Is Foreign Aid Motivated by Altruism or Self'Interest?

30 Pages·2013·0.86 MB·English

Is Foreign Aid Motivated by Altruism or Self-Interest? A
Theoretical Model and Empirical Test
Andrea Civelli Andrew W. Horowitz Arilton Teixeira
(cid:3) y z
University of Arkansas University of Arkansas FUCAPE Business School
June 2013
Abstract
We develop a simple theoretical model of bi-lateral foreign aid that generates falsi(cid:133)able empirical
implications and an explicit test for a signi(cid:133)cant altruistic signal in bi-lateral foreign aid disbursements.
We then estimate the model with OECD donor-data to search for donor-recipient pairs that satisfy the
theoretical condition for altruistic motivation. We (cid:133)nd that approximately 20% of donor-recipient pairs
satisfythetheoreticalconditionforaltruismwithScandinaviancountriesshowing,onaverage,33%more
altruistic transfers than non-Scandinavian countries. We argue that since donor motivation may be an
important unobserved characteristic contributing to endogeneity bias in prior estimates of foreign-aid
e⁄ectiveness, this project may also contribute to more accurate estimates of aid e⁄ectiveness.
JEL Codes: E22, E32, O11, O19
Keywords: Foreign Aid, Altruism, Welfare Analysis, bilateral donors, business cycles
1 Introduction
Imagine an altruistic father who earns $10;000 a month and gives his less successful son $1;000 a month to
supplement the $1;000 the son earns. Utility of both father and son exhibit diminishing marginal utility.
Now an unanticipated income shock reduces both father(cid:146)s and son(cid:146)s earned income by 50% (cid:150)to $5;000 and
$500permonthrespectively. Doesthefathertransfermoreorlessincomeaftertheshock? Whilethereisno
unconditional answer to the question we can show that with su¢ cient altruism transfers will increase (cid:150)that
is,withsu¢ cientaltruismtransfersbecomecounter-cyclical. Weemploythistheoreticalresulttodevelopan
Economics Department,University ofArkansas. E-mail: [email protected].
(cid:3)
Economics Department,University ofArkansas. E-mail: [email protected]
y
FUCAPE Business School,Victoria (Brazil). E-mail: [email protected].
z
1
empiricaltestforaltruisminbi-lateralO¢ cialDevelopmentAssistance(ODAorforeignaid)(cid:150)anissuethat
hasbeensubjecttomuchdebate.1 We(cid:133)ndevidencethatapproximately20%ofdonor-recipientpairsdisplay
oursignalforaltruisticODAmotivationandthatalargeportionofthosepairsinvolveScandinaviandonors.
Scandinaviancountrieshavelongbeenheldasexamplesofaltruisticdonors,thoughatheoreticalfoundation
for these assertions and a rigorous empirical test for altruistic motivation have been largely absent.
MostpriorODAliteraturehasfocusedeitheronthee⁄ectofODAonrecipientcountriesorthemotivation
ofdonors. Weshallarguetheseissuesareinextricablyintertwined. Inparticular,importantrecentworkshave
asserted that earlier estimates of ODA e⁄ects are subject to undermining endogeneity bias (Angus Deaton
(2010), Raghuram Rajan and Arvind Subramanian (2008)). That is, since aid is not randomly assigned
across recipients, the presence of unobserved characteristics which determine both the distribution of aid
and its e⁄ectiveness will critically bias estimates of ODA impact. One of the most potentially important of
those unobserved characteristics is the motivation of donors.
Ourmodelwillidentifycounter-cyclicalaid(cid:135)owsasasignalofaltruisticODAmotivation. Thecyclicality
ofaid(cid:135)owsfrombothdonorandrecipientperspectiveshasbeenaddressedinpriortheoreticalandempirical
literature. However, the prior focus has primarily been on the e⁄ect of aid on recipient business cycles and
its role as stabilizer or destabilizer of recipients. The possibility that cyclical patterns of aid may provide a
signal of ODA motivation has not been considered.
The remainder of the paper is organized as follows: Section 2 provides a review of the literature and
additional background material. Section 3 develops our theoretical model of bi-lateral ODA that yields a
testableempiricalconditionforsigni(cid:133)cantaltruisticmotivation. Section4providesourpreliminaryempirical
results. Section 5 summarizes and suggests future extensions.
2 Literature and Additional Background
Themotivationforbi-lateralO¢ cialDevelopmentAssistance(ODA)haslongbeendebated(see,forinstance,
LeonardDudleyandClaudeMontmarquette(1976);McKinlayandLittle(1979);AlfredMaizelsandMachiko
K. Nissanke (1984); Trumbull and Wall (1994); Javed Younas (2008); Chong and Gradstein (2008)). Many
argue that ODA is ultimately motivated by self-interest (Jean Claue Berthelemy and Ariane Tichit (2004);
Berthelemy (2006); Alberto Alesina and David Dollar (2000); Younas (2008)). This view is prevalent in
the political science literature (Robert A. Packenham (1966); Peter J. Schrader, Steven W. Hook, and
Bruce Taylor (1998); Bruce B. de Mesquite and Alastair Smith (2007); David H. Bearce and Daniel C.
Tirone (2010)). Others argue that the motivations vary signi(cid:133)cantly across countries and that while ODA
1We provide a review of this large literature in Section 2 of this paper. As is standard, our analysis excludes military aid.
O¢ cialde(cid:133)nitions ofallODA terms used in this papercan be found at http://www.oecd.org/dataoecd/36/32/31723929.htm.
2
from most countries is motivated by self-interest, other countries appear altruistic (Jakob Svensson (1999)).
Donors(cid:146)tself-reported motivation should also be noted. Over 95% of reported global ODA was provided
by the subset of the OECD countries belonging to the Development Assistance Committee (DAC). DAC
members adopt standardized accounting methods and assert altruistic motivation for ODA.2 Though it is
natural to discount donors(cid:146)self-reported motivation, falsifying altruism is di¢ cult.
A natural starting point for discerning donors(cid:146)motivation would seem to be measurement of donors(cid:146)
(cid:147)return(cid:148)to ODA. If transfers to impoverished recipients yield no bene(cid:133)ts to the donor, altruism emerges
as the likely motivation by process of elimination. However, even the most impoverished nations have the
capacity to provide a return to donor(cid:146)s ODA in the form of supportive votes in multi-lateral institutions
such as the UN and many authors in both economics and political science have taken this as evidence of
self-interest motivation.3 For example, US e⁄orts to impose sanctions on (presumed) nuclear proliferators
have depended on a sequence of close UN votes. There is little doubt that in such contexts supportive votes
convey considerable value to the protagonists. Nevertheless, measuring the actual donor return ODA is
extremelydi¢ cult. Forexample, ratherthanasupportivevote, donorreturnmaybeintheformofinaction
by a recipient as when a recipient agrees to not sell uranium ore to a proliferator. This return (in the form
of inaction) will not be captured by counting supportive multi-lateral votes or by any explicit balance sheet
entry. Fortunately, we are able to empirically test our altruistic motivation condition without the need for
direct measurement of donors(cid:146)return. We will discuss this in detail in the estimation section.
As noted, most economics literature is focused on the e⁄ect of ODA on recipient countries rather than
themotivationofdonors. AnimportantstrandofthisliteraturelooksattherelationshipbetweenODAand
the business cycle in both donor and recipient countries (Bulir and Hamaan (2008); Kuhlgatz, Abdulai, and
Barrett (2010); Stephane Pallage and Michel A. Robe (2001); Pallage, Robe, and Berube (2007); Dabla-
Norris, Minoiu, and Zanna (2010)). Though these models are related to our work our research objective is
distinct. Speci(cid:133)cally,weseektoidentifyatheoreticalsignalofaltruisticmotivationandthentestempirically
for the presence of this signal.
3 The Model
In this section we introduce a theoretical model that generates a distinguishing empirical signal for altruism
amongdonors. Thetheoreticalmodelpresentedinthissectionisascloseaspossibletotheestimationwewill
undertake. More general derivations of the counter-cyclical altruism signal are possible and are indicated
subsequently.
2http://www.oecd.org/department/0,2688,en_2649_33721_1_1_1_1_1,00.html
3Many ofthe citations above adopt this rationale.
3
3.1 Theoretical Framework
In each period, the donor country planner solves a static utility maximization problem to determine how
much ODA to transfer to each of the R potential recipient countries. The donor derives utility from its
own consumption and from ODA disbursements in a manner to described precisely below. The donor(cid:146)s own
consumption is de(cid:133)ned as income, net of investments, and is assumed to be exogenous at the moment of the
planner(cid:146)s decision. This de(cid:133)nition implies that government expenditures and net exports are fully absorbed
by consumers. With this framework we can focus fully on the donor(cid:146)s ODA dispersement problem across
potential recipients. That is, in our model the donor(cid:146)s decision is whether to forego some consumption in
order to make ODA disbursements to the R potential recipient countries. ODA disbursements need not be
equalacrosstheR potentialcountries. Tokeepanalysistractablewealsoabstractfromstrategicinteraction
among donors.
We (cid:133)rst introduce some notation and the objective function of a generic donor d; the same analysis
would apply to any of the other D donors. The vector of ODA disbursements by the generic donor d is
de(cid:133)ned as A = [A ;A ;:::A ] and the donor(cid:146)s trend income is Y(cid:22). These variables are time series but the
1 2 R
time indexes are omitted for ease of notation; we will explicitly re-introduce them only when necessary. The
utility function, which contains a reference level associated with trend income, is
U A;Y(cid:22) =u C;Y(cid:22) +G(A;Y(cid:22)) (1)
(cid:0) (cid:1) (cid:0) (cid:1)
Notethattotalutilityin(1)includesthestandardownconsumptioncomponentu()andasecondcomponent,
(cid:1)
G(),thatrepresentsthegainfromthefullvectorofODAdisbursements. Globaldiminishingmarginalutility
(cid:1)
from consumption is assumed for u(). All of the model(cid:146)s theoretical predictions work in levels as well as
(cid:1)
relative to a reference level. The resources constraint utilized in the donor(cid:146)s optimization problem links C
to the ODA donations through the standard accounting relation
R
C+ A =Y I (2)
s
(cid:0)
r=1
X
where Y I on the right hand side is the donor(cid:146)s income net of private investment. For later reference, we
(cid:0)
de(cid:133)neC =Y I asdonorincomewhennoODAdonationsaremade. Consistentwithourdiscussionabove
0
(cid:0)
we will refer to this total absorption term as simply "consumption." Finally, ODA disbursements must be
non-negative Ar > 0 for any r = 1:::R and cannot exceed C0. This generates the second constraint of the
4
optimization problem
R
As 6C0 (3)
r=1
X
WeassumethetotalgainfunctionG()canbeexpressedasthesumofindividualgainfunctionsassociated
(cid:1)
with the disbursements to each of the R recipients: A
r
R
G(A;Y(cid:22))= G A ;Y(cid:22)
r r
r=1
X (cid:0) (cid:1)
The gain from each individual transfer, G (0), can be decomposed in two distinct components. The (cid:133)rst
r
component is a direct (non-altruistic) return from an ODA transfer to recipient r, (cid:11) A =Y(cid:22) (for example,
r r
a vote at the UN). The second term is derived purely from altruistic preferences of(cid:0)the do(cid:1)nor towards r,
(cid:14) A =Y(cid:22) . Note that this speci(cid:133)cation allow a donor to be solely motivated by the direct-return from
r r
OD(cid:0)A (sel(cid:1)f-interest), to be altruisic, or any combination of the two motivations.
G A;Y(cid:22) =(cid:11) A;Y(cid:22) +(cid:14) A;Y(cid:22)
r r r
(cid:0) (cid:1) (cid:0) (cid:1) (cid:0) (cid:1)
It is reasonable to assume that there is no gain from either component if no ODA donation is made to a
recipient. Therefore G (0) = (cid:11) (0) = (cid:14) (0) = 0. We also assume (cid:11) ;(cid:14) 0, and (cid:11) ;(cid:14) 0 for any r,
r r r 0r 0r (cid:21) 0r0 0r0 (cid:20)
but only in a positive neighborhood of A =0. It is not necessary to fully characterize the gain function for
r
its entire dominion (0;C ) since all observed individual ODA transfers are very small relative to C (e.g.,
0 0
Section 4 shows that ODA disbursements are typically smaller than :01% of GDP). Hence, we impose only
a minimal set of assumptions on G (A ) close enough to 0 to ensure a solution near A = 0. That is, we
r r r
approximate the solution around (C;A )=(C ;0).
r 0
Empirically, we will also allow the gain functions components to be a⁄ected by pair-speci(cid:133)c shift factors,
X and X . Hence, (cid:11) A ;Y(cid:22);X and (cid:14) A ;Y(cid:22);X are the complete gain component expressions for
(cid:11)r (cid:14)r r (cid:11)r r (cid:14)r
estimation. Examples o(cid:0)f shifters fo(cid:1)r (cid:11) (th(cid:0)e "return"(cid:1)component) in literature are the tightness of the
trade relationship between donor and recipient, geopolitical factors, and colonial relationships. Potentially
important shifters for (cid:14) (the "altruism" component) are the recipient(cid:146)s level of consumption without ODA,
cultural and religous factors, the recipient(cid:146)s population size, political e¢ ciency, and corruption. In our
estimation, we explicitly incorporate the recipient(cid:146)s initial level of consumption in the altruistic component
by making (cid:14)() proportional to the change in the recipient(cid:146)s utility due to ODA donation from a donor.
(cid:1)
We now consider the utility and budget constraint of the recipient as seen from the perspective of the
donor(cid:146)s problem (recall that we derive the local solution in the neighborhood around (C;A ) = (C ;0)).
r 0
5
The recipient(cid:146)s budget constraint is then:
C =C +A (4)
r r;0 r
Equation (4) shows that (cid:14)(A ;X ) can be expressed as a function of C for given C since A = C
r (cid:14)r r r;0 r r
(cid:0)
C . The implicit assumption here is that altruistic donors care about recipient country consumers, but
r;0
do not explicitly consider (cid:133)rms in their altruistic decisions. The recipient constraint implies that ODA
is (cid:147)consumed(cid:148)instantaneously by the government and/or consumers (cid:150)that is, there is full absorbtion of
recipient government expenditures.
Consistent with clear empirical reality, we assume that constraint (3) is never binding for any donor.
Therefor, the local interior (cid:133)rst-order-necessary-conditions of the donors problem are statis(cid:133)ed where the
marginal utility of donor "own-consumption" is equal to the marginal gain (from the total gain function)
for each the recipients. Indirect e⁄ects of transfers across recipients that would be conveyed by the shadow
price of constraint (3), were it binding, are absent. Hence, we can obtain the local qualitative theoretical
signal of altruism utilizing the ODA decision to a single representative recipient, r, taking the donor(cid:146)s ODA
to the other R 1 potential recipients as already optimally determined. Note that the predetermined ODA
(cid:0)
to any (or all) of the other R 1 recipients may also be zero. Finally, we explicitly account for the reference
(cid:0)
level by standardizing the arguments of the utility function by the trend income. To simplify notation, let
Z~ = Z=Y(cid:22) be the ratio to GDP value of variable Z and re-write the utility function (1) after substituting
for constraint (2)
U A~ =u C~ A~ + (cid:11) A~ ;X + (cid:14) A~ ;X (5)
0 r r r (cid:11)r r r (cid:14)r
(cid:0) !
(cid:16) (cid:17) Xr Xr (cid:16) (cid:17) Xr (cid:16) (cid:17)
The (cid:133)rst order condition with respect to the generic donation A to recipient r is
r
u C~ A~ +(cid:11) A~ ;X +(cid:14) A~ ;X =0 (6)
c r;0 r r;A r (cid:11)r r;A r (cid:14)r
(cid:0) (cid:0) (cid:0)
(cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17)
where C~ = C~ A~ . Since we are interested in studying the solution of the problem for a small
(cid:0)r;0 0 (cid:0) j6=r j
positive A , we can tPake a (cid:133)rst order approximation of (6) around A~ = 0. The linear expansions of the
r r
three terms in this equation are
u C~ A~ u (C )+u (C )A~ (7)
c r;0 r c r;0 cc r;0 r
(cid:0) (cid:0) (cid:0) ’ (cid:0) (cid:0) (cid:0)
(cid:16) (cid:17)
(cid:11) (A ;X ) (cid:11) (0;X )+(cid:11) (0;X )A
r;A r (cid:11)r r;A (cid:11)r r;AA (cid:11)r r
’
(cid:14) (A ;X ) (cid:14) (0;X )+(cid:14) (0;X )A
r;A r (cid:14)r r;A (cid:11)r r;AA (cid:11)r r
’
6
In order to keep the notation in the following explanation more compact, we will replace the derivatives
in (7) with over-bar variables. For instance, let us de(cid:133)ne u(cid:22) u (C ) and u(cid:22) u (C ) and adopt
c c r;0 cc cc r;0
(cid:17) (cid:0) (cid:17) (cid:0)
the same convention for (cid:11) and (cid:14) too. Using (7) into (6), we obtain
u(cid:22) +u(cid:22) A~ +(cid:11)(cid:22) +(cid:11)(cid:22) A~ +(cid:22)(cid:14) +(cid:22)(cid:14) A~ =0 (8)
c cc r r;A r;AA r r;A r;AA r
(cid:0)
which returns the solution
u(cid:22) (cid:11)(cid:22) (cid:22)(cid:14)
A~(cid:3)r = u(cid:22) c+(cid:0)(cid:11)(cid:22) r;A(cid:0)+(cid:22)(cid:14)r;A (9)
cc r;AA r;AA
The optimal solution of A~ has a very clear interpretation. Since the second order derivatives evaluated
(cid:3)r
atzeroODAareallnegative,thedenominatorof(9)isnegativeaswell. InordertohaveA 0assolution,
r
(cid:21)
the numerator of (9) needs to be negative (or equal to zero at most). The necessary condition for positive
ODA is then
u(cid:22) <(cid:11)(cid:22) +(cid:22)(cid:14) (10)
c r;A r;A
The marginal gain of setting a positive ODA must overcome the marginal loss due to the fall in the donor(cid:146)s
consumption. If the condition is not satis(cid:133)ed then A =0 and we have a "corner" solution to the problem.
r
Figure 1 represents one of the possible cases in which the direct return is quite low and the ODA donation
decision is mostly explained by altruism.
Figure 1: Optimal ODA decisiion in the linearized framework.
Notes: In this example, a positive, small ODA disbursement to recipient r is optimally achieved thanks to a high
degree of altruism in the donor preferences.
7
3.2 The Counter-cyclical ODA
We explore now the condition for counter-cyclical ODA in this framework which constitutes a signal of an
altruismwhichwewillcall strong-altruism. WeevaluatethederivativedA~ =Y~ applyingtheenvelopethe-
(cid:3)r
oremtothe(cid:133)rstordercondition(9). Beforedoingthis,wepostulatethefollowingreduced-formrelationship
between donor(cid:146)s and recipient(cid:146)s incomes
Y Y
r =(cid:12) +(cid:12) d +’X +" (11)
Y(cid:22) 0 rY(cid:22)
r d
Where the Yi represents the output gap of country i = r;d which is de(cid:133)ned as the ratio of actual GDP Y
Y(cid:22)i i
over its trend income Y(cid:22). On the right-hand-side of equation 11, k is a constant and X can be thought of at
i
this stage as embodying other relevant determinants of the recipient(cid:146)s income. Finally, " is a residual with
mean zero. It is not necessary to impose any restrictions on (cid:12) so that the income of donor and recipient
r
may be correlated positively, negatively, or not at all. In general, (cid:12) will be dictated by the degree of
r
integrationoftherecipientcountrywiththeglobaleconomyaswelltheirtrademixanditwouldvaryacross
donor-recipient pairs.
Letusde(cid:133)ne =u(cid:22) (cid:11)(cid:22) (cid:22)(cid:14) and =u(cid:22) +(cid:11)(cid:22) +(cid:22)(cid:14) , wehavethatthederivativedA~ =dY~ is
1 c(cid:0) r;A(cid:0) r;A 2 cc r;AA r;AA (cid:3)r
dA~(cid:3)r = ddY~ 1 2(cid:0) ddY~ 2 1
dY~ (cid:16) (cid:17) ( )(cid:16)2 (cid:17)
2
The (cid:133)rst derivative term in this expressions is
d du(cid:22) (cid:22)(cid:14)
= c r;A =u(cid:22) (cid:12) (cid:22)(cid:14) (12)
dY~ 1 dY~ (cid:0) dY~ cc(cid:0) r r;Ac
where the fact that (cid:11)() does not depend on the donor(cid:146)s income is used; the parameter (cid:12) in the last term
(cid:1) r
is instead derived from (11).4 The other derivative is
d du(cid:22) (cid:22)(cid:14)
= cc + r;AA =u(cid:22) +(cid:12) (cid:22)(cid:14) (13)
dY~ 2 dY~ dY~ ccc r r;AAc
Putting the two terms together again, we obtain
dA~ 1
(cid:3)r = u(cid:22) (cid:12) (cid:22)(cid:14) u(cid:22) +(cid:12) (cid:22)(cid:14) A~
dY~ cc(cid:0) r r;Ac(cid:0) ccc r r;AAc (cid:3)r
2
h (cid:0) (cid:1) i
4Our de(cid:133)nition of (cid:11)() makes the return independent from the donor(cid:146)s income. This seems to be a fair assumption, even
(cid:1)
though it would be possible to write a model in which (cid:11)() is, for example, proportional to Y and this would determine an
(cid:1)
extra term in 12. However,ourspeci(cid:133)cation is more general.
8
A counter-cyclical ODA dA~(cid:3)r <0 can be found if
dY~
dA~ u(cid:22) (cid:12) (cid:22)(cid:14) u(cid:22) +(cid:12) (cid:22)(cid:14) A~
(cid:3)r = cc(cid:0) r r;Ac(cid:0) ccc r r;AAc (cid:3)r <0 (14)
dY~ u(cid:22)cc+(cid:11)(cid:22)r(cid:0);AA+(cid:22)(cid:14)r;AA (cid:1)
since the denominator of this ratio is always negative, the numerator has to be positive in order for (14) to
be satis(cid:133)ed
u(cid:22) (cid:12) (cid:22)(cid:14) u(cid:22) +(cid:12) (cid:22)(cid:14) A~ >0 (15)
cc(cid:0) r r;Ac(cid:0) ccc r r;AAc (cid:3)r
(cid:0) (cid:1)
However, since our approximation of the solution holds only for for small A~ , the term multiplied by A~
r (cid:3)r
in (15) would be negligible compared to the terms in (12) in the determination of the sign of (15). The
condition we can focus on is then
u(cid:22) (cid:12) (cid:22)(cid:14) >0 (16)
cc(cid:0) r r;Ac
The second derivative u(cid:22) is negative by assumption, therefore if also (cid:22)(cid:14) is negative then condition
cc r;Ac
(16) becomes
u(cid:22)
(cid:12) > cc (17)
r (cid:22)(cid:14)
r;Ac
and it can be satis(cid:133)ed only for (cid:12) > 0. In a baseline scenario, we can expect (cid:22)(cid:14) to be negative. This
r r;Ac
condition tells us that counter-cyclical ODAs are more likely to occur when either u(cid:22) is small relative to
cc
j j
(cid:22)(cid:14) (high donor(cid:146)s consumption relative to the recipient(cid:146)s) or (cid:22)(cid:14) is large relative to u(cid:22) (which would
r;Ac r;Ac cc
j j
(cid:12)occur(cid:12)whenthedonor(cid:146)saltruismtowardrecipientr exceedsthet(cid:12)hresh(cid:12)oldimpliedby(16)foragivenu(cid:22) and
(cid:12) (cid:12) (cid:12) (cid:12) cc
(cid:12) ).
r
However, this does not have to be always the case since (cid:22)(cid:14) also depends on the other shifting variables
r;A
in X and those might change in response to Y~ in a way that makes this cross-derivative non-negative.
(cid:14)r r
For example, suppose that an increase in the recipient(cid:146)s income reduces the degree of corruption of its
government. This would improve the e⁄ectiveness of an ODA donation in the donor(cid:146)s opinion and would
shift the return schedule from the altruistic component of the gain function upward. The total net e⁄ect
on (cid:22)(cid:14) depends on all these partial e⁄ects and we could observe dA~(cid:3)r < 0 even when (cid:12) is negative. This
r;A dY~ r
possibility seems to be fairly common in the data.
Hence, we characterize this form of altruism as strong-altruism to distinguish it from the case where the
donorhasaltruisticpreferencesbutnotlargeenoughtogenerateacounter-cyclicalODA.Insummarystrong-
altruism occurs when voluntary transfers from a richer to a poorer agent move inversely with changes in
bothagents(cid:146)income,asillustratedintheexampleoftransfersfromafathertosonintheopeningparagraph.
9
3.3 Empirical Strategy
Inordertoempiricallyevaluatecondition(16),weaddsomestructuretotheminimaltheoreticalassumptions
above considering some speci(cid:133)c functional form for u(), (cid:11)() and (cid:14)(). The main assumption is that both
(cid:1) (cid:1) (cid:1)
donorandrecipientshaveconstantabsoluteriskaversion. Thisimpliesnegativeexponentialfunctionalforms
for u()
(cid:1)
u C~ = 1 e (cid:27)C~
(cid:0)
(cid:0)
(cid:16) (cid:17)
u C~r = 1 e(cid:0)(cid:27)rC~r
(cid:0)
(cid:16) (cid:17)
where(cid:27) and(cid:27) arethedonor(cid:146)sandrecipients(cid:146)riskaversionparameters. Thistypeoffunctionalformisfairly
r
common in literature because preferences are easily characterize by the curvature parameter only. In our
context, italsoallowsustohaveverysimilar(cid:133)rstandsecondderivativeswhichmakestheoptimalcondition
verysuitablefortheestimationexercise. Ontheotherhand,thereisnomuchguidanceabout(cid:11)()and(cid:14)().
(cid:1) (cid:1)
We choose simple functional forms that satisfy the theoretical properties discussed above. Similarly to the
consumption utility, we parameterize the direct return for the donor from an ODA donation to recipient r
with the same type of negative exponential function as u()
(cid:1)
(cid:11)r A~r;X(cid:11)r =(cid:26)r;0 1(cid:0)e(cid:0)(cid:27)A~r
(cid:16) (cid:17) (cid:16) (cid:17)
in which the curvature parameter (cid:27) is the same as the donor(cid:146)s risk aversion and the new parameter (cid:26)
r;0
represents the direct utility return standardized by donor(cid:146)s risk aversion of ODA associated to A~ = 0.
r
Finally, as mentioned above, we assume the altruism component to be proportional to the change in the
recipient(cid:146)s utility due to the receiving of the ODA donation A~
r
(cid:14)r A~r;X(cid:14)r = (cid:14)r;0 e(cid:0)(cid:27)rC~r +e(cid:0)(cid:27)rC~r;0
(cid:0)
(cid:16) (cid:17) = (cid:14)r;0(cid:16) e(cid:0)(cid:27)r(C~r;0+A~r)+e(cid:0)(cid:17)(cid:27)rC~r;0
(cid:0)
(cid:16) (cid:17)
where (cid:14) expresses the degree of altruism of the donor toward recipient r. As explained above, (cid:11)() and
r;0
(cid:1)
(cid:14)() depend also on a set of shifting variables, which can be thought of as a⁄ecting (cid:26) and (cid:14) . For sake
(cid:1) r;0 r;0
of simplicity in the notation, this dependence will not be explicitly reported.5
5A more complete notation for(cid:26)r;0 and (cid:14)r;0 would be (cid:26)r;0(X(cid:11)r)and (cid:14)r;0(X(cid:14)r)where C~r;0 is not in X(cid:14)r any more.
10