Public Investment in Developing Countries Facing Natural Resource Depletion

Transcription

1 Public Invesmen in Developing Counries Facing Naural Resource Depleion Adrian Aler Inernaional Moneary Fund Dalia S. Hakura Inernaional Moneary Fund Maeo F. Ghilardi Inernaional Moneary Fund January 31, 2015 Absrac This paper analyzes he radeoffs beween savings, deb and public invesmen in a reference developing counry wih looming oil exhausibiliy concerns. Our resuls highligh he risks o fiscal and capial susainabiliy of oil exporing counries from large scaling-up in public invesmen and oil price volailiy in view of a projeced decline in he oil revenue o GDP raio. However, srucural reforms ha improve he efficiency of public invesmen can allow for a relaively faser buildup of susainable public capial and susain higher non-oil growh wihou adversely affecing he deb raio or savings. Moreover, we show ha even if a governmen pursues pruden fiscal policy ha preserves resource wealh and deb susainabiliy in he face of exhausible and volaile resource revenues, low public invesmen qualiy in he form of a misallocaion of resources can hinder aainmen of susainable public capial and posiive non-oil growh. JEL Classificaion: E22; E62; F34; Q32; Q38 Keywords: Public capial; Deb susainabiliy; Invesmen efficiency; Projec selecion The views expressed in his paper are hose of he auhors and do no necessarily reflec hose of he Inernaional Moneary Fund (IMF), is Execuive Board, or IMF policies. Conac: aaler@imf.org; mghilardi@imf.org; dhakura@imf.org; Inernaional Moneary Fund (IMF), h S. NW, Washingon DC, 20431, USA. All remaining errors are our own. 1

2 2 Conens I Inroducion 3 II A cross-counry perspecive 6 III The model 7 A. Households B. Firms C. Governmen D. Marke Clearing IV Calibraion 15 A. Macroeconomic developmens B. Benchmark scenario: public invesmen profile C. Efficiency and absorpive capaciy consrains V Model Simulaions 18 A. Model Simulaions: Invesmen profiles B. Model Simulaions: Efficiency C. Model Simulaions: Oil revenue shock D. Model Simulaions: Projec selecion VI Conclusions 26 Lis of Figures 1 Oil secor relevance, capial expendiure, and resource exhausibiliy (2013) 6 2 Republic of Congo: Oil producion profile and price assumpions 15 3 Fiscal susainabiliy framework: Benchmark invesmen scenario 17 4 Benchmark scenario 19 5 Aggressive scenario 20 6 Consan scenario 21 7 Benchmark scenario: srucural reforms 22 8 Aggressive scenario - srucural reforms 23 9 Benchmark scenario: Oil Shocks (confidence inervals) Projec selecion: public capial and non-oil GDP growh Aggressive scenario: oil shocks (confidence inervals) Consan scenario: oil shocks (confidence inervals) 32 Lis of Tables 1 A cross-counry macroeconomic comparison among developing oil exporers 7 2 Srucural parameers 31

3 3 I Inroducion En roue o becoming emerging markes, resource-rich developing counries mus address povery and infrasrucure gaps. On average, resource-rich developing counries experience povery headcouns in excess of 55 percen, human developmen indicaors in he boom 50 percen, and less han 30 percen of he roads are paved (e.g., Inernaional Moneary Fund (2012)). Despie he abundance of naural resource revenues, hese counries face absorpive capaciy consrains and insiuional inefficiencies o manage public invesmens. The effeciveness of public invesmen depends on insiuional facors, such as he capaciy o implemen, selec, and evaluae projecs. These feaures are srongly linked o he business climae, corrupion and he availabiliy of skilled human capial. Naural resource wealh provides an opporuniy for developing counries o accelerae economic developmen. A he same ime, managing he naural resource wealh poses a challenge because of he exhausible and volaile naure of he resource revenues. The heoreical lieraure of naural resource managemen proposes several public invesmen sraegies. Some heoreical work has advocaed he bird-in-hand approach which argues for counries ha experience resource windfalls o accumulae hese revenues in a Sovereign Wealh Fund (SWF) and consume only he ineres from his fund. As he naural resources deplee, he governmen uses he SWF o smooh is invesmen spending. Oher sudies have called for a porion of he resource windfall o be saved and he res invesed as a way o speed up economic developmen and build essenial public infrasrucure ha provides an impeus for growh and reduces povery (Sachs and Warner (1997)). 1 However, scaling up public invesmen in developing counries may no always enhance growh. Low public invesmen efficiency (a dollar of invesmen ypically ranslaes o 50 cens of public capial in developing counries (Priche (2000)) and absorpive capaciy consrains (from poor infrasrucure, supply chain bolenecks, and lack of qualified workers ha increase he associaed coss, among oher hings) can significanly diminish he growh benefis of public invesmen (Berg e al. (2013) and van der Ploeg (2012)). Also, in resource-rich counries, spending resource revenues domesically may rigger Duch disease effecs, adversely affecing he compeiiveness of raded good secors and, hence, growh (e.g. Sachs and Warner (2001), van der Ploeg and Poelhekke (2010), and van der Ploeg (2011)). This paper assesses he growh and susainabiliy effecs of differen public invesmen pahs for a small open economy ha is a he peak of oil producion and has a relaively shor remaining oil revenue horizon. I uses a Dynamic Sochasic General Equilibrium (DSGE) model along 1 Collier e al. (2010) make he case for developing resource-rich economies o prioriize capial invesmen, afer building up sufficien fiscal buffers o susain exernal shocks. van der Ploeg (2012) claims ha more weigh should be given o curren generaions han in he permanen income hypohesis approach, in order o address he povery gap. He argues ha by managing he naural resource revenues opimally, hese counries could ramp up public invesmen which posiively impacs curren wages and consumpion.

4 4 he lines of Buffie e al. (2012), Berg e al. (2013) and Melina e al. (2014) ha feaures a naural resource secor, deb insrumens, invesmen efficiency and absorpive capaciy consrains, Duch Disease effecs, and a SWF. Taking resource revenue and public invesmen pahs as exogenous, he macroeconomic model simulaes oucomes relaed o growh, public deb, SWF, and he sock of capial, over a period of 15 years (i.e., ). By incorporaing public capial in he producion funcion, his model allows for a direc impac of public invesmen on non-resource GDP growh. In his way, he paper allows an analysis of he radeoffs beween public invesmen decisions, savings and deb for counries wih depleing resources. Berg e al. (2013) has previously sudied he macroeconomic effecs of public invesmen in resource rich counries in a DSGE framework. This work assumes ha public invesmen can only be financed from resource revenues and here is no scope for deb-financed invesmen. By conras, he presen paper examines alernaive invesmen scenarios where public invesmen can be financed from resource revenues and from deb. Hence, he model allows an assessmen of deb susainabiliy and he growh effecs of alernaive invesmen sraegies. Also, exending Melina e al. (2014), which incorporaes a role for deb, his paper focuses on an applicaion o a counry ha is a he peak of he resource windfall raher han a counry ha is expecing a resource windfall. In his way, he paper derives a susainable invesing approach ha combines public invesmen ha mees developmen objecives while a he same ime preserving resource wealh and mainaining macroeconomic sabiliy along he lines analyzed in Berg e al. (2013) and Melina e al. (2014). The paper highlighs he risks o fiscal and capial susainabiliy of large public invesmen scaling up for he reference counry, a gradual reducion in public invesmen is needed o preserve deb susainabiliy and o have sufficien financing o susain public capial afer he resource windfall deplees, including in he face of resource revenue volailiy. The model is applied o he Republic of Congo bu is findings are illusraive of he policy radeoffs faced by any highly oil-dependen counry ha has large social and infrasrucure gaps and faces absorpive and implemenaion capaciy consrains and where resource exhausibiliy is imminen. The paper analyzes he policy radeoffs based on four ses of simulaions. Firs, he paper underakes simulaions o analyze alernaive invesmen pahs aking oil producion and revenues as exogenous. The simulaions sress he imporance of fiscal consolidaion for Congo o preserve macroeconomic sabiliy in he medium- o long-run when oil reserves are exhaused. The paper shows ha an aggressive scaling up of invesmen, could lead o a fas accumulaion of public capial and higher near-erm non-oil growh. However, as more oil revenues are devoed o public invesmen less can be saved, leaving he counry vulnerable o fuure negaive oil price shocks and he oil depleion. Public invesmen can also be financed by borrowing from eiher domesic or foreign sources. A rapid scaling up of invesmen could, herefore, iniially resul in a draw-down of he saving fund in he face of declining oil revenues. Once savings his a minimum accepable lower bound in his case he level of reserves needed o ensure he smooh operaion of he he pegged exchange rae arrangemen he governmen

5 5 can choose o borrow o close he fiscal gap. Evenually, however, he rise in public deb would force he ineviable downward adjusmen in governmen spending. The longer-erm effec of posponing he fiscal consolidaion is o run up unsusainable public deb and leave no financial asses o provide a permanen income once oil reserves are exhaused. This paper also explores an inermediae opion where public invesmen is mainained consan for a period of ime before fiscal consolidaion kicks in. Naurally, his opion leads o a lower build up of savings in he long run and a higher build up of deb han he baseline fiscal consolidaion scenario, and increases he vulnerabiliy of he economy o negaive oil price shocks. Second, he paper simulaes he impac of changes in public invesmen efficiency and absorpive capaciy consrains on he susainabiliy of public capial and non-oil growh. We iniially assume a public invesmen efficiency of 0.5 consisen wih findings for developing counries ha are ypically characerized by a difficul business climae, weak insiuions or poor rule of law, and ha efficiency declines once public invesmen exceeds a given hreshold. The simulaions in his secion highligh how srucural reforms ha improve efficiency can conribue o deliver a susainable higher level of public capial wihou requiring addiional public invesmen spending. Third, he paper examines how volailiy of commodiy prices affecs he macroeconomic oulook, in paricular he amoun of public deb and savings. Simulaions ha accoun for he hisorical volailiy of oil prices are used o derive he confidence bands around he pah for he resource revenue. The simulaions demonsrae how he framework can inform on he public invesmen plans in he face of volaile oil revenues: specifically, he paper s findings highligh he downside risk and he upside poenial semming from changes in commodiy prices. Finally, we analyze he impac of he projec selecion process on he macroeconomic oulook and susainable public capial sock. Unlike he second secion which focuses on srucural reforms ha improve invesmen efficiency he amoun of capial produced per dollar invesed and ha can increase he public capial sock, he focus of he simulaions in his secion are on he economic reurn of invesmens over he long erm, i.e. oupu per uni of capial. This secion inroduces wo ypes of projecs in which he governmen can inves low and high produciviy projecs. Our analysis underscores ha inadequae projec selecion processes or a misallocaion of resources o lower-yield projecs (including from weak governance and insiuions) can obviae a susainable public capial and posiive non-oil growh oucome even when public invesmen follows a pah ha preserves resource wealh and deb susainabiliy.

6 6 II A cross-counry perspecive In his secion we presen a cross-counry comparison across developing oil exporers ha are highly dependen on oil. While oil revenues can help o accelerae economic developmen, oil producion has a horizon of less han 20 years in several developing counries (Figure 1) and governmen revenues from oil are expeced o decline over he medium erm. The projeced decline in oil revenue poses challenges o designing susainable public invesmen pahs ha can be properly financed and ha allow a buildup of savings o suppor governmen spending in he pos-oil era. Figure 1 highlighs ha his challenge is paricularly relevan for he African exporers such as Congo, Equaorial Guinea, and Gabon which have relaively shorer horizons of remaining hydrocarbon producion and relaively larger capial expendiure o non-oil GDP raios han heir counerpars in he Middle Eas and Asia. Figure 1: Oil secor relevance, capial expendiure, and resource exhausibiliy (2013) Noe: Three-leer counry codes correspond o he following counries: AGO - Angola, ARE - Unied Arab Emiraes, AZE - Azerbaijan, CMR - Cameroon, COG - Congo, DZA - Algeria, GAB - Gabon, GNQ - Equaorial Guinea, KAZ - Kazakhsan, KWT - Kuwai, LYB - Libya, IDN - India, IRQ - Iraq, SAU - Saudi Arabia, NGA - Nigeria, OMN - Oman, TCD - Chad, TKM - Turkmenisan Table 1 compares developing oil exporers oil GDP o oal GDP raios in 2013 and 2019, capial expendiure o GDP raios, governmen deb o GDP raios, non-oil primary balance o GDP raios, oil dependance and exhausibiliy in The size of he non-oil primary defici is a proxy for he exen of fiscal adjusmen ha would be needed o aain a primary defici ha can be susained once he oil resources deplee. Again, Congo, Equaorial Guinea, and Angola sand ou among he developing counries as having large non-oil primary deficis despie relaively limied horizons of oil producion.

7 7 Table 1: A cross-counry macroeconomic comparison among developing oil exporers III The model The paper uses a medium scale open economy DSGE model along he lines of Buffie e al. (2012) wih a sovereign wealh fund as in Melina e al. (2014) o analyze he feasibiliy of differen public invesmen plans. The model is designed o analyze he nexus of naural resource revenue managemen, public invesmen, and public deb. In paricular, he economy consiues of hree agens: (i) households, (ii) firms and (iii) governmen. To capure he feaures of low income counries households are divided ino opimizing and non-opimizing (hand-o-mouh consumers). The criical difference beween hese wo is ha he former have access o financial markes and can smooh consumpion. The laer consume all of heir disposable income each period. There are assumed o be hree ypes of firms: (i) (non-resource) raded goods producers; (ii) non raded good producers; and (iii) naural resource producers. Governmen provides invesmen, which is producive, and consumpion. Toal spending is financed wih axes, deb, revenues from axes on naural resource producion as well as savings in he resource wealh fund.

8 8 A. Households The economy feaures wo ypes of households: opimizing and non opimizing (OPT) or hand-o-mouh (HTM ). The former have access o financial markes and can smooh heir consumpion over ime. The laer do no have access o financial markes and hey consume all heir income wihin he period. Boh households have idenical preferences which are described by he following uiliy funcion: U(c i, L i ) = 1 ( ) c i 1 σ κ ( ) 1 σ L i 1+ψ 1 + ψ (1) where c i is consumpion and L i is labor. The parameer σ represens he inverse of he ineremporal elasiciy of subsiuion, ψ is he inverse of he ineremporal elasiciy of subsiuion of he labor supply and κ is he disuiliy weigh of labor. The subscrip i indicaes he ype of household i.e. i = OP T, HT M. Boh households consume a baske of raded c T, and non raded goods c N, according o a consan elasiciy of subsiuion aggregaor a la Sigliz-Dixi: c i = [ ϕ 1 χ ( c i N, ) χ 1 χ + (1 ϕ) 1 χ ] χ ( ) χ 1 χ 1 c i χ T, (2) where ϕ indicaes he non raded goods bias and χ > 0 is he inraemporal elasiciy of subsiuion. The price of consumpion is normalized o 1. This implies he following raded and non-raded price aggregaor: 1 = [ ϕ (p N, ) χ 1 + (1 ϕ) (s ) χ 1] 1 χ 1 where p N, is he price of non raded goods and s represens he relaive price of raded goods o he consumpion baske. In our economy, given ha he law of one price holds for raded goods, s corresponds o he real exchange rae, defined as he price of one uni of foreign consumpion baske in unis of he domesic baske. Minimizaion of oal consumpion expendiures subjec o he consumpion basked yields he following demand funcions for each good: (3) c i N, = ϕp χ N,c i (4) c i T, = (1 ϕ) s χ c i (5) Each household provides labor services o he raded and non-raded secor. Therefore, as for consumpion, oal labor is described by a consan elasiciy of subsiuion aggregaor: L i = [ δ 1 ρ ( L i N, ) 1+ρ ρ + (1 δ) 1 ρ ] ρ ( ) 1+ρ 1+ρ L i ρ T,

9 9 where δ is he share of labor in he non raded secor and ρ represens he inraemporal elasiciy of subsiuion beween he amoun of labor supplied o he wo secors. The relaive wages w aggregaor akes he following form: w = [ δw 1+ρ N, + (1 δ) w 1+ρ ] 1 1+ρ T, where w N, is he real wage paid in he non raded secor and w T, is he real wage paid in he raded secor. Maximizaion of oal labor income subjec o aggregae labor yields he following labor supply schedule for each secor: ( ) L i wn, ρ N, = δ L i (7) L i T, = (1 δ) w ( wt, w (6) ) ρ L i (8) Toal consumpion and labor are respecively he sum of consumpion and labor in each household: c = ωc OP T + (1 ω) c HT M (9) L = ωl OP T + (1 ω) L HT M (10) A.1. Opimizing Households Opimizing households maximize he discouned sum of heir lifeime uiliy funcions: E 0 =0 subjec o he following budge consrain: β U(c OP T, L OP T ) (11) (1 + τ c ) c OP T + b OP T s b OP T + i T + i NT = ( 1 τ L) w L OP T + (12) + ( 1 τ K) ( r T K,k T 1 + r NT K, k NT 1) + +R 1 b OP 1 T R 1s b OP 1 T Θ OP T + +s rm + z + µk G, 1 + Ω T, + Ω NT, where β = (1 + ϱ) 1 is he discoun facor, ϱ is he rae of ime preference and τ c and τ L are ax raes on consumpion and labor respecively. The erm rm denoes remiances from abroad, z are ransfers from governmen, µ are use fees paid for he use of public capial k G, 1 and Ω T,, Ω NT, are profis from he firms in he raded and non-raded secor respecively. We assume ha opimizing households hold physical capial k used for producion in he raded and non-raded secor: k j = ( 1 δ j) k j κj 2 ( i j ) 2 i j 1 i j (13) 1

10 10 where he subscrip j = T, N T indicaed he raded and non-raded secor respecively. The parameer δ indicaes he depreciaion rae, κ is he invesmen adjusmen cos. Opimizing households have access o financial markes in he form of domesic bonds b OP T ( and inernaional bonds b OP T. The erm Θ OP T = η 2 b OP T b OP T ) 2 represens porfolio adjusmen coss associaed wih he purchase of foreign liabiliies. The erm η conrols he capial accoun openness and b OP T denoes he seady sae value of privae foreign deb. Finally, we assume ha he reurn on deb conraced exernally pays a premium over he ineres deb on commercial deb R dc, conraced by he governmen: R = R dc, + u (14) Le λ be he Lagrange muliplier associaed wih he budge consrain and q j he lagrange muliplier associaed wih he law of moion of privae capial in each secor. Then, he maximizaion problem delivers he following firs order condiions: λ (1 + τ c ) = ( ) c OP T σ (15) κ (L ) ψ = λ ( 1 τ L ) w (16) λ = βe (λ +1 R ) (17) [ λ +1 s +1 R ] λ = βe s η (b OP T b OP T ) (18) [ q j = E β λ ( +1 (1 δ) q j +1 + ( K,)] 1 τ K) r j (19) λ 1 q j = 1 κj 2 + ( i j ) 2 ( i j i j 1 κ j 1 β λ +1 λ κ j qj +1 q j ( i j ) ( i j +1 i j 1 1 i j ) i j i j 1 1 i j + (20) 1 ) 2 A.2. Non-Opimizing Households Non opimizing households maximize he curren period uiliy funcion: U(c HT M, L HT M ) (21)

11 11 subjec o he following budge consrain: (1 + τ c ) c HT M = ( 1 τ L Saic maximizaion leads o he following labor supply funcion: ) w L HT M + s rm + z + µk G, 1 (22) L = [ 1 1 τ L κ 1 + τ c (c ) σ w ] 1 ψ (23) B. Firms The economy feaures hree producion secors: (i) raded goods, (ii) non-raded goods and (iii) naural resource producion. We refer o he firs wo as he goods producion secors. B.1. Goods Producion Secor Traded and non-raded goods produce goods according o a Cobb-Douglas producion funcion: y j = z j ( k j 1 ) 1 α j ( ) L j α j ( ) k G α G 1 (24) where he subscrip j = T, N T indicaed he raded and non-raded secors respecively. The parameer α j indicae he labor share and α G is he elasiciy of oupu wih respec o privae capial. The erm z j represens oal facor produciviy. We assume ha he raded secor is subjec o learning-by-doing exernaliies: z T z T = ( z T 1 z T ) ρ z + ( y T 1 y T where ρ z, ρ y [0, 1] conrol he severiy of Duch disease as in Masuyama (1992) and Krugman (1987). Profi maximizaion delivers he following firs order condiions for he raded goods producers: r T K, = ( 1 α T ) s y T k T 1 ) ρ y (25) (26) w T = α T y T s L T and he following for he non-raded goods producers: rk, NT = ( 1 α ) NT p NT y NT k 1 NT (27) (28)

12 12 w NT = α NT p NT y NT L NT (29) B.2. Naural Resource Secor Naural resource producion y O is assumed o follow an exogenous process: y O y O = ( y O 1 y O ) ρ y O exp ( ) ε yo (30) where ρ yo is an auoregressive coefficien and ε yo is he resource producion shock. We assume ha resource producion is small relaive o world producion, and, herefore, ha he inernaional price of he naural resource is given and evolves as: p O p O = ( p O 1 p O ) ρ p O exp ( ) ε po (31) where ρ po is an auoregressive coefficien and ε po is he resource price shock. Resource GDP in unis of he consumpion baske can be expressed as: y O = s p O y O (32) The naural resource producer pays a ax on he oupu produced, herefore her profis are equal o: Ω O = ( ) 1 τ O y O (33) C. Governmen The governmen collecs revenues from consumpion, labor and capial. I levies user fees from exising infrasrucures and benefis from windfall revenues. The revenues are spen on infrasrucure needs, governmen consumpion, deb services and ransfers. When revenues fall shor, he defici is covered by borrowing. Formally he budge consrain can be wrien as: τ c c + τ L w L + τ K ( r T K,k T 1 + r NT K, k NT 1) + s gr + (34) +µ k G, 1 + O + b + s d + s d c, + s r RF f 1 = p G g + z + r 1 b 1 + s r d, d 1 + s r dc, dc 1 + s f

13 13 The lef hand side corresponds o he period revenues and he righ hand side o he period expenses. On he revenue side, he erm gr corresponds o inernaional grans, µk G, 1 are user fees which are compued as a fracion f of recurren coss: µ = fp G δ G. The erm O corresponds o naural resource royalies and corresponds o O = τ O s p O y O. The governmen can issue hree ypes of deb: domesic deb b, exernal concessional deb d and exernal commercial deb dc. The ineres rae paid on he domesic deb corresponds o r, o concessional deb r d,. We assume ha he ineres rae paid on commercial deb r dc, is conraced a a premium over he risk free world ineres rae r f, : where ν dc and η g are srucural parameers. ( d+dc, r dc, = r f, + ν dc e ηg y ) d+dc y We assume ha he governmen can consume and inves in he economy. This implies g = g C + g I, where g C is governmen consumpion and g I represens governmen invesmen. The price index of governmen consumpion p G in erms of unis of he domesic consumpion composie can be expressed as: (35) p G = [ ν p 1 χ N + (1 ν ) s 1 χ ] 1 1 χ (36) where ν is equal o: ν = ( p G g ) ν + ( p G g p G g ) ν g p G g (37) Public invesmen is producive and public capial evolves according o a sandard law of moion: k G = ( 1 δ G) k G 1 + g I (38) The erm g I represens effecive public invesmen since public invesmen feaures inefficiency and absorpive capaciy consrains. This implies ha one dollar of public invesmen spending does no ranslae ino one dollar of effecively produced capial. To reflec his, effecive invesmen is given by g I = ɛg I ɛ ( 1 + γ GI) ḡ I + ɛ ( γ GI if γ ) [ γgi 1 + γ GI γ GI] (39) ḡ I if γ GI > γ GI where γ GI gi 1 is he percen deviaion of public invesmen from is iniial seady sae ḡ I and ɛ [0, 1] represens seady-sae efficiency and ɛ ( ) γ GI (0, 1] governs he efficiency of he porion of public invesmen exceeding hreshold γ GI, in erms of percen deviaion from he iniial seady sae. In paricular, we assume ha ɛ ( ) g I akes he following specificaion: ɛ ( g I ) = exp [ ςɛ ( γ GI γ GI)] ɛ (40)

14 14 In oher words, if governmen invesmen expendiure deviaes from he iniial seady sae more han γ GI, he efficiency of he addiional invesmen decreases o an exen proporional o he size of he deviaion. This mechanism capures absorpive capaciy consrains in developing counries. The severiy of absorpive capaciy consrains is measured by parameer ς ɛ [0, ). The erm f in he budge consrain represens he sock of financial asses held in he resource wealh fund. We assume ha in each period i earns ineres income s (r rf 1) f 1. The resource fund evolves according o he following process: f f = max { f floor f, ( f 1 f ) + f in, s f } ou, s where f is he iniial seady-sae value of he fund, f in, represens he oal fiscal inflow, f ou, represens he oal fiscal ouflow, and f floor 0 is a lower bound for he SWF ha he governmen chooses o mainain. Every period, if he fiscal inflow exceeds he fiscal ouflow, more resources are saved in he resource fund. If he sovereign wealh fund is above f floor any fiscal ouflow ha exceeds he fiscal inflow is absorbed by a wihdrawal from he fund. Whenever he lower bound consrain binds, fiscal policy reacs o cover he gap via borrowing. 2 (41) D. Marke Clearing To close he model we impose he marke clearing condiion and he balance of paymen condiions. The marke clearing condiion for non raded goods is defined as: y N, = ϕp χ N, (c + i N, + i T, ) + ν ( pn, p G ) χ g (42) Finally, he aggregae budge consrain of consumers and governmen produce he accoun ideniy ha growh in he counry s ne foreign deb equals he difference beween naional spending and naional income: s [ gr ( f f 1) + (d d 1 ) + (d c, d c, 1 ) + ( b b 1 = c + i N, + i T, + p G g + Θ OP T + s rm + (R d, 1) s d (R dc, 1) s d c, 1 + ( R 1 1 ) s b 1 ( R RF 1 1 ) s f 1 The righ hand side corresponds o he balance of paymen and he lef hand side is he curren accoun defici. )] (43) 2 The paper makes he simplifying assumpion ha he gap is covered by borrowing. However, he governmen can also cover he gap by increasing axes (on consumpion and facor incomes) or cus in governmen non-capial expendiures (governmen consumpion and ransfers).

15 15 IV Calibraion The model is calibraed wih annual daa. Seady sae parameers are presened in Table 2 (Appendix). The iniial seady sae is based on macroeconomic developmens in he Congo a he end of 2013 (Inernaional Moneary Fund (2014a)). Our projecions run over he period , close o he complee depleion of he naural resource windfall. Figure 2: Republic of Congo: Oil producion profile and price assumpions 140 Producion (million barrels) 120 Price (US$/barrel) Noe: WEO projecions and our calculaions A. Macroeconomic developmens Economic developmens in Congo have been closely ied o developmens in he oil secor. Currenly, oil producion accouns for 58 percen of GDP, oil expors accoun for 78 percen of expors, and he governmen s revenues from oil represen 74 percen of oal fiscal revenues. The governmen is drawing on is oil revenues o implemen an ambiious invesmen plan o develop he economy and address social and infrasrucure gaps. As depiced in Figure 2, Congo s oil oupu is projeced o peak in 2017 a around 118 million barrels, wih he coming on-sream of he Moho Nord oil field when oil producion is expeced o surpass is previous peak level of 115 million barrels in However, unless here is a new discovery, oil producion is projeced o decline seadily over he nex 15 years. As a consequence, oil revenues are expeced o decline from around 33 percen of GDP in 2013 o less han 4 percen of GDP

16 16 in Oil prices are calibraed o he IMF s World Economic Oulook (WEO) price forecas (Inernaional Moneary Fund (2014b)).The projeced decline in oil revenues poses challenges in erms of designing susainable public invesmen pahs ha can be properly financed and which allow a build up of savings ha could suppor governmen spending in he pos-oil era. B. Benchmark scenario: public invesmen profile In order o calibrae he benchmark pah of public invesmen, a sandard fiscal susainabiliy framework for resource-rich counries is used. The objecive of his long-erm framework is o seadily reduce he non-oil primary defici. The raionale behind his framework is o delink fiscal policy from he volailiy of oil revenues and o avoid he need o adjus spending abruply when oil revenues are exhaused, which would negaively impac economic aciviy. A he end of 2013, he non-oil primary defici sood a around 26 percen of GDP. A he same ime, capial expendiures represened 24 percen of GDP while oal expendiures oaled 38 percen of GDP. As oil revenues deplee, capial expendiures are projeced o follow a similar pah, sabilizing a around 13 o 14 percen of GDP in he long-run. Non-oil GDP growh is expeced o average around 5 percen per year, allowing non-oil revenues o increase from 12 percen of GDP in 2013 o around 29 percen of GDP a he end of The consolidaed effec of hese developmens delivers a non-oil primary balance close o zero by 2030 which can be susained. The benchmark profile akes ino accoun also he ambiious invesmen program of he Congo. The Naional Developmen Plan ( Plan Naional de Développemen ) for oulines several imporan infrasrucure projecs (e.g., airpors, adminisraive faciliies, he road Poine Noire-Brazzaville, power grid, elecommunicaion sysems). The scale of his program is a consequence of several posiive developmens. Firs, oil revenues have rebounded afer he global financial crisis o around 33 percen of GDP in 2013 (see Figure 3). Second, Congo benefied from HIPC and MDRI deb relief, which reduced he sock of exernal deb by $1.9 billion, o abou 20 percen of GDP in A he end of 2013, he sock of exernal public deb represened 32 percen of GDP. 3 Mos of hese obligaions are concessional bilaeral loans from China. In addiion o allowing he governmen o boos spending, he large oil revenues from consecuive years of high inernaional oil prices have allowed he governmen o se aside subsanial fiscal savings and accumulae foreign exchange reserves. Gross official reserves sood a abou 38 percen of GDP and he Congolese governmen held exernal deposis a China s EXIM Bank esimaed a around 28.5 percen of GDP. Thus, we se he iniial value of he SWF o 66.5 percen of GDP. In order o mainain an adequae level of reserve coverage and fiscal buffers, we se a floor for he SWF a 40 percen of GDP. 3 In our simulaions, we consider a cap on public deb of 70 percen of GDP, in line wih he curren CEMAC s convergence crieria.

17 17 Figure 3: Fiscal susainabiliy framework: Benchmark invesmen scenario Non-oil revenue Oil revenue 0 0 Curren expendiure Capial expendiure Overall balance Non-oil balance Noe: All indicaors are in percen of oal GDP. C. Efficiency and absorpive capaciy consrains Similar o he res of he CEMAC region, he business climae in he Republic of Congo is among he mos challenging in he world, ranking 178h ou of 189 counries in he 2015 World Bank s Doing Business Survey. 4 The criical facors ha influence his ranking are, among ohers, limied access o elecriciy, he ime and coss involved in cross-border rade and in saring a business, and limied access o financial services. These facors and Congo s relaively low PIMI score (see Dabla-Norris e al. (2012)) imply ha he capial formaion process is subjec o absorpive capaciy consrains and governmen inefficiency. Following Priche (2000) esimaes for sub-saharan African counries, he maximum absorpion capaciy parameer is se o 0.5. Furhermore, o capure he idea of rising invesmen coss because of absorpive-capaciy consrains, when public invesmen exceeds 145 percen of he iniial capial invesmen, invesmen efficiency or absorpive capaciy is assumed o fall,unil i reaches he lower bound level of 0.2 depending on he magniude of public invesmen (see eq. (39)). 4 The CEMAC area sands for Communaué Économique e Monéaire de l Afrique Cenrale (Economic and Moneary Communiy of Cenral Africa). This moneary and economic union is par of he CFA franc zone. I comprises of Cameroon, Cenral African Republic, Chad, Republic of Congo, Equaorial Guinea and Gabon.

18 18 Hurlin and Aresoff (2010) and Gupa e al. (2011) esimae he depreciaion rae of public capial in he range of percen. Given he low PIMI rank and he limied mainenance spending in developing counries, he annual depreciaion rae of public capial is assumed o be 5 percen. V Model Simulaions Simulaions consider several scenarios for public invesmen, is efficiency and oil revenues. In paricular, hree scenarios wih differen pahs for public invesmen are examined: Benchmark scenario. This scenario eliminaes he non-oil primary balance by Therefore, public capial spending adjuss a he same pace as oil revenues decline. Public capial invesmen averages 16 percen of GDP during Moreover, he deb-o-gdp raio averages 31 percen and oil revenues decrease from 33 percen in 2014 o around 2.5 percen of GDP in Aggressive invesmen scenario. This scenario analyzes he implicaions of a large scale-up of public invesmen as discussed in Inernaional Moneary Fund (2014a). Public invesmen peaks a abou 35 percen of GDP in 2018 before declining. The pah for public invesmen in his scenario follows he auhoriies projeced oil-producion pah. Consan invesmen scenario. In his scenario public invesmen says consan unil 2020 a a level around 25 percen of GDP, and hen declines o he projeced pah of he baseline scenario. The pace of adjusmen is similar o he baseline scenario, bu he level reached is higher by 2 percenage poins of GDP a he end of he simulaion period. A. Model Simulaions: Invesmen profiles A.1. The baseline scenario The baseline scenario delivers he bes oucome in erms of deb susainabiliy and financialasses accumulaion in he SWF. As Figure 4 shows, he projeced pah of public invesmen delivers a susainable and sizeable accumulaion of public capial. A he same ime, given he projeced oil revenues, i allows for a susained increase in savings in he SWF. There is also a mild bu susainable increase in he level of public deb in he long run owing o he governmen s policy of coninuing o finance invesmens wih concessional foreign borrowing. In he long run, his scenario produces higher non-oil GDP and privae invesmen.

19 19 The invesmen efficiency is below he opimal level unil I reaches he minimum level of efficiency in 2015 when public invesmen peaks a around 26 percen of GDP. Public capial gradually accumulaes and sabilizes a he 2024 level, reaching a level of abou 32 percen higher han in he seady sae. The SWF accumulaes resources unil 2026 when i ops ou a around 150 percen of GDP, and hen declines o a level of abou 125 percen of GDP by Figure 4: Benchmark scenario Noe: The variables are in percen deviaion from a rend-growh pah, unless specified oherwise in parenheses. A.2. The aggressive scenario ( scaled-up ) The aggressive invesmen scenario illusraes he dangers of a more pronounced scaling-up of public invesmen. As Figure 5 shows, he scaling up of public invesmen o almos 40 percen of GDP lowers he efficiency of invesmen and resuls in an unsusainable level of public capial higher invesmen iniially resuls in a larger build up of capial socks bu wihou sufficien invesmen o cover recurren coss, public capial begins o depreciae in fuure periods. The increase in governmen spending also resuls in higher non-oil growh during In he face of declining oil revenues and he large governmen spending, i is assumed ha capial expendiures are financed by firs running down he SWF. Once he SWF reaches he minimum level needed o ensure he smooh operaion of he pegged exchange rae

20 20 arrangemen (assumed o be 40 percen of GDP) in 2023, he governmen increases exernal borrowing o susain higher governmen spending han in he baseline. As a resul, he deb-o- GDP raio is projeced o increase and op 60 percen by 2030.Evenually, he rise in exernal deb, would force he ineviable downward adjusmen in governmen spending. The longererm effec of posponing he fiscal consolidaion is o erode he SWF and pu public deb on an unsusainable pah wihou a beneficial effec in erms of higher non-oil oupu. Figure 5: Aggressive scenario Noe: All variables are percenage poins of GDP, while invesmen efficiency varies from 0 o 1 (wih 1 perfecly efficien invesmen). The red lines refer o he aggressive scenario, while he blue lines refer o he benchmark one. A.3. Consan invesmen scenario Mainaining public invesmen consan unil 2020 a around 25 percen of GDP produces a mixed siuaion. On he one hand, i allows for a higher capial sock and non-oil oupu han he baseline scenario. On he oher hand, his comes wih higher risks for deb and fiscal susainabiliy: unsusainable level of deb and erosion in he SWF (see Figure 6). A pronounced phase of increased public invesmen pus pressure on he SWF which reaches he lower bound. As a consequence public governmen deb increases o he maximum hreshold which consrains governmen abiliy o borrow exernally and limis he fiscal space (over 65 percen of GDP). However, in order o susain he sock of capial and he higher non-oil oupu, he governmen needs o inves resources above he benchmark level. A his poin, he governmen faces a policy dilemma: eiher le public capial o depreciae (i.e., unsusainable capial) and non-oil

21 21 oupu o fall compared o he baseline, or adjus he fiscal sance via sizable effors (e.g., increase axes). Figure 6: Consan scenario Noe: All variables are percenage poins of GDP, while invesmen efficiency varies from 0 o 1 (wih 0 perfecly inefficien invesmen and 1 perfecly efficien invesmen). The red lines refer o he aggressive scenario, while he blue lines refer o he benchmark one. B. Model Simulaions: Efficiency In his secion we explore he implicaions of srucural reforms ha improve he efficiency of public invesmen. This is paricularly imporan in developing counries ha face a difficul business environmen, and absorpive capaciy consrains, such as coordinaion problems, supply bolenecks, and poor projec execuion and planning. More broadly, hese consrains can refer o insiuional policies and/or echnical and managerial capaciies. Firs we explore he effecs of underaking srucural reforms ha improve efficiency in he baseline invesmen scenario under alernaive assumpions on he iming and magniude of he improvemen in efficiency. Second, we analyze he consequences of posponing improvemens in invesmen efficiency in he aggressive scenario. The firs panel in he op row of Figure 7 shows he progressive improvemen in efficiency. This capures he fac ha srenghening of policy frameworks, including public financial managemen, akes imes o be refleced in beer policy oucomes. In his scenario, he maximum absorpion capaciy (or efficiency) parameer is se o 0.6, consisen wih he efficiency level of

22 22 Figure 7: Benchmark scenario: srucural reforms Noe: Invesmen efficiency varies from 0 o 1 (wih 0 perfecly inefficien invesmen and 1 perfecly efficien invesmen). Public Capial is in percen of GDP, while Non-oil GDP refers o growh deviaions from he seady sae. Red lines refer o he aggressive scenario wih srucural reforms, while blue lines represen he aggressive scenario wihou srucural reforms. an emerging marke counry. This policy produces a sizable and susainable increase in public capial which has posiive spillovers o he res of he economy, highlighed by higher non-oil growh. The boom row of Figure 7 depics he scenario in which srucural reforms are delayed by poliical and economic consrains. The scenario illusraes he missed opporuniy o enhance capial and non-oil oupu growh since mos of he invesmen scaling-up phase precedes he implemenaion of he srucural reforms. By 2030 he public capial sock and non-oil oupu growh are slighly higher han in he benchmark scenario he public capial sock is less han 10 percen of GDP above he level reached in he benchmark scenario and non-oil oupu growh is less han one percenage poin above is rae in he benchmark scenario. As shown in Figure 8, he delayed implemenaion of srucural reforms and he scaling-up of public invesmen increase he likelihood of an unsusainable level of capial. The laer is avoided only in he case where srucural reforms succeed in achieving full invesmen efficiency, i.e. an efficiency parameer of 1, which is highly improbable for a developing counry. Moreover, he beneficial effecs of he srucural reforms on non-oil oupu are limied. A comparison of he scenarios in Figures 7 and 8 shows ha he benchmark scenario wih early implemenaion of srucural reforms yields he bes oucome in erms of higher accumulaion of he public capial sock and non-oil GDP growh by 2030.

23 23 Figure 8: Aggressive scenario - srucural reforms Noe: Invesmen efficiency varies from 0 o 1 (wih 0 perfecly inefficien invesmen and 1 perfecly efficien invesmen). Public Capial is in percen of GDP, while Non-oil GDP refers o growh deviaions from he seady sae. The red lines refer o he srucural reform case implemened for he aggressive scenario, while he blue lines represen he baseline efficiency case. C. Model Simulaions: Oil revenue shock revenue shock Using simulaed oil price pahs over he nex 15 years, we generae confidence inervals for he fiscal revenues, SWF, public deb and non-oil oupu growh for each invesmen scenario. Oil revenues are compued as he produc of he price of oil, oil producion, and he governmen s share of he oil revenue. The baseline oil producion pah and governmen share of oil revenue are assumed o be unchanged, and he oil price pahs are generaed from simulaions. For each simulaion we draw a random vecor of shocks (ɛ po ) for which we compue oil price vecors. Inflaion-adjused oil prices are assumed o follow a Gaussian random walk as in Hamilon (2009). We re-wrie equaion 31 for he oil price as follows: 5 ln(p O ) = α 0 + α P ln(p O 1) + ɛ po, where ɛ po i.i.d. N (0, σ 2 po) (44) 5 Using oil price daa from 1970 o 2012, we esimae α P = and α 0 = Wih a 95 percen probabiliy, over he enire simulaion period oil prices are expeced o be wihin he [$25, $235] inerval.

24 24 Figure 9: Benchmark scenario: Oil Shocks (confidence inervals) Noe: Confidence bands are based on 500 simulaions. Solid lines refer o he median pahs. Dashed lines represen one-sandard deviaion confidence inervals and doed lines refer o wo-sandard deviaion confidence inervals. Oil price volailiy increases over ime. This effec dominaes he overall uncerainy regarding oil revenues. As in he benchmark case, he median size of he resource fund reaches a maximum a around 150 percen of GDP in 2026, while a he end of he simulaion period he resource fund is abou 120 percen of GDP. Two-sandard deviaions confidence inervals show ha he SWF builds up o 400 percen of GDP when oil prices are high. However, when oil prices are a he lower bound, he SWF reaches he minimum imposed hreshold of 40 percen of GDP. In his case, public deb builds up o unsusainable levels and can evenually exceed he CEMAC convergence crierion. These resuls emphasize fiscal revenue risks semming from oil price volailiy ha can endanger deb susainabiliy. In erms of non-oil oupu growh he median resuls show an average growh of around 3.5 percenage poins. Confidence inervals for growh show relaive flucuaions in he order of ±2 percenage poins, which are relaed o he deb-saving radeoff. High oil prices allow higher governmen revenues o finance higher governmen spending and boos non-oil growh. By conras, low oil prices lead oil revenues o deplee more rapidly. As a resul, governmen spending needs o be financed by drawing down he resource fund and hen by a build up of deb. The lower oil revenues consrain governmen spending and non-oil oupu. Also, he higher governmen borrowing crowds ou privae secor invesmen and lowers growh poenial.

25 25 In he Appendix, we show ha aggressive and consan scenarios yield similar findings. In hese scenarios, he slower pace of fiscal adjusmen in he face of lower oil prices and declining oil revenues resuls in a quicker draw-down of savings, larger build up in deb and lower non-oil growh hereby emphasizing he vulnerabiliy o an adverse oil shock from slow fiscal adjusmen. D. Model Simulaions: Projec selecion Figure 10: Projec selecion: public capial and non-oil GDP growh Public capial (Level) Non oil GDP Deviaion from he seady sae (%) Weigh on high produciviy projecs Deviaion from he seady sae (%) Weigh on high produciviy projecs Noe: The benchmark case (ς = 1) represens he case in which he enire capial invesmen is allocaed o he high produciviy and low depreciaion projec. The case when ς = 0 is associaed wih he enire capial spending allocaed o he low produciviy and high depreciaion projec. In his secion we explore he implicaions of improvemens in projec selecion capaciy for he build up of capial and he spillovers o he real economy. We assume ha he governmen can allocae is resources beween wo ypes of projecs: (i) projecs which have a differen influence on he economy. The governmen decides how much o inves in highly producive projecs g IH and low produciviy projecs g IL : g IH = ς g I (45) g IL = (1 ς) g I (46)

26 26 where ς represens he share of oal governmen invesmen in projecs wih high produciviy. This implies wo ha he capial sock in he highly producive projec k GH and in he low produciviy projecs k GL evolves according o: k GH = ( 1 δ GH) k GH 1 + g IH (47) k GL = ( 1 δ GL) k GL 1 + g IL (48) Furhermore we assume ha δ GH < δ GL o capure he lower obsolescence of higher qualiy projec. Accordingly, oal public capial is: k G = k GH + k GL (49) As in he baseline case, public capial is producive. However, in his case, he elasiciy of public capial is no fixed bu varies according o he amoun of invesmen in a specific projec. y j = z ( ( ( ) ) j k j ) 1 α j ( ) 1 L j α j ( ) k G α GH α ς GL α GH (1 ς) In his seup, a shif in invesmen owards lower produciviy projecs impacs negaively he elasiciy of public capial wih respec o oupu. By varying ς beween 0 and 1, we obain he full specrum of public invesmen allocaion. As depiced Figure 10, misallocaion of resources owards low produciviy projecs will resul in lower capial sock and oupu growh. According o our simulaions, when more han 1/3 of invesmen is iled owards whie elephan projecs, oupu growh eners ino he negaive erriory. These resuls highligh he risks of resource misallocaion during he projec selecion process. (50) VI Conclusions This paper illusraes he policy radeoffs faced by a highly oil-dependen counry ha has large social and infrasrucure gaps and faces absorpive and implemenaion capaciy consrains and is near he peak of is oil producion. The model simulaions underscore he imporance of fiscal consolidaion o preserve macroeconomic sabiliy in he medium- o long-run when oil reserves are exhaused. The paper shows ha an aggressive scaling up of invesmen, could lead o a fas accumulaion of public capial and higher non-oil growh. However, as more oil revenues are devoed o public invesmen less can be saved, leaving he counry vulnerable o fuure negaive oil price shocks. Public invesmen can also be financed by borrowing from eiher domesic or foreign sources. A rapid scaling up of invesmen could, herefore, iniially resul in a draw-down of he saving fund in he face of declining oil revenues. Once savings hi a minimum accepable lower bound in his case he level of reserves needed o ensure

27 27 coninued smooh operaion of he pegged exchange rae arrangemen he governmen can choose o borrow o close he fiscal gap. Evenually, however, he rise in public deb would force he ineviable downward adjusmen in governmen spending. The longer-erm effec of posponing he fiscal consolidaion is o run up unsusainable public deb and leave no financial asses o provide a permanen income once oil reserves are exhaused. The paper also explores an inermediae opion where public invesmen is mainained consan for a period of ime before fiscal consolidaion kicks in. Naurally, his opion leads o a lower build up of savings in he long run and a higher build up of deb han he baseline fiscal consolidaion scenario, and increases he vulnerabiliy of he economy o negaive oil price shocks. Our resuls highligh he sensiiviy of budgeary revenues o oil price shocks, which could affec boh governmen spending and poenial non-oil oupu growh. Moreover, our simulaions emphasize he posiive impac of improving public invesmen efficiency, which can conribue o a susainable and higher-level of public capial wihou adversely affecing fiscal susainabiliy. Finally, we explore he consequences of invesmen projec misallocaion and show heir negaive effecs on oupu growh and public capial.

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30 30 Appendix Tables Graphs Figure 11: Aggressive scenario: oil shocks (confidence inervals) Noe: Confidence bands are based on 500 simulaions. Solid lines refer o he median pahs. Dashed lines represen one-sandard deviaion confidence inervals and doed lines refer o wo-sandard deviaion confidence inervals.

31 Table 2: Srucural parameers Parameer Definiion Value Parameer Definiion Value 31 expshare Expor (share of GDP) 0.43 ρ z Persisence of TFP in raded secor 0.1 impshare Impors (share of GDP) 0.46 κ j Invesmen adjusmen cos 25 g share C Governmen consumpion (share of GDP) 0.14 ψ Inverse of Frisch labor elasiciy 10 g share I Governmen invesmen (share of GDP) 0.06 σ Inverse of ineremp. elasiciy of subsiuion 2.94 ishare Privae invesmen (share of GDP) ρ Ineremporal subsiuion elasiciy of labor 1 y share O Oil GDP (share of GDP) ω Measure of opimizers in he economy 0.4 f share Sovereign wealh fund (share of GDP) χ Subsiuion elasiciy raded/non-raded goods 0.44 bshare Domesic public deb (share of GDP) 0.01 η Elas. of porfolio adjusmen coss 1 b share Privae foreign deb (share of GDP) 0 f User fee of public infrasrucure 0.5 dshare Public concessional deb (share of GDP) τ L Tax rae of labor income 0.05 dc,share Commercial deb (share of GDP) 0.01 τ C Tax rae on consumpion 0.1 grshare Grans (share of GDP) 0.14 τ K Tax rae on capial 0.2 σpo Sandard deviaion of oil price shock δ G Depreciaion rae of public capial 0.05 R 1 Domesic ne real ineres rae 0.1 δ GH Depreciaion rae of capial in high prod. proj R RF 1 Foreign ne real ineres rae δ GL Depreciaion rae of capial in low prod. proj. 0.1 Rd 1 Ne real in.rae on concessional deb 0 ffloor Lower bound for he sabilizaion fund 0.4 Rf 1 Ne real risk-free rae 0.04 ν Home bias of governmen purchases 0.6 Rdc,0 1 Ne real in. rae on commercial deb 0.06 νg Home bias of addiional spending 0.4 ηg Elasiciy of sovereign risk 0 α G Oupu elasiciy of public capial 0.15 α NT Labor income share in non-raded secor 0.45 ɛ Seady-sae efficiency of public invesmen 0.5 α T Labor income share in raded secor 0.6 ςɛ Severiy of absorpive capaciy consrain 25 δ j Depreciaion rae of privae capial 0.1 γ GI Threshold of absorpive capaciy 0.75 ρ y Learning by doing in he raded secor 0.1

32 32 Figure 12: Consan scenario: oil shocks (confidence inervals) Noe: Confidence bands are based on 500 simulaions. Solid lines refer o he median pahs. Dashed lines represen one-sandard deviaion confidence inervals and doed lines refer o wo-sandard deviaion confidence inervals.