WPS4541
Policy ReseaRch WoRking PaPeR 4541
The Fiscal Impact of Foreign Aid in
Rwanda:
A Theoretical and Empirical Analysis
Kene Ezemenari
Ephraim Kebede
Sajal Lahiri
The World Bank
Africa Region
Poverty Reduction and Economic Management 3 Division
February 2008
Policy ReseaRch WoRking PaPeR 4541
Abstract
The inflow of large quantities of foreign aid into Rwanda optimal tax rate and the proportion of public expenditure
since 1994 can have potential adverse effects such as allocated to public investment. The econometric analysis
aid dependency via a significant negative effect on tax uses time series data on Rwanda to show, in line with
efforts and on public investments. This paper carries other studies in the literature, a negative relationship
out a theoretical and empirical study to examine these between increased aid and the tax rate; but the magnitude
issues. The theoretical part develops a model in which of the effects are extremely small. In the case of Rwanda,
the recipient government decides on the optimal level reforms to the tax administration and expansion of the
of tax and optimally allocates total government revenue tax base have had mitigating effects. As far as the effect
between current expenditure and public investment. on public investment, the overall effect was negative in
The theoretical model makes it possible to empirically the past; however, since 1995 the direction of this effect
test whether an increase in aid is likely to reduce the has changed.
This paper--a product of the Poverty Reduction and Economic Management 3 Division, Eastern Africa 2 Country
Department--is part of the series of background papers that informed the Country Economic Memorandum, "Rwanda-
-Toward Sustained Growth and Competitiveness. Policy Research Working Papers are also posted on the Web at http://
econ.worldbank.org. The authors may be contacted at Kezemenari@worldbank.org, ekebede@worldbank.org and lahiri@
siu.edu.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
The Fiscal Impact of Foreign Aid in Rwanda:
A Theoretical and Empirical Analysis
By
Kene Ezemenari,a Ephraim Kebede a and Sajal Lahiri b
JEL Classifications: F35, H21, H41, O55
Keywords: Foreign aid, Rwanda, Tax effort, public investment, aid fungibility
aAfrica Region (AFTP3), Poverty Reduction and Economic Management,
The World Bank, 1818 H St., Rm J7-133, Washington, D.C. 20433, U.S.A.;
E-mail: KEzemenari@worldbank.org and ekebede@worldbank.org
bDepartment of Economics, Southern Illinois University Carbondale, MC 4515,
1000 Faner Drive, Carbondale, IL. 62901, U.S.A.; E-mail: lahiri@siu.edu
1. Introduction
This paper examines the impact of aid flows on fiscal policy in Rwanda. A tremendous
amount of aid has been transferred to the country to assist in rebuilding the infrastructure
and institutions that were destroyed in 1994. As the country moved from a period of
reconstruction and stabilization toward sustained growth, total overseas development
assistance (ODA) as a share of GDP averaged 29.7 percent and dropped from 95 percent
in 1994 to 19.2 percent in 2004. Between 2005 and 2006, total ODA averaged just over
14 percent of GDP. However, over the past decade, foreign direct investment as a share
of GDP averaged only 0.23 percent of GDP, while average savings as a share of GDP
was -1.4 percent, highlighting the importance of ODA in sustaining the growth
experienced over the past decade.
With the new G-8 initiative on debt forgiveness and an increased focus of donors
on the poorest countries, particularly those in Africa, there are good indications that the
level of support to Rwanda is likely to be scaled up. Over the period, 2007 to 2020, aid
flows could double to as much as 30 percent of GDP, provided the government continues
to maintain sound policies. This would give rise to a substantial inflow of aid to the
economy, while domestic revenue would likely remain below 20 percent of GDP.
To ensure that these high levels of aid lead to sustained growth and macro
stability, it is useful to evaluate the impact of aid on key policy variables, particularly
related to fiscal policy. In this study we will assess the fiscal impact of aid in Rwanda
through an econometric analysis of historical trends over the past, and the impact of these
trends on key variables of fiscal policy in Rwanda, over the period 1980 - 2004.
2
The theoretical and empirical literature to be discussed below shows that aid can
undermine revenue mobilization. This implies that if aid discourages tax effort, it can
perpetuate or even increase aid dependency. Thus, we will examine whether this is the
case in Rwanda. Has aid discouraged tax effort? Secondly, we shall examine if aid has a
negative effect on the proportion of public expenditure allocated to public investment.
Following the seminal work of Heller (1975), there is now a substantial theoretical and
empirical literature on the fiscal consequences of foreign aid (see, for example, Mosley et
al., 1987; Binh and McGillivray, 1993; Feyzioglu et al., 1998; Franco-Rodriguez et. al.;
1998, Swaroop et al., 2000).1 This literature examines the effect on foreign aid on tax
revenue and public investment.2 On the theoretical side, most models work with variants
of the framework developed by Heller (1975) in which the government's objective
function is quadratic in a number of macro variables such as the difference between the
level of public investment and its target value, the difference between tax revenue and its
target value, and so on. This choice of the objective function is somewhat ad hoc. On the
empirical side, the literature covers time-series country studies, cross-country studies, and
also panel data analysis. Although there are some exceptions, on the whole, the literature
indicates that aid has a negative effect on tax revenue, but not so on public investment.
This paper contributes to this expanding literature in two ways. First of all, we
develop a different theoretical framework based on microeconomic and welfare-theoretic
principles with distortionary and revenue-raising effects of taxes. The government in our
framework uses the tax rate and the allocation of total expenditure between current
1See McGillvary and Mossissey (2004) for a review of the literature.
2There is also the broader literature on aid fungibility; fiscal channels being one of many ways in which
full effects of aid may not be realized. See, for example, Khilji and Zampelli (1994), Pack and Packi
(1994), Feyzioglu et al. (1998), and Lahiri and Raimondos-Møller (2004) for the issue of aid fungibility.
3
expenditure and public investments as instruments for maximizing inter-temporal utility.
We also distinguish between private and public investments. On the empirical side, we
focus on a country in Africa, namely Rwanda, which has drawn very little attention in the
literature, but has received large amounts of foreign aid particularly since 1994. Rwanda
has also gone through a significant change in terms of policy regime since 1994. Thus, it
would be interesting to examine if the fiscal effect of aid has changed qualitatively due to
a new policy environment. Finally, whereas the bulk of the literature examines the effect
of aid on the levels of tax revenue and public investment, in this paper we focus on in
both the theoretical and the empirical part -- the effect on the rate of taxation and the
proportion of total government expenditure that is allocated to public investment.
The paper proceeds first by outlining a theoretical model that will enable an
examination of the fiscal effects of increased aid. Regression analysis is used to examine
the effect of increased aid on key fiscal variables.
2. The Importance of Aid in Rwanda
The importance of aid in Rwanda stems from it being the main source of capital flows
and financing for investments (given the extremely low levels of foreign direct
investment), as well as its impact on macroeconomic stability. In the balance of
payments, capital flows are primarily capital grants and net borrowing (on concessional
terms), and aid is the major source of finance for the budget. In addition, aid funds have
led to increased liquidity in the economy which has required close monitoring and
management to maintain macroeconomic stability. Surges in foreign aid, following the
4
1994 crisis, resulted in increases in M2 (narrow money) and large changes in nominal
GDP and inflation.
Figure 1: Public Investment is Defined by Availability of Donor Grants
1994-2004 (percent of GDP)
14
12
10
8
6
4
2
0
1990 1992 1994 1996 1998 2000 2002 2004
Public investment Grant
Source: World Development Indicators and IMF, as cited in World Bank (2007).
These changes were due to several factors. First, the government introduced new
notes and coins, which had the effect of devaluing the national currency by 45 percent.
Second, there was a huge increase in the amount of currency in circulation in a situation
where people were forced to keep their money in very liquid form. These factors
contributed to an average rate of growth of narrow money of 11.4 percent over the period
2000-04 (and contrasts with a growth rate of 14.8 percent during 1990-99, and 3.9
percent over the period 1980-89).
Given the high level of liquidity arising from the large inflow of aid, the
government's approach to sterilizing the excess liquidity also has had an impact on fiscal
5
policy. To control inflation and the growth in the money supply, the government has
resorted to the sales of treasury bills. This has resulted in an increase in domestic debt
from a level of less than 5 percent of GDP, over the past two years, to 6 percent in 2006.
World Bank (2007) reports that there was some indication of potential crowding out of
the private sector, as credit to the economy and net credit to government displayed moved
together in a counter-cyclical fashion, between 1998 and 2003. Up until 2003, this
counter-cyclical trend between the two series (credit to the economy and government),
was more pronounced because t-bills were used mainly to finance the budget. Between
2002 and 2004, shortfalls in budget support, coupled with increased spending (i.e. on
elections), contributed to increased sales of t-bills, as a means of financing the budget.
Since 2005, sales of foreign exchange have become an increasingly important instrument
for sterilization of excess liquidity. However, given government's concern on the
potential effects of exchange rate appreciation on exports, emphasis has been placed on
the use of t-bill sales as a tool for monetary management. In the past year or so, however,
increased liquidity in the commercial banks, arising from buoyant activity in the NGO
sector (as demonstrated through increased disbursements to project accounts), has
provided an additional source of liquidity and therefore eliminated the countercyclical
trend between credit to the economy and government. As a result, the two series have
moved in a pro-cyclical fashion since 2005 (see Quarshie 2007).
The evidence, on the face of it, indicates that increased aid flows have not
adversely affected the level of revenue and that expenditure has been mainly on priority
poverty reduction areas. Revenue as a share of GDP has increased steadily since 1998
from around 10 percent to just over 14 percent of GDP in 2006. In case of priority
6
expenditure, Table 1 shows that there has been an increase in allocation to priority areas
since 1998 (both during the period of decline in aid, between 2002 and 2003, and from
2004-2005 when aid flow increased again).
Table 1: Rwanda: Priority Spending, 1998-2005
(In percentage of GDP)
1998 1999 2000 2001 2002 2003 2004 2005
Total Budget 18.9 19.7 18.7 21.0 21.3 21.9 25.2 26.2
Total priority expenditure of which: 2.8 3.9 5.3 5.3 6.4 6.9 7.0 8.4
Education 2.2 3.2 3.5 3.5 3.6 3.8 3.9 3.9
Health 0.4 0.5 0.7 0.7 0.8 0.8 0.8 0.9
Agriculture 0.0 0.0 0.2 0.2 0.2 0.2 0.2 0.4
Export promotion 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.5
Transport and communication 0.0 0.0 0.1 0.1 0.4 0.5 0.4 0.9
Infrastructure(Energy and water) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.3
Common Development Fund 0.0 0.0 0.0 0.0 0.1 0.3 0.3 0.3
Other* 0.2 0.2 0.2 0.9 0.5 1.0 1.3 1.3
Source: Rwandese authorities and World Bank (2007).
* This category includes spending on internal affairs, local government, commerce, and youth and sports.
In addition, since 1998, the government has adopted reforms to improve the
efficiency of tax administration and revenue. The Rwanda Revenue Authority, charged
with tax collection, was established in 1997. Four years later, the value-added-tax was
implemented and a year later, in 2002, the tax code was revised. The result was that
government revenue, estimated at about 13 percent of GDP in 1992, and which had fallen
to below 4 percent in 1994, began to increase gradually to reach an average of around 10
percent per annum between 1996 and 2001. By 2002, revenues stood at 12.2 percent of
GDP, reflecting the increase in the VAT rate from 15 to 18 percent, and the substantial
strengthening of revenue administration. Revenue as a share of GDP rose further in the
following years and is now just under 15 percent. Thus, the increased share of tax
7
revenue out of GDP reflect past reforms, and further reforms that took place from 2003,
including the taxation of in-kind benefits.
The discussion above, along with the data in Table 1 and the trend in revenue
(compared to that of foreign aid), shown in Figure 2 below, suggest that increased aid has
not adversely affected tax revenue and spending for poverty reduction. It may however,
have increased the level of domestic borrowing. Aid has been spent on the priority areas
identified in the government's Poverty Reduction Strategy. To examine the marginal
impact of aid on these variables, the next section elaborates a theoretical model which is
then estimated econometrically in section 4.
Figure 2: Trend in Foreign Aid (including Grants and Loans), Domestic Revenue
and Borrowing, 1980-2004
18 100
90
d 16
an 14 80
gniworrob 12 70
eu 60
10 DA
50
8 Ot
40
ic evenR Ne
6 30
est
moD 4 20
2 10
0 0
1980198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004
Domestic borrow ing Revenue Net ODA
8
eu 18 140
16 120
evenr 14
d 100
12 n
an
gni 10 80 oal
worrob 8 60 ngier
6
40 Fo
ic 4
est 2 20
moD 0 0
1980198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004
Revenue Domestic borrow ing Foreign loans
140
120
100
PD 80
G
% 60
40
20
0
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Grants Foreign loans Net ODA
Source: World Development Indicators and authors' calculation.
Note: Grants to government include unrequited, non-repayable, noncompulsory government receipts from other governments or international
institutions. Foreign loans represent debt outstanding and disbursed. Net ODA disbursements equal gross ODA disbursements less principal repayments
(amortization) of previous ODA loans. All variables are given as a ratio of GDP
9
3. A Theoretical Model
We consider an open economy lasting two periods, 1 and 2. Since we do not
consider any issue related to trade, for simplicity, we assume that it produces one final
(consumption) good per period. The second-period price is taken as the numeraire, and
we denote by p the relative price of the good in the first period.
There are two types of capital: private and public. The economy starts at t=1 with
K units of private capital. At t=1, the private sector adds to this through investment, I,
which becomes available at t=2.
The government derives its revenue in period 1 from three sources: from foreign
aid T, from consumption tax at the rate , and from lump-sum tax L. A fraction of
government revenue is used to accumulate public capital. The remaining (1-) fraction of
government revenue is used to produce a public good (g) which gives utility to the
people. This expenditure can be thought of as a recurring or social expenditure. The
economy starts at time t=1 with F amounts of public capital. At t=1, the government
adds to this through public investment, F, which becomes available at t=2. Public
investment can be thought as development expenditure such as infrastructural
development.
On the demand side of the economy, utility level u, as previously noted, is
positively affected by the provision of public good. The inter-temporal expenditure
function E(p(1+), 1/(1+r), g, u) denotes the minimum expenditure (in present value)
required to achieve a given level of utility u at constant consumer prices and public good
provision level. r is the rate of interest. The partial derivative of the expenditure function
10
with respect to u, Eu, denotes the reciprocal of the marginal utility of income.3 Since
public good increases household utility, the partial derivative of the expenditure function
with respect to g, Eg, is negative and -E5 denotes the households' marginal willingness to
pay for the public good (e.g., see Chao and Yu, 1999). That is, a higher level of public
good consumption requires a lower level of spending on private goods to mitigate its
positive effects so that a constant level of utility is maintained. The expenditure function
is assumed to be strictly convex in g, i.e. Egg > 0. That is, a higher level of public goods
provision reduces the households' marginal willingness to pay for the public good. It is
also assumed that Egu < 0 , i.e. a higher level of utility increases the households'
marginal willingness to pay for the public good. Formally,
Assumption 1 Egu < 0 , Egg > 0.
The production side of the economy in periods 1 and 2 are given by the
`restricted' revenue function R1(p, g) and a normal revenue function
R2(1, K + I, F + F) respectively, as functions of the producers' price of the aggregate
good and factor endowments.4
The period-2 revenue function is a standard one. However, the restricted revenue
function in period 1 which gives the value of private outputs, needs further explanations.
Let v(= vp + vg ) denote the vector of total factor endowments in period 1, where vp and
3The partial derivative of the expenditure function with respect to a price gives the compensated demand
function for that good. Also Epp where Epp = (2E / ( p(1+ ))2 ) . For more properties of the
expenditure function see Dixit and Norman (1980).
4The endowments of all factors other than private and public capital are omitted as they do not vary in our
analysis. The partial derivative of a revenue function with respect to a price gives the supply function of the
good, and that with respect to an endowment of a factor gives the price of that factor. Rii 0 for i=K,F.
For properties of the revenue function see Dixit and Norman (1980).
11
vg are respectively the vectors of factors used in the production of the private goods and
the public good. The country's maximum value of production of private goods is denoted
by a restricted gross domestic product, or restricted revenue function, R1(p,vp) , defined
as:
R1(p,vp) = max{px : x T(vp)},
x
where T(vp) is the private sectors aggregate technology set, and x is net output of the
private good. Under the assumption of constant returns to scale in public good production
and that the public sector competes with the private sector in factor markets, the cost-
minimization problem in the public sector yields a unit cost function of producing the
public good Cw (w), where w is the vector of factor prices and is given by
g
w = Rvp (p,v p ).
1
It is well known from the properties of the unit cost function that the demand for
factors of production in the public sector, vg , is equal to Cw (w)g (e.g., see Abe, 1992;
g
Hatzipanayotou et al., 2002). Therefore,
v p = v - Cw (w)g = v - Cw (Rvp (p,v p ))g.
g g 1
Solving the above equation for vp , we get vp = vp(p, g,v) , and since v does not
vary in our analysis, we define the restricted revenue function as
R1(p, g) = Rvp (p,v p (p, g,v)).
1
12
It is well known (e.g. Abe, 1992) that - R1g[= -(R / g)] = Cg (w), the unit cost of
producing the public good. For the rest of the analysis, for simplicity, we assume that
Rgg = 0 .5
Having done the ground work, the economy can now be described by the
following equations:
E(p(1+ ),1+ , g,u) + I = R1(p, g) - L + (1- )G + 1
1 1 R2(1,K + I,F + F), (1)
r + r
G = pEp +T + L, (2)
F = G (3)
(1- )G = -R1g g, (4)
RK =1+ r,
2 (5)
B = p(1+ )Ep + I - R1() - L + (1- )G
= R2() - E1 (6)
,
1+ r
where E1 denote the partial derivative of E with respect to the second argument and it
represents the private consumption in the second period.
Equation (1) describes the inter-temporal budget constraint for the representative
consumer. Total discounted present value of consumptions expenditure (left hand side) is
equal to the sum of total factor income from private production in period 1 (first term on
the right hand side), factor income form the public sector in period 1 (third term), and
5This assumption implies that changes in g which change factor supplies available to produce private
goods, do not affect its unit cost of production. It is to be noted that most of our results will go through
when Rgg is not zero (the more general assumption is that Rgg 0 (see Abe 1995 for the properties of
the restricted revenue function when Rgg is negative).
13
discounted value of factor income in period 2 (fourth term), minus lump-sum taxes paid
(second term). Equation (2) says that government revenue in period 1 is equal to the sum
of consumption tax revenue, foreign aid and lump-sum taxes. Public investment in period
1 is a fraction of government revenue (equation (3)). Equation (4) states that the total
amount allocated for the production of public good in period 1 (left hand side) is equal to
the total cost of producing the public good (right hand side). Private investment I is
determined optimally by the representative consumer by setting u/I=0, yielding
equation (5). Finally, equation (6) defines the amount of borrowing that the representative
consumer makes in period 1: it is defined either to be its excess consumption expenditure
over income in period 1, pr equivalently to be its discounted value of excess income over
expenditure in period 2.
This completes the description of the model. The six equations (1)-(6) determine
six endogenous variables in u, g, G, I, F, and B. The policy instruments are , L and ,
and the exogenous variables include T, r and the price p.
3.1. Optimal Policies
Having developed the model in the preceding section, we shall now characterize the
optimal policies. Since a government's ability to raise lump-sum taxes is usually limited
(see, for example, Wilson, 1991), we shall take lump-sum tax L to be exogenous and
determine optimal values of consumption tax rate and allocation parameter (between
public good production (social expenditure) and public investment) .
Before proceeding further, it may be useful to state a few assumptions. First we
assume that the public good and the taxed private good are taken to be independent in
14
consumption, and all the adjustments of a change in the public good provision (at a given
utility level) fall on the numeraire good (see Wilson (1991, p.159) for a discussion on the
separability between public and private goods). Second, we assume that income effect
does not fall on the taxed consumption good (see, for example, Keen, 1987; Lahiri and
Raimondos-Møller, 1998). Finally, we assume that private and public capital are
complements. Formally,
Assumption 2 Epg = Epu = 0 , RKF > 0.
2
Differentiating (1)-(5), we get:
2
Eudu = -Egdg - pEpd + 1+ dF,
RF (7)
r
dG = p(Ep + pEpp )d + dT, (8)
dF = Gd + dG, (9)
- R1gdg = -Gd + (1-)dG, (10)
dI = RKF
2
dF. (11)
RKK
2
Equation (7) says that welfare is positively related to the level of public good g
and of public capital F, but decreases with consumption tax because of a decrease in
consumers' surplus. Note the welfare does not depend directly on the level of private
investment I as it is optimally chosen by the private sector (envelope theorem). An
increase in foreign aid T increases total government expenditure G (equation (8)). An
increase in has two opposite effects on G: it raises tax revenue for every unit of initial
consumption level, but it also reduces the level of consumption and thus the level of tax
revenue for a given level of the tax rate. An increase in increases public investment by
15
diverting funds from social expenditure (first term in (9)). An increase in G increases
public investment for a given level of (second term in (9)) An increase in G also
increases the level of public good provision g (social expenditure) for a given level of
(second term in (10)). An increase in decreases g by allocating less of public
expenditure to social expenditure. Finally, equation (11) shows that an increase in public
investment increases the level of private investment if the two types of investments are
complementary, i.e., if RKF > 0 .
2
We now examine how the policy parameters and , and the level of foreign aid
T affects welfare. For this, substituting (8)-(11) in (7), we derive:
Eudu = -GR1g - 1
Eg RF2 2
+ r d + (1-)Eg
+
R1g 1+ r
RF dT
(12)
+ p(Ep + pEpp) (1-)Eg 2
+ 1+ r
RF -
R1g Ep d
An increase in has two opposite effects on welfare: it decreases the provision of
public good and increases public investment. An increase in foreign aid T, for a given
level of , increases both the provision of public good and the level of public investment,
and thus it has unambiguous positive effect on welfare. An increase in has two effects.
First, it reduces consumers' surplus and thus welfare. This is the marginal cost of
consumption tax. The second effect is via its effect on tax revenue. It increases tax
revenue, i.e., if p(Ep +pEpp ) > 0 , and then it has the same positive effect as foreign aid
via increases in both the provision of public good and the level of public investment. This
is the marginal benefit of consumption tax.
16
From (12), setting u/=u/=0 and simplifying, we get the following two first
order condition for the determination of the optimal values of and :
Eg = RF
2
, (13)
R1g 1+ r
p + r
1+ =1-1RF , (14)
2
where 2 (= -Epp p(1+)/ Ep = -(Ep / (p(1+)))(p(1+)/ Ep ) ), is the compensated
price elasticity of demand for good 2.
The left hand side of (13) gives the marginal cost (decrease in social spending) of
increasing and the right hand side the benefits (increase in public investment). Since in
a poor country, the rate of return to public capital is high and the marginal willingness to
pay for a public good is low, one would expect the optimal value of to be rather small
in order for optimality condition (13) to hold. From (14) it also follows that here there
will be under provision of the public good as compared to the Samuelsonian rule
( Eg = R1g ) if and only if RF > RK =1+ r .
2 2
The optimality condition for is similar to the well-known inverse-elasticity rule
of optimal commodity taxation under a revenue constraint (see, for example, Diamond
and Mirrlees, 1971). Since there are two possible use of government revenue here and the
allocation between the two is also optimal, the exact formula for optimal commodity
taxation is somewhat different from the ones found in the literature. Since an increase in
consumption tax increases, inter alia, public capital, the rate of return to public capital is
positively related to the level of optimal consumption tax. This observation will be shown
to have some important implications for the effect of foreign aid on public investment.
17
3.2. Fiscal Impacts of Foreign Aid
Having characterized the optimal values of and in the preceding section, in this
section we shall examine the effect of an exogenous change in the level of foreign aid on
the optimal values of and , private investment I, public good provision g, public
investment F, and the level of borrowing B. These will tell us how foreign aid affects tax
efforts, recurring expenditure, development expenditure, private investment, and
borrowing.
Differentiating (13) and (14) and using (8)-(14), we get:6
11d +12d =13dT, (15)
21d +22d =23dT, (16)
where
11 = G Egg - (R1g )2 2 < 0, 2 = RKKRFF -(RKF )2 > 0,
2 2 2
Eg RKK (1+ r)
2
12 = - pE(1+ r) (1- )Egg + (R1g)22 , 13 = (R1g)22 -Egu > 0,
RF Eg
2 RKK (1+ r)
2 RFF Eg (1+ r)
2 Eu
21 = G2 (1- )pEp (1+ r)2 - p (1- )2 < 0.
(RF )2 RKK
2 2 < 0, 22 = < 0, 23 =
(RF ) RKK
2 3 2 (1+)2 (RF ) RKK
2 3 2
Solving (15) and (16) simultaneously, we derive:
d = - 13p + u pEp(1+ r)2 + (1-)pEp(1+ r)2g < 0, (17)
dT (1+ )2 g(RF ) RKK
2 3 2 g(RF ) RKK
2 3 2
6Note that 2 > 0 as revenue functions must be negative semi-definite in factor
endowments. The fact that 11 < 0 and 22 < 0 go toward confirming that the second-
order conditions for the government's optimization problem are satisfied. See also see the
sentence below (18).
18
d = G2 [g -u ] (18)
dT (RF )2 RKK g
2 2
where u = -(Eu /g)(g / Eu) > 0 and g = -(Eg /g)(g / Eg) > 0, and
= a11a22 - a12a21 > 0 in order for the second order condition for the government's
optimization problem to be satisfied. u is the home country's marginal propensity to pay
for the public good, g is the elasticity of the marginal willingness to pay for the public
good with respect to the public good provision.
From assumptions 1 and 2, it follows that d/dT <0. That is, an increase in
foreign aid will raise the proportion of government revenue going to the production of
public good and reduce the proportion going to public investment. Formally,
Proposition 1 An increase in foreign aid would reduce the proportion of government
revenue that is allocated for public investment.
The above result can be explained intuitively as follows. Since Egu < 0
(assumption 2), an increase in foreign aid increases the marginal cost of increasing
(given by the left hand side of (1)). Foreign aid, by increasing public investment for given
value of , also reduces the marginal benefit since RFF < 0 .7 Therefore, an increase in T
2
unambiguously decreases the optimal level of .
Turning now to the effect on tax efforts, from (18) we find that an d / dT < 0 if
and only if g >u . That is, if this condition is satisfied, an increase in foreign aid
decreases tax efforts. In the special case of preferences where
7There are second round effects which are dominated by these initial direct effects. For example, an foreign
aid-induced increase in F increases domestic investment which increases marginal cost of since
RKF > 0 (assumption 2).
2
19
E( p(1+),1/(1+ r), g, u) = E( p(1+),1/(1+ r),u - f (g)) with f '> 0 > f '',8 it can be
verified that g =u - (gf ''/ f ') and thus when the optimal level of is large (which is
expected to be the case, as argued before) the condition is indeed satisfied.
Our result on tax effort is stated formally in the following proposition.
Condition 1 g >u
Proposition 2 Under condition 1, an increase in foreign aid reduces the optimal level of
consumption tax rate.
The above proposition can be explained as follows. The direct effect of an
increase in T is to reduce the optimal value of . An increase in T, for a given level of ,
increases government budget and therefore public investment F. This reduces the rate of
return to public investment RF and therefore the right hand side of (14) (the marginal
2
benefit of ). However, there is an indirect effect which works via changes in . As we
have seen above, an increase in T reduces the optimal level of -- the proportion of
government budget allocated to public investment, and this increases RF and thus 2
increases the optimal level of . It can be verified that the magnitude of this indirect
effect increases with u and decreases with g . An increase in T increases g and
therefore Eg , reducing marginal cost of (left hand side of (13)). The magnitude of this
reduction depends on the magnitude of g . An increase in T also increases u reducing
Eg and therefore increasing the marginal cost of . The magnitude of this increase
8This will be the case if the utility function is additively separable in private and public consumption.
20
depends on the magnitude of u . It so happens that the direct effect of an increase in T
dominates the indirect effect if and only condition 1 is satisfied.
Differentiating (4) we find
- R1gdg = -Gd + (1- ) pEp (1+ r) d + (1- )dT. (19)
RF2
Substituting (17) and (18) in (19), we obtain
(-R1g ) dg = (1-) - G13 p -u pEp(1+ r)2 > 0. (20)
dT (1+)2 (RF ) RKK g
2 3 2
That is, an increase in T unambiguously increases the provision of public good.
Even though the effect of T on and therefore tax revenue is ambiguous, the effect of a
foreign aid-induced increase in 1- dominates.
Tuning to the effect of public investment, differentiating (5) and (14) we get:
2dF = RKK (RF ) p
2 2 2
(1+)2 d. (21)
Thus, under condition 1, an increase in T increases F and therefore from (11) private
investment I. Formally,
Proposition 3 An increase in foreign aid increases the provision of public good, and
under condition 1, also increases both public and private investments.
As noted before, the optimal level of is positively related to the rental rate of
public capital RF which in turn is negatively related to the level of public capital. Thus,
2
under condition 1, the level of public investment increases via a decrease in the
consumption tax rate. Finally, since public and private capital are assumed to be
complementary, foreign aid also decreases private investment via a decrease in public
21
investment. An increase in foreign aid reduces tax efforts under condition 1, i.e., crowd
out tax revenue but not to the full amount and therefore both social expenditure and
public investment increase. Note that since F=G, an increase in T must increase total
government expenditure G as it increases F and decreases .
As for the effect on borrowing, differentiating (6), we get:
(1+ r)dB = RKdI + RFdF - p2E1 d - E1 dg - E1 du,
2 2 (22)
p g u
where from (12)-(14) we have:
Eudu = RF
2
dT. (23)
1+ r
Since both private and public investments go up as a result of foreign aid, period-2
income go up on these counts. These effects are given by the first two terms on the right
hand side of (22). Since foreign aid decreases consumption tax in period 1 and thus the
consumer price in that period, it shifts some private consumption from period 2 to period
1, reducing expenditure in period 2. This effect is given by the third term on the right
hand side of (22). The penultimate term on the right hand side of (22) will also increase
borrowing comes via an increase in social expenditure. An increase in g must reduce
private consumption in order to keep utility constant. Since we assume that the effect of
an increase in g falls entirely on the numeraire good (assumption 2), E1 < 0 . All these
g
effects will tend to increase net income over expenditure in period 2 and therefore the
demand for borrowing in period 1. The last term gives the positive income effect on
period-2 expenditure, since foreign aid unambiguously increases inter-temporal real
income given by u (equation (23)). This is the only term which will reduce the demand
22
for borrowing. It may be reasonable to assume that this effect will be dominated by the
other positive effect on borrowing.
4. Empirical Analysis
In this section we develop and test an empirical framework suitable to analyze two of the
hypothesis derived from our theoretical model. The key predictions of the theoretical
model are that an increase in aid reduces the tax efforts of the government (proposition 2)
and the proportion of public expenditure that is spent on public investment (proposition
1). Using a time series data set for Rwanda, we will test these two hypotheses in the
context of an econometric model derived as a reduced form of the theoretical model.
We consider linear regressions of the form:
PUBINV /TOTEXP = 0 + 1ODA/GDP + 2EXP /GDP + 3LAB
+ 4DUMMY(96+) + 5(ODA/GDP)*DUMMY(96+)+1 (24)
TAXREV /GDP = 7 + 7ODA/GDP + 8EXP /GDP + 9LAB
+ 10DUMMY(96+)+ 11(ODA/GDP)*DUMMY(96+)+2, (25)
where
PUBINV/TOTEXP = Public investment as a percentage of total public expenditure,
TAXREV/GDP= Tax revenue as a percentage of GDP,
ODA/GDP = Overseas development assistance as a percentage of GDP,
EXP/GDP= Exports as a percentage of GDP,
LAB= Labor force (number of people who meet the ILO definition of the economically
active population),
23
DUMMY(96+) = Takes the value 1 for 1996 onward, and zero otherwise.
PUBINV/TOTEXP represents the variable , TAXREV/GDP is a proxy for the
tax rate , and ODA/GDP is foreign aid T, in our theoretical analysis. We have added
other explanatory variables such as EXP/GDP and LAB as control variables. As
mentioned before, the economy of Rwanda went through very significant changes after
the genocide of 1994; in particular many of the changes in terms of the policy regime
came into effect in 1996. Thus, the qualitative effect of aid on the endogenous variables
can be different after1996 compared to what it was before then. To capture this effect we
have included an intercept dummy (DUMMY(96+)) as well as a slope dummy that
interact with ODA/GDP. Based on proposition 1 and 2, we expect a negative signs for
both 1 and 7.
Before discussing the results, it is useful to discuss the data.
Description of Data
The data used in this study come from the World Development Indicators (WDI, 2006).
Table 2 summarizes the mean, median and standard deviation of the variables used in the
regression. As can be seen from the above table, all the variables display fair degree of
variations.
Table 2: Descriptive Statistics of the Variables
PUBINV/TOTEXP TAXREV ODA/GDP LAB EXP/GDP
Mean 40.81 9.85 20.29 2.99 8.32
Median 39.42 10.08 17.24 2.82 7.65
Maximum 60.29 12.67 95.05 4.18 14.44
Minimum 19.23 3.62 9.54 2.28 5.15
Std. Dev. 10.31 1.92 18.3 0.59 2.71
Skewness 0.21 -1.32 3.12 0.75 0.66
Kurtosis 2.55 5.81 12.65 2.29 2.29
24
Before we commence on model estimation, we need to determine the stationarity
nature of the variables of interest. In view of that, we begin our analysis by performing
unit root test for each variable using Augmented Dickey-Fuller (ADF) and Phillips-
Perron (PP) unit root tests. While we are doing the ADF test we pick the lag length on the
augmentation term based on whether the exclusion of lagged term causes serial
correlation in the test equation's error term. As for the PP test, on the other hand, we use
a truncation lag of one given the fact that the frequency of our data is annual.
Table 3: Results of Dickey-Fuller test
Variable ADF ADF PP PP Critical value
( Levels) ( Differences) ( Levels) (Differences) (5%)
PUBINV/TOTEXP -2.91 -6.8** -2.91 -9.77** -3.61
TAXREV -1.79 -4.64** -1.79 -4.64** -3.74
ODA/GDP -2.91 -7.26** -2.89 -8.75** -3.58
LAB -2.91 -6.8** -2.91 -9.77** -3.61
EXP/GDP -1.79 -4.64** -1.79 -4.64** -3.74
Note: ADF is the augmented Dickey Fuller test and PP is Phillips-Perron test. The null hypothesis is that the series is
non-stationary. The asterisks (**) represent a rejection of the null hypothesis at 5% level. PubInv represents public
investment as a share of total government expenditure, TaxRev is the ratio of tax revenue to GDP, PubInv_T is
PUBINV/(100-PUBINV/TOTEXP_T is (PUBINV/TOTEXP)/(100-PUBINV/TOTEXP), TAXREV_T is
TAXREV/(100-TAXREV), ODA is the ratio of official development assistance to GDP, Labor is total labor force and
Export is the ratio of total exports in GDP.
Table 3 presents the estimated ADF statistics. All variables appear to have at least
one unit root, since the nonstationarity test is not rejected for these variables in levels. To
check for a second unit root we carried out a further unit root tests on first differences of
the variables. When the variables are differenced once, all of the ADF statistics are
significant at one percent level. Now, we can proceed with the analysis under the
assumption that no variable contains more than one unit root and the first difference of
each variable is stationary. Table 2 includes columns that describe the value for the test
25
statistics and the critical values for rejecting or accepting the null hypothesis of a unit
root. Both the ADF and PP unit root test results suggest that all variables are non-
stationary at 1% level, and integrated of order one I(1). Therefore, we use first
differences of the variables in our estimations.
Empirical results
Table 4 presents results from the estimation of the basic regression equations (24) and
(25).9 LAB and EXP/GDP were included separately in both regressions as control
variables. Since the explanatory variable ODA/GDP can itself be endogenous a country
receiving more aid in response to its economic difficulties we run OLS as well IV
(2SLS) regressions where the variable ODA/GDP is instrumented with its lagged value
and all other explanatory variables as instruments. As the results show, the coefficient of
ODA/GDP is consistently negative and significant at 99% confidence level. Our finding
on the effect of foreign aid on tax efforts is consistent with many other studies, cross-
section and time series for other countries (see, for example, McGillvary and Morrissey
(2004)).
The value of the coefficient of D(ODA_GDP) in PUBINV/TOTEXP equations is
roughly -0.31 and that in TAXREV/GDP equations is -0.06. This means that one
percentage point increase in ODA/GDP results in a reduction in PUBINV/TOTEXP by
0.31 percentage points and in TAXREV/GDP by 0.06 percentage points. Thus, effects are
significant but very small.
9Since the values of our dependent variables are between 0 and 100, we also run the regression after
transforming the dependent variables into (TAXREV/GDP)/(100-(TAXREV/GDP)) and
(PUBINV/TOTEXP)/(100- (PUBINV/TOTEXP)). The results which are similar to those in table 4 are
presented in table 5.
26
The other interesting finding is that the estimated coefficient of
(ODA/GDP)*DUMMY(96+) is significant and positive for PUBINV/TOTEXP
equations, and positive but insignificant for TAXREV/GDP equations. The magnitude of
the coefficient (ODA/GDP)*DUMMY(96+) in the PUBINV/GDP equations is +0.30
meaning that the effect of ODA/GDP on PUBINV after 1996 is not significant.
To summarize, we find that aid inflow is negatively associated with the
government's tax efforts in the sense that it reduced the average tax rate (as measured by
the share of total tax revenue to GDP). It also had a small negative effect on the ratio of
public expenditure going into public investment until 1995, but aid has had virtually no
effect on the ratio of public expenditure going into public investment since 1996. This
seems to imply that aid inflows during (and post) policy reform period (1996-2004) was
efficient in a sense that it had a positive contribution to development projects through
public resource allocation.
27
Table 4: Estimates of the Fiscal Impact of Aid
Sample: 1981-2004
Dependent
Variable D(PUBINV/TOTEXP) D(TAXREV/GDP)
Regression OLS IV OLS IV OLS IV OLS IV
Method
Equation No. 1 2 3 4 5 6 7 8
Constant 0.69 1.32 0.87 1.38 -0.1 -0.0911 -0.03 -0.03
(0.29) (0.53) (0.76) (0.99) (0.39) (0.390) (0.13) (1.40)
D(EXP/GDP) 1.16*** 1.33*** 0.10 0.11
(2.54) (2.58) (1.25) (1.40)
D(LAB) -25.54 -31.45 -0.85 -0.91
(1.62) (1.61) (0.55) (0.60)
D(ODA/GDP) -0.32*** -0.53*** -0.31*** -0.6*** -0.06*** -0.07*** -0.06*** -0.07***
(3.56) (6.05) (3.15) (13.19) (26.78) (7.78) (18.54) (6.50)
Dummy(96+) 3.50 3.99 -1.98 -2.56 -0.7 0.71 0.44 0.43
(0.68) (0.78) (0.89) (1.09) (1.38) (1.37) (1.07) (1.14)
D(ODA/GDP)* 0.27 0.49*** 0.32* 0.61*** 0.0006 0.003 0.0008 0.001
Dummy(96+) (1.40) (2.77) (1.82) (4.40) (0.03) (0.13) (0.33) (0.36)
R-Squared 0.41 0.24 0.46 0.16 0.72 0.72 0.73 0.73
F-Statistics 3.34 1.97 7.2 3.81 12.24 5.36 13.02 5.39
D-W 1.91 2.23 1.81 2.12 2.02 2.03 1.89 1.9
S.E. 7.76 8.84 5.77 7.17 0.88 0.88 0.86 0.86
*** Significant at 99% confidence level
** Significant at 95% confidence level
* Significant at 90% confidence level
Instruments in the IV method are: Constant, D(ODA/GDP)(-1), Dummy(96+), D(ODA/GDP)* Dummy(96+), and
either D(LAB) or D(EXP/GDP). Notations: PUBINV_TOTEXP is Public investment to total government expenditure (recurrent
public expenditure plus public investment) ratio (multiplied by 100). TAXREV is tax revenue to GDP ratio (multiplied by 100). D(.)
denotes first difference. ODA_GDP is ODA to GDP ratio (multiplied by 100). ODA_GDP_Dummy is in fact D(ODA_GDP) times the
dummy variable for 1996-2005. PUBINV_T is PUBINV/(100-PUNINV). TAXREV_T is TAXREV(100-TAXREV)
28
Table 5: Estimates of the Fiscal Impact of Aid
Sample: 1981-2004
Dependent
Variable D((PUBINV/TOTEXP) (100- D((TAXREV/GDP)/(100-(TAXREV/GDP)))
(PUBINV/TOTEXP)))
Regression OLS IV OLS IV OLS IV OLS IV
Method
Equation No. 9 10 11 12 13 14 15 16
Constant 0.01 0.026 0.02 0.04 -0.001 -0.001 -0.001 -0.0004
(0.14) (0.33) (0.65) (0.89) (0.42) (0.42) (0.156) (0.15)
D(EXP/GDP) 0.04*** 0.05*** 0.001 0.001
(2.65) (2.72) (1.25) (1.38)
D(LAB) -0.72 -0.86 -0.01 -0.01
(1.31) (1.47) (0.51) (0.55)
D(ODA/GDP) -0.01*** -0.01*** -0.01*** -0.01*** -0.001*** -0.001*** -0.001*** -0.001***
(3.17) (4.94) (2.8) (10.09) (28.72) (7.39) (18.18) (6.1)
Dummy(96+) 0.11 0.12 -0.06 -0.07 0.01 0.009 0.01 0.01
(0.64) (0.71) (1.13) (1.32) (1.33) (1.32) (1.06) (1.15)
D(ODA/GDP)* 0.005 0.01** 0.01* 0.01*** -2.66E-05 -6.92E-06 6.35E-05 7.33E-05
Dummy(96+) (1.001) (2.18) (1.66) (2.72) (0.13) (0.03) (0.23) (0.24))
R-Squared 0.25 0.13 0.39 0.19 0.68 0.68 0.7 0.7
F-Statistics 1.62 1.19 5.43 3.77 10.23 4.62 10.98 4.66
D-W 1.92 2.14 1.81 2.04 2.00 2.01 1.87 1.87
S.E. 0.25 0.27 0.18 0.20 0.01 0.01 0.01 0.01
*** Significant at 99% confidence level
** Significant at 95% confidence level
* Significant at 90% confidence level
Instruments in the IV method are: Constant, D(ODA/GDP)(-1), Dummy(96+), D(ODA/GDP)* Dummy(96+), and
either D(LAB) or D(EXP/GDP). Notations: PUBINV_TOTEXP is Public investment to total government expenditure (recurrent
public expenditure plus public investment) ratio (multiplied by 100). TAXREV is tax revenue to GDP ratio (multiplied by 100). D(.)
denotes first difference. ODA_GDP is ODA to GDP ratio (multiplied by 100). ODA_GDP_Dummy is in fact D(ODA_GDP) times the
dummy variable for 1996-2005. PUBINV_T is PUBINV/(100-PUNINV). TAXREV_T is TAXREV(100-TAXREV)
29
5. Conclusion
Rwanda has made major strides toward a sustained economic recovery following
the genocide of 1994 and the subsequent formation of a civilian government. The inflow
of large quantities of foreign aid into Rwanda has made the extent of recovery and
growth possible. However, scaled-up foreign aid can have some potential adverse effects
such as aid dependency. This may particularly happen if aid has a significant negative
effect on tax efforts of the government and on public investments. In this paper, we carry
out a theoretical and empirical study to examine the above issues as a first step toward
designing the interventions to support the effective use of aid. The results from the paper
hopefully provide insights to the effective use of aid to support growth.
The theoretical part develops an optimizing model in which the recipient
government decides on the optimal level of tax and optimally allocates total government
revenue (tax revenue and foreign aid) between current expenditure and public investment.
Our theoretical prediction is that an increase in aid is likely to reduce the optimal tax rate
and the proportion of public expenditure allocated to public investment.
The empirical analysis uses time series data on Rwanda, to estimate that an
increase in aid is associated with a reduced average tax rate in Rwanda, but the
magnitude of the effect is very small. A 1 percentage point increase in aid to GDP ratio
has reduced the rate of taxation by only 0.05 percentage point. It would appear that the
reforms put in place to strengthen the efficiency of revenue administration have mitigated
the impact of ODA. As for public investment, we find that an increase in aid also had a
negative effect on the proportion of public expenditure allocated to public investment
30
until 1995, although the effect is again not very large: a one percentage point increase in
aid to GDP ratio reduces the proportion of public expenditure allocated to public
investment by 0.3 percentage points. However, since 1995 the direction of this effect has
changed. The pattern of government spending and reforms adopted indicate that there
was strong political will to adopt appropriate measures and policies to mitigate the
potential adverse fiscal effects of aid. As a result, in the case of Rwanda, as far as fiscal
effects are concerned, foreign aid does not seem to have had a negative impact,
particularly since 1995.
31
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