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ALTERNATIVE ESTIMATES OF THE REAL COST OF AID*
by
Jagdish N. Bhagwati
Number 37
February 1969
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
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FEB
'.TECH
3
1969
DEWEY LIBRARY
ALTERNATIVE ESTIMATES OF THE REAL COST OF AID
by
Jagdish N. Bhagwati
Number 37
February 1969
* The views expressed in this paper are the author's sole responsibility, and
do not reflect those of the Department of Economics, nor of the Massachusetts
Institute of Technology.
.
Alternative Estimates of the Real Cost of Aid
Jagdish N. Bhagwati
Economists have been properly concerned recently about the overall
net deterioration in the real worth of the foreign aid flow to the developing
countries.
This has been partly due to the near stagnation in the gross aid
flows, the growth in amortization and interest payments on past aid flows 9
and the rise in the price level of the commodities which aid enables
recipients to purchase.
Furthermore, it has also resulted from a general
net deterioration in the terms and conditions of foreign aid.
the broadest sense, terras and conditions include:
(1)
Defined in
the mix of leans and
grants in the gross flow, as also the terms of the loans relating to maturity,
interest and grace periods on interest and amortization; (2) the tying of
aid by source;
the tying of aid by projects, "maintenance" or non-project
(3)
uses, and by commodity specification (including P.L.480 type, direct com-
modity assistance)
;
and (4) political strings which may involve sacrifice of
non-economic objectives or economic policy conditions which may result in the
imposition of (objectively) sub-optimal economic policies on the recipient
countries by messianic but inept experts assisting the donor countries or
staffing the multilateral institutions which dispense aid.
I wish to thank Carol Gerstl and Andrea Beller for assistance with
the computations which were carried out at the International Economics Workshop of Columbia University; and Loda Berlage for computational assistance
financed by the M.I.T. Center for International Studies. Detailed breakdowns of primary and intermediate information, for 1962-1966, are contained
in Tables 7-66, not printed here but available from the author on request.
Paul Rosenstein-Rodan, C. P. Kindleberger and Paul Streeten have made
va luab 1 e c ommen t s
,
.
-2-
In this paper, I wish to concentrate on just one dimension of the terms
and conditions of foreign aid:
diverse terms of the loans.
its division between loans and grants and the
Furthermore,
from the donor country's viewpoint.
point of view, grants are
mors-,
I
wish to examine this question
While it is clear that, from the donor's
expensive than loans and that "softer" terms
on the loans imply, in general, higher cost than "harder" terms, the question
of the "real cost" of aid burden to the donor country requires greater pre-
cision, especially if we are to discuss important questions relating to
(i)
the absolute level of the aid-burden borne by individual donors, say 9 in
relation to their G.N. P. levels and (ii) the associated problem of the distribution of the overall aid burden among different donors.
It has become customary, since the empirical work of John Pincus to
deflate the figures of the flow of foreign assistance by adjusting them for
the present discounted value of the stream of repayments and interest payments
involved in loans as distinct from grants.
2
The procedure involves choosing alternative discount rates by which
the stream of amortization and interest is discounted back to current value
and then deducted from the
cost" of the aid.
nominal value of the aid flow to give the "real
The rates chosen vary from the country's own long-term
rate (which presumably measures the return that the donor country would have
earned if the sum had been invested domestically instead of given abroad via
aid) to the profit rate earned by private foreign investors (which presumably
2
The estimates by Little and Clifford [3] follow essentially the
procedures as devised by Pincus [4].
These methods were suggested originally
by Rosenstein-Rodan [5].
Note that "non-economic" returns such as political
"influence" are being ignored in the analysis.
So also is the possibility
that aid may involve zero opportunity cost under conditions of Keynesian
unemployment
.
-3-
measures the cost that the recipient country might have had to pay to borrow
foreign capital if the aid had not been forthcoming)
3
This paper (1) examines the Pincus-type approach critically and outlines an alternative approach to the method of deflation which is analytically
superior (Part I); (2) develops alternative estimates of the real cost of
foreign aid to the major O.E.C.D. donor countries for 1962 to 1966 to illustrate the
new approach developed here; and (3) compares these estimates (i) with those
reached by using the Pincus-approach and (ii) with those resulting from the
use of unadjusted, nominal flows of official aid.
I:
Methodology
The correct procedure in estimating the real cost of foreign aid,
leaving aside for the time being the thorny questions associated with the
tying of aid, is to ask what would happen if the aid were not forthcoming.
Clearly, there will be a multiplicity of possibilities and effects.
But
at minimum , one could proceed to consider as a realistic possibility that
some part of the aid flow would be borrowed, and allowed to be borrowed, on
commercial terms whereas the res t would have to be absorbed domestically by
the donor country.
Given the current annual magnitudes of official assistance,
it seems highly dubious and unrealistic to argue that the same level of funds
would be borrowed fully (or not at all) at the commercial terms that would be
demanded for private lending to the less developed countries (LDC's).,
3
Note that the benefit the recipient country receives by virtue or
foreign aid, and hence the cost to it of withdrawing it, has no relevance
in itself to the cost that the donor country suffers from undertaking the
aid operation.
Hence, taking the private foreign rate of return on capital
as the discount rate has no meaning insofar as it is used because it is
considered to indicate the benefit to the borrowing country (which, incidentally, it does not).
,
:
-4-
Consider, for example, the idealised Figure 1, which illustrates a
hypothetical schedule of demand for foreign funds by LDC's, D'D, and a
supply schedule of such funds from private sources to the LDC's assuming
the withdrawal of aid
FQ.
.
Aid is assumed to be given at "price" OF, in amount
If it were withdrawn, the amount "commercially borrowed" would be FL
and the volume of funds QL would be the rest of the aid flow that would
then be ploughed back domestically.
It has been argued, so far, that it
seems unlikely that QL will be zero.
But, for analytical completeness (in the methodological discussion)
let us distinguish between (i) Case
I
:
QL =
and (ii) Case II
;
QL > 0*
These cases are discussed successively now.
Case I
Borrowing replaces aid totally (QL = 0)
:
In this case, since aid has been fully replaced by private borrowing
on commercial terms, we have a neat case where we can readily identify the
difference between the terms on which a given amount was granted as foreign
aid and the (stiff er) terms on which it would have been otherwise borrowed.
Since the "terms" involve the maturity of a loan, the rate of interest
charged and the time profile of repayments (including grace periods)
,
the
cost of aid, defined as the benefit foregone by giving foreign aid as against
not giving it, will be equivalent in our present case to a time stream of
differences between (i) the aid stream of amortization and interest payments
and (ii) the commercial-borrowing stream of such amortization and interest
payments.
Thus, for any given value of foreign capital, if Time Stream I
Y1
represents the time profile of amortization and interest payments
...
Y
under foreign aid, the Time Stream II
;
Y-
Y
;
the time profile thereof
under commercial borrowing, then the (opportunity) cost of foreign aid is
Figure
(1)'
Price of
Foreign Funds
Volume of Foreign
Funds
is the demand schedule for foreign funds for the recipient countries and
the supply schedule of funds to them if aid is not given.
Aid is assumed
offered at price OF and at level OR « QF.
If it were withdrawn, the amount
borrowed would be FL which would be below the aid level by LQ.
DD'
SS'
:
-5-
represented by Time Stream III
:
(Y^ -
yJ)
,
(y!J
- Y^)
, =
. ,
(Y^_
n
- Y*
)
,
Since time profiles such as this are not easy to deal with, it would
be useful if they could be discounted back to their current value.
that there
is_
Assuming
a discount rate which measures the productivity of capital to
the donor country in question, such a discount rate could be used for reducing
Time Stream III to a single , workable figure of the real cost of foreign aid.
Note, therefore, that we would require, for our calculations, if we
are to end up with a single number:
the a ctual Time Stream I of amortization and interest payments;
(i)
(ii)
payments
;
the hypothetical Time Stream II of amortization and interest
and
(iii) a relevant discount rate which measures the productivity of
resources to the donor country in question.
Case II
:
Borrowing is less than aid flow (QL > 0)
In this case, clearly two stages of calculation would be involved.
First , for the overlapping part (i.e. FL in Figure I), which is equal
to the amount borrowed,
Case
the same analysis and calculation would apply as in
I.
However, to this cost, we would have to add the second element of
cost which relates to the part that is not borrowed when the aid is with-
drawn (i.e. QL in Figure 1).
To the stream of repayments and interest charge
associated with this "unborrowed" part of the aid flow (QL) we would then
apply the same, relevant discount rate and reduce it to its discounted current
value, deduct it from the aid flow (QL)
this part (QL) of the aid flow.
,
and thus arrive at the real cost of
-6-
Thus, in this realistic case we would need to know, in addition to the
three items required for Case
(iv)
I:
the proportion of aid flow that would be (commercially* borrowed,
International Comparisons
:
Are the estimates of real cost of aid to donor
countries, thus derived, dir ectly comparable from the viewpoint of determining
the distribution of the aid burden ?
to be pointed out,
(1)
Two qualifications of significance need
if such comparisons are attempted.
The single numbers of cost of foreign aid, derived by the procedures
detailed above, hide an important dimension:
namely, the rates of discount
(equivalent to the domestic productivity of resources) which are used to arrive
at these numbers.
Are $X million, calculated as the real cost of aid to the
United States at, say, 5% discount rate, equivalent to $X million, similarly
calculated to be the real cost of aid to the United Kingdom at, say, 6%
discount rate?
Clearly not:
for, the same adjusted flow of aid to the United
States will be less productive than to the United Kingdom (6% > 5%).
Hence,
unless the discount rate used for all donor countries is identical (which
would certainly be an unrealistic assumption in an imperfect world), the
mere comparison of the real-cost-of-aid-f igures will be misleading in its elf
in judging comparative burdens of aid flow among the donor countries.
(2)
Moreover, while different rates of discount may be used, cor-
responding to the domestic productivity of resources, for computing the aid
burden, if the resulting figures are to be compared we would have to assume
that the social time rates of discount are identical between the donor countries
(unless the capital markets are perfect and the time rate of discount is
adequately reflected by the rate of interest).
Do we also have to assume that identical utility weights are to be
used in making such international comparisons?
This would be necessary, of
-7-
course, except that we can alternatively compare the distribution of the aid
burden, computed without such adjustment, with what we would wish it to be
jlf_
utility weights were assigned on different ethical principles such as,
for example, progressive burden-sharing on the basis of per capita incomes.
Limitation of Pincus- type Procedures
:
4
How does the analysis presented above
compare with the procedures of computation used by Pincus [4] and later
writers?
(1)
Their procedure implicitly amounts, in essence, to assuming either
that all aid, if withdrawn, will be put to domestic use; or (2) that if
any aid is commercially borrowed, on withdrawal, it will be lent at the same
rate as the discount rate used to reduce the time stream of costs to their
current value.
Only under either of these assumptions, it will make sense to
use a unique rate of discount to deduce the real cost of aid, by the Pincustype procedure.
But neither of these implicit assumptions seems plausible:
all aid
surely will not be put to domestic use, and the (net-of -recipient-country-tax)
commercial lending rates on private foreign loans and investment cannot be
expected, in an imperfect market, to equal the (gross-of-own-tax)
domestic productivity of resources.
,
marginal
Hence, the computational procedure for
making calculations of the real cost of foreign aid must be adjusted so as to
allow for the possibility of some aid being borrowed commercially and the (net)
terms of this borrowing being different from the (gross) domestic productivity
4
The
This is, in essence, what is done by Kravis and Davenport [2],
desirability of progressivity in international aid-burden sharing has been
stressed by several liberal economists, including Thomas Balogh and Paul
Rosens tein-Rodan.
In the following discussion, attention is confined to the methods of
discounting used in these writings.
It should be pointed out here, however,
that the qualifications noted in the text, in discussing the question of international comparisons, apply equally to these writings. While these qualifications
are noted here for the first time, the new calculations to be presented in
Section II will abstract from the resulting complications.
-8-
of resources in the donor country.
More realistic calculations will have to
proceed, therefore, by making alternative assumptions with respect to (1)
how much of foreign aid, if withdrawn s can be expected to be borrowed; aad
(2)
at what (net-of-recipient-country-tax)
,
marginal terms it would be
borrowed.
II:
Alternative Calculations
We proceed now to present new estimates of the real cost of aid to
donors.
These estimates, as also those of earlier writers , need to be treated
with reasonable skepticism, and are equally more illustrative than definitive,
for they rest at several stages on assumptions which are seriously debatable.
Since a major purpose of the calculations is to examine the diff erences that
emerge in the ranking of donor countries, when the method of discounting is
adjusted as argued above, from those resulting from earlier work, we will
continue to make identical assumptions except where our method departs from
earlier ones.
In what follows, we will work with the following assumptions:
(1)
three alternative assumptions concerning the proportion of foreign
aid loans that will be borrowed commercially:
one-fourth, half and three-
fourths;
7
(2)
three alternative discount rates:
(3)
two alternative terms of the commercial borrowing at:
3%, 4% and 5%;
6% interest
The trade-offs between private investment and official aid could be
guessed at by cross-section and time series analysis of recipients, for example;
Ky Areskoug at Columbia University is attempting this.
These are again assumptions with respect to the productivity of domestically used resources; they could have been taken to be approximated by the
long-term bond rates, as suggested by Pincus [4] and Little [3], but this seems
dubious too.
;
-9-
Q
rate and 5 years maturity; and 15% interest rate and
(4)
5
years maturity;
and
identical application of the preceding three specifications to
all donor countries, thus ruling out international variations arising from
this source.
Note that no allowance is made for the reduction in real cost of aid
resulting from aid-tying by source or by commodity or project specification.
The estimates are made for each of the years 1962-1966
data produced by the Deve lopment Assistan ce Committee (DAC).
eleven major donor countries.
,
10
using O.E.C.D.
They cover
In common with Little and Clifford
[3J, the
following assumptions are made in dealing with the different entries in the
tables on flow of official assistance; the only differences being those intro-
duced from the changed methods of discounting:
(1)
"Grants" are treated at full value;
(2)
"loans repayable in local currencies, net" and "sales for recipients'
currencies, net" are taken as either grant-equivalents (Assumption A) or as in-
volving zero real-cost (Assumption B)
(3)
"multilateral contributions" are treated as grant-equivalents; and
(4)
private capital transfers are excluded altogether.
Furthermore, since the DAC estimates of aid flows give only the total flows
The first terms have been taken simply from the stiffest average terms
among donor countries in 1962, of Austria; the second set of terms are much
stiff er and hypothesised.
9
This eliminates one of the two major difficulties noted concerning
international comparisons.
Aid- tying by source, when effective, amounts to a transfer of real
resources from the recipient to the donor country, insofar as the former effectively subsidises the exports of the latter instead of the latter having to
do so.
Twenty percent seems to be around the upper limit of such transfers,
according to recent estimates. Cf. Bhagwati [1].
-10-
and the average interest rates and maturity on loans for each DAC country, we
have worked with two alternative estimates of actual time-paths of loan repayments, based on the alternative assumptions that the grace-period on repayment
of principal is one year or five years
[3].
We have altogether therefore three alternative estimates of the rate of
discount, four of the proportion of aid that would be borrowed (including the
option of zero lending assumed by Pincus) two of the terms on which commercial
borrowing would occur and two of how commodity assistance is evaluated.
Further, we have worked with two estimates of the actual time profile of amor-
tization and repayments.
Hence, for each country, we can have altogether 72 +
12 (on zero-lending terms) = 84 estimates for each year, of its cost of aid.
In practice, however, only United States and Germany have commodity
assistance during the years chosen, so that for each of the remaining countries
we have only 36 +
6 = 42
alternative estimates.
These measures constitute
essentially a set of "sensitivity" exercises, designed to see how far the ranking
of countries by calculations of the real cost of their aid can be treated as a
reasonably acceptable, statistical index for reaching policy ocnclusions with
respect to actual distributions of the aid burden.
T he Results
:
The resulting estimates of the real cost of aid, turned into
percentages of the GNP of respective donor countries, have been reproduced in
Tables 1-5 along with the ranks of the different donor countries under each
alternative estimate.
Furthermore, for comparison, the ranks of the donors
by nominal, unadjusted aid flows have also been calculated.
Table
6
records the
It should be noted, however, that the ex post actual time profile will
frequently differ from the ex ante time profile which is considered in the calculations presented here, thanks to debt-rescheduling adjustments.
-11-
weighted average maturity periods and interest rates which have been used in
these calculations.
Among the important conclusions which emerge from our calculations are
the following:
(1)
The real-cost estimates often have a striking impact on the aid-flow
estimates as percentage of GNP:
cases.
the burden reduces dramatically iu several
Austria, in 1966 for example, shows only one-eighth of its nominal
burden if we take the zero-lending assumption at 4% discount rate and a one-year
grace period, and as little as one-fourteenth if we take a five-year grace
period (Table 5)»
In the same table, Italy's burden is practically halved for
nearly all the estimates.
For Portugal, the burden almost disappears at 3%
discount rate, zero-lending and a five-year grace period in 1964 (Table 3); and
similar calculations in Table
1
show the burden even turning negative (at -0„3%
of GNP in 1962 for 3% discount rate, zero-lending and five-year grace period),
underlining the moral that "aid" is not always as altruistic as it may appear.
Among the nations which seem to emerge rather well, however, are the United
States (whose terms and conditions for loans are reputedly soft) and France
(whose percentage-of-GNP aid burden continues to be in the range of three-fourths
of one percent despite the alternative adjustments).
(2)
Another important consequence of our deflation is that the ranking
of donors by their real cost of aid as a percent of GNP is strikingly different
from that for nominal, unadjusted aid figures, generally regardless of the real
cost estimates chosen.
Among the sensitive countries is Portugal which drops
sharply from the first rank in 1964 and 1966 (and second in 1965) by the
nominal aid estimates to fairly near the bottom of the scale for some real-cost
estimates and does only a little better for estimates based on the assumption
either that 50% or 75% would be lent at the highly favourable interest rate of
-12-
15% or that the discount rate is at 4% or 5%.
On the other hand, Canada rises
steeply to a higher rank in 1965 and 1966 by most adjustments.
(3)
Finally, the results are sometimes sensitive to changes in the
assumptions about the proportion of aid that would be lent to LDC's if aid were
withdrawn, the terms and conditions on which such lending would accrue, and
the discount rate chosen.
This is indeed what we would expect from the different
combinations of grants and loans, and the different terms and conditions of loans,
among the donor countries.
12
The ranks of several countries are admittedly
fairly, though not totally, stable:
France, for example, remains at the top
through all variations whereas the United States varies at maximum from the
fourth to the sixth rank (in 1966).
On the other hand, a few countries show
remarkable volatility in ranking as the assumptions change.
Portugal , for
example, goes from the first to the eighth rank in 1965 at 3% discount rate
(Table 4); and Canada goes from the fifth to the eighth rank in 1965 at 3%
discount rate (Table 4).
It is clearly,
therefore, somewhat hazardous to rank donor countries by
their aid/GNP shares and deduce conclusions about donor-generosity and aid
policy even when the nominal aid flows have been adjusted to real-cost
equivalents.
The zero-lending Pincus-adjustment itself represents only one of
several possible ways of aiming at "real-cost" estimates from which choice
must be made, since the results can, and (as we have shown) in actual practice
do, vary with the adjustment-method adopted.
12
The precise manner in which changes in ranks are brought about can be
inferred by examining the behavior of the loans in response to alternative
methods of adjustment to get their real-cost equivalent. These data have been
stencilled, for the years 1962-1966, for each donor country, along with the
grants and grant-equivalent estimates, (as Tables 7-66), and are available from
the author on request.
References
[1]
Bhagwati, J.
The Ty ing of Aid.
UNCTAD Secretariat, 1st November 1967;
prepared for and forthcoming in Proceedings of the second UNCTAD
Conference in New Delhi; reprinted in J. Bhagwati and R. So Eckaus
(ed.), Foreign Aia
Penguins (Modern Economics Series), 1969.
„
[2]
Kravis,
"The Political Arithmetic of InterI. and M. W. S. Davenport.
national Burden- Sharing ," Journal of Political Economy August
1963, pp. 309-330.
.
I. M. D., and Clifford, J.
Unwin, 1965.
International Aid
[3]
Little,
[4]
Pincus, J. "The Cost of Foreign Aid," Review of Economics and Statistics
November 1963, pp. 360-67.
[5]
Rosens tein-Rodan, P. N.
"Determining the Need for and Planning the Use of
External Resources," Center for International Studies M.I.T.,
Cambridge, 1962.
.
London;
,
Allen &
,
General Notes to Tables 1-5
In each table, the countries are listed according to
their ranks, in descending order, given by the
percentage of nominal aid to G.N. P. level.
The A-estimates, for U.S.A. and Germany, represent estimates
of "real cost" of aid, assuming that "loans repayable in
local currencies, net," representing primarily commodity
assistance for the U.S.A., are to be treated at full,
nominal value. Under the B-assumption, however, they are
treated as having zero opportunity cost and thus assigned
only zero "real cost." The ranks assigned, when there
are both A and B estimates, are by A estimates only. The
ranks change sometimes, if B estimates are used,, but not
always.
3.
The ranks of the countries for each estimate presented,
are given in brackets, directly under the percentage
estimates.
4.
The primary information, on unadjusted loan and aid flow
levels, and the processed information on the real cost
equivalents of loans (as distinct from overall aid) are
given separately in the countrywise tables which start
from Table 7.
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