Working paper No.4 A small model of the UK economy

Transcription

1 Working paper No.4 A small model of he UK economy Jamie Murray July 2012

2 Crown copyrigh 2012 You may re-use his informaion (no including logos) free of charge in any forma or medium, under he erms of he Open Governmen Licence. To view his licence, visi hp:// or wrie o he Informaion Policy Team, The Naional Archives, Kew, London TW9 4DU, or psi@naionalarchives.gsi.gov.uk. Any queries regarding his publicaion should be sen o us a: obrenquiries@obr.gsi.gov.uk ISBN PU1342

3 A small model of he UK economy Jamie Murray Office for Budge Responsibiliy Absrac This paper presens a small calibraed New-Keynesian model of he UK economy exended o ake accoun of credi risk premia and unconvenional moneary policy. I can be used o run simulaions or provide alernaive economic scenarios in erms of differences from he Office for Budge Responsibiliy s cenral economic forecas. The model can be applied o provide some indicaion of how he sance of moneary policy migh adjus in response o fiscal policy announcemens. I am graeful for helpful commens from Seve Farringon, Seve Nickell, Alex Tucke, Andrew Gurney, Konsaninos Mouraidis, my colleagues a he Office for Budge Responsibiliy (OBR) and members of he OBR s Advisory Panel. The opinions expressed in his paper are my own and do no necessarily reflec hose of he Budge Responsibiliy Commiee. JEL references: E12, E13, E17, E3, E43, E47, E52 Keywords: Macroeconomic model, New Keynesian IS-LM model, economic forecasing, simulaion, moneary policy, fiscal policy.

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5 Conens Secion 1 Inroducion...1 Secion 2 A four-equaion model...3 IS relaion...5 Philips curve...8 Uncovered ineres pariy condiion...10 Cenral bank reacion funcion...11 Secion 3 Exensions...15 Credi spreads...15 Unconvenional moneary policy...18 The public finances...21 Secion 4 Calibraion and model properies...23 Calibraion...23 Simulaion properies...31 Secion 5 Fiscal policy announcemens and ineres rae forecass...33 Annex A References...36 Annex B Simulaion chars...40 Annex C Model equaions and daa...44 Model equaions...44 Model daa...48 Annex D Esimaion resuls...52 Single equaion ordinary leas squares...52 Three-sage ordinary leas squares...53 Vecor auoregression resuls...53

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7 1 Inroducion 1.1 In 2010, he Office for Budge Responsibiliy began o publish illusraive economic scenarios alongside is cenral forecas. Since hen, he ools used o produce hem have been developed. In his paper, I presen a simple calibraed model of he UK economy which can be used o produce alernaive forecass, o conduc simulaions and as he framework underpinning he OBR s scenario analysis. 1.2 Secion 2 describes he heoreical srucure of he model, beginning wih a sandard New-Keynesian model and describing how he model presened here differs from i. Secion 3 explains how I have exended his model o allow for he effecs of credi risk premia and unconvenional moneary policy. I also provides a very simple characerisaion of he dynamics of he public finances. Secion 4 describes he approach aken o calibraion and ses ou he simulaion properies of he model. Secion 5 looks a one simple applicaion of he model o a forecasing issue how moneary policy migh be expeced o respond o a series of anicipaed fiscal policy shocks. 1 A small model of he UK economy

8 A small model of he UK economy 2

9 A four-equaion model 2 A four-equaion model 2.1 There are a number of ways in which o develop a model of he economy, he suiabiliy of which depends upon is inended use. The sors of models produced by academic macroeconomiss ypically adhere sricly o he prescripions of heir microeconomic foundaions. Tha is o say ha, wheher i s a model wih hree equaions or weny, he laws of moion of he economy are governed by he opimising behaviour of agens operaing wihin i. These models are primarily concerned wih he assessmen of policy, and ofen, he appraisal of wha consiues opimal policy. The policy prescripions ha follow from such an approach depend criically on he inernal consisency of he models used and he srucural sabiliy of hose models in he face of changes o policy regimes. 2.2 There exiss a differen class of models, such as he large-scale macroeconomic model used by he Office for Budge Responsibiliy, ha is primarily concerned wih forecasing. 1 These models are no usually derived from microeconomic foundaions and rely more heavily upon a good fi wih he daa. I is widely known ha such models are vulnerable o he Lucas criique because he behavioural relaionships observed in he daa canno be considered srucural and could change when he operaion of policy changes. 2 This is a problem for policy analyss bu less so for forecasers, who are no ypically asked o forecas he effec of significan changes o he macroeconomic policy framework The OBR s main macroeconomic model allows a forecaser o apply judgemen in a srucured and consisen way. Tha judgemen can improve he accuracy of forecass is well-documened and, herefore, is an imporan feaure of he approach aken. 4 The size and scope of he main model are also vial for generaing forecass of he numerous variables required o underake a rigorous fiscal forecas. 1 See OBR (2011) for more deails on he model and he forecas more generally. 2 See Lucas (1976). 3 Neverheless, forecasers rely on models fied o pas daa and care mus be aken o idenify wheher ha daa may have been generaed by a differen policy regime. 4 Wallis and Whiely (1991), Clemens and Hendry (2002) and Groen e al (2009) all explore he applicaion of judgemen o forecass. 3 A small model of he UK economy

10 A four-equaion model 2.4 The model presened here is no designed for he same purpose. Is inended use is o provide quick and easily-undersood forecass of core variables wihou he applicaion of judgemen, which can readily be presened in erms of differences from he cenral forecas. This faciliaes he simple assessmen of alernaive economic scenarios. 2.5 Given he rade-off beween models ha replicae he inerial responses of oupu, inflaion and ineres raes and hose which mos closely adhere o he forward-looking behaviour expeced of agens in he economy, i sands o reason ha he model wih he greaes pracical flexibiliy migh be one which draws from boh of he classes described above. This issue is described a lengh in Pagan (2003). 2.6 Given is inended use, he model presened here sis broadly beween he wo classes of model described above - borrowing he more desirable feaures of micro-founded models bu relaxing some of he sricer assumpions o allow a beer fi wih he daa. 2.7 There is always a empaion o expand any model because i is desirable o idenify he effecs of differen ypes of shock and a larger model permis a wider assessmen of hese. However, a smaller model need no imply a less accurae forecas. 5 And is size can be a srengh; smaller models make i easier o race he ransmission of shocks hrough he model ono key variables, and i is also easier for he modeller o experimen wih alernaive assumpions, such as he degree of forward-looking behaviour ha agens exhibi. 2.8 The four key variables of ineres are he oupu gap, Bank Rae, he inflaion rae and he exchange rae; given by he invesmen-saving (IS), Taylor, Phillips and uncovered ineres pariy relaions respecively. I also include an equaion ha capures changes in he cyclical componen of he governmen s primary balance. In wha follows, I se ou he funcional forms adoped for he core equaions and idenify where he assumpions are consisen wih he microeconomic heory upon which hey are founded and where hey deviae from i. For reference, a complee se of he equaions ha consiue he model can be found in Annex C. 5 Del Negro and Schorfheide (2012) assess he forecas performance of he medium-sized Smes and Wouers (2003) DSGE model, augmened o include he effec of financial fricions, and a small scale DSGE model more like he one presened in his paper. They find ha while he shor-erm forecas performance of he SW is slighly beer han he small-scale model, he medium-erm forecas performance of he smallscale model is slighly superior. A small model of he UK economy 4

11 A four-equaion model IS relaion 2.9 The IS equaion relaes oupu in he economy o deviaions of he real ineres rae from he level consisen wih sable oupu and inflaion in he medium erm. Equaions of his form are a saple of macroeconomic modelling and appear, in some form, in all New-Keynesian models. The forward-looking IS relaion is given by, c c z. (2.1) c j r j 2.10 Equaion 2.1 represens he baseline consumpion Euler equaion ha arises from he represenaive household s opimisaion problem. I has been log-linearised around is seady sae so c represens he deviaion of consumpion from is seady-sae growh pah, c j is he expeced deviaion of consumpion from is seady sae, condiioned on informaion available a ime, z j is he expeced real ineres rae gap condiioned on informaion available a ime and is an independen, idenically-disribued consumpion shock The consumpion Euler equaion simply saes ha, in equilibrium, he represenaive household is unable o increase is uiliy by shifing consumpion beween periods ha is, he marginal uiliy of consumpion oday is balanced wih he discouned marginal uiliy of consumpion omorrow To ge from he consumpion Euler equaion o he IS equaion I assume ha he behaviour of he consumer can explain whole-economy behaviour. This is a common assumpion in small models of he economy bu is no compleely saisfacory given, in paricular, he conribuion of business and invenory invesmen o he cyclical volailiy of oupu Wihou deriving he behaviour of firms explicily from microeconomic foundaions here, i suffices o say ha he change in oupu associaed wih firms responses o changes in real ineres raes is in he same direcion as ha implied by he response of households. Inuiively, if he real rae of ineres falls, his lowers he cos of borrowing and increases he overall rae of reurn of an invesmen projec. Therefore, any profi-maximising firm has a greaer incenive o inves. 6 6 Tobin s Q heory of he invesmen decision, Tobin (1969), operaes in a similar way. Lower expeced ineres raes decrease he rae a which income sreams are discouned, increasing he valuaion of companies ne asses. When he marke value of asses exceeds he book value, here is a profi opporuniy and companies expand heir invesmen unil such a ime ha book prices are equal o marke prices. 5 A small model of he UK economy

12 A four-equaion model 2.14 There are a number of exensions o hese simple heories, which highligh he role of uncerainy and irreversible coss in he invesmen decision - see Leahy and Whied (1995) and Pyndick and Solimano (1993), for example. However, hese are beyond he scope of his paper. While he effecs of uncerainy are no included in his model, one of is feaures is ha he cyclicaliy of business invesmen and is conribuion o oupu volailiy should already be capured in he IS relaion, o he exen ha he invesmen decision is dependen on he real ineres rae gap Aggregaing he consumpion Euler equaion o he whole economy level gives equaion 2.2. I also include a erm for changes in he rade-weighed real effecive exchange rae, which is inended o capure he effec on oupu of changes in relaive prices which serve o shif he allocaion of resources o and from he expor-facing secor, y y y j z r j er er j 7. (2.2) 2.16 y is he oupu gap, y j is he expeced oupu gap a ime and z j is he expeced real ineres rae gap, er j is he real expeced exchange rae and is an independen and idenically-disribued aggregae demand shock Having presened he baseline IS equaion, i is worh commening on is srenghs and limiaions. The srengh of his approach is ha he oupu equaion is based on opimising behaviour and so should be robus o changes in policy i is characerised by deep or srucural parameers. Generally, criicisms fall ino wo caegories, concerns over he applicaion of represenaive agen heory and he assumpion of raional expecaions The developmen of models based on he opimising behaviour of a represenaive agen was promped by concerns raised by Lucas (1976) abou he radiional approach o macroeconomic modelling which depended on an assumpion of sabiliy in he saisical relaionships beween variables. The represenaive agen approach is a simplificaion ha saves having o capure he complex behaviour of millions of individual agens. Such models are now commonplace bu mos ignore he heerogeneiy of agens in he economy, which may have a significan bearing on aggregae behaviour. 8 I absrac from his consideraion here while acceping ha he validiy of aggregaion conribues o 7 See Gali & Monacelli (2005) for a deailed derivaion of he open economy IS curve under domesic inflaion argeing. 8 For criiques of represenaive agen heory see Kirman (1992) and Harley (1996). A small model of he UK economy 6

13 A four-equaion model he already significan uncerainies associaed wih any small model, which necessarily makes dramaic simplificaions of realiy The second criicism of he IS relaion concerns he assumpion of raional expecaions. Esimaed forward-looking IS relaions end o underperform simple auoregressive models and, quie ofen, lile empirical suppor is found for he relaionship beween oupu and expeced real ineres raes. 9 This is parly because he oupu gap moves wih a degree of ineria ha is inconsisen wih he adjusmen pahs implied by forward-looking, raional expecaions models. In hese models, i is he raional bu immediae adjusmen of households expecaions o innovaions which implies a jump response in consumpion, which, in pracise, is rarely seen in he daa Some aemps have been made o explain why consumpion reacs so slowly in response o changes in ineres raes. One such endeavour is he habi formaion model of Fuhrer (2000). Fuhrer posulaes ha he uiliy derived from consumpion depends boh on he absolue level of consumpion and he level of curren consumpion relaive o pas consumpion ha households do no like consuming less han hey have been and iniially resis changes, before evenually adjusing. This modificaion was shown o subsanially improve he fi of he model Oher work, predominanly concerned wih why he behaviour of consumpion appears o invalidae he permanen income hypohesis, such as Muellbauer (1988), suggess ha households may be myopic in heir consumpion choices. Campbell and Mankiw (1989) offer he hypohesis ha households do no have he resources o engage in producing full forecass and so i is opimal for hem o use a rule of humb when updaing heir consumpion plans in response o income shocks Tha lagged oupu improves he fi wih he daa is imporan, bu wheher one acceps he habi formaion sory, he rule of humb hypohesis or simply assumes ha households are less forward-looking han is ofen suggesed, is less imporan for he specificaion of he IS relaion. In empirical work, an assumpion of habi formaion or myopia in household consumpion choices is no uncommon and boh Baini and Haldane (1999) and Smes and Wooers (2003) allow for i in heir respecive models of he UK and he euro area economies. Indeed, neiher Baini and Haldane nor Carlin and Soskice (2010) include expeced oupu in heir baseline IS relaions, an approach which I follow 9 See Fuhrer and Rudebush (2004). 10 See, for example, Giannoni and Woodford (2003) for a formal derivaion of he habi formaionaugmened NKIS relaion. 7 A small model of he UK economy

14 A four-equaion model here. Therefore, he baseline IS relaion employed here includes lags of oupu, real ineres raes and exchange raes bu no expecaions hereof, y y y j r z j erer j. (2.3) Phillips curve 2.23 The New Keynesian Phillips Curve (NKPC) relaes curren inflaion o expecaions of fuure inflaion and marginal cos pressures. Tha he inflaion process is forward-looking follows from he price-seing behaviour of firms, which is assumed o follow Calvo (1983). The basic premise is ha in each period a firm has a fixed probabiliy ha i will keep is price unchanged, so firms se prices now wih a view o he fuure because hey know ha hey may no be able o change heir prices in he subsequen period. 11 The probabiliy of changing/no changing price each period is independen of he ime elapsed since he firm las changed is price, and his aribue simplifies he aggregaion of individual firm behaviour o he whole-economy level. This gives an equaion of he form, y 1 y (2.4) where is he rae of inflaion and 1 is he expecaion of inflaion condiioned on informaion available a he curren ime I assume ha real marginal cos pressures drive he inflaion process, consisen wih Gali and Gerler (1999) and ha hese cos pressures are well-represened by he oupu gap, y. There are oher measures which could be used Baini e al. (2005) use he labour share of income in heir esimae of he Phillips curve, which has he advanage of being direcly observable. 12 Bu using he labour share for forecasing wih his model would no be possible because i does no capure he evoluion of he labour marke, so he oupu gap is preferred. The error erm,, is an independen, idenically-disribued inflaion shock As wih he IS relaion, he purely forward-looking version of his equaion fis he daa poorly failing o capure he observed ineria of inflaion. The equaion specificaion implies ha a high degree of persisence in eiher movemens in 11 Noe ha his probabiliy is independen of he general level of inflaion. This seems unlikely, and has implicaions for he model, such as he poenial non-neuraliy of money. 12 I is also he case ha, under cerain assumpions, he labour share (he average produc of labour) is proporional o real marginal cos in an economy characerised by a Cobb-Douglas producion funcion. A small model of he UK economy 8

15 A four-equaion model he oupu gap or changes in inflaion expecaions could produce an inerial pah for inflaion, bu leaves open he possibiliy of large jumps. I also implies ha inflaion should lead he oupu gap, which is he opposie of wha we observe in he daa; boh empirical evidence and convenional wisdom suggess ha moneary policy affecs inflaion only wih a lag, raher han insananeously A model ha does no adequaely capure he persisence of inflaion would be of lile use o forecasers. Therefore, in wha follows, I relax he resricive assumpion ha households and firms are compleely forward-looking. This approach is consisen wih he approach I have aken o expecaions in he IS relaion The hybrid version of he New Keynesian Phillips Curve, used in a number of empirical esimaes of he equaion (Gali and Gerler (1999)) modifies he sandard NKPC formulaion by allowing a proporion of firms o use a rule of humb when seing prices. This modificaion provides a heoreical jusificaion for he presence of an inflaion lag in he firs order condiion of he NKPC. Inuiively, he inclusion of lags of inflaion serves o ac as a proxy for he raional expecaion of fuure values of he driving variable. The resuling equaion herefore includes a backward-looking erm and a coefficien,, ha deermines he weigh placed on pas inflaion relaive o inflaion expecaions in he inflaion process, j (1 ) y y j. j (2.5) 2.28 The resricion placed on he inflaion coefficiens summing o uniy (effecively imposing a discoun facor of one) means ha money is super-neural in his model. I also implies ha he coefficien can be inerpreed direcly as he proporion of firms in he economy ha se prices in a backward/forward looking manner In his paper I ake a slighly differen approach o he Gali and Gerler se-up and adop he prior expecaion ha agens in he economy expec ha moneary policy is able o reurn inflaion o arge a some ime horizon (ypically assumed o be around wo years). Therefore, I use equaion 2.6 and se equal o he * inflaion arge,, * j (1 ) y y j ee j. (2.6) 2.30 To allow for he effec of exchange rae pass-hrough o prices, I include he change in he rade-weighed nominal effecive exchange rae. Tha he Phillips 1 9 A small model of he UK economy

16 A four-equaion model curve can be augmened in his way is demonsraed formally in Baini e al. (2005). Uncovered ineres pariy condiion 2.31 There is a vas lieraure surrounding he performance of models concerned wih forecasing movemens in exchange raes. In heir seminal paper, Meese and Rogoff (1983) show ha he forecas performance of economic models of he exchange rae is ypically worse han simply assuming he fuure exchange rae will be whaever i is a he momen a random walk model A more recen sudy, Cheung e al (2005), compared he forecas performance of a wide range of models pu forward in he 1990s and showed ha lile progress has been made. Emphasising ha while some srucural models appear o ouperform a random walk model a very long horizons, shor-erm movemens remain unpredicable. This finding reaffirms he Obsfeld and Rogoff (1995) observaion ha deviaions from absolue purchasing power pariy - which simply saes ha he prices of radable goods and services across counries should be equal - can persis for decades. 13 Furhermore, Hauner e al (2011) find ha he forecass produced by a number of models of exchange raes are only weakly correlaed wih Consensus forecass of he exchange rae Wih his in mind, I make no serious aemp o forecas he exchange rae here, beyond he simples possible specificaion of a no arbirage condiion uncovered ineres pariy (UIP). Nowihsanding hese forecasing difficulies, he exchange rae has an imporan bearing on economic developmens: he recen hisory of he serling exchange rae is one of prolonged periods of relaive sabiliy, puncuaed by relaively rapid and subsanial adjusmens (in 1992, and ), and I herefore include i in he IS and Phillips relaions. This should improve he model s shor-erm unconsrained forecas, bu also permi he simulaion of exchange rae shocks Equaion 2.7 is he UIP condiion ha gives he forecas ineres rae, which is consisen wih he equaion used in he OBR s main macroeconomic model, e e 1 i i (2.7) f 13 Which is why, hey sugges, ha movemens in he exchange rae should no appear in a moneary policy rule. A small model of he UK economy 10

17 A four-equaion model f where e is he log nominal exchange rae, i is he foreign ineres rae, i is he domesic policy rae and is an independen and idenically-disribued exchange rae shock The equaion is based on he idea ha, if an ineres rae differenial exiss, he nominal rae of reurn on domesic and foreign asses is equalised by movemens in he nominal exchange rae. 14 In his model foreign ineres raes are assumed o be exogenous and, in seady-sae, are equal o he seady-sae domesic nominal ineres rae For he purposes of including changes in he real exchange rae in he IS relaions i is necessary o have a forecas of foreign inflaion. This is inpu o he model exogenously and assumed o have a seady-sae rae consisen wih he domesic inflaion arge. This, combined wih he ineres pariy condiion, ensures he sabiliy of he seady-sae real exchange rae. This is a similar assumpion o ha made by Carlin and Soskice (2010) For he purposes of augmening he IS relaion, he change in he real exchange rae is given by he ideniy, er ( e e 1 ) (2.8) f where he change in he log real exchange rae er is given by he change in he log nominal exchange rae, e e 1, and he relaive rae of inflaion. Foreign prices are an exogenous inpu o he model. Cenral bank reacion funcion 2.38 Taylor (1993) observed ha he conduc of moneary policy can be well-capured by a simple rule relaing ineres raes o inflaion and he oupu gap. Following Taylor s paper here began a concered academic effor o assess his class of policy rules and heir implicaions for opimal moneary policy. However, some form of Taylor s original rule, which is enirely backward-looking, remains he defaul specificaion for he behaviour of he cenral bank in many economic models. 14 Noe ha he UIP condiion is only an argumen abou he expeced change in he exchange rae i does no pin down is level. 15 This assumpion seems reasonable given ha, for example, he US and he euro area are approximaely argeing he same medium erm inflaion rae, and exhibi broadly equivalen produciviy growh. 11 A small model of he UK economy

18 A four-equaion model 2.39 The IS and Phillips relaions described above operae wih a lag. Tha is o say, i akes ime for ineres raes o affec he oupu gap and, in urn, for inflaion o respond o he oupu gap. The lag srucure embodied in hese equaions means ha moneary policy should be conduced wih a view o he fuure. Therefore, given he involvemen of he Bank of England in forecasing he economy and he lags associaed wih he conduc of policy, I specify a forward-looking form of he Taylor rule which is consisen wih he oher equaions in he model he Bank s expecaions are assumed o be model-consisen As well as being a reasonable empirical descripion of he conduc of moneary policy, Svensson (1997) and ohers have shown ha he Taylor class of rules can also be derived from he inflaion argeing cenral bank s opimisaion problem. Simply allowing for he lag srucure associaed wih he moneary ransmission mechanism gives he forward-looking Taylor rule specified in equaion 2.9, i = i- j + yy j + k - * (2.9) where i is Bank Rae, oupu gap forecas a he relevan ime horizon and deviaion of inflaion from arge. 16,17 i - j is he equilibrium nominal rae of ineres, k y j is he * - is he forecas 2.41 Unlike he IS and Phillips relaions, I do no include an exchange rae erm in he specificaion of he Taylor rule. In his model, he cenral bank responds o movemens in he exchange rae only indirecly, via is effec on oupu and domesically-generaed inflaion. This is consisen wih he Taylor (2001) finding ha he inclusion of exchange raes does lile o improve he sabilisaion of oupu and inflaion and is possibly derimenal A subsanial lieraure also exiss on he observed ineria of ineres rae seing by cenral banks around he world, see for example Goodfriend (1991). In wha follows, I adop he same approach as Clarida, Gali and Gerler (1999), which is o assume he presence of a policy rae smoohing parameer in he cenral bank s reacion funcion. They sugges his smoohing arises from a desire o avoid he credibiliy coss associaed wih large policy reversals, a desire o 16 The specificaion is slighly differen from he original Taylor rule bu consisen wih Nelson and Nikolov (2002). 17 I use effecive bank rae in place of acual bank rae o accoun for he effecs of credi spreads and unconvenional moneary policy on lending raes o he wider economy. I discuss his in more deail from secion 3.1. A small model of he UK economy 12

19 A four-equaion model minimise disrupion o capial markes and he ime i akes build a consensus o suppor a policy change Laer discussions have idenified ways in which ineres rae smoohing migh be opimal for a cenral bank in he presence of parameer uncerainy. Svensson (1999), for example, shows ha parameer uncerainy for an inflaion-argeing cenral bank dampens he policy response, confirming wha Brainard (1967) firs described. Sodersrom (2002) exends his analysis o a dual-mandae cenral bank wih oupu in is loss funcion. He finds ha uncerainy over inflaion dynamics ends o heighen he response o inflaion deviaions (in case expecaions become unanchored) bu uncerainy over oupu dynamics encourages cauion Regardless of he precise moive, he inclusion of cenral banks smoohing of policy raes in heir reacion funcions significanly improves he fi wih he daa. Equaion 2.10 capures ineres rae ineria as in Clarida e al (1999), i * -1 where i is he ineres rae se, is he smoohing parameer, i * is he ineres rae implied by he reacion funcion (absen smoohing) and i -1 is he ineres rae se in he preceding period Subsiuing he generalised Taylor rule in o equaion 2.10 as he i * erm gives he cenral bank reacion funcion wih policy rae smoohing equaion 2.11, * j - i -. (1- )i i (2.10) i (1- )i (1- ) yy j (1- ) 1 (2.11) 2.46 The funcional form presened in equaion 2.11 implies ha he cenral bank is more forward-looking han oher agens in he economy. This assumpion is consisen wih he observaion ha cenral banks spend a subsanially larger share of heir resources aemping o forecas he evoluion of oupu and inflaion han do households or firms. This choice of modelling approach implies ha he cenral bank could exploi he adapive expecaions of privae agens - he classic ime-inconsisency problem. 18 In a raional expecaions conex, Woodford (2003) shows ha i can be opimal for a cenral bank o move he curren policy rae less in response o demand and inflaion shocks if, a he same ime, he changes are characerised by a high level of persisence. Such an argumen criically depends upon he forward-looking expecaions of agens in he economy, which is no a feaure of his model. 13 A small model of he UK economy

20 A four-equaion model 2.47 This is one of he ineviable drawbacks of building a model ha reains some use for forecasing. However, he primary purpose of his model is no o assess he effecs of moneary policy regime change. The macroeconomic framework is well-esablished in he Unied Kingdom and his suppors he validiy of using a model of his ype. A small model of he UK economy 14

21 Exensions 3 Exensions Credi spreads 3.1 Since he onse of he recen financial crisis, a rise in he perceived degree of risk associaed wih lending and borrowing has significanly widened he gap beween he ineres rae se by he Bank of England and he price of credi available o he wider economy. As a resul, moneary policy has subsequenly aken serious accoun of he effec of credi spreads on he behaviour of agens in he economy. 3.2 The inclusion of credi spreads in he model presened here is based on a simple principle: he Bank of England is ulimaely concerned wih he ineres raes paid by household and firms in he economy. So if he spread of ineres raes experienced by agens in he wider economy over policy raes is 200 basis poins higher han usual, his implies ha he Bank would se policy raes around 200 basis poins lower han usual. Therefore, raher han argeing policy raes, in his model, he Bank akes credi spreads ino accoun direcly and arges an adjused policy rae, described here as Effecive Bank Rae, i e. 3.3 By exending he New-Keynesian model of he economy o include a measure of credi spreads, Curdia and Woodford (2009) show ha agens in he economy respond in a similar fashion o increases in borrowing raes arising from changes in he defaul risk premium as hey would o an increase in Bank Rae. 1 Imporanly, he Curdia-Woodford model shows ha, so long as cenral bankers ake credi spreads ino accoun, he Taylor class of policy rules remains opimal in choosing he sance of moneary policy. 3.4 To consruc a measure of he credi spread, I use a selecion of quoed household borrowing and deposi raes and subrac from hose he relevan reference rae of ineres. 2 For example, I ake he average ineres rae quoed for 1 Curdia and Woodford creae a model which assumes ha banks are able o finance hemselves by issuing deposis which mus arac he same rae of ineres as governmen bonds of he same mauriy o avoid arbirage opporuniies. In his paper I assume ha he relevan spread is over he cos of borrowing, as se by he cenral bank. This approach is moivaed by he observaion ha he Bank arges a policy rae defined in erms of very shor-erm governmen borrowing raes he gil repo rae. And QE is conduced by buying and selling governmen bonds. 2 Ideally, a measure of credi spreads would also include corporae secor borrowing and deposi raes, bu here is lile daa available wih which o consruc such a measure. 15 A small model of he UK economy

22 Exensions a 2-year fixed-rae morgage and subrac from his he wo-year gil rae. This gives he spread over expeced policy raes a he relevan ime horizon. 3 Full deails of he daa series and weighs used o consruc his series are conained in he annex. 3.5 One issue worhy of noe is ha in using quoed ineres raes I migh no be capuring oher imporan informaion abou he credi environmen. Firs, he quoed rae may no be represenaive of he acual rae paid by borrowers for new lending. In aking ou a morgage I migh be old ha I could borrow from as lile as hree per cen bu, by he ime my income and oher characerisics are aken ino accoun, I may be required o pay four per cen. Ideally I would use daa abou he acual cos of new borrowing bu his is no available a he same level of deail as quoed rae daa. Therefore I simply assume ha quoed raes are represenaive of acual lending raes Second, while he price of lending and he reurn o saving are clearly imporan o he consumpion choice, he availabiliy of credi is also relevan. During he financial crisis, he price of lending, relaive o policy raes, rose subsanially bu a he same ime he amoun of lending conraced sharply. I remains unclear wheher he very slow growh in credi since he crisis represens a demand response o he weaker growh oulook and wider credi spreads or a reduced willingness o lend. In eiher case, he impaired funcioning of he banking secor probably had significan effecs on oupu hrough channels beyond hose considered here or in he Curdia-Woodford paper. 3.7 In his paper, he model is presened in erms of deviaions around a seady-sae. Therefore, he credi spread series should also be expressed in erms of deviaions around a seady-sae. For simpliciy, I assume ha he seady-sae credi spread is saionary around is long-run average value. The credi spread deviaion can be decomposed ino conribuions from is consiuen pars, which is shown in Char Insofar as he wo-year gil rae is a good proxy for expecaions of policy raes. 4 This is likely o be more of a problem for lending raes han deposi raes. A small model of he UK economy 16

23 Exensions Char 3.1: Conribuions o he credi spread deviaion from seady-sae Per cen Source: ONS, OBR Secured Unsecured Deposi Aggregae 3.8 Char 3.1 shows how he credi spread has deviaed from is sample average value and he weighed conribuions of secured, unsecured and deposi spreads o ha deviaion. Looking a he char, i is clear ha he credi spread was above is mean in he lae nineies and fell below is mean for much of he following decade. An alernaive explanaion is ha he sample mean is a poor proxy for he seady-sae credi spread and ha, insead, his rae has been falling over he sample period. 3.9 There are reasons o believe ha he seady-sae credi risk premia may have fallen over his period. There exiss a subsanial lieraure on he subjec which looks a he evoluion of saving behaviour on a global scale. Caballero e al. (2006) and Bernanke (2005) posulae he exisence of a global savings glu which aced o reduce no jus he cos of borrowing for safe crediors, such as governmens, bu also he ineres raes experienced by riskier lenders. This argumen poins o a srucural fall in he risk premium over he sample period as global saving preferences changed Ohers, such as Taylor and Williams (2009) and Obsfeld and Rogoff (2009), are more scepical arguing ha global saving as a share of world GDP has been relaively sable over he pas couple of decades and ha low nominal bond yields have been a global phenomenon. Looking a Char 3.1, if he firs hypohesis were relevan o he UK experience, one migh expec o see negaive or falling conribuions o he deviaion from he sample mean from each of he 17 A small model of he UK economy

24 Exensions hree componens. Bu, as i happens, he change is dominaed by movemens in unsecured borrowing spreads Wihou convincing evidence in eiher direcion, I have chosen o use he simples specificaion in he model presened here, which is a consan, mean-saionary, seady-sae credi spread. 6 The evoluion of he credi spread is given by equaion 3.1, cs ( cs 1 ) (3.1) cs where cs is assumed o be an auoregressive process ha revers o an equilibrium mean value of zero Following he recen esablishmen of he Financial Policy Commiee (FPC), here may be cause o revisi his specificaion of he credi spread. A richer model would include a Taylor-ype policy rule for he FPC, supporing he decision rule of he MPC in achieving he desired effecive ineres rae pah Char 3.1 also shows ha composiion of he wider credi spread since he onse of he financial crisis has been evenly disribued across he hree weighed lending and borrowing measures. This lends some suppor o he hypohesis ha a widening of credi spreads is similar o a ighening of moneary policy because one would also expec higher policy raes, or expecaions hereof, o feed ino all hree raes. If he rise in he credi spread were aribuable only o deposi raes, for example, his would sugges ha credi spreads were no affecing he economy in he same way as changes in convenional policy raes. Unconvenional moneary policy 3.14 As ineres raes fell o he lower nominal bound in 2009, he Bank of England began o use unconvenional moneary policy ools, such as he approach commonly known as quaniaive easing (QE), o provide addiional suppor o 5 This may also reflec increased compeiion in he domesic unsecured lending marke among banks. 6 I is also likely ha changes in regulaory policy have influenced he credi spread, an area worhy of furher research. 7 i.e. i is exogenous, as in he Curdia-Woodford model. 8 A he ime of wriing, he Bank has revealed ha i is considering a number of insrumens wih which o conduc macroprudenial policy including: Those ha limi he size of banks balance shees, hose ha influence he erms and condiions associaed wih loans and hose which affec he srucure of he marke, Bank of England (2011). A small model of he UK economy 18

25 Exensions aggregae demand. 9 In he model presened here, he Bank uses QE o achieve is argeed effecive policy rae when convenional policy ools are unavailable The operaional mechanics of QE are similar o he way in which he Bank conducs is convenional open marke operaions. For convenional policy, he Bank announces a arge shor-erm ineres rae and conducs open marke operaions he buying and selling of shor-erm governmen deb insrumens such ha he chosen ineres rae is achieved. In he case of QE, he Bank announces a specific amoun of longer-daed governmen bond purchases and allows he marke o arrive a an ineres rae pah consisen wih he size of he announced purchases I assume a policy rae equivalence, calibraed o he impac of QE, as esimaed by Joyce e al (2011). This allows he specificaion of a policy rule in erms of he effecive policy rae described in he credi spreads secion above, i e i cs qe. (3.2) qe 3.17 Equaion 3.2 defines Effecive Bank Rae, i e, as a funcion of Bank Rae, i, he credi spread, cs and he quanum of QE in billion erms, qe, a ime. This is he ineres rae ha he Bank of England arges and agens in he economy respond o. The Bank is able o achieve any effecive policy rae i chooses by selecing some combinaion of Bank Rae and Quaniaive Easing policy One complicaion is ha he operaion of QE may affec he credi spread direcly, hrough confidence effecs. Bu I do no consider his channel here. Tha is o say ha he Bank s asse purchases displace cash from gils ino oher asses - boosing asse prices more generally and supporing oupu hrough ne wealh effecs, for example To show why i is imporan o include credi spreads and he effec of QE, Char 3.2 illusraes hree versions of he effecive policy rae in he UK since The firs is Bank Rae, he second is Bank Rae adjused for he esimaed impac of quaniaive easing and he hird is Effecive Bank Rae adjused for he esimaed effec of QE and credi spreads my preferred measure. The choice of measure leads o very differen conclusions surrounding he sance of moneary policy and herefore he model s forecass for oupu and inflaion. 9 And more formally known as he Asse Purchase Faciliy. 19 A small model of he UK economy

26 Exensions Char 3.2: Differen measures of he effecive nominal ineres rae per cen Source: ONS, OBR Bank rae Bank rae + QE Bank rae + QE + credi spreads 3.20 The operaion of moneary policy is characerised in his model by he assumpions presened in Table 3.1. There are seven equaions in his model which capure each evenualiy and are presened in he annex. The desired policy rae and acual policy rae are given by equaions 3.3 and 3.4 respecively, i d i e i cs, (3.3) e i cs qe. (3.4) qe Table 3.1: QE policy assumpions Desired policy rae above or below he lower bound? Policy ighening or loosening? Sock of ousanding QE? above loosening yes no change above loosening no no change above ighening yes shrinking above ighening no no change above no change yes shrinking above no change no no change below loosening yes expanding below loosening no expanding below ighening yes shrinking below no change yes no change QE A small model of he UK economy 20

27 Exensions The public finances 3.21 In using a small model of he economy o run simulaions, i is useful o hink abou he possible implicaions for he public finances. For he purposes of producing he OBR s economic scenarios, economic deerminans from a small model are used, ogeher wih off-model periphery equaions, o ready-reckon he effecs on he public finances. 10 These are inended o roughly capure he effecs of he composiion of expendiure and urnover in he housing marke, for example, on he public finances. Bu including some aggregae measures of he public finances direcly in he small model presened here provides a quick and simple guide o he effec of economic simulaions on he public finances wihou having o ready-reckon hem This can be achieved by applying he OBR s cyclical adjusmen mehodology, Helgadoir e al (2012), which gives an indicaion of how far one migh expec he cyclical componen of he primary balance (ne borrowing) as a share of GDP o move when he degree of spare capaciy in he economy changes. i.e. how he auomaic sabilisers can be expeced o increase or decrease expendiure and axaion dependen on he economic cycle Equaion 3.5 relaes he cyclical componen of he primary balance as a share of nominal GDP, cb, o he oupu gap, cb (3.5) 1 y j where 1 is he cyclical adjusmen parameer The public finances par of he model does no feed back o he oher equaions in any way he effecs of governmen deb, he srucural balance or he effecive gil rae on oupu are no modelled here and here is no fiscal policy rule. Therefore, his par of he model can be viewed as an add-on ha gives a very rough indicaion of he implicaions of he economic scenarios and simulaions for he public finances Finally, he sock of governmen deb as a share of acual nominal GDP is given by he, now familiar, deb dynamics ideniy, gdeb 1 grae 1 ny 1 gdeb 1 sb cb. (3.6) 10 The OBR s approach o esimaing he fiscal effecs of alernaive economic scenarios is presened in OBR (2012). 21 A small model of he UK economy

28 Exensions 3.26 The sock of governmen deb as a share of acual nominal GDP, gdeb, is a funcion of deb in he preceding period, he effecive gil rae, grae, he growh rae of nominal GDP, ny, he cyclical balance and he srucural balance, sb, which is an exogenous inpu o he model. While running simulaions, he pahs of sb and grae can be fixed exogenously or sourced from he cenral forecas, while cb, gdeb and ny are provided by he model presened here I is beyond he scope of his paper o model he effec of differen moneary or fiscal policy pahs on he pah of he effecive gil rae, which depends, among oher hings, on he pah of policy raes, he quanum of QE and he risk premium associaed wih governmen deb. Therefore, he sylised pahs he model reurns should be inerpreed wih cauion. 11 The model here is described enirely in erms of deviaions around a seady sae and no aemp is made o model he supply side of he economy. However, he public finances equaions described below depend on he level of acual and poenial nominal GDP which, in urn, depend on he pah of poenial oupu and inflaion. Poenial oupu can be exogenously fixed on o he model bu oherwise will grow a a rae consisen wih is hisorical average. A small model of he UK economy 22

29 Calibraion and model properies 4 Calibraion and model properies Calibraion 4.1 While some models are parameerised using esimaed coefficiens, ohers are calibraed o fi cerain aspecs of he daa. Wih a model his small, incomplee specificaion is unavoidable here are feaures of recen economic hisory ha canno be explained wihin he very narrow modelling framework considered here. Bu his does no mean i canno be used for he quaniaive assessmen of economic developmens. I simply implies ha acceping he esimaion resuls presened in Annex D wihou some sensiiviy o informaion ha is available ouside he small model would likely lead o bias. Therefore, in calibraing he model presened above, I draw from a wide range of available informaion. Coefficiens are seleced based on he empirical work of ohers, he esimaion resuls presened in Annex D and, imporanly, wih a view o he simulaion properies of he model. 4.2 As a cross-check on he empirical performance of he model I have also esimaed a four-variable, wo-lag VAR (of he oupu gap, ineres rae gap exchange rae and he inflaion gap 1 ) and he impulse response funcions are shown in Annex D. In a number of cases he VAR resuls provide furher suppor for he choice of parameer size in he calibraion and he lag srucure of he model. IS relaion Coefficiens 4.3 In he IS relaion, hree coefficiens: βy, βr and er need o be calibraed. βy is he coefficien on he auoregressive erm and can be inerpreed as he speed a which he oupu gap can be expeced o close in he absence of moneary policy acion. This is deermined by srucural facors such as he degree of real wage flexibiliy in he economy, which acs as a force o resore oupu o is poenial level. I is no simply he observed empirical persisence of he oupu gap and should, herefore, be characerised by a higher degree of persisence. 1 This is also he Cholesky ordering of he variables in he impulse response funcions. 23 A small model of he UK economy

30 Calibraion and model properies 4.4 Baini and Haldane (1999) selec a parameer of 0.8 for he persisence of he oupu gap, which hey consider o be empirically plausible, based on quarerly daa. I choose a higher coefficien of around 0.96 reflecing he fac ha he oupu gap series I use has a persisence of around 0.9 o begin wih and he coefficien should be higher han his because i represens only he effecs of real wage adjusmen, no he effec of moneary policy on oupu. Empirical evidence of he condiional persisence of he oupu gap from he esimaed VAR also poins owards a larger coefficien. 4.5 The sensiiviy of oupu o he real ineres rae gap, βr, is he second parameer o be calibraed in he IS relaion. Nelson and Nikolov (2002) find ha, from a posiion of equilibrium, a one percenage poin increase in he real ineres rae gap leads o a negaive oupu gap in he nex quarer of around 0.1 per cen. This is consisen wih he effec of a one-year ineres rae shock building o have a maximum effec on he oupu gap of roughly 0.4 percenage poins. 4.6 As repored in Nelson and Nikolov, here exiss a wide range of esimaes of his elasiciy, which is of key imporance o he model, and heir esimae is a lile smaller han he ohers hey discuss. Bu mos oher sudies perain o US daa and here are very few empirical esimaes of he slope of he IS curve for he UK. The esimaion and VAR resuls presened in Annex D are consisen wih a negaive oupu gap of 0.05 per cen following a rise of one percenage poin in he policy rae in he preceding quarer, consisen wih a maximum effec on he oupu gap of beween 0.2 and 0.3 percenage poins. The oupu dynamics of he Bank of England s Quarerly Economic Model (BEQM) are consisen wih a slighly higher coefficien. 2,3 I have chosen a parameer ha is consisen wih he evidence presened by Nelson and Nikolov bu which falls wihin he 95 per cen confidence inerval of he single-equaion esimaes presened in he annex. 4.7 Inclusion of he change in he real exchange rae wihin single-equaion esimaes of he IS relaion ofen resuls in insignifican or incorrecly signed coefficiens. However, he resuls more closely accord wih heory when longer lags are included as is he case in he OBR s main macroeconomic model. The VAR resuls, oo, offer lile suppor for he inclusion of he real exchange rae. 4.8 One reason for he weak empirical evidence is ha he real exchange rae ends o be sable for long periods before making subsanial adjusmens. A hese imes here are likely o be oher hings happening ha are relevan o oupu, such as he collapse in world rade during he recen crisis, when serling 2 Bank of England (2005) 3 I use his as a reference because he simulaion properies of he Bank s new model, COMPASS, are no publicly available. A small model of he UK economy 24

31 Calibraion and model properies depreciaed around 25 per cen, or a change in he macroeconomic framework, as followed he UK s ejecion from he European Exchange Rae Mechanism in he early 90s, when serling depreciaed around 15 per cen. The exchange rae could well have had a posiive effec on oupu over hese periods, ceeris paribus, bu he model is no sufficienly rich o capure i i would need o disenangle his from he negaive effecs associaed wih he global financial and exchange rae crises. 4.9 Given he uncerainies, I include a erm in he IS relaion for he real exchange rae bu aach a relaively small coefficien o i, which is consisen wih he single-equaion esimaes a longer lags. The effec of he real exchange rae on he oupu gap is jus over one hird as srong as he effec of he real ineres rae. Lag srucure 4.10 Due o he slow adjusmen of prices in he economy, a change in nominal ineres raes leads o a change in real ineres raes, incenivising consumpion now over consumpion omorrow. I is well-known ha moneary policy affecs he economy wih a lag and, probably, differen lags a differen imes. This complicaes he analysis of he ransmission mechanism and may parly explain why he saisical relaionship beween real ineres raes and oupu is ofen found o be so weak There is a wide range of esimaes of he horizon over which moneary policy is effecive. The esimaion resuls are consisen wih a lag of one quarer for a change in real ineres raes o begin having an effec. The lag on he auoregressive componen of he equaion is simply one quarer. As menioned above, I include he lagged real exchange rae in he IS relaion. I is likely ha firms ake a long ime o respond fully o he changes in relaive prices ha migh promp hem o orienae oward or away from he expor secor paricularly if here is uncerainy surrounding wheher he movemen in he exchange rae is permanen or emporary. Furhermore, here is lile evidence ha agens in he economy respond quickly o changes in relaive prices, paricularly wih regard o subsiuion away from impors o domesically-produced goods. The relaively slow pass-hrough of he exchange rae o domesic prices may also explain some of he slow response of oupu o changes in he real exchange rae. Phillips relaion Coefficiens 4.12 The esimaion resuls are consisen wih an effec on he annual rae of inflaion from a one percen, one-year posiive oupu gap of around 0.4 percenage poins. This is a lile smaller han he coefficien presened in BEQM, bu 25 A small model of he UK economy