Welfare Gains of Aid Indexation in Small Open Economies

Transcription

1 WP/08/101 Welfare Gains of Aid Indexaion in Small Open Economies Anubha Dhasmana

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3 2008 Inernaional Moneary Fund WP/08/101 IMF Working Paper African Deparmen Welfare Gains of Aid Indexaion in Small Open Economies Prepared by Anubha Dhasmana Auhorized for disribuion by Andrew Berg April 2008 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. Foreign aid flows o poor, aid-dependen economies are highly volaile and pro-cyclical. Shorfalls in aid coincide wih shorfalls in GDP and governmen revenues. This increases he consumpion volailiy in aid dependen counries, hereby causing subsanial welfare losses. This paper finds ha indexing aid flows o exogenous shocks like a change in he erms of rade can significanly improve he welfare of aid-dependen counry by lowering is oupu and consumpion volailiy. Compared o he benchmark specificaion wih sochasic aid flows, indexaion of aid flows o erms of rade shocks can reduce he cos of business cycle flucuaions in he recipien counry by four percen of permanen consumpion. Moreover, use of indexed aid can allow donors o reduce he aid flows by hree percen wihou lowering he level of welfare in he recipien counry. JEL Classificaion Numbers: F30, F32, F34, F35, F37, F41, F42, F43, F47 Keywords: Aid, Volailiy, Welfare, Terms of Trade, Business Cycle. Auhor s Address: adhasmana@imf.org

4 2 Conens Page I. Inroducion...2 II. Primary Commodiy Expors and Price Volailiy...5 III. The Benchmark Model...8 IV. Model Calibraion and Comparaive Saics...13 V. Dynamics...14 VI. Resuls...19 VII. Conclusion...22 Tables 1. Dynamic behavior of Aid Share of he leading primary commodiy expor (97 99) Share of he Top Three Primary Commodiies, ( ) Insabiliy indices of prices of major primary commodiies during Welfare cos under alernaive model specificaions Welfare gains from indexed Aid Welfare gains from indexed Aid Welfare gains from indexed Aid...35 Figures 1. Resource flow as a percenage of GDP Seady sae values Sensiiviy analysis Saionary capial disribuion...33 References References...36

5 3 I. INTRODUCTION Aid flows o poor, aid dependen counries are highly volaile and pro-cyclical 1. Table 1. gives an idea of he volailiy (relaive o he volailiy of governmen revenues) and procyclicaliy of aid flows for a group of 72 aid-dependen counries. The firs row gives he measure of relaive volailiy of aid flows for he period For he enire sample, he average of his measure is close o 4 which implies ha, on an average, aid flows o hese counries are four imes more volaile han he fiscal revenues of he governmen (where boh aid flows and revenues are normalized by he level of GDP). For counries wih he average raio of aid o revenue greaer han 10 percen over he enire ime period, relaive aid volailiy is 4.96 and i increases furher o 7.4 in counries where average raio of aid o revenue is above 50 percen. Thus, aid flows are vasly more volaile han governmen revenues and he relaive volailiy of aid flows increases wih he level of aid dependency of he recipien counry. The second row gives he average correlaion coefficien beween derended aid and revenue series. The average correlaion coefficien is posiive for all he groups, wih he size of he correlaion coefficien increasing wih he raio of aid o governmen revenues. Given ha hese counries have lile or no access o inernaional capial markes and ha hey are dependen on one or wo primary commodiies wih highly volaile prices for heir expor revenues, volailiy and pro-cyclicaliy of aid flows have imporan implicaions for heir growh and welfare. On he oher hand, adjusing aid flows o cushion he exogenous shocks faced by hese counries has he poenial o reduce heir income and consumpion volailiy and hence improve heir welfare. This paper sudies he poenial for innovaive aid indexaion schemes o reduce he macroeconomic volailiy and he resulan welfare loss in aid-dependen counries. To give a brief overview of he model and he key resuls, I sudy he problem of an aiddependen counry using a hree secor, dynamic general equilibrium model of a small open economy (SOE hereafer) wih no access o inernaional capial markes. The SOE faces produciviy and erms of rade shocks and receives an exogenous sochasic ransfer of radable goods known as aid every period. As observed in he daa, aid flows are assumed o be more volaile han he oupu and mildly pro-cyclical. The SOE can no borrow abroad o smooh consumpion bu i can inves in he domesic capial sock. The represenaive household engages in precauionary saving hrough accumulaion of capial sock. However, capial is no a perfec means of consumpion smoohing in he face of exogenous shocks as i is subjec o diminishing marginal produc which implies ha as he SOE builds up is capial sock o buffer iself agains exogenous shocks, reurns o he incremenal capial sock 1 See Bulir and Hamann (2003).

6 4 decline a he margin, making i coslier for he SOE o proec is income agains exogenous decline by accumulaing more and more capial. In his se-up, presence of capial adjusmen coss increases he welfare cos of aid volailiy subsanially (abou four imes) 2. Indexing aid flows o emporary erms of rade shocks, while keeping he average level of aid consan, significanly reduces he volailiy of disposable income and consumpion and hence, lowers he cos of business cycle flucuaions, in he aid recipien counry. Compared o he benchmark case wih sochasic aid flows, he reducion in he cos of business cycle flucuaions due o he use of indexed aid is abou four percen of he permanen consumpion. Alernaively, compared o he benchmark, he same level of welfare can be provided o he recipien counry wih hree percen less aid by indexing aid o erms of rade shocks. These resuls are noeworhy for several reasons. Firs, in he absence of access o inernaional financial markes, aid has become he main source of foreign capial for many of hese counries, replacing official deb. As can be seen from Figure 1, since he mid 1990s real resource ransfers on deb (as a percenage of GDP) have been close o zero or negaive, wih ourigh grans gaining in relaive imporance 3. Aid is also a major source of disposable income for hese counries (accouning for 12.5 percen of disposable income on average in Africa). Highly volaile and unreliable aid flows can herefore deer invesmen and make fiscal planning difficul in he aid-dependen counries, affecing heir growh adversely. Second, pro-cyclical aid flows imply ha poor counries are forced o raise axes or curb heir expendiures a he ime when hese economies are going hrough recession, hereby dampening heir growh even furher 4. Pro-cyclicaliy of aid flows by iself may no be compleely undesirable and could, in fac, be an opimal oucome in he presence of asymmeric informaion and divergen preferences amongs benevolen donor and recipien counries (Pallage and Robe, 2003). However here is no empirical evidence o sugges ha his is indeed he case. On he conrary, he evidence shows ha aid flows are dicaed by poliical and sraegic consideraions much more han by economic prudence and policy performance of he recipiens (Alesina and Dollar, 2003). Finally, hese resuls show ha in he presence of erms of rade shocks and capial adjusmen coss he direc impac of aid volailiy on he welfare of aid-dependen counries hrough higher consumpion volailiy can be subsanial and should herefore be aken in o accoun while designing aid programs. 2 Welfare cos of aid volailiy is defined as he percenage increase in consumpion a all daes ha is required o compensae he represenaive household for he resuling higher volailiy in consumpion. 3 Ne resource ransfers on deb are defined as disbursemens of loans o he developing counries less deb service paymens and deb amorizaion. 4 Gemmell and McGillivray (1998) record ha shorfalls in aid are ofen followed by reducions in governmen spending indicaing ha he recipien counries are no able o make up for he reducion in aid flows by higher revenues.

7 5 My paper is closely relaed o Arellano e.al (2005) who examine he effecs of aid volailiy on consumpion, invesmen, and welfare in a wo-secor general equilibrium model and find ha aid volailiy can resul in subsanial welfare losses for a counry wih limied access o inernaional capial markes (hough no large enough o compleely offse he effec of aid iself). However, heir analysis ignores wo imporan facors ha are likely o affec he welfare coss of aid volailiy in poor counries volailiy in he relaive price of heir main expors and capial adjusmen coss. This paper akes he analysis of Arellano e.al. (2005) a sep furher by looking a he welfare cos of aid volailiy in he presence of erms of rade shocks and capial adjusmen coss. I hen explores he poenial of using aid flows o provide insurance o SOE agains emporary erms of rade shocks by indexing aid flows o exogenous erms of rade shocks 5. II. PRIMARY COMMODITY EXPORTS AND PRICE VOLATILITY The problem of aid volailiy in poor counries is compounded by he fac ha he majoriy of hese counries are heavily dependen on one or wo primary commodiies for heir expor evenues and he prices of hose primary commodiies are highly volaile. As a resul heir expor revenues, which are he only oher source of financing radable consumpion and purchase of impored inpus besides aid, are very volaile oo. Tables 2 and 3 give an idea of he exen of his primary expor dependence. Table 2 liss average shares of he main primary commodiy expor in oal expors and GDP of he counry beween for 17 Highly Indebed Poor Counries (HIPC s), which are also major recipiens of aid. Table 3 does he same for he op hree primary commodiy expors. Of he 17 counries under consideraion, 14 have more han 20 percen of heir expor revenues coming from a single commodiy while 15 counries earn more han 30 percen of heir expor revenue from jus hree commodiies. For 16 ou of he 17 counries, expor revenues from he op 3 commodiies consiue more han 5 percen of heir oal GDP. To give an idea of he relaive price volailiy of he key primary commodiies expored by hese counries I calculae insabiliy indices for individual commodiies over he period The insabiliy index for each commodiy is defined as he percenage sandard deviaion of he naural logarihm of is price (which is deflaed by The Economis s Manufacured Uni Value Index 6 o ge he real value) around he Hodrick-Presco filered 5 The idea of using concessional resource flows as an insurance mechanism has been discussed before in several papers. Saring from Bailey (1983), Shiller (1993), Borenszein and Mauro (2004) and Tabova (2005) sugges indexing concessional deb service of HIPCs o some measure of counries abiliy o pay such as, GDP, consumpion or price of heir primary expors. Berube e.al., 2004 sugges using aid flows o insure developing counries agains adverse shocks. 6 M.V.I is calculaed as he nominal indusrial commodiy price index (dollar based, weighed by he value of developed counry impors), deflaed by he G.D.P deflaor of he US. (coninued )

8 6 rend. The indices hus calculaed give an idea of he volailiy of primary commodiy expor prices relaive o he volailiy of manufacured goods impored by hese counries. Resuls from his exercise are presened in Table 4. The price for sugar seems o be he mos volaile (average annual percenage deviaion of around 40 percen) followed by he price of cashew nus. The average annual percenage deviaion for all he primary commodiy prices is around 20 percen wih 10 ou of he 14 commodiies having volailiy above 15 percen. Given ha he average share of he leading primary commodiy in oal expors is abou 40 percen for counries in he sample, commodiy price volailiy on is own would resul in an annual volailiy of 4 o 16 percen (depending upon he commodiy in quesion) in expor revenues. Thus, flucuaions in commodiy prices are an imporan source of macroeconomic volailiy in hese developing counries. This volailiy in primary commodiy prices is refleced in he volaile erms of rade for developing counries (Bidrakoa and Crucini, 2000). In he discussion ha follows I use he words erms of rade o denoe he Ne Barer Terms of Trade which measures he number of unis of expors ha can be exchanged for a uni of impors. A. Case Sudy: Coon In he face of such volaile commodiy expor prices and revenues one obvious quesion o ask agains exogenous income shocks such as adverse erms of rade. I look a he case of Burkina Faso o examine his poin. The choice of Burkina Faso was dicaed by he availabiliy of daa and he naure of is primary expor coon. I is a small open economy dependen on primary commodiy expors, wih coon expors accouning for 65 of is oal merchandise expors and nine percen of is oal GDP. I s also a price aker in he world marke for coon. The able below describes some imporan feaures of he relaionship beween aid flows, governmen revenues (excluding O.D.A.) and world coon prices for Burkina Faso. As we can see from he firs row, aid flows are abou five imes more volaile han he governmen revenues in line wih he overall resuls for aid dependen economies. Second row gives he rank correlaion coefficien beween aid and governmen revenue. Again, in line wih he overall resuls his correlaion coefficien is posiive. Nex wo rows give he correlaion beween world coon price on he one hand and aid and governmen revenue on he oher. Governmen revenue is posiively correlaed wih he level of coon prices. This reflecs he fac ha for many developing counry governmens, ax on commodiy expors is a major source of revenue. As he price of heir major commodiy expor goes down so does he revenue, and vice versa. Clearly, if aid flows o Burkina Faso

9 7 were o provide her wih some cushion agains exogenous shocks o income, one would expec hem o be negaively correlaed wih he price of coon. On he conrary, I find ha aid flows o Burkina Faso are posiively correlaed wih he world price of coon. In fac, for all he coon exporing counries ha have he daa (Benin, Burkina Faso, Burundi, Chad and Mali), I find his correlaion o be posiive, wih he average correlaion coefficien being equal o 0.3. Case Sudy: Burkina Faso 7 Volailiy and Correlaions Value Relaive Volailiy of AID-Revenue 4.92 Correlaion Coefficien for Revenue-AID 0.12 Correlaion Coefficien for Revenue-Price 0.33 Correlaion Coefficien for AID-Price 0.18 Anoher way o look a he same issue is o check wheher aid flows have hisorically responded o negaive shocks o income of he recipiens. All ha is required for aid o ac as an insurance is for i o go up a he ime of he decline in he recipien s income. Looking a he five coon exporers over he period I find ha ou of he fory-nine cases of decline in GDP by five percen or more, only seveneen were accompanied by an equivalen increase in aid flows of 5 percen or more. Furher, ou of he fify-nine cases of reducion in GDP by one percen or more, only weny-nine cases were accompanied by an increase in aid flows, he remaining hiry cases saw a reducion in aid flows. In shor, a decline in GDP was almos as likely o be accompanied by an increase in aid as by a decline in aid. Empirical evidence presened in he above paragraphs suggess ha he problem of aid volailiy combined wih volaile erms of rade and lack of expor diversificaion are crucial facors underlying he macroeconomic insabiliy in a large number of developing counries. Since mos developing counries have no conrol over he price of heir main expors and impors, i is poenially useful o look a he problem of aid volailiy in conjuncion wih he problem of erms of rade volailiy as is done in his. The res of he paper lays ou he model and is main resuls and policy conclusions in deail. The paper is organized as follows: Secion 3 describes he benchmark model and he alernaive schemes for indexing aid flows. Secion 3 describes he soluion procedure. Secion 4 presens some comparaive saic resuls. Secion 5 presens he sochasic model. Secion 6 presens he resuls and secion 7 concludes. 7 As in Table 1. boh aid flows and revenues are expressed as a percenage of GDP.

10 8 III. THE BENCHMARK MODEL The model used in his paper is based on he SOE real business cycle model developed by Mendoza (1995). The economy is inhabied by an infiniely lived represenaive household ha derives uiliy from consuming hree differen ypes of goods: exporable goods, imporable goods and non-radable goods. The household sells is labor o firms and invess in capial in reurn for wages and renal income, respecively. Firms produce exporable and non-radable goods. Capial is secor specific and is he only asse available for invesing savings in he economy. Toal amoun of labor in he economy is normalized o one and i is freely subsiuable across secors. To model he behavior of aid in he economy I follow he mehod used in Arellano e.al (2005). Besides domesic producion, he economy ges a sochasic ransfer of foreign resources labeled as aid in every period. There are hree sources of uncerainy in he economy, produciviy shocks, aid shocks and erms of rade shocks. These shocks moivae raional individuals o adjus heir savings and invesmen in order o smooh consumpion and o adjus secorial employmen in response o changes in real wage rae. In he following secions I describe he model in deail. Unlike Mendoza (1995), he economy in my paper does no have access o any oher foreign asse. Impors are used as numeraire good hroughou he paper. A. Household The infiniely lived represenaive household in he economy maximizes is expeced lifeime uiliy which depends on he aggregae consumpion level C : U = E 0 = 0 β ( ) 1 σ C 1 σ where σ is he coefficien of risk aversion and β denoes he subjecive discoun facor. The aggregae consumpion funcion C is of consan elasiciy of subsiuion form given by: 1 T μ N μ [ ϖ ( C ) + ( 1 ϖ )( ) ] μ C (III-1) C = (III-2) T EX ς IM Where ( ) ( ) 1 C = C C is he composie radable good, IM C ς EX C is he consumpion of exporable goods, is he consumpion of imporable goods and ς is he share of exporable goods in radable goods expendiure. The household rens capial and provides labor o he firms. In reurn i earns renal income r and wage w. Besides wage and renal

11 9 income, i receive a sochasic ransfer of radable goods from abroad. The price of expors is exogenously given o he SOE. The overall resource consrain of he household is herefore: p C + p C + C = w + rk + AID s (III-3) EX EX N N IM where s is he household saving, k is he amoun of capial sock, EX p is he sochasic erms of rade (relaive price of expor in erms of impors) which is subjec o exogenous shocks. While hese shocks migh be shor lived for some counries, hey may have permanen effecs in case of oher counries. In he discussion ha follows, I assume ha shocks o he erms of rade are persisen bu emporary, i.e., heir effec dies down afer a N finie number of ime periods. p is he price of non-radable goods, also expressed in erms of impors, and AID is he exogenous sochasic ransfer of radable good. The household can inves is savings only in he domesic capial sock as he SOE lacks access o inernaional capial markes. B. Firms Firms produce non-radable and exporable goods using capial and labor services (hey do no produce imporable goods bu he exporable goods can, in principle, also be impored). Boh he secors face Cobb-Douglas producion echnology η ( ) ( ) 1 Y = A k L (III-4) N N N η α ( ) ( ) 1 Y = A k L (III-5) EX EX EX where A is he common produciviy shock affecing boh he non-radable and he exporable secor, and α and η are shares of capial in exporable and non-radable secors respecively. Firms and households have he same informaion se; boh know he disribuion of shocks. Labor is perfecly mobile across secors. The oal amoun of labor is divided beween he wo secors as follows N EX L + L = 1 Capial, however, is assumed o be somewha secor-specific implying ha shifing capial from one secor o anoher involves a ransformaion cos which is capured by he facor ransformaion curve given below (see Mendoza and Urine, 2000): α (III-6)

12 10 (, ) k k k k k υ υ EX N EX N = κ = + Where, k is he aggregae capial sock in he economy, secor, k is he sock of capial in non-radable secor and 1/ ( 1 υ ) N 1 υ (III-7) EX k is he capial used in exporable + is he elasiciy of EX N subsiuion beween k and k. Perfecly homogenous capial is he special case where υ = 1. The assumpion of secor specific capial is in line wih he specific-facors models developed in he rade lieraure and i allows us o replicae he large changes in he relaive price of non-radable goods resuling from changes in he inflow of aid, as winessed in he daa. Firms face quadraic capial adjusmen coss. The assumpion of quadraic adjusmen cos is necessary o mach he volailiy of invesmen observed in he daa wih ha produced by he model. The capial accumulaion equaion is herefore given by: φ k = k + i k k 2 ( 1 δ ) ( ) (III-8) where i is aggregae invesmen and φ is he adjusmen cos parameer. Invesmen in his model akes place only using impored goods which can be purchased eiher by using aid inflows or by using expor revenues. This is a simplifying assumpion ha capures he fac ha impored capial goods and inermediae inpus are imporan ingrediens in he developing counry's producion process ha can no be subsiued by domesic capial sock (Lee, 1994). In fac, capial goods and inermediae inpus form he majoriy of impors for hese counries. This assumpion gives us he following equaion : ( ) i = p Y C + AID C (III-9) EX EX EX IM Thus, invesmen ges affeced by flucuaions in boh, he relaive price of expors and he aid flows. Marke clearing condiions in he non radable and radable secors ensure ha saving is equal o invesmen in his SOE. The marke clearing condiions for he wo secors are: C N = Y (III-10) N p C + p C + C = w + rk + AID s (III-11) EX EX N N IM In equilibrium, marginal produciviy of boh he facors are equalized across secors. Firs order opimizaion condiions give us he following equaions:

13 11 ( 1 ) EX ( EX ) ( EX α ) ( 1 η) N ( N ) ( N ) α α η η w = p A k L = p A k L (III-12) r ( ) ( ) ( ) ( ) EX EX EX α 1 N N η 1 / η / N p EX N EX N κ1 k, k κ2 k, k αp A k L A k L = = (III-13) Equaions (III-12) and (III-13) say ha he wage rae of labor is equal o he marginal produc of labor in he wo secors and similarly he renal rae of capial is equal o he marginal produc of capial in he wo secors. Combining he firs order opimizaion condiions of he household and firms we ge he following iner-emporal Euler equaion: Here ( / ) (, ) EX EX EX α 1 σ σ C C α p 1 A k L + = β E + 1 δ C C EX N p p + 1 κ1 k k C p is he CES price index for aggregae consumpion: ς ( ) ( 1 ς ( ) ( ) ) ς μ/1 ( + μ) μ/1 ( + μ) p = ως 1 ς p + 1 ϖ p (( ) ) C EX N ( 1 + μ )/ μ (III-14) (III-15) Equaion (III-14) equalizes he marginal cos of sacrificing curren consumpion wih he marginal benefi of allocaing he resuling exra savings ino he aggregae capial. Equaion (III-15) is a funcion of elasiciy s of subsiuion, he erms of rade of non-radable goods N p. C. The Seady Sae EX p as well as he price The following paragraphs describe he seady sae of his economy. Profi maximizaion by firms implies ha in he equilibrium, wage rae equals he marginal produc of labor and renal rae equals he marginal produc of capial in he wo secors. Since capial is secorspecific, he effecive rae of reurn in each secor incorporaes he degree of facor subsiuabiliy beween he wo secors given by he derivaive of κ wih respec o he secorial capial. α ( ) ( ) κ η ( ) ( ) EX EX α 1 N N 1 k / L η k / L N p EX N EX N 1 k, k κ2 k, k = (III-16) ( 1 )( EX / EX α α k L ) p N ( 1 η)( k N / L N ) = (III-17) η

14 12 The iner-emporal equilibrium condiion implies ha he seady sae reurn on capial sock, which is he marginal produc of capial ne of depreciaion, is equal o he discoun facor β. This can be wrien as: EX EX α 1 1 α ( k / L ) = (III-18) EX N β κ1 ( k, k ) Uiliy maximizaion by consumers gives us a se of firs order condiions which, afer sligh algebraic manipulaion, can be rewrien as follows: ς C 1 ς C IM EX = 1 (III-19) p N = ϖ N μ 1 ( 1 ϖ )( C ) (( ) ( ) ( ) μ 1 EX IM 1 EX IM C C ) ( 1 ς)( C ) ( C ) ς ς ς ς (III-20) Equaion (III-19) equaes he marginal rae of subsiuion beween imporable and exporable goods o heir relaive price or he erms of rade, which we assume o be equal o 1 in he seady sae for simpliciy. Equaion (III-20), similarly, equaes he marginal rae of subsiuion beween non-radable and imporable goods wih he relaive price of nonradable goods in erms of imporable goods. Goods marke clearing condiions are given by he following equaions: N Nη N ( 1 η ) C = k L (III-21) α EX ( 1 α ) + = + (III-22) IM EX EX C C k L AID i Consumpion of he non-radable good is equal o is oupu in every period reflecing he assumpion ha invesmen and saving in he economy can only ake place in erms of radable goods. Toal expendiure on radable consumpion is equal o exporable oupu plus aid flows less he invesmen in domesic capial. Seady sae invesmen is equal o he seady sae capial sock imes he rae of depreciaion. i = δ k (III-23) Equaions (III-24) and (III-29) give he inpu marke clearing condiions. ( EX N, ) k = κ k k (III-24)

15 13 L N EX + L = 1 (III-25) IV. MODEL CALIBRATION AND COMPARATIVE STATICS Parameers of he baseline specificaion are chosen o mimic some of he characerisics of poor aid-dependen counries or aken from oher developing counry business cycle sudies. The model is hen solved numerically, using value funcion ieraion. The elasiciy of subsiuion beween exporable and non-radable consumpion, 1/ ( 1+ μ ), is which is equal o he GMM esimae from he panel sudy of 13 developing counries by Osry and Reinhar (1992). This deermines he responsiveness of non-radable consumpion o relaive price (real exchange rae) changes. Share of expors in radable consumpion ( ς ) is se equal o 0.15, same as in he developing counry benchmark in Mendoza (1995). The value of he risk aversion coefficien ( σ ) has an imporan bearing on he measure of welfare cos of aid and consumpion volailiy and hence on he magniude of gains from aid indexaion. I deermines he ease wih which consumers can rade curren consumpion for fuure consumpion: he smaller he risk aversion coefficien, he greaer he ease of iner-emporal subsiuion of consumpion and hence he smaller he welfare cos of consumpion volailiy due o exogenous shocks. In he real business cycle as well as he consumpion lieraure, he value of his parameer is widely believed o lie beween 2 and 5. I herefore use wo differen values of his parameer in he simulaions and 5. The firs value is he GMM esimae in Osry and Reinhar (1992) and he second value is he one esimaed by Reinhar and Vegh (1995). I presen boh ses of resuls in he paper. The non-radable secor is assumed o be more capial inensive han he exporable secor which is in line wih oher developing counry sudies such as Mendoza (1995) and Arellano e.al. (2003). This reflecs he fac ha for hese developing counries producion of primary agriculural commodiies (which are heir key expors) such as sugar involves relaively large amouns of labor and lile capial while opposie is rue for heir non-radable goods producion which mainly includes physical and social infrasrucure. Capial shares in exporable and non-radable secors, α and η, are herefore se equal o 0.3 and 0.4 respecively. The elasiciy of subsiuion beween capial used in exporable and non-radable secors, 1/ ( 1+ υ ) is se equal o -10, same as in Mendoza and Urine (2000). The rae of depreciaion of capial δ is se equal o 0.09 so ha in seady sae he invesmen rae is se equal o 18 percen of GDP, an average of long-erm invesmen raes aken from he World Economic Oulook. Table 5 liss he parameer values used in he benchmark model. A. Sensiiviy Analysis In his secion I do some sensiiviy analysis o see how seady sae variables change wih differen levels of aid and parameer values. Figure 2 plos he seady sae values of endogenous variables for four differen levels of aid o GDP raio - 0, 1/10, 1/4 and 1/2. More

16 14 aid increases he relaive price of he non radable good (he real exchange rae) lowers he share of labor and capial employed in he exporable secor and lowers he share of exporable oupu in oal GDP. I lowers invesmen as a share of oal income (defined as he sum of GDP and exogenous aid flows) and increases he share of radable goods in oal consumpion. The decline of exporable goods secor as a resul of increased aid reflecs he problem of he Duch` disease whereby increased inflows of foreign resources cause real appreciaion and hence hur he expor producing secor. The share of radable goods consumpion in oal consumpion goes up because aid pushes he relaive price of nonradable goods upwards. This happens because aid increases he availabiliy of radable goods relaive o he availabiliy of he non-radable good. Also, due o he secor specificiy of capial, shifing capial from exporable o non-radable secor pushes up he reurn on capial, and hence raises he relaive price of he good using capial more inensively (i.e. he non-radable good). Lower relaive price of radable goods also explains he increase in heir share in oal consumpion. The reducion in he raio of invesmen o oal income in response o he increase in aid shows ha in he long run a permanen increase in aid will only lead o a permanenly higher level of consumpion wih no change in he level of saving or invesmen. This is because he seady sae capial sock is deermined by he ime preference parameer and he rae of depreciaion and is hus independen of he level of aid. I check he sensiiviy of hese resuls o differen values of capial inensiy and capial subsiuion elasiciy parameers. As can be seen from Figure 3, one key resul he decline in he oupu of exporable goods, remains inac in all he models, while he oher he increase in he relaive price of non-radable goods, remains inac as long as capial is secor specific. Specificiy of capial is necessary for real appreciaion because if capial was perfecly subsiuable hen shifing capial owards he non-radable secor in response o increased supply of radable goods will involve no ransformaion coss. As for he decline in exporable oupu, i occurs even in he absence of real appreciaion since aid, which is a ransfer of radable goods, subsiues for domesic producion of radable goods. The magniude of decline in he raio of capial employed in he exporable secor, in response o an exogenous increase in aid, depends on he elasiciy of subsiuion of capial beween he wo secors. The more secor-specific he capial, he coslier i is o shif capial sock from he exporable o he non-radable secor and hence he smaller is he decline in he share of capial used in he exporable secor. The raio of labor in he exporable secor goes down in all he models wih he size of decline once again deermined by he elasiciy of subsiuion of capial beween he wo secors. Finally, he raio of invesmen o oal income (defined as he sum of domesic oupu and aid ransfers) declines in all he models indicaing ha addiional aid ges consumed insead of being saved. V. DYNAMICS In his secion I describe he properies of he shocks facing he SOE and lay down he soluion procedure for he dynamic model in deail. The benchmark model ses he produciviy, erms of rade and aid shocks o mach he volailiy and persisence of oupu

17 15 and aid flows in he aid-dependen economies. I is assumed ha produciviy shocks affec exporable and non-radable secors equally, wih a sandard deviaion of 4 percen and a firs order auo-correlaion coefficien of 0.4. This seup implies ha 60 percen of any deviaion of produciviy from is mean level dissipaes in each period. Volailiy of aid shocks is se o be five imes he volailiy of produciviy shocks as found by Bulir and Hamann (2003). The correlaion coefficien beween produciviy and aid shocks is se equal o 0.4 o capure he pro-cyclicaliy of aid flows observed in he daa. Terms of rade shocks have a sandard deviaion of 11 percen and persisence of 0.4 (Mendoza, 1995). Seady sae aid o GDP raio is se equal o 12.5 percen for benchmark simulaions. This is equal o he average aid o GDP raio for he seveneen counries lised below. The recursive naure of he problem allows us o rewrie i in he form of a Bellman equaion as follows: s.. (, ) max (, ) β (, ) V k s = U k s + E V k s k + 1 C = k L N Nη N ( 1 η ) α ( ) ( ) ( 1 α ) p C + C + i = p A k L + AID EX EX IM EX EX EX ( ) L + L = 1 and k = κ k, k N EX EX N (V-1) Uiliy in each period depends on he sock of capial, and he sae of naure ( s ) which denoes he se of shocks o produciviy, aid and erms of rade. Solving his equaion under he household s resource consrain gives he opimal pah for capial sock and consumpion. This opimizaion problem does no have an analyical soluion. Hence I use numerical echniques o obain he value funcion and he policy funcion for he problem. Indexaion of aid flows o he erms of rade or GDP inroduces kinks in he household s budge consrain which makes he use of linear approximaion mehods widely used in he RBC lieraure inappropriae. I herefore follow an exac-soluion procedure based on value funcion and ransiion probabiliy ieraions using discree grids o approximae he sae space. A. Indexed Aid As explained earlier, he idea behind indexing aid flows o some macroeconomic indicaor of he recipien counry s income is o provide i (he recipien counry) a cushion agains an exogenous fall in income. Use of such schemes has he poenial o improve he welfare of poor aid recipien counries by reducing heir macroeconomic volailiy. In he following paragraphs I describe hree differen mehods of indexing aid flows in deail and discuss heir pros and cons.

18 16 Terms of Trade Indexed Aid Empirical evidence presened in he beginning of he paper showed ha highly volaile erms of rade are a major cause of macroeconomic insabiliy in developing counries. Increasing aid flows in response o an adverse erms of rade shock so as o cushion he exogenous fall in he income and expor revenue of he SOE can lower his macroeconomic sabiliy. Use of erms of rade for indexing aid flows has several advanages. To lis a couple of hem - few developing counries have significan marke power o affec he prices of heir major expors or impors and so here are no moral hazard problems of he sor which arise when governmens have some conrol over he variable which deermines aid flows. Also, world prices are known wihou any lag and hence a scheme based on such prices would poenially be able o moderae aid flows in a more imely manner as compared o schemes based on oher macroeconomic variables such as GDP or expors, daa for which are subjec o significan lags and frequen revisions. A he same ime, using an index based on erms of rade may no provide complee coverage agains price volailiy because ranspor coss and grade differenials may resul in significan divergence beween he prices a which a counry expors or impors goods and he inernaional prices of hose goods. Furher, quaniy variaion may be as imporan a deerminan of a counry s expor revenue as price variaion and a scheme based on erms of rade alone does no ake ha in o accoun. Finally, reliance on a erms of rade rigger limis applicabiliy of he scheme o counries wih high commodiy concenraion in expors and impors. The firs wo limiaions can be overcome if we index he aid flows o expor revenues insead of erms of rade while he use of a more general macroeconomic indicaor such as consumpion or income growh can allow inclusion of a wider group of counries in he indexing scheme. However, as menioned above, boh hese alernaives involve significan moral hazard risks. The acual choice of he variable for aid indexaion, herefore, involves a rade-off beween he exen of insurance provided agains negaive income shocks and he poenial cos of associaed moral hazard problems. I is herefore useful o compare he poenial welfare gains from using he hree alernaive forms of indexaion. When alking abou providing insurance agains he erms of rade shocks one has o disinguish beween emporary and permanen shocks o he erms of rade. While i migh be worhwhile o ry and smooh over emporary flucuaions in he erms of rade i would be inadvisable o shield developing counries agains secular decline in he relaive price of heir expors. If he laer describes he behavior of he erms of rade facing a paricular counry hen fundamenal shifs in he srucure of producion and expors migh be he only feasible soluion in he long run. Cashin and Paillo (2000) analyze he erms of rade shocks for a group of 42 counries over he period and provide median-unbiased esimaes of heir half life. They find ha ou of he 42 counries in heir sample, 11 have erms of rade shocks ha do no dissipae a all or are permanen. These include Côe d Ivoire, Kenya, Uganda and Zambia. Hence, ou of he 17 counries lised below, hese four are no suiable

19 17 candidaes for insurance schemes rying o sabilize heir income agains erms of rade shocks bu he remaining 13 counries can poenially benefi from such insurance schemes. Deails of he way indexaion of aid flows o he erms of rade works are as follows. A paricular period may be classified as eiher normal (N), adverse (A) or propiious (P) on he basis of a previously agreed upon crierion based on he counry s erms of rade. In his paper he crierion is based on he acual size of he shock in any given period. For he purposes of implemenaion his erms of rade shock can be calculaed as he percenage deviaion from a moving average rend calculaed over las four or five years. If he shock is are less han 0.5 sandard deviaion (hereafer s.d.) in size hen he period is defined as N and aid flows are kep a heir mean level. The use of a normal period defined wihin a band is based on he principle ha any scheme should aim o cope wih only excepional price movemens and no normal price movemens. In he case of a shock lying beween 0.5 s.d. and 1 s.d., he period is denoed as A (P when he shock is posiive) and he aid flows are increased (decreased) by 5 percen. If he shock is larger han 1 s.d. in size, he period is denoed as A * (P * when he shock is posiive) and he aid flows are increased (decreased) by 10 percen. Aid flows under his scheme can herefore be described as follows: 1.1 aid if s 1 s. d aid if -0.5 s. d. s -1 s. d. aid = aid if 0.5 s. d. > s > 0.5 s. d aid if 1 s. d > s 0.5 s. d 0.9 aid if s 1 s. d. (V-2) The choice of one sandard deviaion shock for he ouer limi of he second erms of rade band roughly corresponds o a direc change of 0.5 percen in he GDP. The limi of 0.5 percen of GDP is in urn commensurae wih he I.M.F. s definiion of a large` disaser 8. Translaed ino expor revenues, a one sandard deviaion decline in erms of rade is roughly equal o a direc loss of 3 percen. For he purposes of comparison, I herefore use a cu-off poin of 0.5 percen and 3 percen respecively for GDP and expor indexed aid. Expor-Indexed Aid Expor indexed aid can be seen as a combinaion of a bond and an insurance conrac whose paymens are linked o he value of exporable good oupu in erms of imporable goods. When he value of expors falls (goes up) by more han 3 percen below (above) he seady 8 IMF classifies a disaser as large if i caused a direc damage of a leas 0.5 percen of G.D.P.

20 18 sae level, aid flows o he recipien counry are adjused upwards (downwards), proporionaely. Hence, aid flows o he recipien counry are given by: ( 1 λ ) aid = aid + g (V-3) x EX Where: g EX EX EX EX α EX ( ( ) ( ) ) 1 α Y p A k L EX = max 0, 0.03 Y EX (V-4) aid is he mean level of aid, Y EX is he seady sae level of exporable oupu and g EX is wha I call expors gap - he difference beween he exporable oupu in period and is seady sae level. λ x < 1 is he adjusmen coefficien ha deermines he degree of aid indexaion. The underlying idea behind his indexaion is o sabilize he disposable radable income of he SOE around is long run value. GDP Indexed Aid As in he case of expor-indexed aid, he idea underlying he GDP indexed aid is o adjus aid flows, when he GDP falls below (rises above) is seady sae level by more han a prespecified level (0.5 percen in his case). The GDP indexed aid is herefore given by : ( 1 λ ) aid = aid + g Y Y (V-5) Where: g Y ( Y Y ) = max 0, Y (V-6) Y is he seady sae level of GDP, and Y is he curren level of GDP. Welfare Coss The meric used for he welfare cos in his paper is he CES consumpion. Following Lucas (1987), he welfare cos of consumpion volailiy is defined as he minimum percenage increase in he level of consumpion in every period, needed o render he agen indifferen beween he sochasic consumpion sream and a deerminisic one wih he same mean. In

21 19 hese compuaions, I focus solely on business cycle flucuaions, defined as he cyclical componen of Hodrick-Pressco (HP) filered series. Again, as shown in Lucas (1987), under he assumpions of CRRA uiliy and i.i.d shocks o consumpion, he welfare cos of consumpion volailiy has a closed form soluion ha can be approximaed by: W 1 = σv C 2 ( ) where σ V ( C) is he coefficien of relaive risk aversion and is he variance of he CES consumpion aggregaor around he Hodrick-Presco filered rend. Clearly, he welfare cos of business cycle flucuaions increases proporionaely wih he level of risk aversion and he variance of consumpion. For any given level of risk aversion, a lower level of consumpion volailiy would herefore imply a higher level of welfare ceeris paribus. One cavea in inerpreing he resuls presened below is ha aid volailiy no only changes he volailiy of consumpion, bu also changes he level of consumpion in he long run as a resul of precauionary savings ha enlarge he capial sock. Given my focus on he cos of business cycle flucuaions he welfare calculaions in his paper are solely based on consumpion volailiy, ignoring changes in levels. VI. RESULTS This secion presens he main resuls of he paper along wih some sensiiviy analysis. Firs I compare hree differen specificaions for he benchmark model, looking a heir implicaions for he welfare cos of aid volailiy. For calculaing he cos of aid volailiy, I compare each specificaion o he case wih a consan aid flow (equal o he mean) and produciviy shocks. The firs specificaion has no erms of rade shocks and no capial adjusmen coss. This is similar o he case sudied by Arrelano e.al. (2005) The second specificaion has erms of rade shocks bu no capial adjusmen cos. The hird and final specificaion has boh erms of rade shocks and capial adjusmen coss. Table 6 presens he resuls for he hree specificaions. Looking a he firs row we can see ha he sandard deviaion of consumpion is he lowes for he specificaion wih no erms of rade shocks and capial adjusmen coss and i is he highes in he case when we have boh capial adjusmen cos and erms of rade shocks. While he difference is relaively small for specificaions 1 and 2, i is very large for specificaions 1 and 3. Larger consumpion volailiy ranslaes ino higher welfare losses for he risk averse households, as shown by he second row of Table 6. Compared o he esimaes in Arellano e.al. (2005) he welfare loss of aid volailiy in he presence of erms of rade shocks and capial adjusmen coss are more ha weny imes larger. This shows ha ignoring capial adjusmen coss can lead o subsanial underesimaion of welfare losses due o aid volailiy. As explained in he beginning, he inuiion for his is ha capial adjusmen cos makes domesic capial a less effecive means of consumpion smoohing and hence raises he level of consumpion volailiy which, in urn, ranslaes in o a higher cos of aid volailiy. I herefore choose

22 20 specificaion 3 as he benchmark for compuing he poenial welfare gains from aid indexaion. Nex I look a he impac of he indexaion of aid flows on welfare oucomes of aid. The firs wo rows of Table 7 presen he sandard deviaion and he welfare cos of business cycle flucuaions under he benchmark specificaion and hree differen aid indexaion schemes. Comparing he firs wo columns we find ha indexing aid flows o he erms of rade can reduce he consumpion volailiy in he aid recipien counry by abou en percen. Correspondingly he cos of business cycle flucuaions measured in erms of he compensaing variaion in he CES consumpion is abou four percen less under erms of rade indexed aid. Anoher way o look a he gains from aid-indexaion is o measure he amoun by which donors can reduce he average level of aid flows by indexing hem o he erms of rade in he manner described above. This is equivalen o he reducion in consumpion ha he household would be willing o accep in order o receive he erms of rade indexed aid flows. I calculae his value as he welfare cos above, denominaed in erms of radable goods, as a percenage of mean aid flows. I find ha if aid flows are indexed o erms of rade shocks, donors can reduce aid flows by hree percen wihou reducing he welfare. The nex wo columns show he resuls for GDP and expor indexed aid flows. In boh cases he volailiy of consumpion and he welfare cos of business cycle flucuaions is lower han he benchmark case. Compared o he use of erms of rade, he use of GDP or expors for indexing aid provides slighly greaer reducion in he cos of business cycle flucuaions as i provides a more direc cushion agains an exogenous fall in income (or expor revenues) and hence a greaer degree of insurance. We can undersand his beer by looking a he correlaion beween oupu and aid flows under hese differen specificaions. Under he benchmark specificaion, oupu and aid flows are mildly posiively correlaed as observed in he daa, implying ha, insead of providing cushion agains income shocks aid flows acually conribue o he volailiy of oupu and consumpion. Indexing aid flows o erms of rade shocks makes aid flows couner-cyclical since now aid flows are auomaically adjused upwards in response o a decline in income resuling from an adverse erms of rade shock, hereby miigaing some of he impac of adverse income shock on consumpion and welfare. Under GDP and expor indexed aid his adjusmen is direcly linked o he level of income and expor revenues respecively. Thus any reducion in income (expors) due o produciviy or erms of rade shocks, evokes a response in erms of increased aid inflows. As a resul we ge aid flows ha are more srongly couner-cyclical as compared o he previous case wih erms of rade indexaion. However, overall he gains in welfare are of same order of magniude in he hree cases. Invesmen and oupu are less volaile under models wih aid indexaion han under he benchmark case. Indexaion of aid flows sabilizes he oal amoun of disposable.radable.

23 21 income of he SOE and hus reduces he volailiy of invesmen which, by assumpion, can only be done by using radable goods. Less volaile invesmen in urn leads o less volaile oupu. The insurance agains an exogenous fall in income provided by aid indexaion schemes reduces he need for precauionary capial accumulaion and hus leads o a smaller long run capial o GDP raio, as recorded in he sixh row of Table 7. Figure 4 shows he saionary or long run disribuion of he capial sock for he four specificaions. We can see ha he long run disribuion of capial sock shifs o he lef when aid is indexed o income shocks, indicaing a decline in he precauionary capial accumulaion. Correspondingly, he long run invesmen o GDP raio is also lower wih indexaion of aid han wihou i. The long run consumpion o GDP raio is higher wih aid indexaion han wihou i. This reflecs he fac ha wih insurance he represenaive household devoes a greaer proporion of is oupu o consumpion han o saving and invesmen for consumpion smoohing. The share of exporable goods in he GDP falls in he presence of aid indexaion when compared wih he benchmark case. This reflecs he assumpion ha invesmen in he SOE can only be done by using radable goods. Insurance hrough aid indexaion reduces he level of long run invesmen and hence he demand for radable goods. Reducion in he demand for radable goods resuls in an increase in he relaive price of non-radable goods promping an increase in he share of labor and capial employed in he non radable secor. This in urn reduces he share of exporable oupu in he GDP. To check he robusness of my resuls I do a couple of sensiiviy ess on he benchmark model. The firs es involves using a smaller coefficien of risk aversion (equal o 2.61). Table 8 presens he resuls from his experimen. A lower coefficien of risk aversion implies a smaller welfare loss for any given level of consumpion volailiy. This can be seen by comparing he second rows of Table 8 and Table 7. While he level of consumpion volailiy is roughly he same as before, he welfare loss under he benchmark case is now abou 2 percen (half he previous size). Correspondingly, he gains from indexing aid flows are also smaller bu roughly of he same magniude for all hree specificaions. In all oher aspecs such as correlaions and raios beween key macroeconomic variables, here is no significan change from he benchmark case. On he whole, gains form using indexed aid are sill subsanial, hough no as large as before. The second experimen involves doubling he average level of aid flows. Since several policy makers have emphasized he need for doubling he aid flows o poor counries in order o achieve he Millennium Developmen Goals, i would be ineresing o see he impac of such a policy in a dynamic framework. Comparing he resuls in Tables 9 and 7 we find ha for all specificaions, he volailiy of consumpion and he welfare cos of business cycles as a percenage of permanen consumpion remain relaively unchanged when aid flows are doubled. Indexing aid flows sill provides subsanial welfare gains and, since a permanen

24 22 increase in aid leads o a permanen increase in he level of consumpion, he gains in absolue erms are poenially larger. The raio of exporable oupu o GDP falls and he relaive price of non radable goods rises wih an increase in he average level of aid flows under all specificaions. Thus, he phenomenon of.duch disease. carries over from he saic model presened in secion 4 o he dynamic model. Consumpion o GDP raio goes up in response o increased aid flows reflecing he fac ha a permanen increase in aid flows raises he level of consumpion permanenly. VII. CONCLUSION Volailiy and pro-cyclicaliy of aid flows resuls in subsanial welfare losses for aiddependen economies lacking access o inernaional capial markes. Welfare coss of aid volailiy are significanly higher in he presence of capial adjusmen cos and erms of rade shocks. Rearranging aid flows so as o insure aid-dependen economies agains exogenous erms of rade shocks can subsanially improve welfare by lowering he consumpion volailiy in hese counries. For reasonable values of he risk aversion coefficien, gains in welfare are beween 2 o 4 percen of permanen consumpion. Alernaively, donors can reduce he average level of aid by 1.5 o 3 percen wihou lowering he welfare of he recipien counry, by indexing aid o exogenous shocks. The model used in his paper is simplified in several respecs. I does no ake ino accoun he condiionaliy and fungibiliy of aid flows. I also ignores he absorpion capaciy consrains and produciviy spillover associaed wih he expansion of he exporable secor. I assumes a simplified consumpion behavior, wih a represenaive household maximizing an iner-emporal uiliy funcion characerized by consan relaive risk aversion. Mos of hese facors are however likely o increase he measured welfare gain from indexing and hence my calculaions of welfare gains in he paper can be regarded as a lower bound for he poenial gains from indexing. To sum up, while donor counries move owards increasing he aid flows o poor counries in order o achieve he millennium developmen goals, i is imporan o ensure effeciveness of hese increased flows in raising welfare. One aspec of ha should be designing aid flow srucures ha promoe growh and minimize volailiy.