Aid, Policies, and Growh By Craig Burnside and David Dollar APPENDIX ON THE NEOCLASSICAL MODEL Here we use a simple neoclassical growh model o moivae he form of our empirical growh equaion. Our inenion in doing his is o provide some examples, hough here migh be many more, of models in which he relaionship beween aid and growh resembles he one we esimae in our paper. The neoclassical model we discuss is one in which aid is viewed simply as a lump-sum ransfer from abroad, and here are no sraegic ineracions beween governmens ha need concern us. Laer, we discuss how sensiive he predicions of he neoclassical model would be o he inroducion of sraegic behavior on he par of policy-makers. A series of ineresing experimens can be performed in he conex of a perfec foresigh, one-secor, neoclassical model. We assume ha here is a single good over which households have isoelasic preferences, once hey have saisfied a subsisence level of consumpion. 1 Assuming households are infiniely lived, lifeime uiliy is given by = β ( C C) 1 γ 1 γ 1, where C represens ime- household consumpion, < β < 1 is he discoun facor, γ > is he coefficien of relaive risk aversion and C is a subsisence level of household consumpion. For simpliciy we assume ha each household operaes is own echnology using is beginning of period- capial,, and a single uni of labor which is supplied The World Bank, Washingon DC 2433. Views expressed are hose of he auhors and do no necessarily represen official opinions of he World Bank. 1 As Lawrence J. Chrisiano (1989) and Sergio Rebelo (1992) have argued, including a subsisence level of consumpion in he specificaion of preferences wihin a neoclassical model is a useful way of explaining he posiive empirical relaionship beween income levels and savings raes. 1
inelasically. The producion funcion is assumed o be given by and < θ 1. θ Y = A, wih A > Ne household income is axed on he margin a he rae τ, and households receive lump-sum ransfers from he governmen given by T. Given ha we assume ha here is no inernaional privae capial mobiliy, he household budge consrain is ( τ )( Y ) T, C + I δ δ + 1 where I is ime- invesmen. 2 Capial evolves according o ( ) = + + 1 1 δ I, where < δ < 1. The governmen is assumed o make consumpion purchases G. For simpliciy we have assumed ha hese governmen purchases do no ener ino he uiliy of privae households. If we changed his assumpion, o allow governmen purchases o have a posiive impac on uiliy, i would change some of our conclusions, hough no necessarily hose regarding he impac of foreign aid on growh. We assume ha governmen purchases are financed by axes ne of ransfers as well as by foreign aid. For he purposes of his secion, we assume ha ime- foreign aid is received in he form of a lump-sum ransfer from abroad, F. 3 If we exclude he possibiliy of boh domesic borrowing and prining money, he governmen s flow budge consrain is given by ( Y δ ) T F. G τ + The economy as a whole, herefore, has he resource consrain C + I + G Y + F. I is worh noing ha boh in he model, and in he conex of acual daa, an injecion of foreign aid does no show up insanly as an increase in GDP, and, herefore, GDP growh. In boh he model and acual economies, assuming ha producion akes place on he echnological fronier, GDP depends only on domesic facors of producion and he 2 Sricly speaking he budge consrain should allow for borrowing and lending beween households. However, allowing for his does no change any implicaions of he model for aggregae behavior, since we are assuming ha all households are idenical. 3 An alernaive, bu equivalen, assumpion would be ha he governmen can use inernaional capial markes o conver he gran componen of any loan ino an immediae capial flow. 2
sae of echnology. Assuming labor supply is unaffeced, aid only affecs GDP when i is used o augmen he sock of capial. If i is consumed, here is an increase in GNP inclusive of ransfers, bu no GDP. If some fracion of i is invesed, hen aid causes an increase in capial, and consequenly domesic oupu. We consider several special cases of he model. Firs, suppose ha θ = 1 and ha C =, so ha reurns o capial are consan and subsisence consumpion plays no role in he model. Under hese circumsances i is sraighforward o show ha consumers will choose o have consan consumpion growh given by ~ where R = ( 1 τ )( A δ ) + 1 where R = A δ + 1. C C + 1 = g = ~ ( ) 1 / γ βr,. The iniial level of consumpion is given by R g C = ( R g) + R ( F G ), R So suppose we consider wo economies, one in which F G =, for all, while = = in he oher G = for all, F = for > and F.4 In he firs economy, which receives no aid, C ( R g), C ( R g) + ( R g) F / R > = while in he second economy, which receives aid a ime =. Wha his ells us is ha when he inflow of aid akes place, par of i, ( R g) F / R invesmen., is consumed. The res of i, gf / R, is addiional We can also show ha in he firs economy he growh rae of GDP is consan and equal o g in every period. However, in he second economy, growh beween period and period 1 is given by g + ( ga/ R )( F Y ) insanly o he rae g. /, while growh afer ha reurns I is ineresing o noe ha he impac of aid on he growh rae of oupu depends no only on he size of he injecion relaive o GDP, F /Y, bu also on he level of 4 Boh economies are ones in which axes levied on income are rebaed, in full, hrough lump-sum ransfers o households. 3
disorionary axes hrough he ga/ R erm. The higher are disorionary axes, he less effecive will be he injecion of aid, oher hings held equal. We hink of he effec aid has on growh, in his example, as is direc effec hrough a one ime increase in capial accumulaion. No surprisingly, he size of he direc effec depends on he incenives o accumulae capial. If we mainain he same assumpions bu allow he subsisence level of consumpion o be nonzero we ge oher effecs as well. We will now have he resul ha C C C C + 1 = g = ~ ( ) 1 / γ βr, which implies ha he level of consumpion beyond he subsisence level will grow a he consan rae, g. The model becomes somewha more complicaed o solve, bu i urns ou ha if we repea he experimen wih he wo economies described above, he one receiving aid will have a higher growh rae in period 1 by he amoun of he direc effec: ( ga / R )( F Y ) / ( R g) F / R. This is because, as before, households will consume exacly of he injecion of aid, while he res, gf / R, is invesed in capial. Bu in his case, here are furher effecs. This is because he growh rae of oupu in he model wih subsisence consumpion is no consan bu increases as he capial sock grows and asympoes o g. An injecion of aid raises he capial sock, and by so doing no only raises oupu direcly, bu also moves he counry ono a ransiion pah wih higher growh raes. This indirec effec, which, in our wo economy experimen, is iniially given by R F 1 1 + R F ( g 1), where = C /( R 1), shrinks over ime, and will be smaller he higher he counry s capial sock is a he ime of he aid injecion (he furher i is from he subsisence level of consumpion). I will also be small if he injecion of aid is small relaive o he counry s iniial capial sock. The indirec effec also depends on he ax rae hrough g. Differen indirec effecs occur in versions of he same model wih diminishing reurns o capial, i.e. θ < 1. When here is no subsisence level of consumpion, he 4
model wih θ < 1 implies a monoonically declining growh rae of oupu as he capial sock grows. This is a case in which he indirec effec is negaive. When we combine subsisence consumpion wih θ < 1, for counries wih low capial socks he growh rae rises as he capial sock grows, peaks, and hen declines along he ransiion pah. In his case he indirec effec is posiive or negaive depending on he size of he capial sock a he ime of he aid injecion. The indirec effecs ha arise from differen parameerizaions of he model are illusraed in Figure 1. To summarize his discussion, we have shown ha injecions of aid have wo effecs on economic growh wihin he conex of simple neoclassical models. Firs, here is a direc effec ha depends on how much of he injecion of aid is ransformed ino addiional invesmen. Second, here is an indirec effec arising from he fac ha when aid affecs he capial sock, i also affecs an economy s locaion along is ransiion pah o some long-run seady sae. Boh of hese effecs are a funcion of he magniude of disorions in he economy, which we have modeled here as axes on household income. These findings moivae our empirical specificaion ha allows for he possibiliy ha he impac of aid on growh depends on governmen policies ha affec he size of disorions in he economy. I does his by incorporaing ineracion erms beween measures of aid receips and measures of economic policies. While we form some of our inuiion for he relaionships among policy, aid and growh using he neoclassical model, oher facors can complicae he picure. Firs, he example we gave above ignores incenive issues by assuming ha aid is provided in a lump-sum manner. Suppose, insead, ha some componen of aid were ied o he income level of he recipien, and ha as ha income level rose he quaniy of aid would decrease. In his case, he donor's rule for providing aid would ac as a ax on capial accumulaion in he recipien counry. Overall capial accumulaion would rise as long as he direc impac of donaed capial was greaer han he indirec ax effec, bu he impac of he aid would be less han in he lump-sum case. Second, our simple examples above assume ha he governmen of he recipien counry does no consume he injecion of aid hrough increased governmen spending on goods and services. In he economy ha received he aid injecion we assumed he 5
paern of governmen purchases was idenical o ha in he economy ha received no aid. This means we are implicily assuming ha he injecion of aid is ransferred lump sum o households, who make opimal decisions abou is allocaion beween household consumpion and invesmen. There are many reasons why his implici assumpion may no be reasonable. In realiy foreign aid is inermediaed by governmens, and hese are no always bes hough of as benevolen eniies ha simply ransfer he funds o households or firms. Poliical figures face a variey of incenives ha may cause hem o use aid in socially subopimal ways. Given his, i is possible ha aid would have lile or no impac on overall economic prosperiy in a recipien counry. Paul Mosley and John Hudson (1996) and Jakob Svensson (1996, 1997) have shown ha when he donorrecipien relaionship is modeled as a noncooperaive game, moral hazard can reduce he effeciveness of foreign aid. Aid may simply relax he budge consrain of he recipien governmen, wihou having much impac on he amoun of ha budge ha ulimaely is used o purchase capial. Furhermore, he donor governmen can also be par of his game for reasons oher han benevolence. Donor ineres may lead o he subopimal use of aid and dampen any posiive impac ha i has. While hese facors and many ohers sugges ha he posiive impac of aid is likely o be smaller han wha is prediced by he neoclassical model described above, our priors abou he impac of aid are sill driven by ha example. Whaever marginal conribuion aid makes o growh, we expec aid o be mos effecive in combinaion wih good policy. Furhermore, we expec ha he effecs of good policy would be enhanced by foreign aid. 6
References Chrisiano, Lawrence J. Undersanding Japan's Saving Rae: he Reconsrucion Hypohesis. Federal Reserve Bank of Minneapolis Quarerly Review, Spring 1989, 13(2), pp. 1-25. Mosley, Paul and John Hudson. Aid, Condiionaliy and Moral Hazard. Universiy of Reading Deparmen of Economics and Deparmen of Agriculural Economics and Managemen Discussion Papers in Developmen Economics, Series G, Volume III (1995/96), No. 26, 1996. Rebelo, Sergio. Growh in Open Economies. Carnegie-Rocheser Conference Series on Public Policy, July 1992, 36, pp. 5-46. Svensson, Jakob. Collusion Among Ineres Groups: Foreign Aid and Ren Dissipaion. Working paper, Policy Research Deparmen, World Bank, 1996.. When Is Foreign Aid Policy Credible? Aid Dependence and Condiionaliy. Policy Research Working Paper No. 174, World Bank, 1997. 7
FIGURE 1 INDIRECT EFFECTS OF AID ON GROWTH IN THE NEOCLASSICAL MODEL (a) (b) g g g g (c) (d) g g Noes: Each panel shows he growh rae of oupu, g, as a funcion of he level of capial,, along he economy s ransiion pah. An injecion of aid, o he exen ha i is invesed, causes an increase in he capial sock ha would no oherwise have occurred. Hence, he indirec effec of he injecion of aid on growh is o move he economy ono a differen par of he ransiion pah. Panel (a) uses a model wih consan reurns o capial, and no subsisence level of consumpion, so here is no indirec effec. Panel (b) uses a model wih consan reurns o capial and a posiive subsisence level of consumpion, so he indirec effec is posiive. Panel (c) uses a model wih diminishing reurns o capial and no subsisence level of consumpion, so he indirec effec is negaive. Panel (d) uses a model wih diminishing reurns o capial, and a posiive subsisence level of consumpion, so he effec is ambiguous. 8