The paper augments Holmstrom’s (1982) team production model in the context of aid effectiveness. The analysis shows how donor proliferation leads to inefficient supply of aid in the recipient country because of the free-riding problem faced by the donors. The empirical findings support the theoretical prediction with regard to donor proliferation. However, this raises the question whether the current efforts in the international aid community with regard to donor coordination can in fact solve the aid proliferation problem.

Rahman, Aminur

Sawada, Yasuyuki

English

Research Papers in Economics

Policy Research Working Paper 5251
Can Donor Coordination Solve 
the Aid Proliferation Problem? 
Aminur Rahman
Yasuyuki Sawada
The World Bank
Investment Climate Department
Regulatory Simplification Unit
March 2010
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dProduced by the Research Support Team
Abstract
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development 
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the 
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those 
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and 
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Policy Research Working Paper 5251
The paper augments Holmstrom’s (1982) team 
production model in the context of aid effectiveness. The 
analysis shows how donor proliferation leads to inefficient 
supply of aid in the recipient country because of the 
free-riding problem faced by the donors. The empirical 
This paper—a product of the Regulatory Simplification Unit, Investment Climate Department—is part of a larger effort 
in the department to understand aid effectiveness. Policy Research Working Papers are also posted on the Web at http://
econ.worldbank.org. The author may be contacted at arahman@ifc.org.  
findings support the theoretical prediction with regard 
to donor proliferation. However, this raises the question 
whether the current efforts in the international aid 
community with regard to donor coordination can in fact 
solve the aid proliferation problem. 
Can Donor Coordination Solve the Aid Proliferation Problem?
1 
 
 
by 
 
 
Aminur Rahman 
World Bank Group 
Washington DC 
 
Yasuyuki Sawada 
Faculty of Economics 
The University of Tokyo, Tokyo 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Keywords: aid proliferation, donor coordination, free-rider problem 
JEL codes: F35, O19, O40 
 
                                                  
1  We thank Steve Knack for helpful comments. Financial support from the World Bank's Knowledge for 
Change Program (KCP) is gratefully acknowledged.     2 
 
1.  Introduction 
Aid proliferation or “aid bombardment” is a growing concern among the international 
aid community and the aid recipients.  Often, the presence of a large number of donors and 
projects overwhelm the recipient government’s capacity to manage and administer aid inflows.  
Consequently, the issue of donor coordination has become an important agenda in development 
policies.  In this paper, we examine the inefficiency in aid supply due to donor proliferation, 
which in turn raises the question whether donor coordination can solve the aid proliferation 
problem. 
Several recent studies address the issue of aid proliferation.  Acharya et al. (2006) 
find that countries with the most acute fragmentation of aid inflows are very likely to receive aid 
from the worst proliferators among the donors.    In such a situation, Knack and Rahman (2007) 
analyze the negative impact of donor fragmentation on the quality of government bureaucracy 
in aid recipient countries.   Arimoto and Kono (2008) formalize the mechanism of competition 
over local matching funds through aid proliferation.  In other words, aid proliferation induces 
competition over local experts or available local matching funds for aid and thus results in a 
decrease in the average bureaucratic quality and the effectiveness of aid projects, respectively, 
in the aid recipient countries.    In addition, Roodman (2006) provides a theoretical argument on 
the proliferation of aid projects and the associated administrative burden for recipients.  
Generally speaking, aid proliferation increases the transaction costs for absorbing foreign aid 
that are incurred by the recipient governments; this results in a significant reduction in the 
effectiveness of aid (Acharya et al., 2006). To the best of our knowledge, no study has 
investigated the effect of aid proliferation on the performance of a recipient country, with the 
exception of Kimura et al. (2007). 
This paper aims to theoretically bridge this gap by augmenting a standard team 
production model of Holmstrom (1982) in the context of aid effectiveness.    The paper focuses 3 
 
on the free-riding problem arising from the fact that aid outcomes in a recipient country are a 
combined result of a wide variety of resources that are provided by the donor and the recipient 
countries.    Using this framework, we investigate whether donor coordination can solve the aid 
proliferation problem. 
 
2.  The Model 
 
Consider the basic Holmstrom (1982) model to determine the amount of aid provided 
by donor countries to a recipient country.  There are N donors, who jointly produce a single 
output, g, that is, for example, the aggregate economic growth of the recipient country.  The 
amount of aid from the i-th donor is denoted by ai.  Therefore, the production technology or 
the economic growth function becomes: g = g (a1, a2, a3, ….., aN; X), where X is a matrix of 
variables that is specific to the recipient country.  Let us assume that the utility function of a 
donor (agent) i is expressed as ui = si – ai, where si is the output share of donor i.
2  T h e  
efficiency regime of this economy can be solved as the following problem: 


   
N
i
i N a a X a a a g Max
i 1
2 1 } { ) ; , , , ( .     (1) 
The first-order condition (FOC) of this problem is: 
1 


i a
g
.     (2) 
Note that the Pareto optimal level of aid, ai*, satisfies this FOC.  On the other hand, a Nash 
equilibrium is derived by solving an individual donor’s utility maximization: 
i i a a g s Max
i
 ) (
} {
,     (3) 
                                                  
2  Alternatively, we can employ a general convex disutility function from aid provision, denoted 
by vi(ai). Such a generalization will not change the qualitative results.     
 4 
 
given the technology in equation (1).    The FOC is: 
1 




i
i
a
g
g
s
,     (4) 
where 
g
si


 is a private benefit from enhancing economic growth and 
i a
g


 is the growth 
effect of aid or “aid effectiveness” of Burnside and Dollar (2000).  Equation (4) gives an 
individually optimal aid level, âi.  The main question is whether the joint outcome g can be 
fully allocated in a manner such that the resulting non-cooperative game among the agents has a 
Pareto optimal Nash equilibrium.  This requires the discovery of an allocation rule si  that 
satisfies both the Pareto optimality condition in (2) and the Nash equilibrium condition in (4).  
Mathematically, we need to show the feasibility of   
i
g
si     , 1  


.     (5) 
This feasibility depends on the characteristics of the output, g.    If, for example, we assume that 
the individual donors’ benefit from aid effectiveness is private goods,
3  equation (5) is infeasible, 
because by differentiating the balanced budget condition, i.e.,  g s
N
i  
1
, we have:   
1
1


 

N
i
i
g
s
.     (6) 
It is evident that the requirement of the Pareto optimal Nash equilibrium in (5) and the balanced 
budget condition in (6) contradict each other if N > 1.  At the Nash equilibrium, an agent’s 
effort level, â, is smaller than the social optimal, ai*.  This result indicates that in a situation 
where selfish donors compete among themselves, free-rider problems are likely to lead to an 
insufficient supply of foreign aid. 
                                                  
3 This may apply when donors care about their relative political influence on a recipient 
country.   5 
 
On the other hand, if there is only one donor, i.e., N = 1, equations (5) and (6) hold 
simultaneously.  However, as  N increases, the gap between the Pareto optimal effort level and 
the individually optimal effort level widens.  This result illustrates the inefficiency of aid 
proliferation. 
In contrast, when donors are fully altruistic and the aid effectiveness translates into 
pure public goods, the individual solution becomes socially optimal.  In other words, the 
free-rider problem arises when there are multiple donors who are motivated by self-interest. 
3.  Empirical Results 
 
Empirically, we examine the free-rider problem by estimating the following equation: 
σit = f(Nit) + Xitβ＋ui + εit,     (7) 
where σit is a proxy for the variable, si, which is quantified by the average aid per donor as a 
share of the recipient’s GDP in country i in year t, and N, as before, is the number of donor 
agencies in the recipient country.  X is a vector of country specific controls, such as GDP per 
capita and population size.  The last two terms in the right-hand side of equation (7) are the 
country fixed effects and a well-behaved error term, respectively. 
With regard to the data sources, we employ the Creditor Reporting System (CRS) 
database of the Organization for Economic Cooperation and Development (OECD) to compute 
the average aid per donor.    The CRS provides detailed information on every activity funded by 
the foreign aid provided by member countries of the OECD or the OECD’s Development 
Assistance Committee (DAC).  To calculate the aid variable for each recipient, we use the 
committed amount of bilateral and multilateral foreign aid.  Other macroeconomic data, such 
as GDP per capita and population size, were extracted from the Penn World Table Mark 6.2 
(Heston, Summers, and Aten, 2006).  We use a cross-country data set of 163 countries for the 6 
 
period 2000–2003. 
We first estimate (7) by assuming that the function, f(･) is a linear function.  We 
employ linear OLS and fixed effect estimators, both in the presence and absence of control 
variables (see Table 1).  While the OLS estimate yields insignificant coefficients for the 
number of donors N, after we control for country fixed effects, we obtain negative and 
statistically significant coefficients on N.  This result is consistent with the prediction of our 
theory in which the individual donors’ benefit from aid effectiveness is private goods.  The 
sample mean of the aid per donor as a share of GDP is about 2.5 percent and the average 
number of donors is 16.    Hence, having an additional donor leads to a 0.7 percent reduction in 
the mean aid per donor share in the recipient country. 
In order to test the robustness against the linearity assumption, we also estimate 
equation (7) semi-parametrically with country fixed effects.    The results of the non-parametric 
and parametric parts are reported in Figure 1 and specification (5) of Table 1, respectively.    As 
is evident from Figure 1, the non-parametric regression line has a negative slope.
4  These 
findings are consistent with the free-rider mechanism described in Section 2. 
4.  Concluding Remarks 
In this paper, we first augment Holmstrom’s (1982) team production model in the 
context of aid effectiveness.  We theoretically demonstrate how donor proliferation leads to 
inefficient aid supply in the recipient country because of the free-riding problem faced by the 
donors. Our empirical findings support our theoretical prediction.  This in turn raises the 
question whether the current efforts with regard to donor coordination in the international aid 
community can actually solve the aid proliferation problem.  Since the free-rider problem 
                                                  
4 In order to estimate Equation (9), we use Lokshin’s (2006) algorithm, which is based on the 
differencing method in the estimation of partial linear models introduced by Yatchew (1997). 
The shape of the function is similar when we introduce linear controls, namely, the recipient’s 
GDP per capita and population. 7 
 
arises due to the presence of multiple donors who are motivated by self-interest, the mere 
coordination of aid, such as general budget supports, will not automatically guarantee the 
sub-optimality of aid provisions unless there is a fundamental change in the incentives for aid 
provisions. 
In the spirit of the Holmstrom (1982) model, the principal can eliminate moral hazards 
by administering incentive schemes that do not balance the budget.  For example, a contract 
under which all donors receive g(a*) if g = g(a*), and receive nothing if g<g(a*).  A feasible 
scheme should be based on a recipient-specific evaluation of the donors’ performance.  The 
operationalization of such a contract would be an important task for the future. 
 
 
 
References 
 
Acharya, Arnab, Ana Teresa Fuzzo de Lima, and Mick Moore (2006), “Proliferation and 
Fragmentation: Transaction Costs and the Value of Aid.” Journal of Development Studies, 
Vol. 42, No.1, pp.1–21. 
Arimoto, Yutaka and Hsiaki Kono (2007), “Foreign Aid and Recurrent Cost: Donor Competition, 
Aid Proliferation and Conditionality,” forthcoming, Review of Development Economics. 
Burnside, Craig and David Dollar (2000), “Aid, Policies, and Growth.” American Economic 
Review, 90(4), pp. 847–868. 
Cassen, Robert and Associates (1986), Does Aid Work?, 2
nd ed., Oxford: Clarendon Press. 
Heston, Alan, Robert Summers and Bettina Aten (2006), Penn World Table Version 6.2, Center for 
International Comparisons of Production, Income and Prices at the University of Pennsylvania, 
September 2006. 8 
 
Holmstrom, Bengt (1982), “Moral Hazard in Teams.” The Bell Journal of Economics, vol. 13, 
pp. 324–340. 
Kimura, Hidemi, Yasuyuki Sawada and Yuko Mori (2007), “Aid Proliferation and Economic 
Growth: A Cross-Country Analysis.” RIETI Discussion Paper Series 07-E-044. 
 
Knack, Stephen and Aminur Rahman (2007), “Donor Fragmentation and Bureaucratic Quality 
in Aid Recipients.” Journal of Development Economics, vol. 83, pp.176–197. 
 
Lokshin, Michael. (2006), “Difference-based Semiparametric Estimation of Partial Linear 
Regression Models.” The Stata Journal, 6, 377–383. 
 
Roodman, David M. (2006a), “Aid Project Proliferation and Absorptive Capacity.” Center for 
Global Development Working Paper, no. 75. 
 
Yatchew, Adonis (1997), “An Elementary Estimator of the Partial Linear Model.” Economics 
Letters, 57, 135–143. 9 
 
 
Table 1. 
Aid Proliferation Regression 
Dependent variable: Aid per donor as a share of GDP 
  (1) (2) (3) (4)  (5) 
Estimation method  OLS  OLS  Fixed Effects  Fixed Effects  Semi-parametric 
Fixed Effects 
        
Number of donors  0.001  0.001  –0.007**  –0.007**  （See Figure 1） 
  (0.001) (0.001) (0.003) (0.003)   
Real GDP per capita    –0.010**    –0.017***  –0.012 
(in  thousand  USD)   (0.004)  (0.006)  (0.009) 
Population size    –10.066***    –11.301  –14.650 
(in million people)    (2.892)    (10.913)  (11.424) 
Constant 0.011  0.099***  0.138**  0.264***   
  (0.017) (0.037) (0.054) (0.080)   
No.  of  Observations  652 652 652 652  651 
Number  of  Recipients  163 163 163 163  163 
Note: Standard errors in parentheses. * significant at 10%; ** significant at 5%; and *** 
significant at 1%.10 
 
 
 

Aid Project Proliferation and Absorptive Capacity.” Center for Global Development Working Paper,

Ana Teresa Fuzzo de

and Associates

Difference-based Semiparametric Estimation of Partial Linear Regression Models.”

Donor Fragmentation and Bureaucratic Quality in Aid Recipients.”

Foreign Aid and Recurrent Cost: Donor Competition, Aid Proliferation and Conditionality,” forthcoming, Review of Development Economics.

Penn World Table Version 6.2,

Yasuyuki Sawada and Yuko

Can donor coordination solve the aid proliferation problem ?

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