How Should Donors Give Foreign Aid? A Theoretical Comparison of Aid Modalities

Abstract

Conditionality, and the extent to which it should be associated with development aid, has been a major concern within the donor community over the past decades. Practitioners argue in favour of associating budget support (BS) with some level of conditionality. A scientific analysis by Cordella and Dell’Ariccia confirms this view. The aim of this article is to qualify the circumstances under which conditionality is an effective complement to BS. To do this, we develop a theoretical model based on Cordella and Dell’Ariccia. We show that the optimal use of conditionality depends on the recipient’s developmental preferences, the productivity of the inputs and the level of aid compared with the recipient’s budget: when these parameters are relatively high, conditionality should be enforced. Otherwise, the optimal aid allocation is such that all the aid is given through unconditional BS. We conclude that conditionality does not always improve aid effectiveness.

Abstract

Depuis quelques décennies, la conditionnalité, et la mesure dans laquelle elle devrait être associée à l’aide publique au développement, est un souci majeur pour la communauté des bailleurs de fonds. Les praticiens du développement plaident en faveur d’un certain degrès de conditionnalité associé à l‘aide budgétaire. Une analyse scientifique de Cordella et Dell’Ariccia (2007) renforce cette perspective. Le but de cet article est d’identifier les circonstances dans lesquelles la conditionnalité est un complément efficace à l’aide budgétaire. A cette fin, nous avons développé un modèle théorique dérivé de l’analyse de Cordella et Dell’Ariccia. Nous démontrons que l’utilisation optimale de la conditionnalité dépend des préférences du gouvernement récipiendaire en termes de politique de développement, de la productivité des apports et du niveau de l’aide publique au développement par rapport au budget du gouvernement récipiendaire. Lorsque ces paramètres sont relativement élevés, la conditionnalité devrait être appliquée. En cas contraire, l’aide publique au développement est optimale lorsque l’aide budgétaire est inconditionnelle. Nous en concluons que la conditionnalité n’améliore pas toujours l’efficacité de l’aide budgétaire.

Appendix

Proof of Lemma 1

• The critical level of capital k _M is defined such that the levels of the recipient’s utility when BS is granted and when it is not are equal: V _C(k _M)=V ₀(k ₀ ^*). □

We consider the case where A=0 and B=T.

In that case, k _M is such that f(k _M, α)=0,

Where

We determine the sign of the partial derivative of k _M with respect to α using the implicit function theorem:

We now prove that this partial derivative is positive.

By construction of k _M (see Figure 1), we obtain that k _M>k _B ^*=α(1−a)(T+G).

Moreover, the recipient budget constraint k+e+m⩽G+B together with B=T imply k _M<T+G.

Therefore, at f(k _M, α)=0 (which is the equation defining k _M), we have (∂k _M)/(∂α)>0.

QED.

Proof of Proposition 3

• To solve maximisation problem (16), we distinguish different candidates for a solution, considering the three cases identified with the help of Figure 1. □

• a When the IR is violated and k _C ^*=k ₀=α(1−a)G−(1−α+αa)γA.

The recipient does not accept the conditional level of capital because it is too high (the IR is violated).

Since the conditionality is not respected, no BS will be given: B=0.

One candidate for a solution in that case is thus:

• b. If the conditional level of capital is smaller than the non-conditional one the conditionality is not a constraint and the donor’s problem is equivalent to the one solved in the third section.

Therefore, all the aid is given through BS and the second candidate for a solution is:

• c. If the conditional capital level is between the non-conditionality level k _NC ^* and the critical level k _M, the best-reply capital level is

From the F.O.C. of the donors’ maximisation problem for this case, we obtain:

The optimal level of conditionality is therefore either the capital level that binds the IR or that leaves the IR slack and that is equivalent to the level of observable input in the first-best allocation.

As can be anticipated from Lemma 1, we now prove that for high levels of recipient developmental preferences α, the IR is not binding: (1−a)(T+G)<K _M.

The opposite holds for low α: (1−a)(T+G)>k _M.

Formally, there exists a threshold level decreasing in its arguments, which allows the following subcases to be distinguished, relative to case c above.

• 1 For a candidate for a solution is ; A _C1 ^*=0 and B _C1 ^*=T. The corresponding level of developmental good is:

  

• 2 For a candidate for a solution is ; A _C2 ^*=0 and B _C2 ^*=T. The corresponding level of developmental good is:

  

To prove this useful result, we want to determine whether the critical level of capital k _M is greater or smaller than the first-best level of capital k _FB ^*=(1−a)(T+G).

In fact, if k _M>k _FB ^*, the conditionality is not binding and the optimal level of conditionality is

Otherwise, the conditionality is binding and the optimal level of conditionality is to impose the critical level of capital: for k _M<k _FB ^*,

As in the proof of Lemma 1, the critical level of capital k _M is such that f(k _M, α)=0 and k _M>k _B ^*.

It is thus straightforward that f(k _FB ^*, α)>(<)0⇔k _M>(<)k _FB ^*.

We can rewrite f(k _FB ^*, α)=ln(1+(T)/(G))−g(a, α), with

Moreover, g(1, α)=g(a, 1)=0 and g′_α(a, α)=(1−a)ln((αa)/(1−α+αa))<0.

The function g(a, α) also decreases in the productivity a of the unobservable input: g′_a(a, α)=α ln((1−α+αa)/(αa))−(1−α)/(a)<0.

Therefore, g(a, α)>0.

We can deduce that for low enough values of developmental preferences α,

and then that k _M<(1−a)(T+G).

The opposite holds for high enough values of α.

Consequently, there exists a level such that f(k _FB ^*, α)=0, which allows the two subcases to be distinguished.

Since g′_α<0 and g′_a<0, the threshold depends on a and T/G, and it decreases in its arguments.

Finally, we compare all the candidates for a solution, distinguishing the two subcases identified above.

For the two possible solutions are

Thus, we obtain that s _B ^*<s _C1 ^*⇔α ^1−a<((a)/(1−α+αa))^a, which is equivalent to the following condition:

we obtain that h(α, a)<0 for α<1.

Consequently, s _B ^*<s _C1 ^*. The optimal contract is such that

For there are also two candidates for a solution:

We can now compare the two possible levels of developmental good for this subcase:

From the definition of k _M, we can write: (s _C2 ^*)^α=(s _B ^*)^α[((1−α+αa)^1−α G)/((T+G)^α(T+G−k _M)^1−α)].

We can prove that ((1−α+αa)^1−α G)/((T+G)^α(T+G−k _M)^1−α)<1.

In fact, if T=0, then k=α(1−α)G by the definition of k _M.

In that case, ((1−α+αa)^1−α G)/((T+G)^α(T+G−k)^1−α)=1 and thus s _C2 ^*=s _B ^*.

Moreover, ((1−α+αa)^1−α G)/((T+G)^α(T+G−k)^1−α) is decreasing in T.

Consequently, we obtain that s _C2 ^*<s _B ^*.