Key words: Sectoral balances, flow of funds, macroeconomic modelling. JEL classification: E21, E22, E25, E37. Working Paper No. <xxx> <month>

Transcription

1 Saff Working aper No. < > A dynamic model of financial balances for he Unied Kingdom Sephen urgess () Oliver urrows () Anoine Godin (3) Sephen Kinsella (4) and Sephen Millard (5) Absrac We consruc a new scenario analysis model for he Unied Kingdom using ONS daa from 987 o he presen. The model links decisions abou real variables o credi creaion in he financial secor and decisions abou asse allocaion among invesors for a wide array of financial asses. We develop esimae and calibrae he model from firs principles as well as describing he sock-flow coheren daabase we consruc o validae he model. We impose several scenarios on he model o es is usefulness as a medium erm scenario analysis ool including increases in banks capial raios sudden sops changes in invesmen increases in house prices and fiscal expansions. Key words: Secoral balances flow of funds macroeconomic modelling. JEL classificaion: E E E5 E37. () ank of England. Sephen.burgess@bankofengland.co.uk () ank of England. Oliver.burrows@bankofengland.co.uk (3) Kingson Universiy. A.godin@kingson.ac.uk (4) Universiy of Limerick. Sephen.kinsella@ul.ie (5) ank of England Durham Universiy usiness School and Cenre for Macroeconomics. Sephen.millard@bankofengland.co.uk The views expressed in his paper are hose of he auhors and no necessarily hose of he ank of England. The auhors wish o hank Sean Ryan for excellen research assisance and seminar paricipans a he Cenre d Economie de aris Nord Royal Holloway Universiy of London he Hungarian Insiue for Economics he Hungarian Naional ank and he ank of England for useful commens. Any errors and omissions of course remain he faul of he auhors. Informaion on he ank s working paper series can be found a ublicaions Group ank of England Threadneedle Sree London ECR 8AH Telephone +44 () ax +44 () publicaions@bankofengland.co.uk. ank of England 6 ISSN (on-line) Working aper No. <xxx> <monh> 7

2 RI inflaion (per cen) Inroducion A puzzling feaure of he build-up o he Grea Recession was he apparen calm observed in he evoluion of many key macroeconomic variables a calm widely referred o as The Grea Moderaion. This Grea Moderaion can be seen in he Unied Kingdom in he unprecedened sabiliy in GD growh and inflaion oucomes in he period shown in Char. While i was a period of remarkable sabiliy in aggregae oupu and price growh here were concerns abou he composiion of growh wih secoral financial balances boh wihin and across counries aracing aenion. Alongside debaes abou he causes of The Grea Moderaion ran he puzzle of global imbalances. A a global level his was apparen in he widening deficis and surpluses across counries shown in Char. or naions like he Unied Kingdom and he Unied Saes he domesic counerpars o widening curren accoun deficis included unusually low and falling household savings raes and associaed financial balances as shown in Char 3. While hese imbalances araced aenion and suggesed ha here was more o The Grea Moderaion han immediaely me he eye much of he rerospecive work on he period has focused on he rapid build-up of gross financial posiions underlying he (ne) balances and in paricular he rapid growh of deb shown in Char 4. Char UK annual growh and inflaion oucomes over he pas 5 years Char Global curren accouns as a percenage of global GD Real GD growh (per cen) Source: ank of England er cen Res of world Japan China & Emerging Asia Oher Defici Counries EA surplus counries Oil exporers USA Source: IM As has been poined ou many imes since he crisis he macroeconomic policy consensus a he ime did no provide clear answers as o how policymakers should respond o eiher financial imbalances or he rapid growh of poenially unsusainable deb burdens a a ime when he real economy appeared lanchard and Simon () ouline he key sylised facs for he Grea Recession. enai (6) provides more formal evidence ha he period experienced lower volailiy in inflaion and GD growh han any previous period in 5 years of daa. The lieraure on global imbalances has emerged rapidly since 7. In paricular he papers of Mendoza e al (7) Caballero and Krishnamurhy (9) Obsfeld () and Chinn e al. (4) explore he naure and provenance of global imbalances while ussière e al. (3) and orio (4) highligh he need o model financial imbalances wihin macroeconomic models and summarise he aemps o do so by he profession. Working aper No. <xxx> <monh> 7

3 o be sable. The sandard Dynamic Sochasic General Equilibrium (DSGE) models on which many policy makers relied ypically had lile or no role for financial flows. When he financial crisis sruck hese models had lile o say abou how financial flows had conribued o he crisis and how hey migh evolve pos crisis. Char 3: UK secoral financial balances Char 4: UK secoral deb Source: ONS. NISH = non-profi insiuions serving households Source: ONS. NC = privae non-financial corporaions. Deb securiies and loans are boh included. This paper aims o make a conribuion owards filling in his gap in modelling imbalances by developing a model wih which we can assess how economic and financial imbalances are likely o evolve over longer periods and wheher such an evoluion is likely o be susainable for he UK economy. In addiion we can use he model o examine he evoluion of financial balances under differen scenarios and observe wha he implicaions migh be for moneary and macro-prudenial policy over he medium erm. We argue ha such a model would form a useful addiion o he se ( suie ) of models called upon by policy makers o help hem in heir decision making. 3 Our paper makes wo conribuions o he lieraure. irs we develop esimae and calibrae he model iself from firs principles as well as describing he sock-flow consisen daabase we consruc o validae he model; as far as we know we are he firs o develop such a sophisicaed SC model of he UK economy in recen years. 4 And second we impose several scenarios on he model o es is usefulness as a medium-erm scenario analysis ool. The approach we propose o use links decisions abou real variables o credi creaion in he financial secor and decisions abou asse allocaion among invesors. I was developed in he 98s and 99s by James Tobin on he one hand and Wynne Godley and co-auhors on he oher and is known as he sock-flow consisen (SC) approach. The approach is bes described in Godley and Lavoie () and Caverzasi and Godin (5) and underpins he models of arwell and urrows () Greiff e al. () and Caiani e al. (4ab). Dos Sanos (6) describes how SC models incorporae deailed accouning consrains ypically found in sysems of naional accouns. SC models allow us 3 or a discussion of how he ank of England uses a suie of models in is economic analysis see urgess e al. (3). 4 Such models were popular in he pas; for example Davis (987a 987b) developed a rudimenary sock flow consisen model of he UK economy. Working aper No. <xxx> <monh> 7 3

4 o build a framework for he model where every flow comes from somewhere in he economy and goes somewhere and secoral savings/borrowings and capial gains/losses add or subrac from socks of wealh/deb following Copeland (949). Accouning consrains allow us o idenify relaionships beween secoral ransacions in he shor and long run. The addiion of accouning consrains is crucial as one aspec of he economy we would like o model is he way i migh reac differenly when policies such as fiscal consolidaions are imposed slowly or quickly. Compared wih sandard DSGE Models such as COMASS (see Secion 4 of urgess e al. (3)) hese models have several advanages: hey can be used o analyse he evoluion of gross posiions of financial asses and liabiliies and gross and ne financial flows under differen assumpions; hey allow for feedbacks from financial asse posiions o real economic decisions; variables wihin he models reac differenly o policies imposed slowly or quickly hus finding differen seady saes; hey allow for an imporan and realisic role for money credi and banks; hey ypically (hough no necessarily) impose more realisic specificaions for expecaions and are more realisic han ypical DSGE models in erms of he behaviour and heerogeneiy of agens wihin he model. Table A: ros and cons of using he SC approach raher han he DSGE approach ros Cons Typically use naional accouning consrains o The model equaions are no explicily linked o provide a framework. he opimisaion problems of paricular agens. Allow modelling of gross flow and balance shee The framework is no well-esablished which posiions by secor. makes i harder o ake on board insighs from oher work. Can be used o model feedback from financial asse and liabiliy posiions o he pahs for producion and spending. Can include an imporan role for money credi and he financial sysem. Can offer a framework for exploring differen specificaions for agens expecaions. Arguably SC models have more realisic behavioural assumpions han many models which are micro-founded. The models are complicaed which makes i hard o explain he main economic mechanisms a work. They are hard o ake o he daa: he daa requiremens are large relaive o hose in more sandard DSGE models. The model parameers suffer from he Lucas criique: hey can be affeced by changes in policy regime or ime series properies of he driving processes. The models are no so clearly linked o economic heory. Agains he benefis of SC models DSGE models have he advanage ha he equaions underpinning hem are based more direcly on he underlying problems facing individual economic agens and are more clearly linked o economic heory; he parameers of each DSGE model are srucural in he sense of being invarian o changes in policy or he ime-series properies of he driving processes (ie are Lucas-criique proof ); hey are simple enough ha he mechanisms a work can be explained easily; hey produce (a leas when linearised) a AR represenaion of he endogenous variables ha should in heory be sraighforward o ake o he daa; and echniques for esimaing hese models are well developed and undersood. In addiion here has been an explosion of work rying o Working aper No. <xxx> <monh> 7 4

5 incorporae financial fricions ino hese models in such a way as hey can generae financial crises. (See eg enes e al. (4).) Table A liss he pros and cons of using he SC approach raher han a more sandard DSGE approach. We view hese modelling approaches as complemens raher han subsiues and develop our model accordingly. The remainder of he paper is srucured as follows. Secion describes he model. Secion 3 describes how we consruc he daa we use from UK secoral accouns and flow-of-funds daa and how we calibrae he model using hese daa. We hen discuss a clean forecas produced by he model in secion 4 before using i o examine several scenarios for how he UK economy may evolve in he nex few years in secion 5. Secion 6 concludes. Model Our SC model of he Unied Kingdom conains six secors. Each secoral variable is indicaed by a subscrip in brackes. We model households (H); non-financial companies (NCs); he governmen (G); banks (); insurance companies and pension funds (ICs); and a simplified res of he world secor ().. Households We firs lay ou he main behavioural equaions for he households. (The housing marke will be described on is own laer.) Households consume ou of heir disposable income YD composed of wages W plus governmen ransfers T H ineres received on deposis i D. D as well as any income from annuiies Ann less axes H pension conribuions ens and paymens relaed o heir morgages namely ineres paid on morgages i Mor. Mor. Taxes are levied in a fixed proporion H o he wage bill pension conribuions are a fixed proporion of expeced household disposable income. YD W i Mor ens i D T Ann () H H H W ens = ρ. E(YD) Mor D H We implemen a Haig-Simons consumpion funcion which relaes consumpion C o expeced disposable income and ne wealh accrued in he pas NW H. The marginal propensiies o consume ou of boh expeced disposable income and curren ne wealh are assumed o be fixed. H () (3) C = α. E(YD) + α. NW H (4) Ne wealh will be given by he sum of deposis D housing wealh h H ne of morgage deb Mor and pension wealh ITR. Household pension wealh will be equal o he liabiliies of he IC secor which we discuss in secion.4 below. NW H D H ITR H Mor h (5) The change in aggregae deposi sock is given by household-secor ne lending NL H (adjused for Working aper No. <xxx> <monh> 7 5

6 pension conribuions) less he ne upake of new morgages (ie new morgages aken ou Mor new less old morgages repaid Mor rep ). In urn household-secor ne lending will be given by disposable income less consumpion and invesmen in housing I h. Hence: ΔD H = NL H + Mor new Mor rep ens (6) NL YD ens C (7) H I h We nex discuss he housing marke specifically. We assume ha he sock of housing grows a an exogenous rae and ha housing ransacions (H sold ) depend on house price inflaion: H H H g H sold h (8) (9) The price of a house is proporional o he household deb o income raio imes expeced disposable income divided by he oal sock of housing. And we assume ha he deb o income raio grows a a consan rae. uing his ogeher we have: p H = r s DTI E(YD) H DTI = DTI + ζ () () New morgages are a funcion of he loan o value raio LT iself he exogenous raio of new morgages Mor new o he value of Morgage repaymens Mor rep which grow in line wih he (lagged) growh in new morgages and he relaion shown in equaion (9). Mor new = LT. p H. H sold Mor = Mor new Mor rep Mor Mor rep rep e Mor Mor new new () (3) (4) inally nominal invesmen in housing is assumed o be a simple linear funcion of (lagged) new morgages and (lagged) house prices: I Mor H new 3 h (5). irms irms have o make a se of inerrelaed decisions abou how much o produce invesmen employmen and finance. 5 Their oupu will be demand driven bu we ensure ha in he long run demand grows a he same rae as producive poenial. We assume a flexible labour marke and a Cobb-Douglas producion funcion. In his case he labour share is consan: 5 Our descripion of firms draws srongly on Chaper of Godley and Lavoie (). Working aper No. <xxx> <monh> 7 6

7 W GD (6) Where GD is defined as gross oupu Y less impors M: GD Y M (7) We allow firms o accumulae producive capial by invesing and ha his invesmen I will depend upon capial uilisaion and he cos of financing invesmen by bank loans. Hence: k k I k k GD g k Y u r i L ir (9) k k The raio of GD o he capial sock k proxies capial uilisaion and i L is he ineres rae on bank loans while i R is he risk-free ineres rae (ha paid by he cenral bank on reserves held wih i). irms are also assumed o hold deposis D hese are assumed o grow in line wih nominal GD according o: (8) D D GD GD () Demand comes from consumpion invesmen in physical capial and housing I H governmen spending and expors X and will equal gross oupu: Y C I I H G X () Since firms use impors as inermediaes in producion we assume ha demand for impors depends on oupu and he exchange rae e: M M Y exp ln 3 e e () Y irms are assumed o reain a consan proporion of heir (pos-ax) profis as reained earnings U and disribue he res as dividends Div. Hence T il L id D Y M W (3) U Div s s Where are axes paid by firms T are governmen ransfers o firms and L is he (end-of-period) sock of ousanding bank loans o firms. Taxes are levied as a fixed percenage of pre-ax profis: (4) (5) Working aper No. <xxx> <monh> 7 7

8 L D Y M W i L i D (6) Dividends are disribued o he holders of firm equiy ICs and he res of he world in proporion o he value of heir equiy holdings IC and RoW respecively: Div Div IC RoW Div Div IC RoW (7) (8) irms issue equiies v a a price again o ICs and he res of he world in order o finance a relaively small proporion of heir invesmen spending. (The lower case v denoes a volume measure.) The price a which hey issue he equiies equaes he nominal demand for hem wih he supply: v v I E v IC RoW (3) (9) Any remaining invesmen spending ha canno be financed ou of reained earnings is hen financed by bank borrowing: L L NL NL v D (3) Noice ha in he firs insance new loans o firms (as well as loan wrie-offs NL) will be mached by a rise in firms bank deposis. As he money is spen i will move ou of firm bank deposis ino changes in firms ne lending and equiy such ha equaion (3) will coninue o hold. This means ha our model is compaible wih he banks as creaors of money hrough lending way of hinking abou banks sressed by Jakab and Kumhof (5). y definiion ne lending of he corporae secor will be given by: NL Div I (3) And wrie-offs NL are given by: NL L (33).3 Governmen We assume governmen expendiures G are exogenously deermined in order o examine he effecs of differen pahs for fuure governmen spending. Given is expecaion of he price a which i will be able o sell hem he governmen issues enough bonds b G o cover is defici. These bonds are held by he res of he world he IC secor and for moneary policy purposes by he ank of England. So Working aper No. <xxx> <monh> 7 8

9 nominal demand for governmen bonds will be given by: G IC RoW C (34) Once he price of hese bonds is revealed he governmen finances any furher borrowing by issuing shor-erm bills Gbills which we assume o be non-ineres-bearing. Ne lending by he governmen NL G will be given by he difference beween governmen revenue including profis remied from he cenral bank and expendiure including ineres paymens on is deb: NL G G T T i (35) H H C Hence he real supply of governmen bonds will be given by: NL Gills b b E E Their price will be given by: (36) b G G (37) And he supply of bills will be given by: Gills E (38) b Transfers o households and firms are assumed o grow in line wih nominal GD. And finally he ineres rae paid on governmen bonds is relaed o heir price according o: i * (39).4 IC secor We assume ha he agens have defined conribuion pensions. A reiremen hey ake heir po of savings and spend i on an annuiy. We assume ha annuiy paymens depend on accumulaed pension wealh: Ann ITR (4) The IC secor faces marke risk on is balance shee. Is asses A IC consis of bonds issued by he governmen he banks IC and he res of he world as well as domesic and foreign equiies : A IC IC IC IC (4) Working aper No. <xxx> <monh> 7 9

10 Where we can noe ha and are denoed in domesic currency. ICs profis IC consis of reurns on heir invesmens less he annuiy paymens hey make o households. We assume ha when deciding on dividends Div IC which are paid ou o invesors in he res of he world ICs arge a share of heir expeced ne worh. IC i Div IC IC i Div IC Ann IC sic E AIC ITR AIC AIC ENLIC ens i Div (43) E (44) NL IC IC Div IC (45) (4) Where NL IC denoes ne lending of he IC secor and we can noe ha Div is denoed in domesic currency. The change in household pension wealh will hen be given by: ΔITR = A IC NL IC (46) The IC secor faces a porfolio allocaion problem in ha i needs o allocae is funds across domesic and foreign bonds and domesic and foreign equiy. We assume ha he change in he proporion of is asses held in a paricular asse class depends on he relaive raes of reurn on each asse class. This approach is similar in spiri o he mehod used by rainard and Tobin (968) excep ha we allow for he presence of rends in invesor senimen owards paricular asse classes reflecing wha we observe in our daa. 6 As wih rainard and Tobin we impose he condiion ha hese shares mus sum o uniy in every period by definiion. IC IC RoW IC RoW A A A A A IC IC IC IC RoW IC IC IC RoW IC IC IC IC 3 IC 4 IC 5 IC IC IC 3 IC 4 IC 5 IC IC IC 3 IC 4 IC 5 IC 3 IC 3 IC 33 IC 43 IC 53 IC 4 IC 4 IC 34 IC 44 IC 54 IC 5 IC 5 IC 35 IC 45 IC 55 r r E r r r RoW RoW EA (47) IC Where he acual and expeced reurns on he ICs asses are defined by: 6 y implicaion we expec hese ime rends o coninue over he horizon of he scenarios we consider hough we can always aim off hem when acually using he model for scenario analysis. Clearly for he model o have a well-defined seady sae hen he consans mus all equal zero i.e. hese rends mus sop a some poin and he asse shares wihin he porfolio remain consan from ha poin onwards. Working aper No. <xxx> <monh> 7

11 Working aper No. <xxx> <monh> 7 G G G G E E i r E (48) G G G G i r (49) E E i r E (5) i r (5) e e E E i r E RoW RoW (5) e e i r RoW RoW RoW (53) E Div E r E (54) Div r (55) e e E Div E r E RoW RoW (56) e e Div r RoW RoW (57).5 anks anks se heir bond issuance a he beginning of each period in order o make heir balance shees balance a he end of he period given he price a which hey expec o be able o sell hem. Demand for bank bonds comes from he IC secor and from he res of he world. In nominal erms we have simply ha: IC (58) Once he price of hese bonds is revealed he banks finance any furher borrowing by issuing shorerm non-ineres-bearing bills ills. Ne lending by he banking secor NL will be given by: H D L Mor Div i D D i L i Mor i NL (59) The supply of bank bonds will be given by: H E ills NL NL D D L Mor b b (6) Where denoes bank equiy assumed o be privaely-held and no raded by invesors in he res of

12 he world and he supply of bills will be given by: ills E (6) b The price of bank bonds maches up demand and supply: b (6) The ineres rae paid on bank bonds will be given by: i i (63) Turning o bank equiy we fix is price implying ha is reurn will be given by: r Div (64) where Div denoes dividends paid ou by he banks o heir foreign shareholders. anks equiy will evolve as: NL NL (65) anks will se heir equiy so as o arge a risk-weighed capial raio greaer han he regulaory minimum υ min which depends on risk-weighed asses: Mor L T min (66) Where and denoe he risk weighs on morgages and loans respecively. We assume ha he banks disribue dividends o ensure a consan reurn on heir equiy: Div (67) We can define he banks aggregae regulaory capial raio and heir leverage raio lev by Mor L and lev Mor L respecively. We assume ha banks in aggregae adjus o deviaions of capial from is arge level by adjusing he mark-up hey charge on loans. Specifically banks se he ineres rae on loans as a mark-up over Working aper No. <xxx> <monh> 7

13 average funding coss and on deposis as a mark down on he rae of ineres he cenral bank pays hem on heir holdings of reserves i R. y seing he ineres rae hey are making a supply decision and giving us some leverage over supply wihou having o le price clear he marke. The mark-up on loans depends on he deviaion of acual capial from is arge level. i Mor = χ Mor + χ. E(i D ) + χ. E(i ) + χ 3. E(r ) ξ. i L = χ L + χ. E(i D ) + χ. E(i ) + χ 3. E(r ) ξ. i D = χ D i R χ D T. ( T. ( ) (68) ) (69) D where χ = H χ D H + + = χ D H = and he χ D H + + i incorporae a measure of he riskiness of he various asses and E(r ) is he expeced reurn on bank equiy..6 Res of he world The rade balance is deermined by he demand for impors from firms and he exogenous demand for UK expors emanaing from he res of he world X. The curren accoun which will be he negaive of ne lending by he res of he world denominaed in serling NL is hen composed of he rade balance and dividends and ineress paymens by domesic firms and banks as well as exogenous flows of dividends and bonds paymens from he res of he world o he IC secor: (7) NL M X Div Div Div IC i i i Div (7) We assume ha he growh in res of he world dividend paymens o he Unied Kingdom is equal o he growh in he value of res of he world equiy ha is dividend yields are consan. And we assume ha he ineres rae on res of he world deb is given by: i i 3 i (7) y definiion domesic asses (in serling erms) held by he res of he world will be given by: A bills Gills (73) oreign invesmens are disribued over he asses in he model via a porfolio demand equaion: A A A r E r r E A (74) Working aper No. <xxx> <monh> 7 3

14 where again we assume ha he change in he proporion of is asses held in a paricular asse class depends on he relaive raes of reurn on each asse class and where we again allow for he presence of rends in invesor senimen owards paricular asse classes reflecing wha we observe in our daa. Serling-denominaed liabiliies of he res of he world o domesic invesors (specifically he IC secor) consis of bonds and equiy: Liab (75) The supply of hese liabiliies is assumed exogenous. And so he UK Ne Inernaional Invesmen Liab A osiion as a percenage of GD will be given by. GD We use a flexible exchange rae closure of he model where he movemen in he exchange rae moves o equalise he reurns on domesic vis-à-vis foreign bonds: e e r r RoW RoW r RoW RoW (76).7 Cenral bank The cenral bank s asses are governmen bonds and is liabiliies are he reserves of he banking secor. Is demand for governmen bonds is assumed o be exogenous. I doesn pay ineres on reserves so is profis will equal he ineres i earns on governmen bonds. Moneary policy is assumed o se his rae of ineres according o a nominal GD growh argeing rule where we assume he rule has a form ha ensures he ineres rae never falls below zero (is lower bound). G C R (77) i (78) C C ln R R 3 i lni lngd (79).8 Expecaions inally we assume adapive expecaions hroughou he model: E(X) = X + υ. (E(X) X ) (8) 3 Daa and calibraion In his secion we explain how we have used UK daa o calibrae and operae he model. The model is a non-linear backward-looking model of he ype explained in secion 6..7 of urgess e al. (3). A daa annex explains more abou how we have sourced he daa for he model. The following secions describe wo specific challenges we had o overcome in maching he model o he daa. Working aper No. <xxx> <monh> 7 4

15 3. Challenge : maching he model s ransacion flow marix o he UK naional accouns Table shows he model s ransacion flow marix (TM). Alhough our behavioural model is large and complicaed (probably a he upper limi of racabiliy) i is significanly simpler han he full se of naional accouns published by he ONS. This is rue in wo paricularly imporan respecs. irs he number of rows in boh he income and financial accouns is significanly lower in our model han in he published naional accouns. The ONS lue ook for example conains around 65 series for he seven secors in our model. The equivalen number in our TM is around. Second he behavioural equaions impose a number of zero resricions on he behaviour of paricular secors. or example because we assume ha all business invesmen is carried ou by NCs and do no have equaions for invesmen in oher secors we are implicily assuming ha invesmen by banks ICs and OIs is zero whereas in pracice hey accoun for abou 5% of business invesmen. Table : Transacions flow marix See Table E in Annex for more informaion on variable mnemonics. These are boh poenial obsacles o our goal of modelling he financial balances for each secor of he UK economy. The financial balance ( ne lending ) of each secor is a balancing iem which is ulimaely a funcion of every oher series in ha secor s income or financial accoun. If we leave ou some rows of he accouns or aribue spending o one secor ha is acually being carried ou by anoher we will ineviably only be able o model he ne lending of each secor wih some residual error. or he model o be a useful lens o look a he economy i is no imporan ha his residual be zero. Working aper No. <xxx> <monh> 7 5

16 Many enries in he naional accouns are small and would be exremely challenging o model using behavioural equaions derived from economic heory. However for pracical applicaions i is imporan ha we ensure ha our behavioural equaions are explaining he majoriy of he ineresing variaion in he secoral financial balances over he period for which we ake daa (ie ha he remainder is jus noise or a fairly consan wedge ha we can explain) and ha when we use he model o forecas we rea hese residual componens rigorously. ecause hese small residual componens are no modelled explicily in he TM and here is no an auomaic offse in anoher secor here is a risk ha hey could lead o a violaion of imporan accouning ideniies when using he model for simulaions. Wha we do is o rea he residual for each secor as an AR() process when simulaing he model. Since he residuals mus sum o zero in he las period of back daa holding hem all fla when simulaing will ensure ha ha relaionship is mainained in forecass. The residuals mus all sum o zero over he pas because he sum of he ne lending balances in any se of naional accouns is zero and because he variables which are accouned for explicily in our TM all lead o double enries by consrucion. 7 Char 5: The exen o which our model s behavioural equaions allow us o replicae secoral financial balances over Households Non-financial corporaions Ne lending in he naional accouns Governmen er cen of GD Ne lending according o he series capured explicily in our TM Ne lending in he naional accouns er cen of GD Ne lending according o he series capured explicily in our TM anks Ne lending in he naional accouns er cen of GD Ne lending according o he series capured explicily in our TM Ne lending in he naional accouns er cen of GD Ne lending according o he series capured explicily in our TM This is rue once he saisical discrepancy beween income and expendiure has been accouned for. In our model we add his o he ne lending balance for OIs for convenience. We do no model he OI secor explicily bu we do keep rack of is financial balance for accouning reasons. Working aper No. <xxx> <monh> 7 6

17 ICs Res of he world Ne lending in he naional accouns er cen of GD Ne lending according o he series capured explicily in our TM Ne lending in he naional accouns er cen of GD Ne lending according o he series capured explicily in our TM Char 5 shows he exen o which our behavioural equaions successfully model ne lending for each secor. In each case he blue line shows ne lending as published in he laes vinage of he UK Economic Accouns published by he ONS and he red line shows he series implied by he TM we are using. This is herefore no a measure of fi in an economeric sense: wha i really shows is he deail ha we lose by discarding he roughly 65 series in he relevan par of he naional accouns and using insead he or so series ha are needed o run our behavioural equaions. To ake he governmen secor as an example if one ook daa for governmen consumpion and invesmen ineres paymens and axes from and ransfers o households and NCs one would expec o ge close o he governmen s ne lending posiion bu no o mach precisely because of he much greaer deail in he naional accouns. This is indeed wha we find. Given he relaive parsimony of our TM we regard he closeness of fi for four of he secors (households NCs governmen and res of he world) as being exremely good. The fi is less good for banks and ICs. Tha may be due parly o daa limiaions: he financial flows associaed wih hese secors are exremely large and we know ha even he published saisical discrepancies beween he esimaes of ne lending from he income and financial accouns for hese secors can be very large. 8 u anoher reason is likely o be ha our model is imposing srong resricions on hese secors. or example ICs are assumed o hold all of he UK s equiy claims on he res of he world in our TM whereas in pracice we know many of hose are held by NCs hrough foreign direc invesmen (DI) so earnings on DI are mosly being wrongly aribued o ICs in our model. Noe ha here is a corresponding bias in mos ime periods in he NCs char. or fuure work we will consider exending he model o address his perhaps by including behavioural equaions for DI. However one would need o be very wary of he need o keep he model racable: his model is already as far as we aware he larges model of is ype buil for he UK and here is a danger ha furher significan exensions would risk making he model oo complex o use When aligning measures of ne lending from he income and financial accouns he ONS allow here o be a deviaion beween he wo and hey publish a saisical discrepancy. u hose are o some exen engineered: he published ne lending balances are hemselves adjused judgemenally so he saisical discrepancies implied by raw daa could be much larger. Working aper No. <xxx> <monh> 7 7

18 3. Challenge : ensuring ha sock-flow consisency is mainained in simulaions As described in he inroducion one of he key srenghs of our approach is ha he model is sockflow-consisen as defined originally by Godley and Cripps (983). We can simulae he evoluion of balance shees for each secor in a way which is compleely consisen wih heir real economy aciviy and he ransacions aking place beween economic agens. One necessary condiion for sock-flow-consisency is ha real economic ransacions are associaed wih wo enries in he corresponding financial accouns one for he payee secor and one for he secor receiving he funds. To a large exen his is ensured by he srucure of our model. or example if households purchase goods from NCs for consumpion purposes ha will be refleced in lower ne lending of households and higher ne lending for firms all else equal. The way our model is specified his will auomaically feed hrough o a reducion in household deposis and a reducion in firms borrowing because he changes in hose financial socks depend explicily on he secors ne lending. The only addiional check ha is needed relaes o he residual erms for each secor ha are no explicily modelled in our TM (see previous secion). In he model we add an accouning check variable which sums he ne lending balances across all secors and here is a flag if his ever becomes non-zero during simulaions. Anoher necessary condiion is ha he sock of each financial insrumen evolves in a way ha can be accouned for using he ransacions in ha sock and any revaluaion effecs. Specifically (and using governmen bonds as an example): Sock (end of period ) = Sock (end of period -) + Ne issue of new governmen bonds in period + Revaluaion effec due o change in bond prices 9 (84) where ignoring complicaions o do wih inra-period ransacions we have Revaluaion effec = Sock (end of period -) * (rice() / price(-)) (85) In our model revaluaion effecs only arise for hree main insrumens: governmen bonds bank bonds and NC equiies. or mos financial insrumens his necessary condiion will hold auomaically because he updaing equaions for he socks are defined in erms of previous periods socks and he ne lending balances for he curren period. However here is a complicaion wih governmen bonds and bank bonds which needs careful aenion. or hose wo secors he problem is ha hey use bond liabiliies as heir buffer insrumen o ensure ha hey are sufficienly funded o mee all heir paymen obligaions in he curren period. However he prices of hose insrumens are assumed o depend on he curren period s supply as well as nominal demand. anks and he governmen herefore base heir bond issuance on expeced prices and hey can subsequenly be surprised when asse markes clear. If prices are ou of line wih heir expecaions hen equaion (84) above will be violaed. (Noe ha he same issue does no arise for NCs because in heir case loans raher han equiies is he 9 This can also include wrie-offs and oher volume changes. In our model we only aemp o consider wrie-offs on NC loans. Working aper No. <xxx> <monh> 7 8

19 buffer sock; so i is no a problem for sock-flow-consisency if heir expecaion for equiy prices urns ou o be incorrec.) To avoid his we inroduce he plausible assumpion ha banks and governmen also have access o one-period sources of funding o mee such unexpeced shor-erm shifs in cashflow. We inroduce wo unobservable variables bank bills and governmen bills which mop up he difference beween expeced and acual financing needs and are added o he new financing requiremen in he nex period. or simpliciy we rea hese bills as non-ineres-bearing. They are also ideniies in he model so i is no necessary o supply daa for hem. These adjusmens o he model are documened fully in Secion. As Char 6 shows when we run he model wih hese addiional variables he funding ha hese wo secors are assumed o mee wih bills raher han bonds is very small in almos all ime periods. Char 6: Esimaed socks of governmen and bank bills relaive o bonds Char 7: Illusraion ha he model is sockflow-consisen over he forecas for he governmen secor ank bonds ank bills er cen of GD Governmen bonds Governmen bills Governmen ne lending - income accoun bn Governmen ne lending - adjused change in balance shee socks Char 7 shows he governmen financial balance (red line) over he pas and he forecas. The blue line hen shows he change in he sock of governmen liabiliies adjused for explici revaluaion effecs. Over he pas he daa are no perfecly sock-flow-consisen because here are effecs in he naional accouns daa oher han explici revaluaions which can cause he flows o deviae from he changes in socks. Over he forecas however our model imposes his auomaically meaning ha he wo lines are he same. The equaions deermining hese socks of bills are laid ou in Secion. To ensure ha sock-flow-consisency holds for all secors in simulaions of he model we have inroduced six furher check variables which evaluae equaion (84) for each secor. Once we have added hese shor-erm bills for governmen and banks we find ha sock-flow-consisency does indeed hold when we forecas using he model. An example is shown in Char 7 for he governmen secor. As an aside i is worh noing ha hese ideniies do no always hold over he pas. This is because of oher volume changes (like reclassificaions) in he naional accouns daa and because our asse price indices which are indicaive series aken from non-ons sources will no be a perfec proxy for he revaluaion effecs ha are implied by he socks and flows in he naional accouns. This is clear from he hisorical comparison in Char 7. Working aper No. <xxx> <monh> 7 9

20 3.3 Calibraion and esimaion We derived our parameer values via a win approach of calibraion and esimaion. In all cases we used UK daa over he period 998 Q o 4 Q4. An annex conains deailed descripions of all he variables used. Saring wih hose parameers we calibraed we se he parameer deermining he weigh on pas errors when agens are forming heir adapive expecaions o. in line wih Hommes (3) and Evans and Ramey (6). We se he ax rae on household income H o 8.5% and he average rae of pension conribuions o 9% heir average values in our daase. We se he quarerly nominal depreciaion rae of capial o.3%. This is done so ha he derived esimae of he capial sock roughly maches he esimaes for he Unied Kingdom in Oulon and Wallis (5). The growh rae of he deb-o-income raio is se equal o.3 and he raio of housing wealh o morgage deb r s equal o.9 heir average values in our daase. The seady-sae share of capial is se o.35 implying a labour share of.65 equal o is average in our daase. The share of reained earnings s is se o 74% and he ax rae on corporae profis is se o 6% heir average values in our daase. The parameer he proporion of new invesmen financed by issuing equiy should be equal o he seady-sae proporion of oal firm liabiliies ha consis of equiy. In our daase which excludes corporae deb his proporion is 84%. u given his value seemed unrealisically high o us we used a value of %. We se he proporion of non-performing loans o.% is average value in our daase. inally for he impors equaion we calibrae he coefficien on he exchange rae in such a way ha he response of he curren accoun o an exchange rae change is roughly in line wih ha used in IM esimaes of curren accoun adjusmen. The implied values are.4 and.5 for and 3 respecively. or he block of he model deermining banks dividends and equiy we assume a arge level of equiy of en percenage poins above he bare regulaory minimum which is likely o be a reasonable approximaion for he sysem as a whole once all addiional loss-absorbing buffers are aken ino consideraion. Tha is we se o % and min o 8%. The relevan risk weighs on morgages and loans respecively are se o.35 and. When he banks equiy level is on arge we assume a reurn on equiy of around 8% is average value in our daase. or he ICs he only parameer we need o se oher han he coefficiens in he porfolio equaions is he share of oal asses ha are reained s IC. We se his parameer o.999 is average value in our daase. or he moneary policy rule we used a quarerly ineria coefficien of.9 roughly in line wih ha in COMASS (urgess e al. (3)) and we se he oher coefficiens in such a way ha nominal ank rae is around 5% when nominal GD growh is around 5%. The implied values of and 3 are -. and 36.5 respecively. The porfolio equaions are esimaed in differences raher han levels. Specifically we regress he change in he porfolio weigh on all he raes of reurn and a consan in order o be able o accoun for long-erm rends in porfolio weighs. Where OLS emis a coefficien which appears o be he wrong sign we se ha coefficien o zero. This is mainly an issue wih he off-diagonal enries in equaion (47) where i is hard o esimae a specificaion in which hey are all negaive. The resuling Working aper No. <xxx> <monh> 7

21 porfolio equaions are as follows: IC IC RoW IC RoW r r E r r. r G RoW RoW E A IC (86) and r.e r r G E A (87) In each case one equaion was no esimaed raher we imposed he budge adding-up consrains: AIC G IC IC IC EARoW RoW RoW E (88) (89) We esimaed he remaining parameers of our model using ONS daa over a sample period of Specifically we use OLS esimaion of he behavioural equaions of our model o esimae he model parameers. In his version of he model he equaions are esimaed one a a ime. The resuling parameer values are shown in Table C. Table C: arameer values esimaed by OLS Equaion Dependen variable arameer values number 4 Consumpion Housing ransacions Morgage repaymens Housing invesmen Growh rae of capial Governmen bond.55.7 yield 4 Annuiy paymens Morgage ineres rae Loan ineres rae Deposi ineres rae y u mor L D D ank bond yield 7 Res of he world bond yield r.64 Working aper No. <xxx> <monh> 7

22 4 Using he model o forecas In his secion we use he model o produce a simple forecas for he nex en years. We ake in a full daase up o 4 Q4 and hen allow he model o projec he enire se of variables ou o 5 Q4. Clearly we do no expec he forecass o be accurae a such long horizons bu using a long horizon allows us o assess wheher or no he soluion is explosive and he manner in which imbalances migh unwind. In order o produce such a forecas we need o ake a sand on he fuure pahs of our wo exogenous variables which are governmen spending and expors. As he purpose is o show how he model can be used o produce a forecas raher han produce our bes forecas for he nex en years we adop he simple assumpions of growing governmen spending and expors a consan raes in line wih heir long run average growh raes. orecasing also involves making a judgemen abou how variables will evolve when hey deviae from heir behavioural equaions in he las period of back daa. Typically forecasers eiher lock in any deviaion (perhaps because hey are aware of a srucural break) or unwind i perhaps because i is hough o be due o noise in he daa. In our hands-free forecas we adop he simples possible approach: we le all variables rever o heir model-implied pahs in he firs quarer of he forecas ( seing all he residuals o zero ). The only excepion we make is for he income flows for each secor which are no explicily modelled (see discussion around Char 5) where hese need o be se o non-zero values. We se hese equal o heir values over he 3-4 period in order o avoid puing oo much weigh on heir values in he final period of daa (4 Q4). This is a simple and ransparen approach o forecasing which has wo advanages. irs i allows easy inerrogaion of he long run properies of he model. Second i provides a ransparen baseline agains which we can run simulaions (see nex secion). However i is likely ha in policy applicaions forecasers would wan o ake a more sophisicaed approach o managing hese residuals. In many cases variables may have deviaed from heir model predicions for a long ime and for good reason and a more sensible approach migh be o unwind he differences slowly over a imespan of years. 4. Shor-erm forecas Our forecas is shown in Char 8. In he firs year of he forecas he economy slows down. House prices and housing invesmen are currenly above he levels implied by heir equaions in he model and so when heir residuals are unwound hey fall. This leads o negaive wealh effecs on consumpion and a direc fall in GD growh (from housing invesmen). However he model is se up wih posiive rend produciviy growh and we are inpuing profiles for he exogenous expors and governmen spending pahs which have growh raes in line wih heir hisorical averages. The real economy herefore recovers once he forecas reaches 6 and revers o more normal growh raes. Wihin our model here is no self-equilibraing mechanism ha would necessarily bring balance shees back ino equilibrium if hey were subjec o shocks; ie i is quie possible ha deb socks will sar o grow in an unsable way. We hink his is useful since if a scenario suggess deb socks would sar o grow unsusainably hen ha suggess ha he cenral bank migh wan o ake macroprudenial seps o deal wih his. Working aper No. <xxx> <monh> 7

23 In financial balances space he shor erm is characerised by a rise in household saving. The fiscal defici widens bu he curren accoun defici narrows. Char 8: eaures of a hands-off forecas using he model GD consumpion business invesmen and ank rae and effecive exchange rae impors ercenage change on previous year er cen Jan 5 = Consumpion Invesmen GD Impors Effecive exchange rae (LHS) ank rae (RHS) Secoral financial balances er cen of GD Households NCs Governmen anks Ins comps & pens funds Res of world Morgages NC loans and banks cusomer funding gap Loans o NCs Morgages anks' cusomer funding gap er cen of GD Working aper No. <xxx> <monh> 7 3

24 anks equiy and deb relaive o GD Capial-oupu raio er cen of GD er cen ank deb ank equiy Minimum equiy requiremen Capial-GD raio rices of bank bonds governmen bonds and equiy prices Index Governmen bond prices (RHS) ank bond prices (RHS) Equiy prices (LHS) Index Socks of equiies and bonds relaive o GD Effecive ineres raes Effecive rae on NC loans Effecive rae on morgages Effecive rae on household deposis Effecive rae on bank bonds Effecive rae on governmen bonds Ne inernaional invesmen posiion er cen Sock of bank bonds Sock of governmen bonds Sock of NC equiies er cen of GD er cen of GD Ne inernaional invesmen posiion Working aper No. <xxx> <monh> 7 4

25 4. Long-erm forecas urher ou he financial balances evolve in ways which are similar o heir recen behaviour in he Unied Kingdom reflecing he fac ha he model is calibraed on recen daa. Thus he governmen remains in defici as does he curren accoun and saving by NCs is parly offse by household dissaving. ICs remain big dissavers relying on invesmen income reurns o offse heir negaive ne lending posiion. Wha happens o financial variables in he exended forecas? The privae secor deleverages wih corporae savings being used o pay off loans and he fall in house prices and slower housing marke urnover han in he pas leads o morgages falling as a share of GD. anks deposi funding is more han sufficien o fund loans and morgages and banks are obliged o hold less capial. ank deb generaes higher reurns han oher asses (see below) and he price of bank deb rises driving is yield down. This means ha he ineres rae on bank bonds does no rise even as ank rae is raised during he recovery. The higher bank rae is passed hrough ino lending raes however. The forecas also shows a fall in he prices of NC equiies and governmen bonds. or equiies his occurs because ICs sell heir holdings of equiies progressively over he forecas. Tha is parly based on an exrapolaion of rends from he pas where ICs have swiched from equiies ino bonds capured in he porfolio equaions in he model. Alhough he demand for governmen bonds remains solid he persisen governmen deficis over he forecas imply a rising supply of bonds which drives down he price and drives up he yield.. Invesors herefore hold more bonds and fewer equiies. (Our porfolio equaions do no have any adjusmen o expeced reurns o ake accoun of he risk associaed wih he differen asse classes.) Wih domesic bond yields high he exchange rae depreciaes gradually o equalise reurns. This leads o a rise in he UK s ne inernaional invesmen posiion reflecing is high share of foreign currency denominaed overseas asses. 5 Some simulaions In his secion we produce specific simulaions relaive o his baseline. In each case we apply judgemens o a suiably chosen endogenous variable and hen inver he model on a given residual (shock) o allow he judgemen o feed hrough o all he oher endogenous variables. The idea is o show how he model can be used o examine he possible effecs of such scenarios on financial flows raher han o provide precise forecass of how he economy will acually respond o hese changes. 5. A rise in banks capial requiremens An ineresing quesion for macroprudenial policy is he impac of a sysem wide one percenage poin increase in banks capial requiremens. We can simulae his in our model and also have he abiliy o impose oher judgemens simulaneously for example o specify wha happens o banks Working aper No. <xxx> <monh> 7 5

26 disribuions. In his simulaion we choose o hold he dividend payou rae of banks fixed as hey raise more capial. Char 9: The effec of a one percenage poin rise in sysem-wide capial requiremens ank capial raio bank bond yields and loan Loan volumes and GD raes Change from baseline pp Change from baseline % Change from baseline % Eff rae on bank bonds Eff rae on morgages Acual capial raio Eff rae on NC loans Minimum capial raio GD (RHS) olume of morgages (RHS) olume of NC loans (LHS) Char 9 shows he effec of his change. Since he dividend payou rae is fixed he cos of equiy finance is he same. u he weigh of equiy in banks overall average funding coss rises pushing up heir average funding coss. This however is offse by a fall in bank bond yields as hey do no need o issue so much deb. anks also raise he margin on heir loans o ry o boos heir profiabiliy. The ne effec of hese is relaively small: loan raes are 5 basis poins higher a heir peak. This feeds back hrough o he real economy hrough weaker invesmen demand and leads o lower GD and lower loan volumes. The effec on morgage raes is lower due o he lower risk weigh. Table D: Illusraive esimaes of he impac of a one percenage poin increase in banks headline capial requiremens (peak impacs) Loan raes (bps) Loan volumes (%) GD (%) Aiyar Calomiris and Wieladek (4) [ ] ridges e al. (4) -3.5 Ellio (9) [4.59.] rancis and Osborne () Macroeconomic Assessmen Group () [5.5.] [ ] urgess urrows Godin Kinsella and Millard (6) +5 (corporae) -4 (corporae) -. Source: Harimohan and Nelson (4) Table D pus our esimaes in he conex of oher recen sudies of he effec of higher capial requiremens. Those in our model are broadly in line wih he exising lieraure alhough we do no include any quaniy raioning. Tha said as Harimohan and Nelson (4) noe hese effecs are The only asses in our model which are relevan for capial raios are morgages and corporae loans. We impose a risk weigh of 35% for morgages and % for NC loans. Working aper No. <xxx> <monh> 7 6