Journal of Development Economics
Vol. 64 Ž2001. 147–171
www.elsevier.comrlocatereconbase
An equal-opportunity approach to the allocation
of international aid
Humberto G. Llavador a , John E. Roemer b,)
b
a
Department of Economics, UniÕersitat Pompeu Fabra, Barcelona, Spain
Departments of Political Science and Economics, Yale UniÕersity, 124 Prospect Street,
P.O. Box 208301, New HaÕen, CT 06520-8301, USA
Abstract
How should international aid be distributed? The most common view is according to
some utilitarian formula: in order to maximize the average growth rate of aid recipients or
the growth rate of income of the class of recipient countries.
Recently, the The World Bank wThe World Bank, 1998. Assessing aid, World bank
policy research reportx has published a study demonstrating the importance of good
economic management, within a recipient country, in transforming aid into economic
growth. We identify good economic management with effort, and ask, how should aid be
distributed to equalize opportunities wamong recipient countriesx for achieving growth,
according to Roemer’s theory of equal opportunity wRoemer, J.E., 1998. Equality of
Opportunity. Harvard University Press, Cambridge, MAx q 2001 Elsevier Science B.V. All
rights reserved.
JEL classification: D61; D63; O19
Keywords: International aid; Equality of opportunity; Utilitarianism
1. Introduction
From the viewpoint of justice, how should international aid be distributed? At
present, considerations other than justice are perhaps primary in the determination
)
Corresponding author. Department of Political Science, Yale University, 124 Prospect Street, P.O.
Box 208301, New Haven, CT 06520-8301, USA. Tel.: q1-203-432-5249; fax: q1-203-432-6196.
E-mail address: [email protected] ŽJ.E. Roemer..
0304-3878r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 8 7 8 Ž 0 0 . 0 0 1 2 8 - 0
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H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
of the distribution of aid, especially bilateral aid: rich countries, for example,
predominantly give aid to countries which are important with regard to their
international economic and military interests. Considerations of justice, however,
are arguably more prominent in the decisions of multi-lateral agencies.
The question of how to distribute aid efficiently, as it is often posed, can be
viewed as a form of the question we posed initially. Suppose there is a set of N
countries, potential recipients for aid, and suppose the growth rate of country i’s
GDP is a function g i Ž x ., where x is the fraction of its GDP that it receives as aid.
A given budget, A, of international aid, will determine a feasible set, X, of aid
allocations Ž x 1, x 2 , . . . , x N .. Let Ž Y 1, . . . ,Y N . be the initial levels of GDP of the
recipient countries, and let Y s ÝY i. There are several notions of efficiency used
N
by researchers: to distribute aid to maximize 1rN Ý is1
g i Ž x i ., the average growth
N
i Ž i .Ž i .
rate of recipient countries. To maximize Ý is1 g x Y rY, or to produce a
vector Ž g 1 Ž x 1 ., . . . , g N Ž x N .., which is undominated as a point in R N . The first of
these concepts corresponds to utilitarianism, where the utility function of a country
is taken to be its growth rate; the second is equivalent to maximizing total income
of the class of recipient countries, and corresponds to utilitarianism where the
individuals are people rather than countries, and the utility function of an
individual is taken to be his income; the third is Pareto efficiency across countries,
where the utility function is taken to be the growth rate. The first two concepts
must be motivated by utilitarianism as a political philosophy; the third, Paretianism, is the only measure that is traditionally viewed as being value-free Žand, of
course, it is not single-valued..
One could, moreover, adopt some other utility function for individual persons
and countries than income or its rate of growth; alternative country measures could
be the rate of infant survival Žone minus the rate of infant mortality. or the
non-poverty rate Žone minus the poverty rate.. Now let Y i be the population of
recipient country i, and let g i be its rate of infant survival, and assume that the
N
fertility rate is the same in all countries; then maximizing Ý is1
g i Ž x i .Y irY means
maximizing the fraction of live infants born in the class of recipient countries Žto
transpose this social welfare function into one in terms of individual persons, we
could give every pregnant woman a utility of one if she bears a live infant and a
utility of zero if she bears one who dies. The latest formulation is utilitarianism
with respect to the class of pregnant women in the universe of countries under
consideration..
But varying the interpretation of the functions g i is only one possibility: the
other is to vary the conception of justice from utilitarianism to some other
conception. In this article, we shall substitute for utilitarianism the objective of
equal opportunity. In particular, we shall ask: How should international aid be
distributed to equalize opportunities of recipient countries for growth? The
distinction between equalizing growth rates and equalizing opportunities for
growth hinges upon the fact that countries are, at least in part, responsible for the
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
149
ways in which they use aid, and the lending agency should have no ethical
mandate to compensate specially countries with ‘low effort’ governments.
We compute both utilitarian-growth policy and equal-opportunity policy, which
unlike utilitarian policy, is non-welfarist and does not seek to maximize the
average growth rate. We find that both policies differ substantially from actual aid
policy, which allocates more to African countries and less to the East Asian tigers.
We find that the equal-opportunity policy is more egalitarian than both the
utilitarian policy and the actual allocation, at present levels of world aid.
We could as well take as the objective of the equal-opportunity functional the
rate of infant survival or the non-poverty rate of countries—and perhaps one of
those kinds of ‘utility’ is better than the growth rate from a view-point of justice
—but we take the growth rate for illustrative purposes, and because of the
availability of a useful data set with which we can make the computation with
growth rates.
2. The theory of equal opportunity
We use the equal opportunity theory of Roemer Ž1998., which we review here
briefly. Primary to the conception of equal opportunity is the distinction between
two attributes of the ‘individuals’ among whom opportunities for some objective
will be equalized—their ‘circumstances’ and their ‘effort’. The circumstance of an
individual Žour individuals will be ‘countries’. are attributes which influence the
degree to which it Žor he. can achieve the objective in question Žfor us, a growth
rate., and which are beyond its control, or are not changeable in the short run. In
contrast, ‘effort’ refers to actions the individual takes, which also influence the
degree to which it achieves the objective, but which are deemed to be ‘within its
wor hisx control’ or are changeable in the short run.
The degree to which individual i achieves the objective in question is, then, a
function of three arguments, denoted uŽ C i ,e i , x i ., where C i denotes the circumstances of the individual, e i denotes its effort, and x i denotes the level of a
resource which it receives, or more generally, the value of a policy, determined by
the interventionist agency Žin our case, x will be a measure of aid.. The idea of
equalizing opportunities for the acquisition of the objective u is to choose that
policy which compensates individuals with low values of C, so that the levels of u
finally achieved will be reflective only of their effort. In terms of a common
metaphor, to equalize opportunities means to level the playing field, where the
troughs and gulleys in the field are the disadvantages countries suffer with respect
to achieving u due to poor circumstances. Once the playing field is leveled by
application of a judicious policy Ž x ., then the differences in outcomes Ž u i . will be
due only to differences in efforts Ž e i .. Equality of opportunity does not compensate individuals for differential outcomes ascribable to differential effort. In this
sense, it differs from an equal-outcome ethic.
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H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
We proceed to state, but not to derive, the manner in which the view just
described is translated into the equal-opportunity social welfare functional, which
can be optimized, given the appropriate data. We first partition the set of
individuals into a set of types, where all individuals of a given type have
Žapproximately. the same circumstances. Let the types be denoted 1,2, . . . ,T. The
typology is such that there are many individuals in each type—we assume, in this
paragraph, that there is a continuum of individuals in each type. Given a policy x,
which in our application will be a distribution of aid, there will ensue a
distribution of efforts among the individuals in each type. We define the indirect
utility function Õ t Žp , x . as the value uŽ C t ,e t Žp , x ., x ., where e t Žp , x . is the effort
expended by the individual at the p th quantile of the effort distribution of its type,
and p is any number in the interval w0,1x. We call p a degree of effort. The equal
opportunity welfare functional is
1
t
Õ Ž p , x . dp .
H0 min
t
Ž 2.1 .
Thus, the problem is to choose the policy x from among a set of feasible
policies which maximizes Ž2.1.. We call the policy that solves this maximization
the EOp policy.
Roughly speaking, Ž2.1. tries to equalize the value of the EOp objective Ž Õ . for
all individuals who expend the same degree of effort, across types; further, it gives
equal weight to doing this for every effort quantile of individuals in the population. Again, roughly speaking, Ž2.1. puts a premium on reducing differential
outcomes in so far as they are due to differential circumstances Žtype., but does
not try to reduce differential outcomes in so far as they are due to differential
effort. It is ‘Rawlsian’ in its treatment of differential outcomes due to differential
circumstances, and ‘utilitarian’ in its treatment of differential outcomes due to
differential effort. A detailed justification of formula Ž2.1. is found in Roemer
Ž1998, Section 4..
The EOp functional is non-welfarist. A welfarist social welfare function has, as
its arguments, only the individual welfare Žor utility. levels of the individuals in
question. ŽThus, utilitarianism, in its simplest form, sums these levels; an equalwelfare ethic maximizes the minimum of these levels.. In contrast, one cannot
compute the value of the EOp functional knowing only the welfare levels of the
individuals in question—one must also know the distribution of efforts within
types. Thus, unlike welfarist social-choice theory, the equal-opportunity view
recognizes as ethically significant the efforts expended by individuals, not just the
outcomes they achieve.
3. Application to the problem of international aid: the policy frontier
Our application is based upon The World Bank Ž1998. study Assessing Aid,
and the related work of Burnside and Dollar Ž1997.. The main point of the former
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
151
is that the effectiveness of aid in stimulating growth depends upon there being a
set of practices, in the country, which the authors identify with ‘good economic
management’. Economic management is the weighted average of three macroeconomic markers: budget surplus relative to GDP, inflation, and Sach and Warner’s
Ž1995. trade openness variable.
We shall identify good economic management with ‘high effort’. The Bank
study presents a number of regressions, for a universe of 56 developing countries,
of the growth rate against variables which, in our lingo, can either be characterized
as ‘circumstances’ or ‘effort’. Generically, we write such a regression equation as
J
g i s Ý b j c ji q a 1 e i q a 2 e i x i q a 3 x i q e ,
Ž 3.1 .
js1
where there are J variables denoting the circumstances of a country, and c ji is the
value of the jth circumstance for country i. e i is the value of the economic
management Žeffort. variable for country i, and x i is dollars of aid received as a
fraction of the country’s GDP. We take the regression Eq. Ž3.1. to define the
function uŽ C, e, x ..
We shall use as our policy instrument a disbursement of aid to countries, so that
a country that expends effort e i will receive aid in amount be i q c, for some fixed
Ž b, c ..
We shall assume that the behavior of politicians or planners in country i is
governed by a utility function of the form:
1
r Ž g , j . s g y b ji 1q h ,
Ž 3.2 .
where g is the growth rate and j is the effort expended by the politician or
planner. Effort should be interpreted as those actions by plannersrpoliticians that
lead to growth, but that go against the interests of powerful domestic Žor
international. groups, and hence may be politically dangerous to pursue.
We shall proceed as follows.
Ž1. Estimate the parameters b i and h of Eq. Ž3.2..
Ž2. Compute the space of feasible policies. Suppose countries were offered aid
according to the formula be q c. By substituting the growth Eq. Ž3.1. into the
right-hand side of Eq. Ž3.2., we can compute the optimal effort, e i Ž b, c ., of each
country planner. Thus, we view a country’s effort as chosen by its
politiciansrplanners, to maximize their utility. The aid a country will then receive
is max w0, be i Ž b,c . q c x Y i. Since the units of aid are Adollars per unit GDPB, the
policy is budget-balancing if
Ýmax
0,be i Ž b,c . q c Y i s A.
Ž 3.3 .
i
Our method will be, for a sequence of numbers b j, to compute c j at which Eq.
Ž3.3. holds. We will then have computed the boundary of the policy space as a
sequence of ordered pairs Ž b j, c j ..
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H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Ž3. Now find the point on the boundary of the policy space that maximizes the
EOp objective.
Ž4. Do the same for Žone of. the utilitarian objectiveŽs..
In the remainder of this section, we present the details of steps 1 and 2.
First, note that country effort as it is measured by the World Bank, lies in range
wy1,1x, but for our utility function ŽEq. Ž3.2.. to make sense, effort must be a
positive number Ž j .. We therefore transform measured effort into politician’s
effort by the monotone transformation:
j s Exp w e x .
Thus, writing our utility function ŽEq. Ž3.2.., after substituting in from Eq. Ž3.1.,
we have:
J
r Ž g ,e . s Ý b j c i j q a 1 e i q a 2 e i x i q a 3 x i y b i Exp w e i x
1q
1
h
.
Ž 3.4 .
js1
We assume that, historically, aid disbursements have not depended on effort,
and so the plannersrpoliticians in country i view x i as constant. Their present
effort result from optimizing Eq. Ž3.4., which leads to a F.O.C. which, after taking
logarithms, can be written:
1
1
ž / ž /
ln w a 1 q a 2 x i x s ln b i 1 q
q 1q
h
h
ln w e i x .
Ž 3.5 .
Because effort is the dependent variable, and we are viewing past aid as fixed, we
now rewrite Eq. Ž3.5. in a form amendable to estimation, as:
1
y1
1
ž / ž /
i
ln w e x s y 1 q
h
ln
1q
h
b
i
y1
1
ž /
q 1q
ln w a 1 q a 2 x i x .
h
Ž 3.6 .
Our next step is to run regressions to estimate h , which we assume is constant
across countries, and the individual country parameters b i. We describe the
econometric work in the next section. We estimate a value of h s 0.0582, and
values b i ŽTable 6, column 2..
We now suppose that aid will be disbursed according to a formula be q c,
where Ž b,c . is announce. Thus, the country planners now face an optimization
problem where they choose e to maximize:
a 1 e q a 2 e Ž be q c . q a 3 Ž be q c . y b i Exp w e x
iŽ
1q
1
h
.
Ž 3.7 .
We define e b,c . as the unique maximizer of Eq. Ž3.7., and now, for b fixed,
find that value of c that solves Eq. Ž3.3.. ŽThis is a tractable problem with
Mathematica.. We proceed to map out the policy frontier, by doing this calculation for a sequence Žgrid. of b’s.
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
153
Fig. 1. Planner’s utility as a function of e for Indonesia, at bs 2.3, csy0.06068.
We have just described the ideal procedure for computing the Žboundary of the.
policy space. In actuality, the problem is somewhat more complex, because, for
some pairs Ž b, c . and countries i, the set of maximizers of Eq. Ž3.7. contains two
elements. Fig. 1 graphs the utility function for Indonesia’s planner, at the values of
Ž b, c . in the figure’s title, as a function of e. We see that there are two
maximizers. The double-humped utility function occurs because aid is assigned
according to the formula max w0, be q c x. To compute his optimal effort, the
planner must make two calculations: Ži. first, his optimal effort if he expends
enough effort to receive aid Žthat is, if e ) yŽ crb ..; Žii. second, his optimal effort
if he does not expend enough effort to receive aid Žthat is, if e F yŽ crb ... This
leads to the camel-shaped utility function.
Now consider the problem of finding a value c which solves Eq. Ž3.3., for the
value of b s 2.3 Žthat value for which the Indonesian pathology occurs.. As c
moves from just below the value y0.60608 to just above that value, Indonesian
effort takes a saltus up, from zero to a non-infinitesimal positive number. Thus,
the left-hand side of Eq. Ž3.3. takes a saltus up. It turns out that there is no
solution, c, to Eq. Ž3.3. when b s 2.3 Žindeed, this happens for many values of
b ..1
Therefore, the best that we can do, in general, is to compute, for each b, the c
that minimizes the positive difference A y Ý i max w0, be i Ž b, c . q d x Y i. In other
words, for some values of b, the lending agency will have a budget surplus.2 This
is what we have done.
1
This is consistent with the Maximum Theorem Žsee Mas-Colell et al., 1995, p. 963., which asserts
that the set of maximizers of Eq. Ž3.7. is an upper-hemi-continuous function of c. Indeed it is: but that
correspondence contains no continuous selection, which leads to the problem we discuss.
2
One might have hoped to eliminate this technical problem by a suitable choice of planner’s utility
function ŽEq. Ž3.2.. and growth regression ŽEq. Ž3.1... Our approach, on the contrary, has been to
stipulate a reasonable utility function and growth regression, and then to live with the mathematical
difficulties.
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H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
4. Fitting the model
The empirical analysis uses the data from Burnside and Dollar Ž1997.. The
database consists of panel data on 56 countries over six 4-year time periods from
1970–1973 through 1990–1993. An observation is a country’s performance
averaged over a 4-year period. Some countries are missing data in some time
periods, so that we end up with a total of 272 observations.
We want to estimate Eq. Ž3.1., in which growth depends on: variables denoting
the circumstances of a country, the economic management variable, foreign aid,
and aid interacted with economic management. The econometric analysis follows
Burnside and Dollar Ž1997..
First, we describe briefly the set of variables. Besides foreign aid and economic
management Ždescribed below., Burnside and Dollar include six more variables in
the regression of growth: initial income, ethnolinguistic fractionalization, assassinations Žto capture civil unrest., ethnolinguistic fractionalization times assassinations, money supply ŽM2. as a fraction of GDP Žas a proxy for distortions in the
financial system., and institutional quality.3 We will associate these variables with
the circumstances of a country. For a detailed explanation and justification of the
variables, see Section 3.1 in Burnside and Dollar Ž1997.. Nevertheless, the
inclusion of institutional quality among the circumstances of a country needs a
little explanation. Institutional quality captures security of property rights and
efficiency of the government bureaucracy, and it is measured using the 1980
international Country Risk Guide ŽICRG. presented in Knack and Keefer Ž1995..
Burnside and Dollar use each country’s 1980 observation Aon the assumption that
institutional factors change slowly over timeB Žp. 15., thus they cannot be affected
in the short run. We maintain the assumption and include institutional quality
among a country’s circumstances.
Foreign aid is measured by the Effective Development Assistance ŽEDA., Aan
aggregate measure of aid flows combining total grants and the grant equivalents of
all official loansB ŽChang et al., 1998.. EDA aggregates annual flows from both
bilateral and multilateral donors. More importantly, it does not include loans with
a clear non-development purpose, namely military and defense-related loans
ŽChang et al., 1998, p. 10.. The aid data are presented in constant 1985 dollars
using the unit-value of import price index from the IFS.4 To calculate aid as a
fraction of GDP, the aid data figure is divided by real GDP in constant 1985
prices.
3
Time dummies to account for the world business cycle, and regional dummies for Sub-Saharan
Africa and East-Asia are also included in the regression.
4
We obtain then a measure of aid that is constant in terms of its purchasing power over a
representative bundle of world imports, as argued by Dollar and Burnside.
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
155
Finally, we define economic management as the weighted average of the
following set of policy variables: budget surplus relative to GDP; inflation, as a
measure of monetary policy; and Sach and Warner’s Ž1995. trade openness
dummy variable. To determine the weights, we run a regression of growth against
the circumstances and the policy variables ŽTable 1., and let the coefficients of the
policy variables determine their relative importance in the economic management
index. Thus,
Eco.Managements 0.0473 Budget surplusy 0.0156 Inflation
q 0.0212 Openness.
We are now in the position to run regression ŽEq. Ž3.1.. of the growth rate against
‘effort’, foreign aid ŽEDA., and the variables describing ‘circumstances’. We
Table 1
OLS panel growth regression I
Variable
Coefficient
Standard error
t-Statistic
Prob
C
INITIAL RGDPPC
ETHNIC FRACT.
ASSASSINATIONS
ETHNF=ASSASSIN
ICRGE
M2rGDP
Sub-Saharan Africa
East-Asia
GOV. CONSUMP
Time Dummy 2
Time Dummy 3
Time Dummy 4
Time Dummy 5
Time Dummy 6
BUDGET SURPLUS
INFLATION
SACH–WARNER
y0.014981
y0.000003
y0.0000615
y0.00375
0.0000669
0.007046
y0.000231
y0.012306
0.007674
y0.060126
0.025043
0.024852
0.011871
y0.008731
0.005403
0.04727
y0.015644
0.021225
0.011237
0.0000013
0.0000807
0.003056
0.0000631
0.001749
0.000174
0.006478
0.007169
0.048085
0.007808
0.007286
0.007171
0.007106
0.006454
0.034418
0.00525
0.006003
y1.333179
y2.313779
y0.762549
y1.227164
1.060532
4.029801
1.325242
y1.899679
1.070442
y1.250402
3.207354
3.41081
1.655535
y1.228748
0.837183
1.37339
y2.979774
3.535518
0.1837
0.0215
0.4464
0.2209
0.2899
0.0001
0.1863
0.0586
0.2854
0.2123
0.0015
0.0008
0.0991
0.2203
0.4033
0.1708
0.0032
0.0005
R-squared
Adjusted R-squared
SE of regression
Sum squared resid
Log likelihood
Durbin–Watson stat
0.402077
0.362059
0.028787
0.210485
588.3719
1.918205
Mean dependent var
SD dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob Ž F-statistic.
0.011841
0.036042
y4.193911
y3.955292
10.0473
0
Dependent Variable: REAL GDP PER CAPITA ŽRGDPPC. growth rate.
Method: Least Squares.
Sample: 1 272.
Included observations: 272.
156
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Table 2
OLS panel growth regression II
Variable
Coefficient
Standard error
t-Statistic
Prob
C
INITIAL RGDPPC
ETHNIC FRACT.
ASSASSINATIONS
ETHNF=ASSASIN
ICRGE
M2rGDP
Sub-Saharan Africa
East-Asia
GOV. CONSUMP
Time Dummy 2
Time Dummy 3
Time Dummy 4
Time Dummy 5
Time Dummy 6
EFFORT
EFFORT=EDAGDP
EDAGDP
y0.016087
y2.71Ey06
y5.51Ey05
y0.003737
6.61Ey05
0.007168
0.000221
y0.014087
0.008627
y0.073116
0.025987
0.025663
0.012475
y0.00823
0.005563
0.958812
1.124706
0.095085
0.010916
1.33Ey06
7.99Ey05
0.003015
6.24Ey05
0.001734
0.000167
0.006453
0.00724
0.047792
0.007203
0.006827
0.006689
0.006727
0.006363
0.233905
6.071722
0.125253
y1.473783
y2.034886
y0.689097
y1.239606
1.058539
4.133429
1.318151
y2.182947
1.191556
y1.529874
3.607657
3.759168
1.864868
y1.223466
0.874249
4.099156
0.185237
0.759146
0.1418
0.0429
0.4914
0.2163
0.2908
0
0.1886
0.03
0.2345
0.1273
0.0004
0.0002
0.0634
0.2223
0.3828
0.0001
0.8532
0.4485
R-squared
Adjusted R-squared
SE of regression
F-statistic
Prob Ž F-statistic.
0.403631
0.363716
0.028749
10.11238
0
Mean dependent var
SD dependent var
Sum squared resid
Durbin–Watson stat
0.011841
0.036042
0.209939
1.848049
Dependent Variable: REAL GDP PER CAPITA ŽRGDPPC. growth rate.
Method: Least Squares.
Sample: 1 272.
Included observations: 272.
perform a Hausman test to check for the endogeneity of aid, and accept the null
hypothesis of consistent ordinary least square ŽOLS. estimates.5 Table 2 reports the
results of the OLS regression of growth.
Using this regression, define the index for the circumstances of country i as the
growth not explained by effort or aid. For a country with growth rate g i , effort e i ,
and aid x i , let C i s g i y Ž e i Ž a 1 q a 2 x i . q a 3 x i .. In other words, C i is the effect
of country-specific circumstances on the rate of growth plus the country-specific
error term: C i s Ý Jjs1 b j c ji q e , see Eq. Ž3.1.. We have decomposed then the
growth rate into three components: circumstances Žthe sum of obserÕed circum-
5
Collier and Dollar Ž1999. reach the same conclusion and also regress growth against aid using
OLS.
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
157
stances Ž Cˆ i and the error, i.e., C i s Cˆ i q e .; the total effect of effort Ž e i Ž a 1 q
a 2 x i ..; and the direct explanatory power of aid Ž a 3 x i .. Plugging in the estimation
from the growth regression in Table 2, we obtain:
g i s C i q e i Ž 0.959 q 1.125 x i . q 0.095 x i .
We present in Table 3 and Figs. 2 and 3 the share of the rate of growth
attributed to each component. Note that some components contribute negatively to
growth. For example, the Dominican Republic average growth is 2.66%, although
the observable circumstances report a higher growth rate. Namely, with neutral
economic management and no foreign aid the Dominican Republic’s GDP would
grow at a rate of 2.87%. However, bad economic policies produce more that
one-quarter of a point negative growth, which is only partially compensated for by
the positive direct effect of aid Ž0.02%..
Figs. 2 and 3 present the relative importance of the different components in
explaining growth. We have graphed in Fig. 2 the percentage of each component
in total growth. Fig. 3 takes the absolute values. Observe that, in general,
circumstances account for the largest share of the rate of growth. However, and
more importantly, effort does play a significant role in explaining growth. The
modest participation of aid in current growth is due to the small amounts of aid
actually distributed: the average aid is just 1.5% of GDP, and in more than 50% of
the observations a country received less than 0.6% of its GDP in aid.
Table 4 summarizes our calculations so far. For each one of the 55 countries,
we have identified an effort level Žcolumn 4., an amount of aid received as
percentage of GDP Žcolumn 3., and an index of circumstances Žcolumn 5., all of
them averaged over the available observations.6
Before proceeding to compute the EOp and the utilitarian policies, we need to
calibrate the utility functions of the politiciansrplanners ŽEq. Ž3.2... In the
previous section, we wrote the observed level of effort as a linear function ŽEq.
Ž3.6.. of aid with the same slope for all countries but particularized intercepts. We
set up the following regression equation:
55
EFFORTs Ý u j Dj q k AID q Ýf h X h q e ,
Ž 4.1 .
js1
where EFFORT is the observed effort level Žin logs.; AID s lnŽ a 1 q a 2 x .; Dj is
a dummy variable that takes the value 1 for country j and 0 otherwise, and which
6
Because India has a large potential for growth, makes reasonably good policy efforts and has a
very large population Žmore than one half the population of all the other countries together., it would
absorb all the available aid under the EOp and the utilitarian criteria. We decide therefore to carry the
analysis constraining India to its present level of aid. That is, we exclude India from the sample and
reduce the total aid by the amount that India currently receives.
158
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Table 3
Growth decomposition
Country
RGDPPCgw,
g Ž%.
Algeria
Argentina
Bolivia
Botswana
Brazil
Cameroon
Chile
Colombia
Costa Rica
Cote d‘Ivore
Dominican Rep
Ecuador
Egypt
El Salvador
Ethiopia
Gabon
Gambia
Ghana
Guatemala
Guyana
Haiti
Honduras
India
Indonesia
Jamaica
Kenya
Korea
Madagascar
Malawi
Malaysia
Mali
Mexico
Morocco
Nicaragua
Niger
Nigeria
Pakistan
Paraguay
Peru
Philippines
Senegal
Sierra Leone
Somalia
Sri Lanka
Syria
Tanzania
2.81
0.55
y0.04
7.48
2.39
0.84
2.09
2.13
2.18
y2.59
2.66
2.63
3.76
y0.31
y4.74
1.26
0.25
y0.74
0.58
y0.36
0.10
0.87
2.07
4.90
y2.92
1.33
6.99
y1.74
y1.10
4.35
4.64
1.40
1.74
y3.45
1.46
0.78
2.79
2.19
y0.72
0.88
y0.18
y0.39
0.60
2.86
3.13
0.26
CIRCUMST.,
Ž C . Ž%.
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
2.91
1.83
y0.48
4.72
3.89
0.76
1.27
1.79
1.84
y2.04
2.87
1.63
4.24
y0.63
y4.75
1.36
y0.82
y1.05
0.28
0.03
0.15
0.68
2.43
3.08
y2.17
1.44
5.13
y1.70
y1.07
2.73
3.10
1.38
1.21
y1.62
1.28
1.15
3.18
1.92
0.40
0.62
y0.26
0.28
0.79
2.62
3.36
0.49
EFFORT,
eŽ a 1 q a 2 x . Ž%.
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
y0.17
y1.28
0.27
2.27
y1.51
y0.10
0.80
0.32
0.33
y0.63
y0.27
0.97
y0.70
0.15
y0.34
y0.29
0.40
0.13
0.25
y0.75
y0.22
y0.01
y0.39
1.79
y0.89
y0.33
1.83
y0.29
y0.56
1.61
0.81
0.02
0.44
y2.13
y0.33
y0.39
y0.47
0.20
y1.16
0.23
y0.27
y0.83
y0.61
0.13
y0.40
y0.78
AID,
a 3 x Ž%.
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
0.07
0.00
0.17
0.49
0.00
0.18
0.01
0.01
0.01
0.08
0.06
0.03
0.23
0.18
0.36
0.18
0.67
0.18
0.05
0.36
0.17
0.21
0.02
0.04
0.13
0.22
0.02
0.26
0.54
0.02
0.73
0.00
0.09
0.30
0.51
0.01
0.07
0.07
0.04
0.04
0.35
0.16
0.42
0.11
0.18
0.56
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
159
Table 3 Ž continued .
Country
RGDPPCgw,
g Ž%.
Thailand
Togo
Trinidad y Tobago
Tunisia
Turkey
Uruguay
Venezuela
Zaire
Zambia
Zimbabwe
5.18
y0.24
0.59
1.26
3.78
1.24
y0.52
y1.94
y2.04
y0.70
CIRCUMST.,
Ž C . Ž%.
s
s
s
s
s
s
s
s
s
s
3.30
y0.17
0.78
0.66
2.69
1.70
y0.68
y1.59
y1.50
y0.30
EFFORT,
eŽ a 1 q a 2 x . Ž%.
q
q
q
q
q
q
q
q
q
q
1.86
y0.57
y0.19
0.52
1.06
y0.47
0.16
y0.58
y0.99
y0.63
AID,
a 3 x Ž%.
q
q
q
q
q
q
q
q
q
q
0.02
0.51
0.01
0.09
0.03
0.01
0.00
0.22
0.46
0.22
captures country-specific characteristics. We also include several variables, X h , to
be sure that we control for non-aid related factors on effort.7 We run a 2SLS
regression, instrumenting for aid,8 and obtain h s 0.0582 from the estimated
coefficient k . Finally, once we know h , and under our assumption that, historically, aid has not depended on effort, we calculate b j from the F.O.C. of the
utility maximization problem of the plannerrpolitician ŽEq. Ž3.5...9 The values of
b are reported in Table 6, column 2.
5. Optimization
In this section, we compute the EOp policy and the utilitarian policy. We first
partition the set of 55 countries into four types according to their circumstances,
where type 1 countries enjoy the best circumstances Žsee Table 5..
In our description of the theory, given above, we assumed a continuum of
individuals, but here we have 55. We thus create four effort quartiles in each type,
by dividing the interval of efforts computed into four equal intervals, for each
type, and then assigning each country an effort quartile, q Ž i; b j, c j .. Thus, a
country’s effort quartile depends not only on its type, but on the policy. Now let
eŽ q, t; b j, c j . be the average effort expended by countries of type t in effort
7
In particular, we include initial GDP per capita, assassinations ŽAssassin., ethnolinguistic fractionalization ŽEthnic., Ethnic=Assassin, and money supply as a fraction of GDP Žlagged..
8
Instruments: Pop ŽLog of population., Pop2, Inf Žinfant mortality., Inf2, Pop=Effy1ŽLog lagged
effort., Inf=Effy1 , arms imports Žlagged., dummies for Egypt, franc zone countries, Central American Countries.
9
That is, for js1, . . . , 55, b j s Ž a 1 q a 2 x j .rw1qŽ1rh .4Exp e j1qŽ1rh .44x.
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Fig. 2. Decomposition of the rate of growth Ž% of total growth..
160
Fig. 3. Relative importance of the components of growth Žin absolute values..
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
161
162
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Table 4
Effort and circumstances Žaverage over observations.
Country
Number of
observations
Aid,
x Ž%GDP.
Effort Ž e .
Circumst. Ž C .
Algeria
Argentina
Bolivia
Botswana
Brazil
Cameroon
Chile
Colombia
Costa Rica
Cote d’Ivore
Dominican Rep
Ecuador
Egypt
El Salvador
Ethiopia
Gabon
Gambia
Ghana
Guatemala
Guyana
Haiti
Honduras
India
Indonesia
Jamaica
Kenya
Korea
Madagascar
Malawi
Malaysia
Mali
Mexico
Morocco
Nicaragua
Niger
Nigeria
Pakistan
Paraguay
Peru
Philippines
Senegal
Sierra Leone
Somalia
Sri Lanka
Syria
Tanzania
2
3
6
3
6
5
6
6
6
1
6
6
5
6
2
6
6
6
6
6
5
6
6
6
3
6
6
4
4
6
1
6
6
6
2
6
6
6
6
6
4
6
2
6
5
2
0.767
0.020
1.800
5.121
0.026
1.876
0.156
0.122
0.153
0.845
0.600
0.323
2.392
1.865
3.745
1.909
7.081
1.921
0.494
3.737
1.771
2.189
0.259
0.392
1.416
2.338
0.201
2.704
5.647
0.201
7.649
0.016
0.941
3.145
5.381
0.138
0.765
0.686
0.411
0.439
3.631
1.698
4.441
1.169
1.856
5.857
y0.0018
y0.0133
0.0027
0.0224
y0.0158
y0.0010
0.0083
0.0034
0.0034
y0.0066
y0.0028
0.0100
y0.0071
0.0015
y0.0034
y0.0029
0.0038
0.0013
0.0026
y0.0075
y0.0023
y0.0002
y0.0040
0.0186
y0.0091
y0.0033
0.0191
y0.0030
y0.0055
0.0167
0.0078
0.0002
0.0045
y0.0214
y0.0033
y0.0041
y0.0048
0.0021
y0.0120
0.0023
y0.0027
y0.0085
y0.0061
0.0013
y0.0041
y0.0077
0.02909
0.01828
y0.00485
0.04728
0.03894
0.00762
0.01274
0.01792
0.01020
y0.02036
0.02875
0.01630
0.04242
y0.00639
y0.04748
0.01366
y0.00848
y0.01062
0.00276
y0.00003
0.00151
0.00674
0.02432
0.03077
y0.02170
0.01439
0.05133
y0.01700
y0.01074
0.02727
0.03105
0.01379
0.01216
y0.01578
0.01285
0.01153
0.03184
0.01919
0.00401
0.00616
y0.00258
0.00284
0.00788
0.02619
0.03360
0.00486
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
163
Table 4 Ž continued .
Country
Number of
observations
Aid,
x Ž%GDP.
Effort Ž e .
Circumst. Ž C .
Thailand
Togo
Trinidad y Tobago
Tunisia
Turkey
Uruguay
Venezuela
Zaire
Zambia
Zimbabwe
6
4
5
3
1
6
6
5
6
3
0.243
5.359
0.066
0.907
0.328
0.126
0.015
2.350
4.805
2.335
0.0193
y0.0056
y0.0020
0.0054
0.0111
y0.0049
0.0017
y0.0059
y0.0098
y0.0064
0.03303
y0.00178
0.00782
0.00656
0.02690
0.01704
y0.00685
y0.01585
y0.01494
y0.00296
quartile q. We now let Õ t Ž q, x ŽŽ q, t; b j, c j .. be the growth rate of a Žhypothetical. country, representing the average of countries in quartile q of type t, gotten
Table 5
Classification of countries in type according to their circumstances
164
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
by substituting effort eŽ q, t; b j, c j . into the growth equation, when the aid
disbursed to this country is
x Ž q,t ;b j ,c j . s max 0, Ž b j e Ž q,t ;b j ,c j . q c j . Y q t .
Here, Y q t is the GDP of countries in quartile q of type t Žwe take the average of
the circumstances in the countries in this quartile-type for the hypothetical
country.. We now write the discrete analog of Eq. Ž2.1. as:
max Ýg qminÕ t Ž q, x Ž q,t ;b j ,c j . . .
Ž b j ,c j . q
t
Ž 5.1 .
The literal analog of Eq. Ž2.1. would take the coefficients g q to be the fraction of
countries that lie in effort quartile q, but we shall modify this, and take g q to be
the fraction of total population of the target countries that live in countries of
effort quartile q.
To compute the utilitarian policy, we find the policy that solves:
max Ýß q t Õ t Ž q, x Ž q,t ;b j ,c j . . ,
Ž b j ,c j . q ,t
Ž 5.2 .
where ß q t is the fraction of total GDP of target countries which is earned in
countries of effort quartile q of type t. Thus, the utilitarian objective ŽEq. Ž5.2..
aims to distribute aid to maximize the growth rate of the total GDP of the 55
countries.
Next, given the current amount of total aid ŽUS$14.6 billion., we find the EOp
and utilitarian allocations. As explained in Section 3, we calculate the sums in
Eqs. Ž5.1. and Ž5.2. for a grid of b’s Žand their corresponding c’s in the policy
frontier., and choose the policy that maximizes the objective functions. We can
observe in Fig. 4 that the EOp objective reaches a maximum at b , 0.3, while the
utilitarian objective’s maximum is obtain for b , 3. Finally, Table 6 and Fig. 5
present the EOp, the utilitarian and actual allocations of aid.
The main observations from these tables and figures appear to be as follows.
Ž1. There is a sizeable number of countries, which are mainly in Africa, which
receive more aid than is recommended by either the EOp or the utilitarian
allocation.
Ž2. Korea and Thailand receive much less aid than is recommended by either
the EOp or the utilitarian allocations. Malaysia, Indonesia and 10 other countries
would also receive more aid under the EOp rule.
Ž3. Both the EOp and the utilitarian allocations leave some countries without
aid: Zambia, Tanzania, Nicaragua, Brazil, and Argentina in the EOp allocation; all
but three countries in the utilitarian allocation.
Ž4. The utilitarian allocation allocates more than 95% of total aid to two
countries, Korea and Thailand. The reason is that total growth is utilitarianism’s
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
165
Fig. 4. EOp and utilitarian objectives.
only concern, and these countries are the most AproductiveB countries in generating growth.10
Ž5. The EOp allocation is more egalitarian than either the actual or the
utilitarian allocations. We have represented in Fig. 6 the Lorenz-type curves for
the three allocations. The Gini coefficients from these graphs are G EOp s 0.40,
GActual s 0.67, and G Util.s 0.85.
Ž6. The utilitarian allocation is by far the most unequal distribution.
Observations 1, 2 and 3 are all aspects of the meta-observation that the actual
pattern of aid is in a sense far more compensatory than either the EOp or
utilitarian rules recommend, because in actuality, African countries get Žfar. more
10
Observe that our data ends in 1994, before the Asian crisis.
166
Table 6
Actual, EOp, and utilitarian aid allocation
Algeria
Argentina
Bolivia
Botswana
Brazil
Cameroon
Chile
Colombia
Costa Rica
Cote d’Ivore
Dominican Rep
Ecuador
Eqypt
El Salvador
Ethiopia
Gabon
Gambia
Ghana
Guatemala
Guyana
Haiti
Honduras
Indonesia
Jamaica
Kenya
b
0.055
0.067
0.051
0.037
0.070
0.055
0.045
0.050
0.050
0.060
0.056
0.044
0.062
0.052
0.059
0.057
0.053
0.053
0.051
0.063
0.056
0.054
0.038
0.063
0.058
Ž% of GDP.
Žin milions of US$.
Actual
AidrGDP
EOp
AidrGDP
Utilitarian
AidrGDP
Actual
AID
EOp
AID
0.767
0.020
1.800
5.121
0.026
1.876
0.156
0.122
0.153
0.845
0.600
0.323
2.392
1.865
3.745
1.909
7.081
1.921
0.494
3.737
1.771
2.189
0.392
1.416
2.338
0.292
0
0.420
1.007
0
0.295
0.642
0.479
0.479
0.130
0.262
0.695
0.081
0.378
0.175
0.231
0.347
0.371
0.445
0.039
0.254
0.315
0.980
0.034
0.208
0
0
0
3.487
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
264.83
30.34
164.11
49.02
48.76
220.14
77.37
110.94
97.25
152.12
76.12
73.20
2,134.02
153.70
489.20
58.39
38.51
202.14
76.07
31.25
85.14
112.45
1,183.03
72.12
370.38
100.83
0
38.28
9.64
0
34.60
318.64
435.33
303.56
23.41
33.25
157.35
71.89
31.18
22.91
7.06
1.89
39.01
68.42
0.33
12.20
16.18
2,956.58
1.76
33.01
ŽUS$ per capita.
Utilitarian
AID
0
0
0
33.38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Actual
AID
EOp
AID
17.29
1.16
29.84
47.94
0.39
23.00
6.76
4.03
5.37
18.91
13.00
8.91
45.73
34.02
11.69
75.54
56.57
17.32
10.52
40.88
15.97
30.14
7.74
33.82
21.30
6.58
0.00
6.96
9.43
0.00
3.61
27.84
15.82
16.75
2.91
5.68
19.15
1.54
6.90
0.55
9.14
2.78
3.34
9.46
0.43
2.29
4.34
19.35
0.82
1.90
Utilitarian
AID
0.00
0.00
0.00
32.64
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Country
0.037
0.057
0.062
0.039
0.050
0.053
0.049
0.081
0.060
0.057
0.058
0.051
0.066
0.051
0.058
0.063
0.062
0.052
0.058
0.065
0.037
0.062
0.055
0.048
0.043
0.058
0.051
0.060
0.067
0.061
0.201
2.704
5.647
0.201
7.649
0.016
0.941
3.145
5.381
0.138
0.765
0.686
0.411
0.439
3.631
1.698
4.441
1.169
1.856
5.857
0.243
5.359
0.066
0.907
0.328
0.126
0.015
2.350
4.805
2.335
1.001
0.211
0.066
0.921
0.469
0.375
0.498
0
0.145
0.229
0.192
0.424
0.000
0.436
0.201
0.049
0.071
0.387
0.192
0
1.007
0.069
0.300
0.529
0.731
0.202
0.425
0.121
0
0.105
3.410
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3.481
0
0
0
0
0
0
0
0
0
515.59
169.49
224.43
147.78
332.06
63.04
405.87
118.57
178.88
103.42
952.96
48.27
159.57
386.15
225.31
52.00
248.23
370.11
659.16
701.17
408.34
96.66
6.90
200.90
709.66
17.10
13.51
286.10
201.42
251.01
2,565.86
13.21
2.63
676.81
20.38
1,502.32
214.93
0
4.83
171.95
239.25
29.81
0
383.58
12.49
1.49
3.97
122.45
68.15
0
1,691.81
1.24
31.25
117.17
1,582.12
27.47
395.72
14.78
0
11.28
8,741.32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5,849.57
0
0
0
0
0
0
0
0
0
13.42
18.25
29.31
10.30
42.07
0.92
20.24
40.69
34.60
1.37
10.66
14.60
9.00
7.73
43.68
15.30
40.90
24.50
72.31
31.63
8.70
35.21
6.39
26.39
12.27
5.80
0.88
10.67
33.11
27.61
66.79
1.42
0.34
47.19
2.58
21.84
10.72
0.00
0.93
2.28
2.68
9.01
0.00
7.68
2.42
0.44
0.65
8.10
7.48
0.00
36.04
0.45
28.94
15.39
27.36
9.31
25.73
0.55
0.00
1.24
227.53
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
124.60
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Korea
Madagascar
Malawi
Malaysia
Mali
Mexico
Morocco
Nicaragua
Niger
Nigeria
Pakistan
Paraguay
Peru
Philippines
Senegal
Sierra Leone
Somalia
Sri Lanka
Syria
Tanzania
Thailand
Togo
Trinidad y Tobago
Tunisia
Turkey
Uruguay
Venezuela
Zaire
Zambia
Zimbabwe
167
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
Fig. 5. Actual, EOp, and utilitarian aid allocations Ž% of GDP..
168
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
169
Fig. 6. Lorenz-type curves of the actual, EOp and utilitarian allocations.
than they ‘should’, and the East Asian tigers get less than they should. Does this
mean that the African countries are receiving too much aid and the East Asian
tigers too little? Not necessarily. For there are other possible objectives, even
within the rubric of equal opportunity.
Suppose our objective were not to equalize opportunities for growth, but rather
to equalize opportunities for GDP per capita. This means we would allocate aid to
try, roughly speaking, to equalize the distribution of GDP per capita, across
different types of country Žwithin each type of country, there will be a distribution
of GDP per capita, due to differential effort. We would allocate aid to try to
equalize those distributions across types.. One must first ask: over what time
horizon do we wish to equalize opportunities for GDP per capita? If the time
horizon were long, then present GDP per capita has almost no influence—differences across countries in GDP per capita in the long run will be determined
entirely by differentials in their rates of growth, and the equalizing opportunities
for GDP per capita is equivalent to equalizing opportunities for growth. Therefore,
the objective we have studied above is indeed equivalent to equalizing opportunities for GDP per capita in the long run. If, however, we adopt a short time horizon,
then the overwhelming determinant of cross-country differences in GDP per capita
170
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
is present GDP per capita, not the growth rate, and we would equalize opportunities for GDP per capita by spending aid primarily on the low GDP-per-capita
countries. Then the EOp allocation would give substantially more to the African
countries, and substantially less to the Asian tigers than the EOp-for-growth
allocation.
Now turn to the utilitarian rule. Here, the story is different. The allocation of
aid that maximizes the growth rate of GDP per capita of the class of developing
countries is exactly the same as the allocation that maximizes the GDP per capita
of the class of developing countries 1 year from now!11 So changing the
equalisandum from growth rates to levels makes all the difference in the short run
in the EOp formulation, but no difference in the utilitarian formulation. Formally
speaking, this is because the utilitarian objective function pays attention only to
rates of change and not to levels, whereas EOp pays attention both to levels and
rates of change. Finally, maximizing total GDP of the class of Žpresent-day.
developing countries in the long run means choosing that policy x that maximizes
ÝŽ1 q g i Ž x .. r Y i , for r large. This implies using the policy that maximizes the
maximum rate of growth Žmaximax. across the class of countries, a policy that
most would find abhorrent. Indeed, we see that, even when r s 1, we get almost
the maximax solution, in the sense that only three countries receive aid in the
utilitarian optimum.
6. Conclusion
We review our main points, both theoretical and empirical.
Ž1. What is often called efficient aid policy 12 is in fact utilitarian aid policy.
The distinction is important, because AefficiencyB bears the connation of valuefreeness, whereas utilitarianism, a political philosophy, is embedded with a view
about distribution—namely that that distribution is most desirable which maximizes the sum of utilities. The nomenclature AefficiencyB is better reserved for
Pareto efficiency.
Ž2. We introduce equal-opportunity policy, which differs in two ways from
utilitarian policy in conception—it is non-welfarist, and it does not seek to
maximize total income or the average growth rate. EOp seeks to equalize across
types of country, but maximize averages across effort quartiles of country.
Ž3. We compute both the EOp policy for growth, and the utilitarian-growth
policy. These policies differ; notably, at present levels of world aid, the utilitarian
policy would deny aid to all but three countries while the EOp policy would deny
11
Just observe that maximizing over x the expression ÝŽ1q g i Ž x ..Ž Y i r Y . is equivalent to
maximizing Ý g i Ž x .Ž Y i r Y ..
12
Most prominently, see The World Bank Ž1998..
H.G. LlaÕador, J.E. Roemerr Journal of DeÕelopment Economics 64 (2001) 147–171
171
aid to only a handful of countries. The EOp policy is more egalitarian than both
the utilitarian policy and the actual allocation, at present levels of world aid.
Ž4. Both policies differ substantially from actual aid policy, which allocates
more to African countries and less to the East Asian tigers, than either of the
policies in Ž3..
Ž5. Is there a way of ‘rationalizing’ observed policy, that is, of explaining it as
the outcome of maximization of a Žsocial welfare. function? We suggest that the
observed policy might resemble a policy that equalizes opportunities for per
capita GDP, rather than for growth. We explained that this can be interpreted as a
concern with average consumption Žper capita GDP. in the short run, as opposed
to the long run.
Ž6. In addition, the observed policy differs from the policies in 3 because it is
Žobviously. not drawn from a unidimensional policy space. That is, our optimization exercise, with a unidimensional policy space, precludes the variation in policy
among countries that one observes in reality, and that one might like to have.
Introducing more dimensions into our policy space is in principle possible, but
would complicate the analysis substantially.
Acknowledgements
We wish to thank Oscar Jorda for his advice and suggestions. Humberto
Llavador gratefully acknowledges financial support from the Fundacion
´ Ramon
´
Areces.
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