South African Reserve Bank Working Paper

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1 WP/13/01 Souh African Reserve Bank Working Paper The pace of poenial oupu growh in he Souh African economy N Ehlers, L Mboji and M M Smal March 2013 Working Papers describe research in progress and are inended o elici commens and conribue o debae. The views expressed 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 or opinions conained herein.

2 Souh African Reserve Bank WP/13/01 Souh African Reserve Bank Working Paper Research Deparmen The pace of poenial oupu growh in he Souh African economy Prepared by N Ehlers, L Mboji and M M Smal 1 Auhorised for disribuion by C Loewald March 2013 Absrac In a flexible inflaion-argeing framework he oupu and inflaion gaps are key measures of inflaionary pressures and play an imporan role in deermining he opimal policy ineres rae. The esimaion of poenial oupu is, however, a challenge since i canno be direcly observed. This noe explains he mehodologies currenly used by he Souh African Reserve Bank o esimae poenial oupu growh and discusses changes o he esimae since he onse of he global financial and economic crisis. JEL classificaion: E23, E24, C32 Keywords: HP filer, MV filer, poenial oupu, producion funcion Corresponding auhor s address: nelene.ehlers@resbank.co.za 1 The auhors would like o hank V Anvari and S de Jager for heir valuable conribuions.

3 Conens 1 Inroducion Esimaion echniques De-rending smoohing echniques Srucural and semi srucural echniques Esimaes of poenial oupu... 7 Figures 1 Acual and poenial oupu level (R billions) Acual and poenial oupu growh (per cen) Oupu gap...11 Tables 1 Souh Africa s acual and poenial oupu (per cen)... 9 Abbreviaions EAP ECB GDP HP MPC MV HP NAWRU PGDPM PGEM SARB US economically acive populaion European Cenral Bank gross domesic produc Hodrick Presco [filer] Moneary Policy Commiee mulivariae Hodrick Presco [filer] non-acceleraing wage rae of unemploymen Poenial Gross Domesic Produc Model Poenial General Equilibrium Model Souh African Reserve Bank Unied Saes ii

4 1 Inroducion In a flexible inflaion-argeing framework he oupu and inflaion gaps are key measures of inflaionary pressures and play an imporan role in deermining he opimal policy ineres rae. The esimaion of poenial oupu is, however, a challenge since i canno be direcly observed. This noe explains he mehodologies currenly used by he Souh African Reserve Bank o esimae poenial oupu growh and discusses changes o he esimae since he onse of he global financial and economic crisis. While he hisorical inflaion gap calculaion is fairly simplisic (measured by he difference beween he known inflaion arge and expeced price inflaion), he oupu gap is expressed as he deviaion beween he acual level of oupu and an esimae for he poenial level of oupu of he economy. Poenial oupu is no direcly observable. The long-erm rend in real oupu generally shifs upwards as more resources primarily labour and capial become available, and as echnological progress allows more efficien use of exising resources. However, real oupu also displays a shor-erm variaion around ha long-erm rend largely because of he influence of he business cycle, bu also because of severe shocks ha may cause a more pronounced deerioraion of facors of producion and resource use. Depending on he exen of he shock, his can resul in a emporary, albei prolonged, deviaion from is previous rend. Alhough poenial oupu measures he producive capaciy of he economy, i should no be viewed as a shor-erm echnical ceiling on oupu ha canno be exceeded. Raher, i is a measure of susainable oupu, in which he exen of resource use is no adding o, or subracing from, inflaionary pressure. When forecasing, he challenge of he poenial oupu calculaion is amplified. No only mus he curren poenial oupu and he oupu gap be esimaed, bu he pace of he poenial oupu growh needs o be assumed over he forecas horizon. When an economy is subjeced o a serious and prolonged negaive shock, such as he curren global crisis, he facors of producion may deeriorae well below heir poenial levels, causing he curren poenial oupu level o deviae subsanially from is long-run rend. 1

5 This noe provides esimaes of he oupu gap by means of an aggregae measure for he level of poenial oupu over he pas few years. 2 Esimaion echniques The informaion conen of observable macroeconomic daa is cenral o he esimaion of poenial oupu and wheher demand and supply shocks can be accuraely idenified. This involves exploiing saisical and/or srucural approaches o separae emporary (demand) and permanen (supply) influences on oupu. Buler (1996) suggess a se of crieria o asses mehods used o esimae poenial oupu. These crieria include economic consisency; he abiliy o incorporae addiional judgemen flexibly; and he abiliy o reduce and quanify uncerainy abou he curren level of poenial oupu and specificaion robusness. However, i should be noed ha i is highly unlikely ha one esimaion mehod could be expeced o mach all of he lised crieria. For ha reason, we se ou single-mehod esimaes and compare hem o a separae measure ha aggregaes he esimaes. 2.1 De-rending smoohing echniques One class of echniques involves he applicaion of simple de-rending (smoohing) echniques o acual developmens in real gross domesic produc (GDP). These derending mehods are saisical and resuls are ofen referred o as rend growh and he oupu gap as a deviaion from rend. Usually when here is a significan change o he acual observed oupu, poenial oupu is revised accordingly. The widely used Hodrick Presco (HP) filer decomposes an observed shock ino a supply and a demand componen (Hodrick and Presco 1980, 1997). This filer applies he disincion ha supply shocks have permanen or lasing effecs on oupu, while demand shocks are considered o be emporary. However, i is imporan o noe ha persisen demand shocks may have longer-erm supply-side effecs which he filer canno disinguish. The choice of he degree of cycle versus rend o include in he esimaion procedure (se by choosing a value for he 2

6 smoohing parameer, ofen referred o as he so-called lambda), is chosen subjecively and is ofen prone o debae. 2.2 Srucural and semi srucural echniques Producion funcion echniques Anoher class of esimaion echnique incorporaes srucural informaion as se ou in a ypical producion funcion specificaion. These measures of poenial oupu inegrae srucural frameworks by including informaion concerning capial sock, working populaion, rend paricipaion raes, srucural unemploymen and developmens in facor produciviy. The SARB s Poenial Gross Domesic Produc Model (PGDPM) a highly aggregaed, small supply-side model was used o esimae poenial oupu. Here poenial oupu is he level of oupu ha resuls when he facors of producion and oal facor produciviy are a heir respecive poenial levels. 2 Any revision o poenial oupu is hen due o a change in he producion facors lised above. Typically, a producion funcion may be represened by he following expression: Y A K N (1) where Y is acual GDP a facor cos; A is unobservable oal facor produciviy (TFP); K is he acual capial sock, and N is acual employmen. and represen he capial and labour share parameers respecively, where consan reurns o scale are assumed, ha is, + = 1. The poenial level of oupu is deermined by esimaing he poenial levels of all he variables of equaion 1. The superscrip * is used o denoe poenial levels of all variables, and poenial oupu Y * is derived from: Y * A * * K N * (2) 3

7 The poenial level of oal facor produciviy A* is approximaed using a Solowresidual approach, and a neoclassical (Jorgenson) approach is used o esimae he desired capial sock K*. Specific aenion is paid o he susainabiliy of noninflaionary growh associaed wih he labour marke by uilising boh acual raes and underlying naural raes of unemploymen (i.e., he non-acceleraing wage rae of unemploymen, or NAWRU). The labour inpu is consequenly adjused for he gap beween acual unemploymen and he NAWRU o obain N*. 3 This srucural model, inclusive of he disaggregaed capial sock channels, was simulaed o deermine he poenial oupu for he Souh African economy, assuming some level of srucural unemploymen esimaed o range beween 25 and 28 per cen (using he expanded definiion of unemploymen). These srucural unemploymen numbers broadly correspond o hose calculaed by he Organisaion for Economic Co-operaion and Developmen (OECD 2010) in is economic survey of Souh Africa 2010/11 repor (OECD 2010, 98) Mulivariae HP filer The mulivariae Hodrick Presco filer (MV HP filer) is a semi-srucural approach ha augmens he saisical properies of he HP filer wih srucural relaionships from an Okun s Law, Phillips curve and capaciy uilisaion relaionships (see Conway and Hun 1997). The inclusion of a Phillips curve in his approach allows for he hypohesis ha producion consrains in he economy play a role in he inflaion process and helps o separae ou he differen impac of supply and demand shocks on inflaion. The equaion is specified as follows: e ( y 2 2 ) 3( m 1 m 3) / 2, (3) 2 See Box 2 in he SARB, Moneary Policy Review (Preoria: SARB, May 2006). This is a model based on annual daa. I is updaed annually and he poenial oupu is hen re-esimaed. 3 The poenial level of employmen is defined as he level of labour resources ha migh be employed wihou resuling in addiional inflaion, assuming some naural rae of unemploymen (NAWRU). According o his definiion, poenial employmen (N*) is he difference beween he economically acive populaion (EAP) and he fracion of EAP ha is naurally unemployed, ha is, N*=EAP(1-NAWRU). 4

8 e In equaion 3 he variables π, π, y, Φ and m represen consumer inflaion, consumer inflaion expecaions, he log of acual real oupu, he log of poenial oupu and he log of nominal effecive exchange rae a ime. The residual erm is represened by ε π. Backward-indexed consumer inflaion expecaions are assumed in his equaion and he nominal effecive exchange rae is included o reflec he impac of impored prices on domesic prices. Okun s Law represens he relaionship beween he disequilibria in he goods and labour markes. According o equaion 4, his relaionship allows a fall in acual unemploymen o a level below is rend, o be inerpreed as a posiive shock o he oupu gap. U U p, ( y ) U, (4) In his equaion, U is he unemploymen rae 4, U p is rend unemploymen (measured by an HP filer) and he residual erm is represened by ε U, a ime. The uilisaion of producive capaciy in he economy is also used as a condiion in he mulivariae filer, specifically in erms of he deviaion of capaciy uilisaion from is longer-erm rend. The inuiion being ha when capaciy uilisaion exceeds is longer-erm rend i indicaes a posiive shock o he oupu gap. C C p, ( y ) C, (5) In equaion 5, C represens capaciy uilisaion in he manufacuring secor and C p is is rend, proxied by an HP filer, a ime. Deviaions of capaciy uilisaion from is 4 The unemploymen rae was compiled by incorporaing evidence from he Ocober Household Surveys, he midyear populaion esimaes, he Surveys of Toal Employmen and Earnings, he Quarerly Employmen Surveys and he Labour Force Surveys as published by Saisics Souh Africa. The unemploymen series is herefore calculaed as he difference beween he economically acive populaion and employmen. 5

9 rend ransfer ono he same change in he oupu gap, since he parameer is se equal o one. The HP filer mehodology is augmened by incorporaing hese srucural equaions as resricions in he opimisaion procedure. The exen o which he esimae of poenial oupu is influenced by he srucural equaions is condiioned by weighing each of he residual error erms. The well-known smoohing parameer lambda ( ) is specified as a ime series so ha he smoohing characerisics of he filer can be alered hrough ime if deemed necessary. To avoid circulariy, he procedure of opimisaion requires an iner-emporal ieraive process ha is repeaed unil he changes beween ieraions saisfy some pre-specified convergence crieria General equilibrium approaches General equilibrium approaches are increasingly used o esimae poenial oupu. The SARB s Poenial General Equilibrium Model (PGEM) 5 makes use of a general equilibrium approach o modelling he poenial oupu level of he Souh African economy. The PGEM is a gap model and incorporaes acual oupu, inflaion (boh acual and expeced), unemploymen and capaciy uilisaion daa in an effor o esimae he unobservable poenial oupu using a mulivariae Kalman filer. Specifically, each of he four key variables has an implied equilibrium or seady sae level, and acual deviaions from hese levels are considered gaps. The SARB model is augmened wih a global componen, which allows changes o global poenial growh o aler Souh Africa s own poenial growh rae. One way of moderaing biases associaed wih each esimaion echnique is o aggregae he differen echniques o creae an addiional esimae of Souh Africa s poenial oupu and he exen of he oupu gap. 5 This model is based on a core srucure of a model ha was firs developed by he Inernaional Moneary Fund, which uses a Kalman filer o esimae poenial oupu on economic relaionships and observable daa, wih some adapaions by he SARB o reflec Souh African condiions. 6

10 3 Esimaes of poenial oupu Since he global financial crisis, he global and domesic economic recoveries have been longer han previously anicipaed. This slower pace has promped a reassessmen of poenial oupu growh used in he SARB suie of models. Figure 1 shows he level of acual and poenial oupu as calculaed by he various echniques described above, and he combined average. The figure illusraes ha here is no maerial difference beween he various smoohing mehodologies and he PGEM model, as he lines are in close proximiy o one anoher. The level of poenial oupu as calculaed by he PGDPM (producion funcion) more or less racks he rajecory of acual oupu, bu appears o be on a higher level, in par influenced by he magniude of full employmen, adjused for naural unemploymen. The oher esimaes employ smoohing mechanisms, o differen degrees, rendering hese o be less volaile measures of poenial oupu. The impac of he 2008/09 slowdown is visible in he level of acual oupu (blue line), and i is imporan o noe ha acual oupu has remained below every measure of poenial oupu since The measure of poenial oupu used in furher references is calculaed from he aggregae of he various mehodologies using equal weighs (he doed line in Figure 1). 7

11 Figure 1: Acual and poenial oupu level PGDPM = Poenial General Equilibrium Model; PGEM = Poenial General Equilibrium Model; MV HP = mulivariae Hodrick Presco; HP = Hodrick Presco By heir naure, he annual growh raes in poenial oupu (see Figure 2) as esimaed hrough he various de-rending echniques exhibi a smooher profile han ha arrived a by using he PGDPM supply-side echnique and do no flucuae as much. Neverheless, all he mehodologies show a slowdown in poenial growh raes from The resuls obained from he PGDPM echnique display a more pronounced decline in 2008 (as employmen and produciviy conribuions decline sharply), before recovering o more or less he same level as hose of he de-rended filers. By using an average, he exremes are smoohed so ha he evenual resul is no as volaile as would be he case if only he supply-side model were used. A he same ime, hey are no so sable ha deep economic shocks are dilued by he derending mehods. These variaions in he aggregae poenial oupu raise quesions abou he characerisics of he long-run level, he pace of poenial oupu and he magniude of he oupu gap. When esimaing he pace of poenial oupu, we calculae an average over a period ha covers he full business cycle, and no by merely aking he laes reading. 8

12 Figure 2: Acual and poenial oupu growh (per cen) 7 Per cen Acual PGDPM PGEM MV HP filer HP filer Poenial PGDPM = Poenial General Equilibrium Model; PGEM = Poenial General Equilibrium Model; MV HP = mulivariae Hodrick Presco; HP = Hodrick Presco Table 1 summarises he esimaes of he long-run poenial growh rae of he Souh African economy over various ime periods. For purposes of comparison, he resuls from he various echniques are also shown, ogeher wih he poenial oupu as calibraed from he differen echniques (las column in Table 1). Table 1: Souh Africa s acual and poenial oupu (per cen) Period Acual oupu Mehodology HP filer MV HP filer PGEM PGDPM Poenial (average of mehods) ,7 3,5 3,6 3,5 3,9 3, ,2 3,4 3,4 3,4 3,6 3,5 Calculaed over a period comparable o he ECB sudy: Souh Africa Euro area ,3 3,7 3,8 3,7 4,6 3,9 1,9 2, ,7 3,3 3,0 3,1 2,0 2,8 0,9 1,8 ECB = European Cenral Bank; PGDPM = Poenial General Equilibrium Model; PGEM = Poenial General Equilibrium Model; MV HP = mulivariae Hodrick Presco; HP = Hodrick Presco US 9

13 The SARB laes esimae of annual long-run poenial oupu growh is 3,5 per cen. Noably, over he longer horizon of (he laes full se of annual daa ends in 2011) he average esimaes from he differen echniques do no differ maerially. The average deceleraion of poenial GDP from 1998 o 2008 and from 2009 o 2011 was caused by he deerioraion in he conribuion by labour and oal facor produciviy, which was no fully offse by he improvemens in he conribuion of he capial sock. Our esimaes for Souh Africa (see Table 1) over he same period as he ECB sudy reflec a decline from an average of 3,9 per cen o 2,8 per cen; more or less similar o he esimaed magniude of decline in he euro area and he Unied Saes. The European Cenral Bank (ECB) has noed in a sudy ha he financial crisis could have a longer-erm impac on poenial oupu for a number of years o come as he facors of producion were severely affeced by he crisis (ECB 2011, 75). According o he ECB sudy, euro area poenial growh deceleraed from an average of around 1,9 per cen over he period o an average of 0,9 per cen over he period A similar decline in poenial oupu growh is quoed for he US economy over hese wo periods a 2,5 per cen o 1,8 per cen. The sudy explains ha for he euro area he decline is aribuable o lower conribuions from labour and capial inpus, while he oal facor produciviy conribuion changed only marginally. A change in he rajecory of poenial oupu will impac boh he magniude of he oupu gap and he opimal ineres rae pah as indicaed by a Taylor-ype moneary policy reacion funcion. Figure 3 shows he rend of he oupu gap level esimae resuling from he equally weighed average of he differen echniques explained o calculae he poenial oupu. This graph illusraes ha he negaive oupu gap from 2009 o 2011 is roughly beween 1,5 per cen and 2,0 per cen. 10

14 Figure 3: Oupu gap level As he economy recovers and facors of producion gradually expand, he esimae of long-run poenial oupu growh will rise relaive o curren esimae. However, such a revision can only be ascerained by he evidence from forhcoming daa. I should also be noed ha in order o close he oupu gap, acual oupu growh mus exceed poenial oupu growh for a period. Bibliography: Buler, L A Semi-Srucural Mehod o Esimae Poenial Oupu: Combining Economic Theory wih a Time-series Filer. The Bank of Canada s New Quarerly Projecion Model (QPM), Par 4. Oawa: Bank of Canada. Conway, P. and B. Hun Esimaing Poenial Oupu: A Semi Srucural Approach. Reserve Bank of New Zealand Discussion Paper No. G97/9. Wellingon: Reserve Bank of New Zealand. ECB see European Cenral Bank. European Cenral Bank. Trends in Poenial Oupu. European Cenral Bank Monhly Bullein No. 01/2011, January. Frankfur: ECB. 11

15 Hodrick, R. J. and E. C. Presco Pos-war U.S. Business Cycles: An Empirical Invesigaion. Discussion Paper 451. Pisburgh: Carnegie-Mellon Universiy. Hodrick, R. J. and E. C. Presco Pos-war U.S. Business Cycles: An Empirical Invesigaion. Journal of Money. Credi and Banking 29:1 16. Mohr, M A Trend-Cycle (Season) Filer. European Cenral Bank Working Paper No Frankfur: ECB. OECD see Organisaion for Economic Co-operaion and Developmen. Organisaion for Economic Co-operaion and Developmen OECD Economic Surveys: Souh Africa, July. Paris: OECD. Smi, B. W. and L. Burrows Esimaing Poenial Oupu and Oupu Gaps for he Souh African Economy. Sellenbosch Economic Working Papers No Sellenbosch: Universiy of Sellenbosch. 12