South African Reserve Bank Working Paper Series WP/17/01

Transcription

1 Souh African Reserve Bank Working Paper Series WP/17/1 The Quarerly Projecion Model of he SARB Byron Boha, Shaun de Jager, Franz Ruch and Rudi Seinbach Auhorised for disribuion by Chris Loewald Sepember 217

2 Souh African Reserve Bank Working Papers are wrien by saff members of he Souh African Reserve Bank and on occasion by consulans under he auspices of he Bank. The papers deal wih opical issues and describe preliminary research findings, and develop new analyical or empirical approaches in heir analyses. They are solely inended o elici commens and simulae debae. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he Souh African Reserve Bank or Souh African Reserve Bank policy. While every precauion is aken o ensure he accuracy of informaion, he Souh African Reserve Bank shall no be liable o any person for inaccurae informaion, omissions or opinions conained herein. Souh African Reserve Bank Working Papers are exernally refereed. Informaion on Souh African Reserve Bank Working Papers can be found a hp:// Enquiries Head: Research Deparmen Souh African Reserve Bank P O Box 427 Preoria 1 Tel. no.: SARB ( ) Souh African Reserve Bank All righs reserved. No par of his publicaion may be reproduced, sored in a rerieval sysem, or ransmied in any form or by any means wihou fully acknowledging he auhor(s) and his Working Paper as he source.

3 The Quarerly Projecion Model of he SARB Byron Boha Shaun de Jager * Franz Ruch Rudi Seinbach Sepember 217 Absrac The macroeconomic modelling and forecasing process a he Souh African Reserve Bank makes use of a suie of models. This paper provides an updae of he Quarerly Projecion Model (QPM) a so-called gap model which has played an inegral role in he suie since 27. Deails of he srucure and funcioning of he QPM model, wih paricular focus on he four mos imporan gaps he oupu gap, real exchange rae gap, real ineres rae gap, and inflaion gap (or inflaion from arge) are provided. The model is hen used o decompose hese four gaps in order o ell a coheren sory of Souh Africa s macroeconomic dynamics since he incepion of inflaion argeing. From he perspecive of he policy maker, he QPM provides a ool ha quanifies he consequences of is acions on he economy, while adequaely highlighing he rade-offs ha are faced in he process. JEL Classificaion: E5, C53, Z Keywords: Forecasing; Moneary Policy; Souh Africa; Macroeconomic models Corresponding auhor s address: Shaun.DeJager@resbank.co.za *Corresponding auhor. Souh African Reserve Bank, PO Box 427, Preoria, Souh Africa, 1. Tel: +27() Shaun.DeJager@resbank.co.za. The auhors wish o hank Jaromir Hurnik for his invaluable guidance and conribuions o he developmen of his version of he Quarerly Projecion Model.

4 Conens 1 Inroducion 1 2 The four gaps: A bird s-eye view of he QPM Oupu gap Exchange rae gap Inflaion gap Real ineres rae gap How does moneary policy work in he QPM? 4 4 The model Real economy Prices and wages Headline CPI Relaive prices and heir rends Core inflaion Food, elecriciy, and fuel price inflaion Wages Exchange rae Ineres raes Taylor rule Term srucure of ineres raes Counry risk and erm premiums Res of he world Empirical feaures Daa Equilibriums Seady saes Poenial growh Real equilibrium exchange rae Res of world: poenial growh and neural real ineres rae Counry risk premium Neural real ineres rae Calibraion Impulse response analysis Policy shock Exchange rae shock Oupu gap shock Hisorical decomposiions Inflaion Oupu Gap Policy rae Forecas comparison Conclusion 36 i

5 Appendices 39 Appendix A Daa 39 Appendix B Shock decomposiion 4 Appendix C Variables names and naming convenion 41 Lis of Tables 1 Model seady saes Calibraed parameers Forecas performance: Roo mean squared error relaive o random walk A1 Daa A2 Shock decomposiion groupings Lis of Figures 1 The four gaps The moneary policy ransmission mechanism in he QPM The relaive price of elecriciy Core inflaion Poenial growh Real effecive exchange rae Foreign moneary policy Foreign poenial growh Counry risk in equilibrium Neural real ineres rae One per cen policy rae shock One per cen real effecive exchange rae shock One per cen GDP shock CPI: Services inflaion CPI: Core goods inflaions CPI: Food inflaion Oupu gap Policy rae equaion decomposiion Hisorical ou-of-sample simulaions ii

6 1 Inroducion The macroeconomic modelling and forecasing process a he Souh African Reserve Bank makes use of a suie of models. All models have heir specific srenghs and weaknesses, and he use of a suie allows he models o complemen each oher in order o generae beer policy oucomes. Over ime, he models have evolved along wih advances in boh economeric heory and compuing power. This paper provides an updae of he Quarerly Projecion Model (QPM) a so-called gap model which has played an inegral role in he suie since The QPM is a general equilibrium model (GEM) ha has is foundaion in modern macroeconomic heory. 2 The underlying assumpion is ha agens in he economy are forward looking, i.e., expecaions abou he fuure maer for decisions ha are made oday. For example, a firm would se he price for he good i produces by aking ino accoun is expecaion for fuure inflaion. In erms of policy making, an inflaion-argeing cenral bank would also se ineres raes oday based on is expecaion for inflaion monhs ino he fuure. An equally imporan characerisic of he QPM is he fac ha he economy evolves around an underlying, bu well-defined, equilibrium pah. The so-called gaps develop when he economy deviaes from is equilibrium pah. In general, hese deviaions from equilibrium are caused by a variey of shocks. While shocks are mosly ransiory, he impacs on gaps (such as he oupu gap) hey induce are quie persisen due o he presence of nominal and real rigidiies. The role of moneary policy is o assis in closing he gaps by guiding he economy back o is equilibrium pah and, mos imporanly, inflaion back o i s arge level. The use of QPM-syle models was pioneered by he Bank of Canada in he 199s. Since hen, many cenral banks wih inflaion-argeing mandaes have incorporaed hese models in heir suies. In general, QPMs provide longer erm economic projecions wih relaive ease. They also enable cenral banks o analyse he naure of he shocks ha are impacing on he economy, as well as he longer erm equilibraing forces ha influence economic behaviour over ime. However, since QPMs generally have he limiaion ha hey are highly aggregaed focusing on GDP as a whole and no he underlying componens of aggregae demand hey need o be complemened wih oher models ha explain he behaviour of specific variables ha are analysed a a more disaggregaed level. This laes revision of he SARB s Quarerly Projecion Model presens furher enhancemens o he iniial model of De Jager (27) and is revised version by De Jager, Johnson, and Seinbach (215). I is imporan o emphasise ha hese various publicaions of he model reflec he sae of hinking a he ime of release. The model will coninue o undergo changes as new empirical evidence is uncovered, or as economic heory evolves. The paper is laid ou as follows: firs, a bird s-eye view of he model is given in he nex secion; hereafer follows a more echnical discussion of he model s key equaions in Secion 4. The various empirical properies of he model, ranging from is parameerisaion o is dynamic responses o shocks, is discussed in Secion 5, before Secion 6 concludes. 1 See De Jager (27) for a deailed descripion of his iniial version of he model, and De Jager, Johnson, and Seinbach (215) for an exended version hereof. 2 Essenially, he QPM is a simplified, user-friendly version of he more rigorous dynamic sochasic general equilibrium (DSGE) models ha are a popular ool in boh academic and cenral banking circles. 1

7 2 The four gaps: A bird s-eye view of he QPM The model is premised on he key assumpion ha moneary policy (in pracice) canno influence he fundamenal long-erm equilibrium rends in he economy, and herefore only affecs he cyclical feaures of he economy, or gaps, as hey are referred o here (i.e., he deviaions from long-erm equilibrium rends). Essenially, here are four gaps ha maer for policy analysis and forecasing in he QPM: (1) he oupu gap; (2) he real exchange rae s degree of over/undervaluaion; (3) inflaion s deviaion from he arge; and (4) he real ineres rae s deviaion from i s neural level. These gaps (or disequilibria) are illusraed in Figure 1, and discussed in more deail below. Figure 1: The four gaps 4 Oupu gap (% pa) 4 Real exchange rae gap (% pa) Inflaion gap (% pa) 3 Real ineres rae gap (% pa) Oupu gap The oupu gap reflecs he deviaion of he level of real GDP from is poenial level. Here, he premise is ha if he curren level of GDP is he same as is poenial level, his gap would be zero and will herefore be a i s equilibrium level, i.e. where here is no excess or insufficien demand pressures impacing on inflaion. The key facors in he QPM ha influence he oupu gap are he real ineres rae gap, he real exchange rae gap, commodiy erms of rade effecs and foreign demand, which is expressed as he oupu gap in he res of he world. 2

8 2.2 Exchange rae gap The real exchange rae gap he deviaion of he real exchange rae from is equilibrium level essenially shows o wha exen he currency is eiher over/undervalued, or he pressure ha he currency is exering on inflaion. A closed gap (i.e. a real exchange rae ha is in line wih is equilibrium level) is consisen wih oupu a poenial, and inflaion a is arge. Exchange raes in he QPM are defined as he price of foreign currency in erms of he rand. A posiive gap herefore reflecs a rand ha has depreciaed beyond is equilibrium level, in real erms. The real exchange rae in he model is deermined by an uncovered ineres pariy condiion (UIP) ha relaes expeced currency movemens o he risk-adjused differenial beween real ineres raes a home and abroad. Similarly, he equilibrium rend of he real exchange rae is defined by an equilibrium UIP condiion (i.e. where he ineres raes a home and abroad are represened by heir neural levels and he equilibrium counry risk premium). 2.3 Inflaion gap The inflaion gap is he deviaion of he rae of headline CPI inflaion from he mid-poin of he inflaion arge band. This is driven, iner alia, by he wo gaps saed above, as well as wage pressures and he expecaions of fuure inflaion. The QPM allows for he headline CPI o be explicily decomposed ino is non-core and core subcomponens, where non-core inflaion componens such as food, fuel, and elecriciy are separaely defined. - CPI food inflaion has a weigh of per cen in he overall CPI baske, and is deermined by inernaional food prices, he exchange rae, domesic demand, and inpu coss relaed o labour and fuel. - Fuel prices accoun for 4.58 per cen of CPI, and are deermined by he inernaional oil price, he exchange rae, as well as axes and margins. - Elecriciy inflaion, wih a weigh of 3.75 per cen, is generally reaed as exogenous, and is assumed o follow a prescribed pah over he forecas. - Core CPI makes up per cen of headline CPI, and is spli ino core services (2/3) and core goods (1/3). Boh subcomponens are largely deermined by real wage pressures, he real exchange rae gap, impored inflaion, he oupu gap and inflaion expecaions. 2.4 Real ineres rae gap The real ineres rae gap reflecs he deviaion of he real (shor-erm) ineres rae from is neural level. The real ineres rae is calculaed, using he Fischer equaion, as he nominal ineres rae minus expeced inflaion (or some forecas of inflaion one-period ahead), i.e. where he nominal shor-erm ineres rae is deermined by he cenral bank s policy reacion funcion using a Taylor-ype rule. The nominal repo rae in his version of he Taylor rule reacs o he deviaion of forecased inflaion from he arge midpoin, as well as he oupu gap. 3

9 3 How does moneary policy work in he QPM? The mechanism by which moneary policy ransmis o he real economy, and ulimaely inflaion, is summarised in Figure 2. 3 To illusrae, assume ha he economy sars in a posiion of equilibrium, i.e., he oupu gap is closed, he real exchange rae is a is equilibrium (fair) value, he real ineres rae is a is neural level, and inflaion is a is arge. If he Bank were o raise he repo rae, inflaion would be affeced via wo channels: (1) he real economy, and (2) he exchange rae. A higher repo rae immediaely increases he real ineres rae as prices are sicky. The real ineres rae now exceeds is neural level. The posiive real rae gap induces a negaive oupu gap, as GDP falls below is poenial level. Hereafer, inflaion sars o decline as he wider oupu gap creaes disinflaionary pressure. Wihin he exchange rae channel, he higher repo rae leads o an appreciaion of he nominal and real exchange rae (he laer due o price sickiness). No only does he sronger exchange rae pu furher downward pressure on inflaion, i also pus he real economy under furher srain hrough a deerioraion of he ne expors posiion. The combinaion of lower inflaion and a wider oupu gap causes he Bank o reduce he repo rae. Reducing he repo rae will: (1) lower he real ineres rae; (2) lif he oupu gap; (3) depreciae he exchange rae; and (4) raise inflaion, closing he four gaps. Figure 2: The moneary policy ransmission mechanism in he QPM This example merely illusraes he workings of he model for one specific shock a sudden change o moneary policy ha causes he repo rae o move firs. However, shocks may emanae from abroad, or in he domesic economy, and cause he exchange rae, inflaion, or oupu o move firs. In realiy, many shocks occur simulaneously. Neverheless, he closing of he gaps occurs hrough he same four basic channels. 3 For he sake of exposiion, cerain key channels in he QPM are omied from his diagram. 4

10 4 The model Before discussing he key equaions of he model, i is worh explaining he noaion ha we have used. Le x represen any variable (in erms of log 1). Where a ha appears above he variable, ˆx, i indicaes ha he variable is a gap, or deviaion from equilibrium. In urn, when a line appears above he variable, x, reference is being made o he variable s equilibrium value. To indicae he seady sae of a variable, a superscrip ss is used and he ime subscrip is no shown (since seady saes remain consan over ime): x ss. Finally, he quarer-on-quarer change in a variable is denoed by a ha precedes i: x. The only excepion here is inflaion he quarer-on-quarer change in he (log) price level where we use π s, as i is he cusom in mos of he lieraure Real economy The real economy is modelled as an invesmen-savings (IS) curve. Here, he oupu gap (i.e., deviaions of oupu from is equilibrium level) is deermined by four fundamenal variables: (1) he real ineres rae gap lr ˆ ; (2) he real exchange rae gap ẑ ; (3) he foreign oupu gap ŷ ; and (4) he deviaion of Souh Africa s expor commodiy price index (real) from is rend value rcom. In addiion, expecaions abou he fuure real economy, E ŷ +1, as well as recen oucomes ŷ 1 maer for he dynamic behaviour of he oupu gap. Finally, he residual erm, εŷ capures demand shocks, while he a s are he parameers ha indicae he direc impac each of he variables above have on he oupu gap: ŷ = a 1 E ŷ +1 + a 2 ŷ 1 a 3 [ a4 lr + (1 a 4 )( ẑ ) ] + a 5 ŷ + a 6 rcom + εŷ, (1) a 1 =.15, a 2 =.6, a 3 =.15, a 4 =.95, a 5 =.15, a 6 =.1 where he oupu gap is defined as he difference beween he log of real GDP and ha of poenial GDP, imes 1, in order o express he gap in percenage erms: ŷ = [ log(gdp ) log(poenal GDP ) ] 1 = y ȳ. (2) 4.2 Prices and wages In he QPM, inflaion is generally modelled as a New Keynesian Phillips curve. I is he modern version of he original Phillips curve ha permeaed macroeconomics since he lae 195s, when A.W. Phillips (1958) documened he relaionship beween wage growh and unemploymen in he Unied Kingdom. Over ime, he original specificaion of his cenral ene ha inflaion is linked o condiions in he real economy evolved ino is modern version. 5 Accordingly, he New Keynesian Phillips curve expresses curren inflaion as a funcion of he inflaion rae ha price seers expec o hold in he fuure, pas inflaion oucomes, as well as price pressures ha emanae 4 See Appendix C for a complee lis of he variables and heir definiions. 5 For example, Friedman (1968) correcly argued ha he Phillips curve is only valid if i also accouns for inflaion expecaions. 5

11 from changes in he real coss of producion commonly referred o as real marginal coss. 6,7 In he model, hese real marginal coss are generally driven by real wages, he real exchange rae, and he oupu gap Headline CPI To ensure ha he underlying dynamics in he headline consumer price index (CPI) are adequaely capured wih sufficien deail, CPI is disaggregaed ino is core and non-core subcomponens. In urn, he core CPI is spli ino is services and goods subcomponens, while non-core CPI is made up by separae equaions for he CPI indices of food, elecriciy and fuel prices. Headline CPI is consruced as follows: p cpi = (1 w f ood w elec + w f ood p f ood + w elec + w per p elec p per w per )p core where he p s denoe he (log) price levels for headline CPI and is subcomponens, and he w s denoe he weighs of he respecive subcomponens. Similarly, core CPI is furher decomposed ino he CPI for services and core goods: p core = w services p services + (1 w services )p coregoods (4) (3) Relaive prices and heir rends When he price a specific good changes relaive o he price of ohers, such relaive price movemens ofen aler consumpion paerns, as consumers would subsiue a less expensive good for he good ha has become more expensive. These relaive price movemens are imporan drivers of overall inflaion dynamics, since, in heory, reduced demand for he good ha has become relaively more expensive, should ulimaely consrain he price change ha caused he iniial relaive price movemen. In he model, he relaive prices of he componens of headline CPI are all expressed relaive o headline CPI: relp i = p i p cpi where i represens food, elecriciy, fuel, and core (which is spli beween services and core goods). While heory would predic ha subsiuion effecs ulimaely correc relaive price changes, his does no hold in he Souh African daa. On average, CPI elecriciy inflaion is higher han CPI food and fuel inflaion. In urn, hese non-core inflaion raes are higher han core inflaion. Wihin core inflaion, services inflaion is generally higher han he inflaion rae of goods. There are various reasons for hese permanen differences in relaive prices. Some are relaed o he degree 6 The pure heoreical New Keynesian Phillips curve absracs from pas inflaion oucomes. However, o mach he empirical persisence of acual inflaion, indexing o pas inflaion oucomes is added o he specificaion 7 Real marginal coss are essenially he increase in producion coss (in real erms) ha are relaed o a marginal increase in oupu a he firm level. 6 (5)

12 Index, Dec 216 = 1 Relaive price o which he consumpion of cerain goods is inelasic o he price of ha good food and ranspor are necessiies. Ohers are srucural. A well-known example would be Souh African elecriciy ariffs (see Figure 3). Figure 3: The relaive price of elecriciy 1 8 Headline CPI Elecriciy CPI 1.9 Relaive price: Elecriciy o Headline For years, Souh Africa had excess capaciy in erms of elecriciy generaion, which reduced he need for elecriciy ariffs o increase (while overall CPI was rising). As a resul, he relaive price of elecriciy was so low, ha Souh Africa enjoyed a considerable comparaive advanage in is energy-inensive producion secors (see Mohamed, 1997). 8 Evenually, increasing demand for elecriciy eroded all he excess capaciy. Suddenly, by 28, subsanial increases in elecriciy ariffs were needed in order o finance he required expendiure on new generaion capaciy. Wihin he model, we accoun for hese permanen differences in he relaive prices of he subcomponens of CPI o he headline index hrough relaive price wedges. Over he medium- o long-erm he wedges of all he inflaion componens average o zero (when muliplied by he weighs of he CPI baske). This for example, allows food inflaion o be higher han services inflaion for long periods of ime, wihou eiher being inconsisen wih medium-erm headline inflaion or he longerm inflaion arge Core inflaion Core inflaion is decomposed ino is subcomponens of core goods and services. 9 This disincion is made o allow for he differing roles ha wages and he exchange rae play in he respecive price formaion processes of goods relaive o ha of services. In general, services inflaion is more persisen, and wages play an imporan role in he price seing process. On he conrary, CPI goods are generally more sensiive o exchange rae movemens, as a large porion of he goods iems in he CPI baske are raded across inernaional borders. 8 These secors mosly relae o firs-sage beneficiaion of raw maerials from he mining indusry, such as smelers, ec. 9 All he services in headline CPI are par of core CPI. CPI goods excluding food, elecriciy and fuel consiue core goods. 7

13 Percen Percen Figure 4: Core inflaion Core goods CPI - lhs REER gap Services inflaion The Phillips curve for services CPI is specified as follows: Services CPI - lhs REER gap (scaled and shifed) Nominal wages 6 4 [ π services = b 11 E π cpi +1 + ] relpservices + (1 b11 )π 1 services + b 13 rmc services b 11 =.2, b 13 =.2 + ε πservices (6) where he quarer-on-quarer (annualised) inflaion rae of services CPI, π services is he change in he (log) price level of services CPI: π services = (p services p 1 services ) 4 (7) In Equaion (6), services CPI inflaion is a funcion of he expecaion for headline CPI, E π cpi +1, which needs o be adjused for he difference in equilibrium beween he relaive price of services o headline CPI, relp services. In addiion, o capure he persisence observed in services inflaion, i is driven by is own recen oucomes, π 1 services. The degree of slack in he economy, as measured by he oupu gap ŷ, as well as he gaps for real wages and he real exchange rae, combine o creae he real marginal coss ha price-seers in he services secor face, rmc services : rmc services = b 14 (b 15 ŷ + (1 b 15 )[ rwage relp services ]) + (1 b 14 )(ẑ relp services ). (8) b 14 =.85, b 15 =.61 Finally, ε πservices in Equaion (6) capures supply shocks o services CPI, i.e. idiosyncraic movemens in services CPI ha are no explained by he model. Core goods inflaion The Phillips curve for core goods CPI is specified as follows: π coregoods [ = b 21 E π cpi +1 + ] relpcoregoods + (1 b21 )π coregoods 1 + b 22 π m + b 23 rmc coregoods + ε πcoregoods (9) 8

14 b 21 =.25, b 22 =.4, b 23 =.25 where he quarer-on-quarer (annualised) inflaion rae of CPI for core goods, π coregoods is he change in is (log) price level: π coregoods = (p coregoods p coregoods 1 ) 4 (1) Similar o services CPI, inflaion of core goods prices is a funcion of he expecaion for headline CPI, E π cpi +1, adjused for he difference in equilibrium beween he relaive price of core goods o headline CPI. In addiion, core goods inflaion is parly driven by is own recen oucomes, π coregoods 1. Wha disinguishes core goods from services, is he fac ha cerain goods in he CPI baske are impored as a final produc from abroad, wihou any value necessarily being added in he domesic economy. 1 Price changes for hese impored final goods will herefore reflec direcly in he CPI. Their inflaion rae, π m, is defined as follows: π m = d 1 π m 1 + (1 d 1 ) [ s + π z + relp coregoods ] + ε πm d 1 =.1 Equaion (11) relaes quarer-on-quarer impor price inflaion o is own lag, as well as o changes in he nominal exchange rae, s, and foreign inflaion, π. The las wo erms he rae of equilibrium real depreciaion z and growh in he equilibrium relaive price of core goods ensure seady sae consisency in he long run. I is worh noing ha he presence of he lag erm π m 1 allows for shor-run deviaions from he law of one price in erms of impor price inflaion. Real marginal coss for he price seers of core goods, rmc coregoods, are a funcion of he oupu gap ŷ, and boh gaps for real wages and he real exchange rae: rmc coregoods = b 24 (b 25 ŷ + (1 b 25 )[ rwage relp coregoods ]) + (1 b 24 )(ẑ relp coregoods ). (12) b 24 =.9, b 25 =.43 As before, ε πcoregoods in Equaion (9) capures supply shocks o CPI inflaion of core goods. (11) Food, elecriciy, and fuel price inflaion Food price inflaion In he same vein as services and core goods inflaion, he firs wo erms in he food price equaion are persisence and expecaions of fuure inflaion. Food price inflaion also reflecs changes in inernaional food prices f ood (convered o rand erms by he nominal exchange rae s ), he real marginal cos of food, perol prices, and a supply shock. Similar o he core goods equaion, inernaional food prices are inended o capure impors of final goods. The energy (perol) prices erm is unique o his equaion and akes ino accoun he imporance of fuel prices in he producion of food, from he machinery employed in agriculure o he ransporaion of produc hroughou he producion process. The idiosyncraic supply shock represens deviaions in food prices ha are 1 Among hese impored final goods would be CPI caegories such as appliances, elecronic equipmen, cerain new vehicles, ec. 9

15 no covered by he fundamenals of he equaion. The impac ha a period of drough can have on CPI food prices is an example of such a shock. π f ood = b 31 π f ood 1 + b 32 ( f ood + s ) + b 33 rmc f ood + b 36 π 4,perol + ε π f ood + (1 b 31 b 32 b 36 )(π +1 + relp f ood ) b 31 =.65, b 32 =.12, b 33 =.16, b 36 =.33 Real marginal coss for he price seers of food prices, rmc f ood, are a funcion of he oupu gap, and boh gaps for real wages and he real domesic price of inernaional food. rmc f ood = b 34 [b 35 ŷ + (1 b 35 )( rwage relp f ood )] (13) + (1 b 34 )[ r f ood + ẑ relp f ood )] (14) b 34 =.8, b 35 =.5 Elecriciy price inflaion The elecriciy price equaion is very similar o he oher price specificaions given above, having he simples form a Philips curve migh have in his conex. Namely persisence and expecaions erms, real marginal coss, and an idiosyncraic supply shock. The use of a simplified Phillips curve is moivaed by he fac ha elecriciy prices are regulaed and herefore do no necessarily reac o marke forces. π elecriciy = b 41 π elecriciy 1 + b 42 rmc elecriciy + ε πelecriciy + (1 b 41 )(π +1 + relp elecriciy ) (15) b 41 =.65, b 42 =.1 Real marginal coss for elecriciy prices are a funcion of he oupu gap and he gap for real wages. Since he majoriy of elecriciy supplied is generaed wihin Souh Africa, he real exchange rae gap is omied. 11 In pracice, CPI elecriciy in he QPM is assumed o follow a prescribed pah over he forecas horizon. rmc elecriciy b 43 =.1 = b 43 ŷ + (1 b 43 )( rwage relp elecriciy ) (16) Fuel price inflaion Fuel price inflaion π perol measures he growh rae of he CPI index consising of perol and diesel componens. I is proxied in he model by he official regulaed price of 95 ocane unleaded perol 11 Less han 4 per cen of he domesic elecriciy supplied by Eskom is impored. Counries ha supply elecriciy o Eskom are members of he Souhern African Power Pool (SAPP), and include Mozambique (Cahora Bassa), Namibia and Lesoho. 1

16 in Gaueng, published monhly by he Cenral Energy Fund (CEF). Due o mehodological reasons, and he fac ha diesel is no included in he proxy, here is a shock allowing for deviaions o wha would oherwise be an ideniy. π perol = perol + ε πperol (17) The perol price is made up of wo major componens; he basic fuel price (BFP), b f p, and levies and margins, peax. Their relaive weighs are simply he raio of he respecive componen o he oal price. Over he recen period he weigh of BFP in he perol price has been roughly 45 percen, wih levies and margins accouning for he res. perol = w b f p b f p + (1 w b f p ) peax (18) perol = 4 (perol perol 1 ) (19) The BFP is calculaed by CEF as he combinaion of movemens in inernaional produc prices (sourced crude and refined oils) and he (rand/dollar) exchange rae. These price movemens are proxied by he measure of crude oil and exchange raes used in he model. b f p = oil + s + ε b f p (2) b f p = b f p 1 + b f p /4 (21) Since levies and margins are purely a regulaory componen hey are modelled agnosically as a mean revering process (which converges o is calibraed seady-sae). peax =.75 peax 1 + (1.75) peax ss + ε peax (22) peax = peax 1 + peax /4 (23) Wages The wage channel is an imporan driver of he overall inflaion process in he model. Real wage developmens along wih he real exchange rae and oupu relaive o is poenial ulimaely deermine he real marginal coss ha feaure in he model s price seing equaions. The definiion of real wages is sandard: rwage = wage π, (24) and simply saes ha real wage growh, rwage, is nominal wage growh adjused for conemporaneous inflaion. Imporanly, i is no he absolue growh rae of real wages ha leads o inflaionary pressures, bu raher he degree o which real wages deviae from heir equilibrium level. The equilibrium real wage is pinned down by he heoreical condiion which saes ha in he long run, real wage growh should equal produciviy growh. In his case, produciviy growh is defined as growh in oupu per worker, or GDP growh adjused for employmen growh. In equilibrium, his definiion of produciviy growh would herefore become poenial GDP growh adjused for equilibrium employmen growh. The equilibrium for real wage growh is herefore specified as follows: rwage = (g emp ) + ε rwage, (25) 11

17 where ε rwage is a shock ha can move he equilibrium real wage rae emporarily. Having defined boh he real wage and is equilibrium, he real wage gap which feaures in he real marginal cos componen of he model s Phillips curves is expressed as he difference beween he real wage and is equilibrium value: rwage = rwage rwage. (26) Essenially, he real wage gap reflecs he real uni labour coss ha producers face. I is however a sligh modificaion of he usual uni labour cos definiion. Here, he real wage gap reflecs real wages ha are adjused for equilibrium produciviy, while he more familiar real uni labour cos definiion expresses real wages ha are adjused for conemporaneous produciviy. While real wages are he cause of inflaion deviaing from is arge, i is ulimaely nominal wages ha are seled upon in he labour marke. In he model, nominal wages follow a Phillips curve ha depends on expecaions of fuure wage inflaion as well as recenly realised wage inflaion. Nominal wages furher depend on he real wage gap, rwage, and produciviy. Here he real wage gap plays an equilibraing role: if he real wage gap is posiive, no only are nominal wages growing in excess of headline inflaion, bu real wages are growing in excess of produciviy, and nominal wages will herefore be forced o moderae. An empirical feaure of he Souh African labour marke is he endency of wage-seers o index wage increases o pas inflaion, which is capured by he fifh erm. There is also an idiosyncraic supply shock. wage = (1 w 1 w 3 )E wage +1 + w 1 wage 1 w 2 ( rwage ) + w 2 (ŷ êmp ) + w 3 (π rwage ) + ε wage (27) w 1 =.2, w 2 =.8, w 3 = Exchange rae A key srucural elemen of he QPM, as is rue for all open-economy DSGE models, is he uncovered ineres pariy condiion (UIP). I links domesic and inernaional financial markes, by relaing expeced currency movemens o he risk-adjused differenial beween ineres raes a home and abroad. To ensure no opporuniy for arbirage exiss, he currency wih he higher yield (afer adjusing for he counry risk premium, prem ) should be expeced o depreciae in fuure in order o equae reurns in eiher currency. More formally, he sandard UIP condiion is expressed as follows: Es +1 s = i i prem (28) where s is he (log) price of he foreign currency in erms of he domesic currency. As such, an increase in he exchange rae signifies a depreciaion. A drawback of he sandard UIP specificaion in Equaion (28), is ha i does no mimic he empirical behaviour of he rand exchange rae, which generally shows more persisence and a less 12

18 han one-o-one reacion o he ineres rae. 12 As a resul, exchange rae dynamics in he QPM are deermined using a modified UIP relaionship similar o ha found in operaional QPM models elsewhere. 13 Φ = e 1 Es +1 + (1 e 1 )(s [ z + π arge π arge ]) (29) Φ s = e 2 (i i prem ) + (1 e 2 )( z 1 + π 1 π 1 ) els (3) e 1 =.9, e 2 =.6 The Φ erm is broken up ino wo pars in Equaion (29). The firs, Es +1, represens purely raional agens wih forward-looking expecaions similar o ha found in he sandard UIP specificaion. The second par represens myopic, backward-looking agens. These agens forecas fuure exchange raes based on he equilibrium real exchange rae and he differenial beween he domesic and foreign inflaion arges. Essenially, hese hree erms represen relaive purchasing power pariy (PPP) in equilibrium. In Equaion (3), he sandard UIP condiion in which ineres rae differenials impac he exchange rae on a one-o-one basis, is reduced by he coefficien e 2. Here, a porion of he exchange rae s movemen from one quarer o he nex is ascribed o recen developmens in he inflaion differenial. Togeher, hese modificaions dampen he pass-hrough of ineres raes ono he exchange rae. 4.4 Ineres raes Taylor rule The model uses a sandard, albei slighly modified, Taylor-ype rule employed in srucural models such as hose in use a oher inflaion argeing cenral banks (Benes e al., 216, Szilágyi e al., 213, Kamber e al., 215). i = f 1 i 1 + (1 f 1 ) { i neural + ε i + f 2 [ 1 3 (Eπ4,cpi +3 + Eπ4,cpi +4 + Eπ4,cpi +5 ) Eπarge +4 ] + f } 3ŷ (31) f 1 =.79, f 2 = 1.57, f 3 =.54 An almos universal difference in his syle of model from he rule Taylor (1993) proposed is he auoregressive smoohing parameer f 1, which creaes he necessary persisence in he policy (repo) rae i o fi he observed daa. The policy rae is hen also a funcion of he neural policy (or equilibrium) rae i neural : i neural = r + π arge, (32) which is purely he sum of he neural real ineres rae and he inflaion arge. In erms of macroeconomic condiions, he rule responds o deviaions from he inflaion arge of (smoohed) inflaion expecaions over he nex year and half, and he oupu gap. There is also a policy shock, ε i, o accoun for deviaions of acual policy decisions from his rule This finding is primarily based on he esimaion resuls of a recursively idenified Bayesian vecor auoregression (VAR). 13 See Benes e al. (216). 14 Such deviaions occur for wo reasons, one, he Taylor rule is only a crude approximaion of he MPC s reacion funcion, and wo, when he model filers he daa hrough hisory i uses ex pos informaion ha he MPC would no 13

19 Parameers f 2 and f 3 are he relaive weighs on deviaions of forward-looking inflaion from arge and oupu from poenial. The expeced inflaion erm emphasises he desire o reac over he moneary policy horizon and hus see hrough he noise while concern for he inflaion-oupu rade-off is consisen he SARB s flexible inflaion argeing framework. I is necessary ha f 2 is greaer han 1 for he model o have a soluion. Tha is, he policy maker is required o reac more han one-o-one wih deviaions of expecaions from arge (inducing real ineres raes o rise) in order o effecively anchor expecaions and fuure inflaion oucomes Term srucure of ineres raes While he cenral bank has conrol over he shor-end of he yield curve via he repo rae, i has less conrol over longer mauriies along he yield curve. Longer-erm ineres raes are mosly deermined by expecaions abou he fuure pah of shor-erm ineres raes. Ulimaely, wha maers for aggregae demand is no only he shor-erm ineres rae, bu also ineres raes of longer mauriies, especially for invesmen and governmen spending. Since he QPM is forward looking, i allows for he derivaion of expeced fuure shor-erm ineres raes. As such, longererm ineres raes can be modelled via he expecaions hypohesis of he erms srucure, which saes ha he yield on a long-erm bond should equal he average of expeced shor erm ineres raes over he life of he bond: i n = 1 n 1 i +i + erm n, (33) n i= where i n represens he yield of an n-period bond, he summaion erm reflecs he expeced average shor-erm ineres rae, and erm n is he erm premium required by invesors o hold ha bond.15,16. Using he Fisher equaion: r = i E π +1, (34) which saes ha a real ineres rae is a nominal rae minus inflaion, he expeced average shorerm ineres rae of Equaion (33) can be furher decomposed ino expecaions for boh he average real rae and inflaion over he life of he bond: i n = 1 n 1 r +i + 1 n 1 π 4 n n +1+i + ermn. (35) i= i= The real yield for a bond of n-period mauriy, r n can herefore be calculaed from he firs erm on he righ-hand side of Equaion (33): r n = 1 n 1 r +i. (36) n i= have had a is disposal when hey made heir ineres rae decision, i.e., acual inflaion oucomes are differen from wha was forecas a he ime, and he hen real-ime oupu gap would mos likely have been revised. 15 Since he QPM is a quarerly model, a 1 year bond would consis of 4 quarers, hence n = The inclusion of he erm premium is necessiaed by he fac ha he expecaions hypohesis canno explain he empirical regulariy ha yield curves slope upwards on average. The liquidiy premium heory exends he expecaions hypohesis heory, by posiing ha invesors generally prefer o hold shorer-erm securiies, and herefore need addiional compensaion a erm premium o induce heir holding of longer erm securiies. The erm premium increases wih he mauriy of he bond, and herefore explains he endency of he yield curve o slope upwards. 14

20 In order o deermine he relaive imporance ha yields of differen mauriies have for aggregae demand in he model, we analyse he deb mauriy srucure in Souh Africa. To do his, we consider he lending aciviies by boh banks and non-bank financial insiuions, as well as lending via he bond marke by governmen and corporaions. Formal bank lending oalled R3.35 rillion in June 217, wih abou an equal spli going o households and corporaions. Of his oal, abou 4 per cen are morgage advances, 3 per cen general loans and advances, while he res includes overdrafs, credi cards, insalmen sales, and oher lending. The majoriy of loans occur on a flexible basis, linked direcly o he prevailing shor-erm repurchase rae se by he SARB. As a consequence, he majoriy of his deb, alhough possibly of long mauriy, is linked direcly o he shor-erm policy rae. An esimae of he effecive lending rae from bank lending has a correlaion wih he policy rae of.97. General governmen, on he oher hand, mainly borrows from he bond marke, a he longer-end of he yield curve. In 216/17 fiscal year, governmen had an esimaed erm-o-mauriy on oal deb of 14.7 years. Corporaions ha lend on he bond marke fall somewhere in beween he longer-end lending of governmen and he formal bank lending wih esimaes of an average mauriy of around 6 years. Taking accoun of oal invesmen and governmen spending s shares in real GDP, he effecive long-run real rae, lr, ha eners he IS-curve of Equaion (2) is specified as follows: lr = α 1 r + α 2 r 8 + α 3 r 2 + α 4 r 4, (37) α 1 =.4, α 2 =.3, α 3 =.2, α 4 =.1 where r is he real repo (or shor-erm) rae, r 8 is an 8-quarer (i.e., 2 year) real bond yield, while r 2 and r 4 are he real yields for 5 and 1 year governmen bonds, respecively. The α s in Equaion (37) represen he relaive weighs of he various yields Counry risk and erm premiums The counry risk premium (prem ) in he model is a key feaure of he UIP condiion in Equaion (28). By re-arranging he UIP condiion as follows: prem = (i i ) (E s +1 s ), (38) i becomes clear ha he counry risk premium serves as he wedge ha equaes reurns beween domesic asses and hose abroad. For higher domesic counry risk, inernaional invesors would require greaer reurn from he domesic economy via a higher i. The risk premium iself is modelled in a fairly agnosic (non-srucural) way, i.e. as a sochasic process ha moves around in he even of risk-premium shocks, ε prem, bu, in he absence of such shocks, i will ulimaely rever o is equilibrium value, prem : prem = h prem 1 + (1 h )prem + ε prem (39) h =.8 Similar o he counry risk premium, he erm premiums of he various bond yields from Equaion (33) are modelled as sochasic processes ha ulimaely converge on heir seady sae values: erm n = h 4 erm n 1 + (1 h 4)erm n,ss + h n (prem prem ss ) + ε ermn. (4) h 4 =.8 However, since he same fundamenals ha move he counry risk premium would also drive changes in erm premiums, we enable his co-movemen o occur by allowing for spill-overs from 15

21 he counry risk premium ono he various erm premiums. Finally, he mauriy weighing ha applies o he effecive long-run real rae lr, is also used o deermine he effecive erm premium, lerm : 17 lerm = α 1 + α 2 erm 8 + α 3 erm 2 + α 4 erm 4. (41) α 1 =.4, α 2 =.3, α 3 =.2, α 4 = Res of he world Due o he small size of he Souh African economy relaive o he res of he world here is no appreciable feedback from he domesic economy o he res of he world. Advanage is aken of his fac by reaing inernaional price and oupu variables as exogenously (separaely) deermined via supplemenary models in he SARB s suie of models. These variables include rade-weighed consumer prices, oupu, and ineres raes of he G3 economies (i.e. he Unied Saes, euro area, and Japan) plus China as well as food, oil, and non-oil commodiy prices. The global variables hemselves are modelled in he Global Projecion Model (GPM) (Carabenciov e al., 213) which models he economies of our mos imporan rading parners 18. The srucure of his model is similar in spiri o he QPM, while placing emphasis on he dynamics of cross-counry spillovers of global shocks. Some of he salien empirical feaures of his model are discussed in he nex secion. 5 Empirical feaures This secion discusses he empirical properies of he model, including is ime-varying equilibrium values, seady saes, and he calibraion of parameers. In urn, his allows us o generae impulse response funcions (i.e., he model s dynamic response o a variey of shocks), decomposiions of he key equaions ino he variables and shocks ha drive hem, as well as forecass. In order o generae forecass from he model, a number of seps are required. Firs, as was done in he previous secion, he appropriae model srucure needs o be deermined, which is a fine balance beween complexiy and funcionaliy. Second, he model s parameers need o be calibraed o fi Souh Africa s empirical properies. Third, acual daa on he economy (i.e., CPI, real GDP, ineres raes and he exchange rae, among ohers) is required o filer he model over hisory, in order o generae he ime-varying equilibriums and he accompanying srucural shocks ha lead o hisorical deviaions from hese equilibriums. Fourh, he model is decomposed o deermine he accuracy and appropriaeness of he model s srucure and calibraion using shock and equaion decomposiions, impulse response funcions, and forecas accuracy. 5.1 Daa In order o filer and forecas, he QPM requires daa of he variables of ineres. In he filer sep, for a given calibraion and daase, we esimae he unobserved equilibriums (and he gaps hey imply). Following he Bank s suie of models approach, no all equilibriums are esimaed in he QPM, bu raher imposed as observed. The mos imporan equilibrium generaed from an 17 Since here is no erm premium for he shor rae, i is denoed by a zero in Equaion (41) 18 While he QPM does have a foreign economy block of equaions, he equilibriums of mos foreign variables are aken from he GPM and no filered in he QPM. The forecas of hese variables are also aken from GPM s GPM Nework forecas of which he SARB is a conribuing member. 16

22 auxiliary model is poenial growh. We use a modified version of he finance-neural mehod used by Anvari e al. (214). Table A1 shows all he daa used as inpus ino he QPM. 5.2 Equilibriums The QPM is a general equilibrium model where deviaions from equilibrium he so-called gaps drive economic oucomes. In his general equilibrium conex, i is assumed ha an economy will rever o is long-run equilibrium (seady sae) over ime, usually in he absence of ransiory shocks and oher facors affecing he medium erm. Take for example an economy ha is operaing above is poenial growh rae for a period of ime due o srong demand. This period is characerised by a posiive and growing oupu gap which ends o raise inflaion. The bes Souh African example was he mid-2s, when real GDP growh averaged over 5 per cen, bu poenial growh was likely jus below 4 per cen. This led o a significanly large posiive oupu gap which pu upward pressure on inflaion, i.e. wha s generally referred o as demand-pull inflaion. As a consequence, argeed inflaion rose from 4.5 per cen in he firs quarer of 24 o jus below 8 per cen by he end of 27, and required moneary policy ighening o help bring inflaion back o wihin he arge range. This secion provides deail on some of he key equilibriums ha are defined in he QPM: he neural real ineres rae; real equilibrium exchange rae; he inflaion arge; and ohers. These equilibriums inform he gaps he deviaions from equilibrium ha policymakers ofen speak abou and use o jusify heir policy choices Seady saes I is imporan o disinguish beween he concep of a variable s equilibrium level and ha of a seady sae. Seady saes are a se of fixed values ha represen he fundamenal long-run properies of an economy. The long-run can be hough of as 8 years and beyond. Equilibriums are slowly evolving medium-erm conceps ha generally flucuae around he seady seady over ime. The medium-erm can be hough of as 3-6 years. The above example on he pre-crisis boom in Souh Africa is useful for illusraing his disincion. Assuming ha Souh Africa s (long-run) seady-sae poenial growh rae is around 2,5 per cen, a number of facors helped o emporarily drive acual poenial growh a medium-erm equilibrium concep above his seady sae value during he mid-2s (srong and rising asse prices, growing credi exension, rising erms of rade linked o significan growh in he price of Souh Africa s expor commodiies). Togeher, hese facors explain he rise in Souh Africa s poenial growh from around 2.5 per cen in he lae-199s o o almos 4 per cen during he mid-2s (see Anvari e al., 214). However, following he global financial crisis, poenial growh once again deceleraed. In fac, in recen years, esimaes show ha poenial growh has fallen o below is seady sae. Table 1 provides some of he key seady sae values imposed on he QPM. Two main equaions pin down he relaionship beween seady sae values a home and abroad: a purchasing power pariy (PPP) condiion: 19 s ss = z ss + (π arge π,arge ); (42) 19 The noaion for seady sae values does no have a ime subscrip, since hese values are consan over ime. 17

23 and an uncovered ineres pariy (UIP) condiion in real erms: r ss = r,ss + prem ss + z ss. (43) The seady sae PPP condiion links he depreciaion of he nominal exchange rae ( s ss ) o he real exchange rae s rae of depreciaion ( z ss ) and he inflaion arge differenial beween Souh Africa and abroad. The real UIP condiion, in seady sae, relaes he domesic neural real ineres rae ( r ss ) o he foreign neural real ineres rae r,ss, equilibrium counry risk premium (prem ss ), and equilibrium real exchange rae depreciaion ( z ss ). Table 1: Model seady saes Policy Variables Domesic Foreign Inflaion arge Neural real ineres rae Neural nominal ineres rae Poenial growh Exchange raes Real exchange rae depreciaion Nominal exchange rae depreciaion 2.5 Counry risk premium 2 Moneary policy in Souh Africa operaes wihin an inflaion arge range of beween 3 and 6 per cen. However, such a range canno be implemened wihin he srucure of he QPM. Insead, a poin arge is required. Recen MPC saemens have indicaed a preference by he MPC o focus on he mid-poin of he 3 6 per cen arge range over he medium o longer erm, by saing in is July 217 MPC saemen ha []he MPC would prefer [inflaion] expecaions o be anchored closer o he mid-poin of he arge range. As such, he inflaion arge in he QPM is aligned wih his preference and se a 4.5 per cen. For foreign inflaion, ineres raes and he exchange rae, he G3 economies are used. The inflaion arge for hese combined economies is 2 per cen. To idenify he seady sae neural real ineres raes of he G3 economies is slighly more complicaed. Here we use he las 3 years as a proxy for he long run. Over his period real ineres raes in he G3 economies have averaged around.5 per cen. In order o deermine Souh Africa s seady-sae neural real ineres rae ( r) from Equaion (43), we require esimaes for equilibrium real exchange rae depreciaion and he counry risk premium in seady sae. Equilibrium exchange rae esimaes of De Jager (212) indicae ha he real exchange rae experienced rend appreciaion during much of he early 2s, from higher produciviy growh in SA, compared wih economies such as he US and euro area, and improving fiscal balances. This rend reversed following he global financial crisis. From 21 onwards, SA experienced equilibrium depreciaion in he real effecive exchange rae (REER) as produciviy differenials worsened more quickly in SA compared wih he US. These wo disinc periods of SA hisory complicae he choice of seady sae value for he real effecive exchange rae. On average, over he inflaion argeing period, equilibrium depreciaion of he REER has been closer o 18