificaion described above. All variables are sandardised. Char plos he esimaed facors for world real aciviy, inflaion and nominal ineres raes (blue is he esimaed facors from he Gibbs sampling and magena is he principal componen esimaor). The narrowness of he confidence inerval indicaes ha he facors are esimaed quie precisely. I is ineresing o noe he similariies beween he Gibbs sampling (GS) procedure and he principal componens esimaor (PCE) for he real aciviy and inflaion facors. For he ineres rae facor, he PCE is more persisen and he cyclical flucuaions are less volaile compared Working Paper No. 5 May 3

15 Char : Sandardised foreign facors (ligh blue band is he 95% confidence inervals) World real aciviy World inflaion World ineres rae % CI Gibbs zero PC wih he GS procedure. Neverheless, he cyclical flucuaions beween he wo series are similar. One explanaion for he difference is ha he GS procedure akes ino accoun he auocorrelaion of he idiosyncraic componens of each series, herefore i aribues less of he observed persisence o he common componen. Comparing our esimaes wih previous sudies such as Kose, Orok and Whieman (3), a few paerns are very similar. The indusrialised world experienced, on average, four severe recessions over he sample period: he mid-97s oil price shock; he early 98s recession associaed wih he deb crisis, loose US fiscal policy and igh moneary policy o bring down inflaion; he early 99s downurn; and he downurn in following he burs of he docom bubble. The daes roughly mach hose idenified in Kose e al (3). Ineresingly, by using higher frequency observaions (quarerly daa raher han annual), we idenified he early 98s recession as a double dip in economic aciviy whereas esimaes from Kose e al (3) sugges a prolonged recession. Our esimaes sugges he decline in world economic aciviy in Working Paper No. 5 May

16 he mid-97s was he seepes ou of he four recessions, bu is recovery was very rapid. The rough in he early 98s recession was less severe bu he recovery was slower due o he higher ineres raes over ha period. The magniude and he speed of recovery beween he early 99s and recession was remarkably similar. In boh cases, he fall in he ineres rae may have helped o speed up he recovery. The decline in he measure of inernaional inflaion is consisen wih he noion of global disinflaion pu forward by Rogoff (3). Despie he seady increase in oil and commodiy prices beween 3-5, world inflaion remained relaively sable. World ineres rae peaked in he early 98s, since hen, i has declined significanly reaching hisorical lows in he very recen pas. 3. An unanicipaed increase in world ineres raes 3.. World facors A shock o he world ineres rae facor canno be inerpreed lierally as a foreign policy shock as here is nohing such as a world policy maker. However, a generalised increase in ineres raes may represen a siuaion ha requires cenral banks across he world o deviae from he pah implied by he sysemaic componen of heir moneary policy. The global disinflaion sance in he early 98s and he recen experience of unprecedened low policy raes are examples of such evens. Here, we inerpre he unanicipaed increase in ineres raes across he world as a conracionary moneary policy shock ha occurs, on average, in he foreign block. Char plos he dynamic effecs of he world facors in response o a conracionary moneary shock. The size of he shock is normalised o be a % increase in he world ineres rae facor. The firs column plos he median impulse response funcions (IRFs) o he shock esimaed for he fourh quarer of each year in he sample, while he second and hird columns illusrae he responses in and ogeher wih he 8% error bands (ligh blue band). The increase in world ineres raes generaes a saisically significan conracion in real world aciviy and inflaion. More ineresingly, once we conrol for he ime-varying sochasic volailiy he response of he world facors are very similar across ime. The inflaion response is slighly larger in he laer par of he sample bu he difference is small. Based on hese esimaes, he Working Paper No. 5 May 5

17 World Ineres Rae Inflaion Real Aciviy Char : Response of world facors o a world moneary conracion varying IRF impac of world moneary policy shocks on real aciviy and inflaion has changed lile over he sample period. 3.. UK exernal indicaors The key o undersanding he inernaional ransmission mechanism o foreign moneary shocks res on he behaviour of he exchange rae and he response of relaive prices o he shock. Char 3 plos he ime-varying responses for he UK nominal effecive exchange rae (NEER), erms of rade, rade balance, impor and expor prices. Noe ha he final column of he char compares he disribuion of impulse responses (cumulaed a he one-year horizon) in 97 and. If he majoriy of he draws lie below he 5 o line, ha indicaes he cumulaed response is larger in Working Paper No. 5 May

18 Expor Prices Impor Prices Trade Balance Terms of rade NEER 97 relaive o and vice versa. Throughou he sample, he exchange rae depreciaes in response o higher capial ouflows from he lower ineres rae differenial. 7 Is response was he weakes in he early 99s around he ime of Unied Kingdom s exi from he European Exchange Rae Mechanism (ERM). Char 3: Response of UK exernal indicaors o a world moneary conracion varying IRF Accumulaed response: and In he earlier par of he sample, he median impor price response increases immediaely following he exchange rae depreciaion and hen falls slowly. This is consisen wih he noion of producer currency pricing (PCP) by foreign exporers. More recenly, pass-hrough from he exchange rae depreciaion is smaller wih he median conemporaneous response closer o zero. This lends more suppor owards local currency pricing (LCP) and is consisen wih recen papers ha documen a fall in exchange rae pass-hrough in he Unied Kingdom (see for Noe ha in he ex, by saisical significance we imply a siuaion where he poserior disribuion does no conain zero. 7 Foreign ineres rae is higher han he domesic ineres rae. Working Paper No. 5 May 7

19 Consumpion GDP Invesmen example Campa and Goldberg () and Mumaz, Oomen and Wang ()). As a resul of his shock, he Unied Kingdom s erms of rade deerioraes and he rade balance improves wih a larger response in he early years of he sample. This is consisen wih he earlier explanaion of PCP, high exchange rae pass-hrough and he classic expendiure swiching effec UK real aciviy and inflaion Char : Response of UK real aciviies o a world moneary conracion.3.. varying IRF Accumulaed response: and Char plos he ime-varying response of invesmen, GDP and consumpion. One sriking feaure is he uniform swich in he sign of conemporaneous responses from posiive o negaive among he real aciviy indicaors in he early 99s. Noe also ha, while he posiive impac on invesmen, GDP and consumpion is large and significan in he earlier par of he sample, he corresponding negaive responses oward he end of he sample period are largely insignifican. This change is consisen wih he possibiliy discussed above of a shif from producer o local Working Paper No. 5 May 8

20 GDP Deflaor Wages CPI Inflaion currency pricing and a fall in exchange rae pass-hrough. Under PCP, high exchange rae pass-hrough o impor prices give domesic consumers more incenives o shif consumpion owards relaively cheaper home goods - he expendiure swiching effec. If his expendiure swiching effec dominaes he negaive income effec from he conracion in world money supply, hen domesic real aciviy is posiively affeced as appears o be he case in he earlier par of he sample. On he oher hand, if impors are priced in local currency and exchange rae pass-hrough is low, hen here is less incenive for consumers o swich from impors o domesic goods and he beggar-hy-neighbour effec is amelioraed. See Bes and Devereux (999) for a more deailed explanaion. 8 Char 5: Response of UK inflaion and wages o a world moneary conracion varying IRF Accumulaed response: and Char 5 plos he ime-varying response of nominal wages, inflaion measures based on he CPI 8 We have also invesigaed he possibiliy of changes o he policy sance using Lubik and Schorfheide s (5) model as an alernaive explanaion. However, changes o boh foreign and domesic policy sance canno explain he swich in he sign of domesic aciviies. Working Paper No. 5 May 9

21 Shor erm rae yr Bond FTSE House Prices and GDP deflaor. Boh inflaion measures fall immediaely following he shock and reach heir peak around four quarers. According o he CPI measure, he accumulaed fall is slighly smaller in he earlier sample whereas he GDP deflaor measure shows a similar response across he sample period. The wage response is largely around zero a he beginning of he sample bu falls slighly in he laer sample. 3.. UK asse prices Char : Response of UK asse prices o a world moneary conracion v ary ing IRF Accumulaed response: and Char plos he ime-varying response of 9-day, -year governmen bond yields, and he growh rae of house and equiy (measured by he FTSE index) prices. There is a saisically significan increase in boh he shor and long-erm ineres raes following he shock. The response of house prices is posiive and significan during he 97s and he 98s. However, his response is largely insignifican over he pos-99 period. The FTSE declines in response o he shock in he 97s bu is response is largely insignifican over he res of he sample period. Working Paper No. 5 May

22 3..5 Resuls from recursive idenificaion scheme Char 7: Response of UK variables o a world moneary conracion using recursive idenificaion NEER Terms of rade Trade Balance Impor Prices Expor Prices Invesmen GDP Consumpion CPI Wages GDP Deflaor House Prices Char 7 plos he ime-varying response for various UK variables using he recursive idenificaion scheme (RIS) described in equaion (). The sign and shape of he dynamic responses are largely similar across he wo idenificaion schemes. However, here are some ineresing differences. Firs, he magniude of he NEER and erms of rade responses are smaller in he RIS. For example, he erms of rade now peaks a.5% raher han.% earlier. Second, he responses for wages and he inflaion measures from he RIS reurns o zero much faser, wihin he firs five quarers of he shock raher han over quarers. Third, he swich in he sign of domesic economic aciviy now happens in a much more gradual manner. Neverheless, he iming of he swich are more or less he same. Working Paper No. 5 May

23 Shor erm ineres GDP Wages CPI Inflaion NEER Char 8: Response of key UK variables o a posiive world demand shock varying IRF Accumulaed response: and Inernaional demand and supply shocks Char 8 presens he response of key UK variables o a posiive foreign demand shock. The shock is normalised so ha i increases he world aciviy facor by one uni. 9 The NEER and he erms of rade were virually unaffeced by he shock. A he beginning and he end of he sample, he impac on domesic real aciviy is close o zero. However, for a large par of he sample (beween 98 and 998) domesic aciviy increases in response o he higher world demand albei he impac is relaively shor-lived. The sronges impac is beween Boh nominal wages and CPI inflaion is significanly posiive in he medium erm. The peak response of he domesic shor-erm ineres rae response o his shock is very similar across he sample. Impulse responses o a negaive world supply shock (calibraed o increase he world inflaion facor by %) are presened in Char 9. Boh inflaion and wages increase significanly in 9 Noe ha he normalisaion of he demand and supply shocks on real aciviy and inflaion facors, respecively, is for convenience and simpliciy. These responses could be normalised on oher variables. Working Paper No. 5 May

24 Shor erm ineres GDP Wages CPI Inflaion NEER Char 9: Response of key UK variables o a negaive world supply shock.5 varying IRF Accumulaed response: and response o his shock during he 97s. I is ineresing o noe ha he response of hese variables in he pos-98 period is smaller and less persisen, possibly indicaing he role played by moneary policy in anchoring inflaion expecaions during he Thacher years. UK GDP, falls following he supply shock. The magniude of his fall is smaller since he 99s. 3. Forecas error variance decomposiion Our model allows us o compue a ime-varying forecas error variance decomposiion o assess possible changes in he imporance of foreign shocks for he UK economy, Char plos he decomposiion (he median esimae for he fourh quarer of each year in he sample) for exernal indicaors of he Unied Kingdom. The hree foreign shocks ogeher conribue around % of he oal forecas error variance for he NEER across he sample period, wih foreign moneary policy shocks more imporan in he pre-98 period. Foreign demand shocks appear imporan for impor and expor prices hroughou he sample period, explaining abou % o 3% of he forecas error variance. I is ineresing o noe ha foreign supply shocks played an Working Paper No. 5 May 3

25 Trade Balance Terms of Trade Expor Prices Impor Prices NEER Char : Variance decomposiions of UK exernal secor o foreign shocks 8 Foreign Moneary Policy Shock Foreign Demand Shock Foreign Supply Shock imporan role for he erms of rade before he 99s bu much smaller role more recenly. Char shows ha he foreign shocks are esimaed o have conribued around % of he oal forecas error variance for UK real aciviy. The foreign moneary policy shocks were somewha more imporan during he 97s. On he oher hand, supply shocks appear o have he larges conribuion during he lae 98s and he early 99s. Char presens he forecas error variance decomposiion for wages and inflaion. Foreign demand shocks made an imporan conribuion o he measures of inflaion and wages hroughou he sample period, conribuing around % o 5% especially a long horizons. Foreign supply shocks were imporan during he 97s especially for GDP deflaor inflaion. In Char 3, he foreign moneary policy shocks conribue around % o he forecas error variance of house prices during he 97s, wih a smaller conribuion in he subsequen periods. More recenly, foreign demand shocks have played a more imporan role in deermining house Working Paper No. 5 May

26 Consumpion GDP Invesmen Char : Variance decomposiions of UK aciviy indicaors o foreign shocks Foreign Moneary Policy Shock Foreign Demand Shock Foreign Supply Shock price forecas error variance. The decomposiion for he FTSE shows a similar paern, wih foreign moneary policy and supply shocks relaively imporan during he 97s while foreign demand shocks make a slighly larger conribuion owards he end of he sample period. I is ineresing o noe ha foreign policy shocks were imporan for he shor-erm ineres rae in he pre-99 period. However, demand shocks have remained imporan for he shor and long-erm rae over he enire sample. Working Paper No. 5 May 5

27 GDP Deflaor Wages Inflaion Char : Variance decomposiions of UK inflaion indicaors o foreign shocks Foreign Moneary Policy Shock Foreign Demand Shock Foreign Supply Shock Working Paper No. 5 May

28 ST ineres rae year Gov Yield FTSE House Prices Char 3: Variance decomposiions of UK asse indicaors o foreign shocks 5 Foreign Moneary Policy Shock 8 Foreign Demand Shock 8 Foreign Supply Shock Working Paper No. 5 May 7

29 Conclusions This paper has sudied he inernaional ransmission of srucural shocks in an open economy FAVAR model applied o he Unied Kingdom. Unlike previous conribuions, we use daa on 7 counries and 5 variables, covering prices, aciviy and moneary indicaors, o model he ineracion beween he foreign and domesic blocks of he VAR. In addiion, we allow he relaionships embodied in his model o change over ime by incorporaing ime-varying coefficiens and sochasic volailiy wihin he FAVAR framework. A foreign moneary policy easing has subsanially differen effecs on he Unied Kingdom in he period afer 99. In paricular, he response of he domesic economy in he period before 99 resembles a classic beggar-hy-neighbour scenario, wih decreases in foreign money supply resuling in an increase in UK real aciviy. In conras, he pos-99 period is characerised wih negaive bu insignifican response of UK real aciviy o his shock. A posiive foreign aggregae demand shock have a large posiive impac on UK GDP during he years Is impac over he more recen period have been subsanially smaller. Foreign supply shocks led o a persisen increase in UK inflaion and wages during he 97s, wih he curren impac esimaed o be relaively small. Forecas error variance decomposiion from he model suggess ha he conribuion of foreign shocks o forecas error variance of domesic variables have been relaively modes, ye non-negligible ranging a mos % o 5% in oal for some variables. The conribuions also display ime-variaion: he role of foreign moneary policy and supply shocks have become smaller over he sample period. In conras, foreign demand shocks remain imporan for UK inflaion and asse prices. In his sudy, we have idenified changes o he inernaional ransmission of shocks around 99 which corresponds o significan changes o he Unied Kingdom s moneary policy framework. Fuure research could herefore be direced owards undersanding he ineracions beween moneary policy response and he inernaional ransmission mechanism. Working Paper No. 5 May 8

30 Appendix The empirical model The model consiss of wo blocks, one for he Unied Kingdom and oher for he res of he world, which is ordered firs. The informaion abou he Unied Kingdom and he res of he world are summarised by K unobserved facors, F = [F F U K ], where denoes he foreign economies and U K denoes he domesic economy. The UK shor-erm ineres rae, R, is he only observable facor. This ogeher wih he unobserved common componens form he dynamic sysem ha evolves according o he following ransiion equaion: F B (L) F F U K = B (L) B (L) B 3 (L) F U K + u B 3 (L) B 3 (L) B 33 (L) R where B(L) is a conformable lag polynomial of finie order p, and u = / e wih he srucural disurbances e N(, I ) and = A, ( A, ) is he sochasic covariance of he R (A-) reduced form shocks. The srucure of B(L) reflecs he small open economy assumpion such ha he domesic facors do no impac on world facors, bu no vice versa. The ime-varying covariance marix of he VAR innovaions, u, can be facored as Var(u ) = A ( ) H A (A-) Following Primiceri (5), he ime-varying marices H and A are defined as: H = h, h, (A-3) h n, The erm foreign and world are used inerchangeably. Working Paper No. 5 May 9

31 and A = α, α n, α nn, (A-) wih ln h i,, and he non-zero and non-uni elemens of he marix A is assumed o evolve as drifless random walks ln h i, = ln h i, + µ i,, i =,..., n α i j, = α i j, + ξ i j,, i =,..., n and j =,..., n (A-5) (A-) where he disribuional assumpions regarding [ ] µ, ξ are saed below. The random walk assumpion allows for permanen shifs in he sochasic volailiy erms. Allowing he simulaneous relaions (A ) o vary over ime is crucial for modelling he ime-varying dynamics of srucural VAR models. The unobserved facors are exraced from a large panel of N foreign and domesic indicaors conaining imporan informaion abou he fundamenals of he economies. The facors are assumed o be relaed o he variables in he panel (X ) according o he following observaion equaion: X Y X π X R X U K R = Y π R U K R F Y F π F R F U K R + v (A-7) v = ρ(l)v + ɛ (A-8) where Y, π and R are he facor loadings on foreign real aciviy, foreign inflaion and foreign ineres raes wih size N Y, N π and N R respecively; U K is N U K k marix of facor loadings for he domesic unobserved facors and R, N U K, capures he conemporaneous relaionship beween he domesic indicaors and he shor-erm ineres rae; and ɛ is a (N ) vecor of i.i.d disurbances. The las row of equaion (A-7) is an ideniy which does no have an error erm. Working Paper No. 5 May 3

32 Following Del Negro and Orok (8), he facor loadings Y assumed o evolve as drifless random walks, π, R, U K and R are also Y π R U K = Y + ηy = π + ηπ = R + ηr = U K + ηu K (A-9) (A-) (A-) (A-) R = R + ηr (A-3) All he innovaions in he model are assumed o be joinly normally disribued wih he following assumpions on he variance covariance marix: µ W ξ S ɛ Q η Y M Y V = Var = η π M π η R M R η U K M U K M U K,R M U K,R M R η R (A-) To reduce he number of esimaed parameers, we furher assume he covariance marices for he sochasic volailiy (W ), he off-diagonal non-zero elemens (S) and he idiosyncraic error erms in he observaion equaion (Q) are diagonal. However, we allow for correlaions beween he facor loadings in each equaion bu no across equaions. In principle, one can allow for a much richer covariance srucure among he innovaions in he sysem. Neverheless, here are a leas wo reasons in favour of he simplified srucure described in (A-). Firs, he high number of parameers in he sysem will require specifying sensible priors o preven cases of ill-deermined parameers. Second, as highlighed in Del Negro and Orok (8), a compleely generic covariance srucure will complicae he srucural inerpreaion of he innovaions. The sysem (A-)-(A-) is he FAVAR model proposed by Bernanke, Boivin and Eliasz (5) and exended o he open economy by Mumaz and Surico (8). The main innovaion in his paper is he inroducion of ime-varying facor loadings and sochasic volailiies. This is Working Paper No. 5 May 3

33 imporan in order o examine changes o he inernaional ransmission mechanism. Idenificaion Unobserved facors There are hree facors for he res of he world represening inernaional comovemens in real aciviy, inflaion and shor-erm ineres raes. The inernaional facors are idenified hrough he upper (N Y + N π + N R ) 3 block of he marix in (A-7). We assume ha all real aciviy series in he foreign block of he model share common dynamics and ha such common dynamics are no shared by any oher series in he panel. The inernaional real aciviy facor is idenified as he only facor ha is loaded by all real aciviy series in he res of he world. Similar resricions are assumed for he inernaional inflaion and shor-erm ineres rae facors. The dynamics of he UK variables are capured by k UK facors, where k is assumed o be four. The UK facors are no idenified in a sense ha hey are exraced from he full panel of UK series. The sub-marix U K in (A-7) is a full marix wih he normalisaion assumpion on he firs k series. The reason for leaving he domesic facor loadings unresriced is ha he dynamics of he variables in X U K will depend on he srucure imposed on he loadings. For example, if all domesic aciviy series share a single domesic aciviy facor, hen he response of all domesic aciviy indicaors will also share he common dynamics up o a scale facor pinned down by he loading. One of he goals of his paper is o invesigae any possible heerogeneiy in he responses of domesic prices and aciviies across secors, and herefore i is unsaisfacory o impose a igh consrain on he dynamics of he individual series. The vecor R, measuring he conemporaneous relaionship beween he domesic indicaors and he shor-erm ineres rae is also lef unresriced. The idenificaion scheme described above imposes mos of he srucure on he foreign block while leaving he domesic block, whose responses is he objec of invesigaion, relaively unconsrained. The dynamics of each domesic series is a linear combinaion of all UK facors and he domesic shor-erm ineres rae. The ransiion equaion (A-) links he dynamic responses beween he inernaional and domesic facors. Togeher wih he idenificaion resricions discussed in he nex subsecion, he inernaional facors serve o idenify he foreign Working Paper No. 5 May 3

34 shocks. Esimaion: muli-sep Gibbs sampling The model in equaions (A-) o (A-) is esimaed using procedures described in Kim and Nelson (998), Primiceri (5) and Del Negro and Orok (8) o approximae he poserior disribuion. Essenially, his amouns o reducing a complex problem of sampling from he join poserior disribuion ino a sequence of racable ones by sampling from he condiional disribuion of a subse of parameers condiional on all oher parameers of he model. The muli-sep Gibbs sampling procedure can be broken down o five main blocks. -invarian parameers We iniialise he facors using a simple principal componen esimaor. Given he values for he facors F, he ime-varying facor loadings, he sochasic volailiies H and he off-diagonal covariances A, we can hen draw he ime-invarian parameers for he VAR coefficiens B(L), he auoregressive coefficiens of he error erm in observaion equaion ρ(l) and he hyperparameer Q. Drawing he VAR coefficiens is complicaed by he presence of heeroscedasiciy in he VAR covariance. We derive he condiional poserior disribuion of he VAR coefficiens by rewriing he VAR as sae-space sysem and he parameers are drawn using he algorihm described in Carer and Kohn (99): F = B (L)F + u B (L) = B (L) (A-5) (A-) where B (L) is assumed o be ime-invarian and he covariance of u is. Noe ha he resricions implied by he small open economy assumpion are incorporaed by using an appropriae prior disribuion for B (L) : p (B(L)) N (B, ) where B has all elemens equal o zero excep hose corresponding o he firs lagged dependen variables which are se equal o he auocorrelaion coefficien obained via univariae Working Paper No. 5 May 33