The Macroeconomics of Medium-Term Aid Scaling-Up Scenarios

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1 WP//6 The Macroeconomics of Medium-Term Aid Scaling-Up Scenarios Andrew Berg, Jan Goschalk, Rafael Porillo, and Luis-Felipe Zanna

2 2 Inernaional Moneary Fund WP//6 IMF Working Paper Research Deparmen The Macroeconomics of Medium-Term Aid Scaling-Up Scenarios Prepared by Andrew Berg, Jan Goschalk, Rafael Porillo, and Luis-Felipe Zanna * July 2 Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. We develop a model o analyze he macroeconomic effecs of a scaling-up of aid and assess he implicaions of differen policy responses. The model feaures key srucural characerisics of low-income counries, including varying degrees of public invesmen efficiency and a learning-by-doing (LBD) exernaliy ha capures Duch disease effecs. On he policy fron, i disinguishes beween spending he aid, which is conrolled by he fiscal auhoriy, and absorbing he aid financing a higher curren accoun defici which is influenced by he cenral bank's reserve accumulaion policies. We calibrae he model o Uganda and run several experimens. We find ha a policy mix ha resuls in full spending and absorpion of aid can generae emporary demand and real exchange rae appreciaion pressures, bu also have a posiive effec on real GDP in he medium erm, hrough higher public capial. Full spending wih parial absorpion, on he oher hand, may sem appreciaion pressures bu can also induce adverse medium-erm real GDP effecs, hrough privae secor crowding ou. When aid is very inefficienly invesed and here are srong LBD exernaliies, aid can be harmful, and parial absorpion policies may be jusified. Bu in his case, a welfare improving soluion is o defer spending or even beer if possible raise is efficiency. JEL Classificaion Numbers: E2, E2, F3, O4 Keywords: Aid; Africa; Duch Disease; Fiscal Policy; Moneary Policy; Public Invesmen; Real Exchange Rae; Transfer problem. Mail Auhor s E-Addresses: * The auhors have benefied from commens and conversaions wih Chris Adam, Emanuele Baldacci, Benedice Chrisensen, Yasemin Bal Gunduzmany, Bre House, Enrique Mendoza, Tokhir Mirzoev, Sephen O'Connell, Chris Papageorgiou, Peer Pedroni, Kazuko Shirono and several colleagues in he Fund's African deparmen who firs applied he model, and UNDP colleagues who conribued o he join IMF-UNDP projec from which his model arose. All errors remain ours. The views expressed in his paper are solely he responsibiliy of he auhors and should no be inerpreed as reflecing he views of he Inernaional Moneary Fund.

3 2 Table of Conens Page I. Inroducion...4 II. The Model...7 A. Households...8 A.. Asse Holders...8 A.2. Hand-o-Mouh Consumers... B. Non-Traded Good Secor... C. Traded Good Secor...2 D. The Governmen...3 E. The Cenral Bank...4 F. Aggregaion and he Goods Marke Equilibrium Condiions... III. Calibraion...6 IV. Experimens...2 A. The Baseline Scenario...2 B. Parial Aid Absorpion Policies...22 B.. Reserve Accumulaion Rules under a Flexible Exchange Rae Regime...22 B.2. A Fixed Exchange Rae Regime wih Serilizaion...24 C. Learning-by-Doing Exernaliies, he Efficiency of Public Invesmen, and Parial Absorpion Policies...27 C.. The Efficiency of Public Invesmen...27 C.2. The Learning-by-Doing Exernaliies...28 C.3. Parial Absorpion Policies...3 V. Discussion...3 VI. Conclusions...36 Tables Table. Baseline Calibraion: Preference Parameers...7 Table 2. Baseline Calibraion: Technology Parameers...8 Table 3. Baseline Calibraion: Policy Parameers and Aid Process...9 Figures Figure. Baseline Scenario...2 Figure 2. Parial Absorpion under a Flexible Exchange Rae Regime: Accumulaing Some Aid Flows in Reserves...23 Figure 3. Full Absorpion: A Fixed Exchange Rae Regime wihou Serilizaion...2 Figure 4. Parial Absorpion Policy: A Fixed Exchange Rae Regime wih Serilizaion...26 Figure. The Efficiency of Public Invesmen and Real GDP...28

4 3 Figure 6. The Effecs of Low Efficiency and Srong Exernaliies...29 Figure 7. Parial Absorpion Policies under Low Efficiency and Srong Exernaliies...3 Figure 8. Parial Absorpion Policies under High Efficiency and Srong Exernaliies...32 Figure 9. Parial Absorpion and Parial Spending Policies...33 Figure. Welfare Gains and Absorpion Policies...34 Appendix A. Wriing he Model in Saionary Terms...38 B. The Equaions of he Model...39 B.. The Firs Order Condiions of he Households Problem...39 B.2. The Firs Order Condiions of he Firms Problem...4 B.3. Demand Funcions, Aggregaion, Marke Clearing Condiions, and Oher Equaions...4 B.4. Definiion of Equilibrium...4 C. The Efficiency of Public Invesmen and GDP...42 References...43

5 4 I. Inroducion Aid surges o er boh challenges and opporuniies o recipien counries. Some argue ha hese surges may hur growh by inducing real exchange rae appreciaion pressures, o he derimen of growh-promoing exporing indusries; while ohers believe hey may spur growh by nancing muchneeded public invesmen in infrasrucure. 2 Concerns abou he poenial negaive e ecs of aid surges may rigger policy responses aimed a dampening hese e ecs. For insance, Berg e al. (27) documens how, during aid surges, concerns abou real appreciaion induced several African economies o accumulae much of he addiional aidrelaed foreign currency in reserves. This response may have helped conain he appreciaion pressures. Bu when combined wih a scal policy ha enailed he full spending of he local currency counerpar o he aid, his response urned ou o be problemaic. I led o an increase in he money supply, and di eren serilizaion policies posed new challenges o hese economies: hose ha did no serilize faced high in aion; whereas hose ha did serilize experienced high ineres raes. These di ering views and concerns abou aid surges have creaed he need for a common framework o analyze he shor and medium erm macroeconomic e ecs of aid surges, as well as he appropriae policy responses. This paper proposes such a framework, by developing a dynamic quaniaive model ha can be useful for Fund sa eams and policy-makers in recipien counries. The model has already been used o help formulae counry-speci c aid scaling up scenarios. As par of he Unied Naions Millennium Developmen Goals (MDG) Africa Seering and Working Groups, he IMF was requesed o provide macroeconomic assessmens of Gleneagles aid scaling-up scenarios for several African counries. IMF (28a) and IMF (28b) presen he rs six counry scenarios, ve of which used he model presened here. 3 The novely of our model sems from is srucure, which capures he main mechanisms and policy issues of ineres in low-income counries (LICs). The model feaures a learning-by-doing mechanism (LBD) ha creaes an exernaliy associaed wih he producion of raded goods and capures he noion ha real exchange rae appreciaion may harm produciviy growh in he raded secor; a role for public capial in producion, so ha governmen spending can raise oupu direcly and poenially crowd in privae invesmen; and less-han-full conversion of public invesmen ino useful public capial. 4 The model also allows for separae and possibly uncoordinaed scal spending and reserve accumulaion responses o aid surges, permiing a variey of policy combinaions. By assumpion, he scal See Rajan and Subramanian (2), among ohers. 2 See, for insance, Collier (26). 3 IMF and UNDP (2) describes he full join projec. The assessmens have been developed for Benin, Cenral African Republic, Ghana, Liberia, Niger, Rwanda, Sierra Leone, Togo, Tanzania, and Zambia. The model used for Niger is described in Farah e al. (29). 4 The model also feaures hand-o-mouh consumers o capure nancial marke imperfecions ha can give scal policy larger real e ecs in he shor run; limied access o inernaional capial markes ha gives serilized inervenion an imporan role; and imperfec mobiliy of producive facors across raded and non-raded secors, which a ecs he degree of real exchange rae appreciaion.

6 auhoriy evenually spends all he incremenal aid; he quesion here is abou he e ecs of doing so as he aid comes in, which we de ne as full spending of aid. The moneary auhoriy, on he oher hand, in uences aid absorpion, which we de ne as he use of he foreign currency proceeds from aid o nance higher curren accoun de cis (ne of aid). I does so by accumulaing par of he aid ows in inernaional reserves. In previous work we have shown, using a smaller model wihou privae or public invesmen, ha policies ha are frequenly implemened in response o aid ows can have sriking implicaions for he shor-run behavior of macro variables such as he real exchange and he real ineres rae. Here, we demonsrae ha he same policy responses can someime have adverse medium-erm e ecs as well, depending on he e ciency of public invesmen and he exen of learning by doing exernaliies in he economy. We show hese resuls by calibraing our model o he Ugandan economy and running several experimens. To x ideas, we sar wih a baseline scenario of a exible exchange rae regime, somewha e cien public invesmen, mild LBD exernaliies, and scal and reserve accumulaion rules ha imply he full spending and absorpion of aid. As he governmen spends he aid, demand pressures emerge. These combine wih nominal price rigidiies in he non-raded secor o creae a shor-lived spike in real gross domesic produc (GDP). The real exchange rae subsanially appreciaes and he raded secor su ers a conracion bu recovers in he medium erm. Over ime, price rigidiies dissipae and he demand impulse fades ou, bu GDP coninues o grow on he srengh of higher public capial and he resuling higher privae capial accumulaion. The subsanial shor-erm real appreciaion pressures of he baseline scenario may concern policymakers who are commied o mainaining compeiiveness in he raded secor. We herefore invesigae he consequences of parial absorpion policies ha may help counerac hese pressures: (i) accumulaing some of he aid ows in reserves in he conex of a (managed) oa, and (ii) operaing a xed exchange rae regime. Accumulaing reserves succeeds in miigaing appreciaion pressures bu crowds ou privae consumpion and invesmen in he shor run, hus lowering real GDP over he medium erm relaive o he full-absorpion baseline. The underlying cause of he crowding ou is he aemp o use he same aid resources wice: he cenral bank uses aid in ows o build up reserves, while he scal auhoriy uses he domesic currency counerpar of hese in ows o increase spending. Aid resources can be used eiher by he governmen for increased spending or by he cenral bank for reserve buildup, bu no for boh wihou crowding ou he privae secor. A xed exchange rae regime may also sem appreciaion pressures, depending on he associaed moneary policy. This regime induces he auhoriies o accumulae reserves in resising nominal appreciaion. If he auhoriies do no serilize he associaed moneary emission, he resuling in aion induces a real appreciaion and produces roughly a full-absorpion scenario ha closely resembles he baseline in real erms. E ors o resis he in aion by serilizing he moneary emission will again succeed in narrow erms bu a a cos of parial aid absorpion, higher real raes, and privae secor See Berg, Mirzoev, Porillo, and Zanna (2).

7 6 crowding ou. 6 As before, his implies lower real GDP in he medium erm. Why migh governmens noneheless consider parial absorpion policies? Maybe because, in conras o our baseline assumpions, he e ciency of public invesmen is low, while very srong LBD exernaliies imply a signi can loss in produciviy of he raded secor when oupu in his secor conracs. In his conex, accumulaing some addiional aid in reserves may relieve some of he shor-erm appreciaions pressures wihou inducing adverse medium-erm e ecs on real GDP. To fully undersand his resul, i is necessary o invesigae he roles of he e ciency of public invesmen and he LBD exernaliies and heir ineracion in he model. Consider he role of e ciency, i.e., he exen o which public invesmen is acually convered ino useful capial. In our model, here is a disincion beween he e ciency of seady-sae invesmen and ha of he invesmen nanced by he scaling-up of aid. Wha maers for he e ecs of aid on real GDP (in percen changes) is he e ciency of he aid-surge invesmen spending relaive o seady-sae e ciency. Our focus in his paper is on his relaive e ciency concep. In our model, counries ha are less e cien in his sense enjoy lower medium-erm bene s in real GDP erms, as less public capial is accumulaed and he crowding in e ec on privae invesmen is smaller. Srong LBD exernaliies, on he oher hand, raise he sakes: hey may amplify posiive e ecs of aid on raded oupu and real GDP which we refer o as Duch vigor bu he may also make aid harmful causing Duch Disease. Wheher he srong exernaliies amplify he posiive or negaive e ecs of aid depends on he e ciency of public invesmen, as his will deermine if he shrinkage in he raded secor is emporary or proraced. When e ciency is low and exernaliies are srong, Duch-disease ype e ecs can dominae under full absorpion policies so ha aid reduces real GDP. By limiing he conracion in raded secor oupu, parial absorpion policies can help miigae hese e ecs, even if hey sill crowd ou privae invesmen in he shor run. In hese circumsances, however, here are beer ways o respond o aid surges, while miigaing appreciaion pressures, han parial absorpion policies. Firs, if governmen spending is ine cien and here are srong exernaliies, hen he reserve accumulaion policy could be accompanied by parial spending of aid. Second, if aid were o be used more e cienly, hen he GDP e ec of scaled-up aid would always be posiive, and more so wih full absorpion. 7 We suppor hese ndings wih some simple welfare analysis. Wih low e ciency and srong exernaliies, accumulaing some of he addiional aid in ows in reserves may generae small welfare gains if aid is fully spen, alhough parial spending is preferable. However, wih high e ciency, his resul is overurned, as here are large gains from fully spending and absorbing he aid. 6 The model feaures limied inernaional capial mobiliy making serilizaion policies e ecive in a small-openeconomy se-up, even when he exchange rae is xed. 7 Spending more aid on invesmen raher han consumpion or allocaing more public invesmen owards he raded goods secor are policies ha are no explored in his paper bu ha would like achieving higher e ciency yield beer growh oucomes han parial absorpion in he face of srong LBD exernaliies.

8 7 Our work disinguishes iself from he lieraure by simulaneously analyzing boh shor-erm (demand) and he medium-erm (supply) e ecs, in a conex where scal and cenral bank policies shape he spending and absorpion of aid and maer for medium-erm oucomes. Adam e al. (29), our previous work Berg e al. (2), Bu e e al. (28), and Prai and Tressel (26), among ohers, also focus on he e ecs of various policy responses o aid in ows, bu hey do so in models where secoral oupu is exogenous or capial accumulaion is absen. The absence of capial accumulaion is a noable simpli caion, given ha all he way from he work of Keynes (936) and Hicks (939) o ha of Kydland and Presco (982), macroeconomic heories have underscored invesmen dynamics as an imporan channel for he ransmission of aggregae shocks. By inroducing boh public and privae capial, our work shows ha invesmen spending plays a key role in shaping he e ecs of moneary and scal policies under aid surges. Our work also di ers from papers ha presen real models wih capial, including Adam and Bevan (26), Agenor e al. (28), Agenor and Yilmaz (28), Arellano e al. (29), Cerra e al. (28), and Chaerjee and Turnovsky (27), among ohers. Despie heir imporan conribuion, hey do no model scal and moneary policies and, herefore, do no permi a rich discussion of he ineracion of hese policies and heir implicaions for he shor-o-long run e ecs of aid. In addiion, hese works have no underscored he role of he e ciency of public invesmen, as our work does. 8 These invesmen ine ciencies may have imporan implicaions for he empirical calculaions of capial as well as for growh analysis. 9 Finally, our parial absorpion resuls are reminiscen of hose in Calvo e al. (99), which are derived in a small sylized model: absen inernaional capial mobiliy, prevening he real exchange rae from appreciaing leads o some combinaion of emporary higher in aion and higher domesic real ineres raes. The remainder of his paper is organized as follows. Secion II presens he srucure of he model. Secion III discusses he calibraion o Uganda. Secion IV presens and elaboraes on he resuls of he experimens, saring by he baseline scenario. A discussion of he scope of our resuls, including some welfare analysis, is presened in secion V. Finally, secion VI concludes. II. The Model Consider an in nie-horizon small open economy. The economy has wo goods, a raded good (T ) and a non-raded good (N), and consiss of he following agens: i) wo ypes of households, some paricipaing in asse markes and ohers no; ii) wo secors wih rms producing raded and nonraded goods using labor, privae capial, and public capial; iii) a cenral bank in charge of exchange rae policy and moneary policy, including reserve accumulaion policy; and iv) a scal auhoriy ha is he direc recipien of aid and decides how much of his aid o spend as par of is scal policy. 8 Agenor e al. (28) is a parial excepion using a srucural model ha is no fully microfounded. 9 See Hulen (996) and Priche (2).

9 8 There is exogenous deerminisic growh of he labor-augmening ype, which is he same across secors. The labor produciviy level T grows a he consan facor n so ha T = nt. To faciliae he descripion of he model, we will presen is srucure in saionary erms. This involves rescaling variables by T when required, such ha all he variables are consan in he long run (seady sae). We assume ha he law of one price holds for he raded good. Therefore P T = S P T ; where P T is he price of raded goods, S corresponds o he nominal exchange rae, and P T is he foreign price of raded goods. By denoing he domesic (foreign) Consumer Price Index (CPI) as P (P ), we can express he CPI-based real exchange rae as s = SP P and he relaive price of non-raded goods as p N = P N P : We also de ne real gross domesic produc (GDP) as: y = p N y N + sy T ; () i.e., he sum of he producion of he non-raded good, y N, and he raded good, y T, valued a heir seady-sae relaive prices p N and s. Nex, we describe he objecives and consrains of he di eren agens of his economy. A. Households There is a coninuum of households on he inerval [; ]. A fracion p is represened by households who are forward-looking and smooh consumpion by being able o rade in asse markes. These are asse holders or savers and will be indexed by he superscrip a. The res of he households p have no asses and canno smooh consumpion. They will be indexed by he superscrip h and behave in a hand-o-mouh fashion, fully consuming heir curren labor income. A.. Asse Holders Savers mus decide how o allocae consumpion expendiures among di eren goods. Consumpion of he raded good and he non-raded good, denoed by c at and c an, respecively, are combined ino a CES baske c a = ' + ( ') ; (2) c jn h wih he associaed CPI P = ' P N i + ( ')(P T ) ; where denoes he inraemporal elasiciy of subsiuion, and ' is he degree of home bias in consumpion. This CES aggregaor implies he following demand funcions for raded and non-raded goods: c an = ' p N c a and c at = ( ')s c a : The non-raded good is in urn a composie good wih a coninuum of varieies indexed R by i 2 [; ] saisfying c an = c an i di ; wih measuring he elasiciy of subsiuion of The rs par of he Appendix discusses in more deail how o ransform he model in saionary erms. A recen survey conduced in Uganda nds ha almos 62 percen of he sample does no access formal or informal nancial markes. See Seadman Group (29). c jt

10 9 hese varieies. The demand for variey i is given by: h where p N i P i N R P and P N = Pi N i di : p c an N i = i p N c an ; (3) The represenaive saver maximizes his life-ime uiliy: 2 X ( a ) u a (c a ; m a ) = { a + (la ) + ; (4) wih h i u a (c a ; m a ) log # a (c a ) + ( # a ) (m a ) ; () where c a Ca T refers o a consumpion baske of he ype described in (2), m a M a P T are he holdings of real money balances, and l a is he amoun of labor supplied o rms for he producion of he non-raded and raded goods. The parameer a 2 (; ) corresponds o he subjecive discoun facor of he asse holders, # a 2 (; ) is he share of consumpion in he uiliy u a (:); > measures he elasiciy of subsiuion beween c a and m a, { a is a scale parameer, and > is he inverse of he labor supply elasiciy. We wan o capure he noion ha labor mobiliy is limied across secors and ha inersecoral wage di erenials are possible. Supplied labor is hen de ned as in Bouakez e al. (29): l a = % l an +% % + ( ) % l at +% % +% % ; (6) where 2 (; ) is he share of labor supplied o he non-raded secor, l an, in oal employmen, and % > is he elasiciy of subsiuion beween labor services provided o he wo secors. The index of real wages associaed wih he aggregaor (6) corresponds o: w = h w N +% + ( ) w T +% i +% : (7) The budge consrain of he represenaive agen, de aed by he domesic CPI and expressed in saionary erms, is given by: c a + m a + b ac where b ac Bac P T + s b a + s P a = ( )w l a + ma b ac + i n n + s i b a n + a + s rm + a ; (8) is he saver s real holdings of domesic bonds issued by he governmen, which pay a gross nominal ineres rae i + r and b a Ba P denoes his real holdings of foreign asses ha T pay a gross nominal inernaional ineres rae i and are subjec o porfolio adjusmen coss P a. 2 Because we are wriing he problem of he agen in saionary erms, he objecive funcion should also include he erm ( a ) log(t ): We can omi his erm, since T is exogenous and does no represen a conrol variable.

11 Toal labor income sais es w l a = w N l an + w T l at wih w k W k P T denoing he real wage in secor k = N; T. Moreover, = P P denoes gross domesic in aion, while is foreign in aion; which is assumed o be consan; a denoes real pro s from domesic rms; is an income ax rae se by he governmen; rm are remiances received from abroad and assumed o be consan; and a is a ransfer from asse holders o hand-o-mouh consumers. 3 This budge consrain implies ha spending (lef-hand side) mus equal income (righ-hand side). The porfolio adjusmen coss are given by P a 2 (ba b a ) 2 ; where b a is he seady-sae value of he real foreign asses. These coss serve wo purposes. Firs, hey ensure saionariy of b a. 4 Second, hey allow us o model di eren degrees of inernaional capial mobiliy. When! +; he capial accoun is pracically closed; whereas when < << ; i is parially open. The problem of he asse holders reduces o maximizing (4) wih respec o consumpion, real money balances, labor supply in boh secors, and domesic and foreign asses, subjec o he consrain (8) and a ransversaliy condiion associaed wih all asse holdings. The rs-order condiions of his problem are presened in he Appendix. A.2. Hand-o-Mouh Consumers Households ha do no have access o asse markes rely on labor income, remiances, and ransfers as heir only source of income. The represenaive agen from his group maximizes uiliy as in (4) and (), where c h and l h ake he same form as in (2) and (6). The agen is subjec o a ransversaliy condiion associaed wih money holdings and he budge consrain: c h + m h = ( )w l h + mh n + s rm + h ; (9) wih w l h = w N l hn + w T l ht and h p = p a. Noe ha in principle hand-o-mouh consumers could smooh consumpion by changing heir money holdings. To preven his, we can assume ha heir subjecive discoun facor h is se o zero. In his regard, heir problem becomes saic. The rs-order condiions of his problem are lised in he Appendix. B. Non-Traded Good Secor This secor faces monopolisic compeiion and nominal price rigidiies. Each monopolis produces a variey i of he non-raded good. The echnology of he represenaive producer i is given by: y N i = z N h k N i N (q ) N i N l N i N ; () 3 This ransfer simpli es he analysis of he model by avoiding he need o keep rack of he di eren consumers. They ensure ha consumpion a he seady sae is he same for he wo ypes of households. See Galí e al. (27). 4 See Schmi-Grohé and Uribe (23) for alernaive mehods o ensure saionariy of ne foreign asses. The share of consumpion in he uiliy for hese consumers, # h ; can be di eren from ha of asse holders. In his way we ensure ha real money balances are he same across boh ypes of households, a he seady sae, given ha he demand funcions are no he same for boh ypes, as shown in he rs-order condiions saed in he Appendix.

12 where z N is a consan produciviy parameer; li N is he amoun of labor employed, ki N is privae capial, which is rm-speci c, and q is public capial. The coe cien N indicaes he producion share of labor, while N denoes he share of privae capial in oal capial used in producion. Privae capial is subjec o a depreciaion rae N : I is accumulaed via invesmen x N i, which is a composie 2 of raded and non-raded goods like in (2), and subjec o adjusmen coss Fi N N x N i 2 ; as in Chrisiano e al. (2). Then: x N i nki N = ( N )ki N + Fi N x N i : () The monopolis is subjec o a demand consrain of he Dixi-Sigliz ype described in (3) y N i = p N i p N y N ; (2) where y N is he overall demand for he non-raded good. She also faces price adjusmen coss 2 G i 2 p N y N, where N is he non-raded goods in aion wih he seady-sae p N i p N i N value represened by N. These coss are a varian of hose proposed by Roemberg (982), as hey allow for indexaion o pas values of in aion. The maximizaion problem of he monopolis corresponds o choosing he price level p N i, he amoun of labor, capial, and invesmen in order o maximize he discouned pro s X J ( $)( + N ) p N i yi N G i = w N l N i x N i + ($ N )(p N y N G ) ; subjec o equaions ()-(2), where G corresponds o G i wih p N i = pn. 6 The rs-order condiions are presened in he Appendix. There is a ax disorion $ ha reduces he value of rms sales ne of price adjusmen coss for any given level of producion. This disorion is o se in he aggregae, as he amoun $(p N y N G ) is resiued o each rm, bu i a ecs rms incenive o hire labor and inves in new capial. I is mean o capure a broad se of insiuional feaures ha keep poor counries from invesing a he high raes ha migh oherwise be jusi ed by he very low socks of privae capial. In his way, we mach he observed low invesmen shares in many low-income counries. In addiion, each rm receives a subsidy N per uni produced and ne of price adjusmen coss, which is nanced wih a ax common o he enire secor. This simpli es he seady-sae analysis by ensuring ha disorions arising from monopolisic compeiion are zero a seady sae. 6 The discoun facor J of he pro s is sochasic and relaed o he asse holders marginal uiliy of consumpion, since hey own he rms.

13 2 C. Traded Good Secor The raded secor feaures perfec compeiion and exible prices. The represenaive rm j is endowed wih a similar echnology o ha of he non-raded secor: y T i = z T h k T i T (q ) T i T l T i T : (3) The represenaive rm also accumulaes capial k i T hrough invesmen xt i 2 adjusmen coss Fi T T x T i 2 : Accumulaion is dicaed by x T i which is subjec o nk T i = ( T )k T i + F T i x T i : (4) The rm picks he amoun of capial, labor and invesmen in order o maximize he discouned pro s X J ( $)s yi T w T li T x T i + $s y T ; = subjec o equaions (3) and (4). As in he non-raded secor, sales in his secor are also subjec o he ax rae $: The Appendix liss he rs order condiions. One of he chief concerns wih a scaling up of aid is he possibiliy of Duch disease e ecs. Frequenly, he real appreciaion and shrinkage of he raded secor are inerpreed as evidence of hese e ecs. However boh e ecs may no consiue a disease, as hey are an indispensable par of he ransmission mechanism o shif resources from he raded o he non-raded secor in order o mee higher governmen demand for non-raded goods. Raher, o capure he idea of a disease, we inroduce learning-by-doing (LBD) e ecs ino he raded secor: a decline in he raded secor will impose an economic cos hrough los oal-facor produciviy (TFP) in his secor. 7 More formally, we assume ha he produciviy in he raded secor depends on he hisory of he deviaions of he previous secoral oupus from he seady sae, as can be inferred from! z T z z T = zt y T z T y T! v ; () where z T is he seady-sae value of he produciviy in he raded secor, and z 2 (; ) and v > : This speci caion is a variaion of he one in Masuyama (992) and Krugman (987). 8 I implies ha here are no permanen e ecs of learning by doing on oupu or produciviy. Bu deviaions of raded secor oupu from rend do imply persisen produciviy e ecs. 7 Rodrik (28) models LBD as one of wo broadly equivalen for our purposes reasons why real appreciaion could lower produciviy growh, he oher being ha he raded secor is inensive in public goods such as srong conracing insiuions ha are scarce in many low-income counries. 8 See also Adam and Bevan (26) and Torvik (2), among ohers.

14 3 D. The Governmen Governmens face poenially good opporuniies for public invesmen bu have limied access o exernal capial and nd raising axes very cosly. 9 The governmen is he direc recipien of foreign aid A ; which follows he process A = A + A (A A ) + A ; (6) where A is he seady sae level of aid, A corresponds o an exogenous increase in aid a ime, and A 2 (; ) is a parameer ha measures he degree of persisence of he increase in aid. Governmen consumpion g is a CES baske ha includes raded and non-raded goods and is de ned by g = g N + ( ) g T ; (7) which implies he following governmen price index p g h = p N i + ( )(s ) ; expressed in erms of he CPI. In his speci caion, is he degree of home bias in governmen consumpion, which may di er from is privae counerpar. Using he aggregaor (7), we can derive he following demand funcions: g N = p N g ; and g T = ( )s g : (8) The governmen can nance is spending p g g hrough a variey of sources: axes on labor income w l, using he domesic currency value of aid proceeds, s A, drawing down on deposis held a he cenral bank, d g d g b n, or issuing domesic deb ne of amorizaion b n. This domesic deb (b ) is held by households ha can save (b c ) and by he cenral bank (b cb ). The governmen also pays ineres on he share of governmen deb ha is held by consumers, (i )b c n. Then we can wrie he period-by-period governmen budge consrain as p g g = w l + s A d g d g + n where l = pl a + ( p)l h and b = b c + b cb : b b n (i )b c n ; (9) Governmen spending g, which is endogenously deermined by he consrain (9), can be used for public consumpion or invesmen purposes. 2 We disinguish beween he public invesmen ha is a consan share of seady-sae governmen spending, i.e., x gs = s g wih s 2 [; ]; and he public invesmen associaed wih he increase in aid, i.e., x ga = A (g g) wih A 2 [; ]: These invesmens serve o accumulae public capial q following nq = ( g )q + " s x gs + " A x ga ; (2) 9 On revenue-raising capaciies in low-income counries, see Heller e al. (26). 2 We do no model agency and asymmeric informaion problems beween donors and recipiens ha may deermine aid composiion as in Cordella and Dell Ariccia (27). Neiher do we consider he implicaions of aid for insiuional developmen, excep indirecly insofar as his is relaed o he size of he raded goods secor. On hese issues, see e.g. Johnson, Osry, and Subramanian (27).

15 4 where g is he depreciaion rae of public capial, and " s ; " A 2 [; ] measure he e ciencies of he wo ypes of public invesmen. These e ciency parameers " s and " A capure he idea ha less han one dollar of public capial is creaed for each public dollar spen on invesmen. The radiional perpeual invenory mehod infers he sock of public capial from informaion on public invesmen, and assumpions abou depreciaion raes, using equaion (2), wih he criical implici assumpion ha " s = and " A =. However, his assumpion is fraugh, paricularly in developing economies. Wheher because of wase and corrupion, an absence of marke pressures o ensure ha all projecs have he highes possible rae of reurn, or simply misclassi caion of curren spending (e.g. salary paymens o civil servans) as invesmen, a dollar of public invesmen spending may no always yields a full dollar of public capial, as argued by Priche (2). 2 The scal policy quesion of ineres here is how fas o spend he local currency counerpar o aid in ows. We assume ha aid dollars accrue o he scal auhoriy, which hen sells hem o he cenral bank in reurn for a domesic currency deposi. The accumulaion of governmen deposis is described by he following rule, which depends on he increase in aid: d g = dd g + ( d) d g + ( )s A A ; (2) where A and d g are he seady-sae levels of aid and deposis, and d 2 (; ). In his seup, he governmen will always spend he seady sae amoun of aid. However, an increase in aid A may or may no be spen iniially, depending on he policy parameer 2 [; ]. If aid is no spen, i will iniially accumulae as deposis bu will be gradually spen over ime. Boh d and deermine he speed of spending. To close he scal policy side of he model, we assume ha domesic governmen deb is consan: b = b: E. The Cenral Bank In a ypical aid-dependen counry, he canonical aid-relaed moneary policy problem can be described as follows: when he governmen spends he local-currency counerpar o aid in ows, how should he resuling moneary emission be handled? In paricular, how much should be serilized? And should he serilizaion be done hrough he sale of local-currency open-marke operaions or hrough he sale of foreign exchange? To sudy his problem, we inroduce in he model he cenral bank balance shee m m = b cb b cb d g d g + s R R n n n n ; (22) 2 The speci caion in (2) also capures some of he main insighs from he heoreical lieraure ha invesigaes how ine cien and corrup bureaucracies inerac wih he provision of public infrasrucure services and negaively a ec he produciviy of privae capial and growh. See Chakrabory and Dabla-Norris (29) and Sare (2), among ohers. A di eren approach o model ine ciency considers ha governmens can be viewed as producers of (public) goods. Governmens ha produce more of a paricular good while spending less on inpus can be viewed as more e cien han governmens ha produce less oupu and use more inpus. As an applicaion of his approach o esimae he e ciency of governmen expendiure on educaion and healh in Africa, see Gupa and Verhoeven (2).

16 where b cb are he governmen bonds held by he cenral bank and R denoes he foreign currency m value of reserves. The balance shee implies ha changes in money supply, m ; depend on open marke operaions, b cb b cb n ; changes in deposis, d g by assumpion are fully driven by changes in inernaional reserves, s R d g n n ; and changes in ne foreign asses, which R n The cenral bank implemens he following rule for he foreign currency value of reserves: : R = R R + ( R ) R + (!) A A! s ( S S ); (23) where S is he nominal depreciaion of he currency, and R and S are he seady-sae levels of reserves and nominal depreciaion. The persisence parameer R sais es R 2 (; ), while! s measures he degree of commimen o a nominal depreciaion arge. This rule implies ha he accumulaion of reserves is driven by hree separae facors. Firs, he cenral bank always sells he seady-sae value of aid, bu may reac di erenly o changes in he volume of aid. The coe cien! measures he fracion of addiional aid dollars sold on he marke by he cenral bank, i.e., he degree of immediae absorpion ouside of he seady sae. Second, he cenral bank may also follow a xed exchange rae regime by seing! s very high. 22 Finally, while he amoun of reserves may deviae persisenly from is long-run value, we assume ha he cenral bank arges a paricular long-run value of reserves, provided ha! s is no in nie, which may be calibraed o a counry s hisorical average or o some desired level of reserves. Regarding he moneary policy rule, we assume ha open-marke operaions adjus so ha reserve money always grows a he rae g. This capures he fac ha many low-income counries sill arge money, a leas de jure. Noe ha a he seady sae, reserve money grows a he rae g, and oherwise is growh rae is adjused in response o in aion. More speci cally, open-marke operaions imply he following process for b cb b cb b cb = m g n n : + d g d g n s R R n : (24) Therefore in he even ha aid is spen bu no absorbed, open-marke operaions would increase in order o fully serilize he direc moneary injecion ha would follow from incremenal aid in ows. Noe ha because he previously inroduced porfolio adjusmen coss P a are a funcion of privae secor ne foreign asses, cenral bank serilized inervenions will in general maer in his se-up, as we will see below. F. Aggregaion and he Goods Marke Equilibrium Condiions We aggregae across boh ypes of households, so a = pa a + ( p)a h for a = (c ; c N ; c T ; m ; l ; b ; b c ; rm ; ). We focus on a symmeric equilibrium, so we can drop he sub-indices ha disinguish among rms in he producive secor. The Appendix provides a de niion of equilibrium in his model. 22 Depending on he degree of capial mobiliy, he commimen o an exchange rae arge may be limied by he moneary policy rule.

17 6 Here we only sae he goods-marke equilibrium condiions. The equilibrium in he non-raded goods marke is described by: y N = p N D N ; (2) where D N = ' c + x N + x T + G + (p g ) g ; while he marke-clearing condiion for raded goods can be derived by combining he equilibrium condiion (2) and he budge consrains for all agens, including boh ypes of consumers, he governmen, and he cenral bank: A = c T + g T + x T T + x NT + pp a y T rm (i )b {z n + b } CAD b n {z } KAS + R R {z n ; } RA (26) where x T T and x NT correspond o he raded componens of he invesmens in he raded and nonraded secors, respecively. Equaion (26) also summarizes he possible uses of aid: i can nance a higher curren accoun de ci ne of aid (CAD), a capial accoun surplus (KAS), or an accumulaion of reserves (RA). III. Calibraion Our analysis will rely on calibraed numerical simulaions. 23 Because he model is micro-founded, some parameers can be based on microeconomic evidence, such as he e ciency of invesmen. Oher parameers depend on seady-sae raios ha can be deermined from naional income accouns, public and privae secor balance shees and inpu-oupu marices, or can be informed by moreor-less srucural macroeconomeric esimaes, e.g. money demand parameers. Oher parameers describe he policy response o aid or he policy regime in place and can herefore be reaed as free parameers ha are modi ed according o he policy experimen. Some parameers will remain poorly deermined, wheher because daa are unavailable or because he model s simpli caions imply ha an exac empirical counerpar may no exis. For hese parameers calibraion is based parly on sandard values found in he macro lieraure, and parly on desirable properies for he dynamics of he model following he increase in aid such as smooh hump-shaped responses. For his reason and, more generally, as a check on he overall calibraion, sysem properies of he model, such as on he e ecs of aid or public invesmen on growh, are also compared o reduced form macroeconomeric or case-sudy evidence. We calibrae mos of he parameers of he model o he Ugandan economy. Since here are a large number of parameers, we organize he discussion around hree groups: preferences, echnology, and policy. Tables -3 summarize he calibraion or policy reacions we will sudy below. We now brie y discuss he calibraion of some of he parameers ha are crucial for he policy experimens. The preference parameers are presened in Table. Regarding he value for p; he 29 Seadman Survey nds ha 62 percen of Ugandans do no have access o formal or informal nancial services. The ineracion of such large share of hand-o-mouh consumers wih he money argeing 23 The model was simulaed wih he sofware Dynare. See hp://www.cepremap.cnrs.fr/dynare.

18 7 rule resuls in large spikes in he real ineres rae in he baseline scenario ha do no seem plausible. As a resul, a lower share was chosen. Wih respec o he parameer %; which measures he elasiciy of subsiuion beween hours worked in he wo secors, here are no empirical esimaes for developing economies. We se i o, which corresponds o he economeric esimaes provided by Horvah (2). Table. Baseline Calibraion: Preference Parameers Parameers Value Source/Mehod '. Consisen wih Naional Income Accouns.89 Based on Tokarick (29) esimaes of impor demand elasiciies in Uganda 2 Sandard value in lieraure { a.6 Normalizes employmen of savers o a seady sae { h.6 Normalizes employmen of non-savers o a seady sae 2. Sandard value in lieraure # a.999 Help mach Uganda s annual real ineres rae # h.99 Help mach Uganda s real money balances in percen of GDP.8 Based on regression of real money balances on nominal ineres raes and GDP.6 Maches he share of non-raded producion in value added (6 percen) % In line wih Horvah (2). rm.28 Ensures rade de ci equals.2 percen of GDP a.99 Helps mach real ineres raes in Uganda p.67 Financial survey by Seadman Group (29); sysem properies As for echnology parameers presened in Table 2, we have relied on recen developing economy esimaes by Arslanalp e al. (2) on he impac of public capial on growh. These esimaes approximaely imply ha ( j ) j = : for j = N; T: 24 In he experimens below we assume ha he economy has a closed capial accoun, which makes serilizaion policies more e ecive. Consequenly, we choose a very high value for. The parameers of he learning-by-doing exernaliy, v and z ; are in line wih rm-level paneldaa esimaes of he learning-by-exporing lieraure in developing economies. Mengisae and Paillo (24) nd ha he growh rae of oal-facor produciviy of expor-oriened manufacuring rms in Sub-Saharan counries depends on lagged oal facor produciviy. Their esimaes roughly correspond o z = :: Calibraing v is more challenging, as mos of he learning-by-exporing lieraure esimae represenaions in which he curren produciviy of he rm depends on he dichoomous variable of lagged expor saus, which capures wheher he rm expored or no in he previous period. 2 By adoping his approach, mos of he works implicily assume ha here is also an asymmery in he e ec of lagged expor saus on produciviy. Isgu and Fernandes (27), however, ake an alernaive approach and repor esimaes of learning-by-exporing e ecs for Colombian manufacuring rms 24 The lieraure on he link beween public invesmen (capial) and growh seems o be reaching a consensus ha he link is posiive, bu no as big as originally esimaed by works such as Aschauer (989). 2 See for insance Van Biesebroeck (2), among ohers.

19 8 using he lagged raio of expors o oupu. Following heir esimaes, we se v = :: Table 2. Baseline Calibraion: Technology Parameers Parameers Values Source/Mehod Producion and Price Rigidiies T ; N.7 Uganda Inpu-Oupu ables T ; N.33 In line wih Arslanalp e al. (2) v. In line wih esimaes by Isgu and Fernandes (27) z. In line wih esimaes by Mengisae and Paillo (24) T ; N 2 Ensures smooh impulse responses for invesmen n.7 Maches Uganda s annual growh (7 percen) z T Normalizaion z N.4 Ensures he real exchange rae equals one a seady sae N ; T. In line wih Bu (24) 9 Sandard value in lieraure implying prices are sicky for almos one year Disorions and Subsidies $.74 Helps mach Uganda s invesmen share (6 percen) N.9 Eliminaes monopolisic disorion a seady sae Capial Mobiliy Implies he capial accoun is closed b a Normalizaion We model a emporary bu persisen increase in aid such ha, as a resul of he scaling up, aid is on average six percenage poins of GDP higher han is seady-sae value over he following ve years. Noe ha he coe cien A in he process for aid described in (6) resuls in a half life of he shock of slighly more han a year, which implies he aid increase is fron loaded. Finally he value of he seady-sae e ciency " s is based on work by Areso and Hurlin (26). 26 For our baseline calibraion we assume " s = :4. This assumpion, along wih he parameers ha govern he seady-sae invesmen rae, he depreciaion rae, and he parameers of he producion funcion, implies ha he marginal produc of public capial in he seady sae is 3 percen. One migh also calculae he marginal produc of public invesmen a he seady sae, which corresponds o he increase in oupu due o an addiional dollar of public invesmen. Wih our baseline calibraion, his equals 3" s or :2 percen. 26 Areso and Hurlin (26) ake a close look a he relaionship beween dollars spen on cerain speci c caegories of public invesmen and physical capial indicaors and were able o infer some public invesmen e ciency measures, in our sense, for Colombia and Mexico. They nd ha he relaionship beween public invesmen and he change in he capial sock is indeed linear, as assumed in equaion (2), and ha " s has a value of abou.4 for hese wo counries. Ineresingly, hey nd a value of abou. for he Unied Saes. Priche (2) calculaes, using a very di eren mehodology, ha " s equals abou. in many low-income counries, wih subsanial heerogeneiy across counries.

20 9 Table 3. Baseline Calibraion: Policy Parameers and Aid Process Parameers Value Source/Mehod Aid process A.9 Implies a half-life of he shock of abou one year A.49 Maches curren share of aid in GDP ( percen) A.226 Maches a scaling up on average of 6 percenage poins of GDP in years The Governmen.7 Endogenously deermined o clear non-raded goods marke.237 Helps mach he curren share of governmen spending (8 percen of GDP) s.3889 Maches he curren share of public invesmen (7 percen of GDP) A. Policy parameer b c.69 Maches he sock of ousanding domesic governmen deb (4.2 percen) b cb.828 Helps mach real money balances g.2 Broadly in line wih Arslanalp e al. (2) " s.4 In line wih Areso and Hurlin (26) " A.4 In line wih Areso and Hurlin (26) d.9 Policy parameer d g.28 Based on Uganda s Moneary Survey Policy parameer for he experimens The Cenral Bank R.9 Policy parameer R.298 Maches Uganda s sock of reserves (8 percen of GDP)! Policy parameer for he experimens! s Policy parameer for he experimens g.32 Consisen wih Uganda s in aion (6 percen) Consisen wih a Taylor rule wih an in aion coe cien of. The impac of aid-surge-relaed public invesmen on he percenage deviaions of real GDP from is seady sae is deermined by he relaive e ciency " A "s ; and his wha we generally mean by e ciency in his paper. The reason is simple. Consider a change in he calibraion ha increases boh e ciencies by he same amoun. In his case, he given aid surge yields he same percenage GDP deviaions, because here are wo opposie e ecs. The good news is ha he aid surge will build more public capial, because " A is higher. The bad news is ha he higher value of " s means ha he seady-sae capial sock mus be larger, as implied by equaion (2). Bu he percenage change in oupu is proporional o he percenage change in he capial sock. Thus, a larger capial sock implies a smaller percenage increase in capial and hence oupu for he same dollar incremen o aid. As shown in he appendix, hese wo e ecs exacly o se for he Cobb-Douglas producion echnologies of our model This recalibraion of boh e ciency parameers can be undersood in di eren ways. We have in mind he noion ha he analys revises her assessmen of overall e ciency in a given counry, no ha we are comparing wo di eren counries. In he former case, he level of oupu is observable and unchanged. Thus, he level of oal facor produciviy

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