Back Matter
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Appendix I

I. Evolution of NGO Activity

Since NGOs are private organizations and extremely diversified, it is rather difficult to gather precise and comprehensive data on all NGOs in the world. However, all sources seem to confirm an intensified NGO participation in ODA as well as an increase in their number (Meyer (1995)). For example, World Bank data shows that during the 1990’s, the World Bank-NGO co-operation has been significantly enhanced. The number of “World Bank approved projects including an NGO-participation” which used to be below 20 per year from 1974 tol989 reaches 100 in 1995. The ratio “projects including an NGO participation” on “overall bank approved projects” confirms the same trend. If until 1991, less than 10 percent of all projects were involving NGOs, this ratio is well above 40 percent since 1995.

This trend is validated by OECD data. Net NGO transfers have been multiplied by more than 5 in 10 years; from USD 884 millions in 1985 to USD 5 636 millions in 1999.

Concomitantly, the share of bilateral ODA transferred through NGO is also increasing. OECD data indicates that ODA from its DAC members channelled through NGOs has risen from 0.11 percent in 1982-83 to roughly 3 percent in 1994, reaching more than a billion USD. This figure can even be much higher for some bilateral aid agencies; for example 30 percent of Swedish development aid is conveyed by NGOs (OECD 1999).

Emergency aid is a sector where NGOs gather a particularly significant share of public funding. According to the World Food Program, food aid distributed through NGOs increased from 9.76 percent to 20.96 percent of the overall food aid between 1988 and 1994. This evolution is particularly obvious during periods of crisis: between 1990 and 1994, between 45 and 67 percent of all funds from the European Community Humanitarian Office went to support NGO actions. In 1994, NGOs received USD 116 millions, i.e., around 44 percent of European Union humanitarian action for the Former Yugoslavia and US$ 13 millions, i.e. 44 percent of the emergency aid for Liberia. According to the Humanitarian Department of the United Nations, they have channelled, in 1993, US$ 100 millions to Somalia, which represented 47 percent of all aid to this country, and the same amount to Sudan, i.e., 49 percent of all the aid perceived.

More generally, the increasing participation of NGOs in development aid corresponds to an increase in the number and size of NGOs as well as to a rise of the budgets they are dealing with, as institutional donors “discovered” them as a new way of transferring aid. Hence, this rapid growth and the increasing political and economical importance of NGOs result in a significant part of development aid being channelled through NGOs.

Appendix II

II. Dynamic Optimization

Let us solve the dynamic game by applying the maximum principle.

Let us first consider the traditional hierarchy setting. Let us write that the principal maximizes

ι(B(pt(1pt)αat)12pt2)(1+r)t(A-1)

subject to

xt+1=(1+σ)xtpt(A-2)

and

0pt1(A-3)

The agent maximizes:

s=t(b(βpt+(1pt)at)12at2)(1+r)t(A-4)

s.t.

yt+1=(1σ)yt+at(A-5)

and

0at1(A-6)

where r stands for the constant rate of time preference and we assume r<σ

Let us write Hp and Ha the current-value Hamiltonians of respectively the principal and the agent.

Hp=B(pt+(1pt)αat)12pt2+λt(σxtpt)+g1pt+g2(1pt)(A-7)
Ha=b(βpt+(1pt)at)12at2+πt(σytat)+h1at+h2(1at)(A-8)

with g1 ≥ 0, pt ≥ 0, pt = 0 and g2 ≥ 0,1– pt ≥ 0, g2(1– pt)=0

with h1 ≥ 0, ht ≥ 0 and h1at = 0 and h2 ≥ 0, 1–at ≥ 0, h2(1– at)=0

We consider only interior solutions and the maximum principle yields:

BatαBptλt=0(A-9)
λtλt1=σλt+rλt1(A-10)
xt+1xt=σxtpt(A-11)
bptbalπl=0(A-12)
πtπt1=σπt+rπt1(A-13)
yt+1yt=σytat(A-14)

where λt and πt are costate variables

with transversality conditions: limt→∞ πtyt(1+r)–t = 0 and lim πt(1+r)–t ≥ 0

By solving (25) and (28) in terras of a (t) and p (t), then substituting π (t) and λ (t) by their expressions in (26) and (29) and further manipulating, we obtain

pt+1=(1+r(1+σ))pt+A1xt+1=(1+σ)xtptat+1=(1+r1+σ)at+A2yt+1=(1+σ)ytat

where for notational simplicity:

A1=(σr)(BαBb)(1+σ)(1αBb)A2=(σr)(BbB)(1+σ)(1αbB)

Delegation Following the same method, I obtain

pt+1=(1+r(1+σ))pt+C1xt+1=(1+σ)xtptat+1=(1+r(1+σ))at+C2yt+1=(1+σ)ytat
C1=(σr)(BBb)(1+σ)(1βBb)
C2=(σr)(BβBb)(1+σ)(1βBb)

Appendix III

III. Comparison of the Agents Effort

Let us recall that a¯=bBb(1αBb)and a*=bβBb(1βBb)

Denote E=a¯a*

E=bB(bβ+1βBbαbβ+βBαb)(1βBb)(1αBb)

the sign of E depends on the sign of d = –(bB(bβ+1–βBbαbβ+βBαb)) Solution of d > 0, is:

{signum(Bb2(1+βB))α<signum(Bb2(1+βB))bβ1+βBb+βb(1+βB)}

When b < 1 and B < 1,

we have –1+βB < 0 and bβ1+βBb+βb(1+βB)>1. Hence, for all α, we have E < 0.

When b ≥ 1 and B ≥ 1, then –1+βB>0 and again bβ1+βBb+βb(1+βB)>1 Then for all α, we have a*<a¯.

Appendix IV

IV. Comparison of the Payoffs of the Principal

Let us write u¯pthe long term value of the principal utility in the traditional hierarchy:

u¯p=Bp¯+(1p¯)αBa¯12p¯2

which can be written as

u¯p=BBαBb1αBb+(1BαBb1αBb)αBa¯12(BαBb1αBb)2

which simplifies into:

u¯p=(1β)αBb1αBb

Let us write up* the long term value of the principal utility under delegation:

up*=(1βB)αBb1βBb

denote

F=u¯pup*
F=αB2b(bβ+1βBbαbβ+βBbα)(1αBb)(1βBb)

the sign of F depends from the sign of

f=αB2b(bβ+1βBbαbβ+βBbα)

Solution of f>0, is:

{signum(b+βBb)α<signum(b+βBb)bβ1+βBb+βb(1+βB)}

When b < 1 and B < 1,

we have –1+βB < 0 and bβ1+βBb+βb(1+βB)>1. Hence, for all α, we have F < 0 that is u¯p<up*

When b ≥ 1 and B ≥ 1, then –1+βB>0 and again bβ1+βBb+βb(1+βB)>1. Then for all α, we have u¯p>up*

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1

I am grateful to G. Nancy for guidance and discussions. I would like to thank R. Lagunoff and P. Michel for their comments and technical review. A. Bhatia, A. Feltenstein, A. Mourmouras, S. Nsouli, and participants at an IMF Institute seminar provided many useful suggestions. Errors are solely mine.

2

The game rules out negative payoffs.

3

For an analysis of different factors leading a principal to be overruled by her subordinate, see Aghion and Tirole (1997).

4

Delegation is defined solely as the allocation of autority over the choice of the project to the agent.

5

For the sake of simplicity, we describe the decisions of the players in a sequential manner, but, actually, they play simultaneously.

6

This technical assumption indicates that the players have unlimited access to training.

7

We define trust as the closeness of preferences

Hierarchy and Authority in a Dynamic Perspective: A Model Applied to Donor Financing of NGO Proposals
Author: Boriana Yontcheva