ARE AID FLOWS EXCESSIVE OR INSUFFICIENT?
ESTIMATING THE GROWTH IMPACT OF AID IN THRESHOLD REGRESSIONS
Sarantis Kalyvitisa, Thanasis Stengosb, and Irene Vlachakic
September 2011
Abstract: Existing empirical studies and policy reports provide ambiguous results on the growth effect of
foreign aid flows in the recipient countries. The present paper examines whether there exists an aid
threshold that determines the growth impact of foreign aid. We use a threshold regression methodology to
estimate growth specifications and the associated aid thresholds in a sample of 42 aid recipients covering
the period 1970-2000. Our findings indicate that there is a threshold level of aid, above which the growth
impact of aid becomes positive.
Keywords: growth, aid, threshold regression, endogeneity.
JEL classification: F35, O4, C2.
Acknowledgements: We have benefited from comments and suggestions by two anonymous referees.
We thank Zeb Aurangzeb for excellent research assistance.
a
Corresponding author: Department of International and European Economic Studies, Athens University of
Economics and Business, Patission Str. 76, Athens 10434, Greece. Tel: (+30210) – 8203151. Fax: (+30210) –
8203137. e-mail: [email protected]
b
Department of Economics, University of Guelph, Guelph, Ontario N1G 2W1, Canada. e-mail:
[email protected]
c
Department of International and European Economic Studies, Athens University of Economics and Business,
Patission Str. 76, Athens 10434, Greece. e-mail: [email protected]
1. Introduction
A persistent issue in development economics involves the impact of foreign aid in terms of boosting
economic growth in the recipients. The empirical literature on this issue, surveyed by Kanbur (2006),
McGillivray et al. (2006) and Doucougliagos and Paldam (2008), has provided ambiguous evidence.
Earlier empirical studies, conducted until the 1990s, concluded that aid flows did not have a positive effect
on growth. Subsequent studies have been more favourable to a positive impact of aid on growth under the
assumption of diminishing returns (Hadjimichael et al., 1995; Hansen and Tarp, 2000, 2001; Lensink and
White, 2001; Dalgaard and Hansen, 2001; Clemens et al., 2004; Alvi et al., 2008) or the conditionality of
sound policies in the recipient country (Burnside and Dollar, 2000). Yet, recently, Rajan and Subramanian
(2008) have conducted an extensive study on the growth impact of aid and have found no evidence of a
significant effect over the last decades.1
In parallel to the empirical literature, and viewing the growth-aid nexus from a policy perspective,
several reports have highlighted the role of insufficient aid flows in explaining the poor growth results of
recipients. Perhaps the most prominent manifestation of this claim involves the attainment of the
Millennium Development Goals (MDGs), which require substantial additional funding in terms of foreign
aid to the developing world.2 For instance, Zedillo et al. (2001) have estimated that roughly $50 billion a
year in additional aid would be required to achieve the MDGs in all developing countries. Similarly,
Devarajan et al. (2002) have provided a figure in the range of $40-70 billion, which roughly represents a
doubling of official aid over 2000 levels. The Commission for Africa (2005) has called for an additional
$25 billion per year in aid to African countries by 2010, with a further $25 billion a year to be
implemented by 2015.
The present paper attempts to re-examine the growth impact of aid by addressing the following
1
See, however, Arndt et al. (2010) for a critical review of the Rajan and Subramanian (2008) approach.
In July 2005, the G-8 agreed to double foreign aid to Africa, from $25 billion a year to $50 billion in an attempt to
finance the “big push”, required for African countries to get out of the poverty trap though a large aid-financed
increase in investment. Similarly, the European Commission (2005) issued an “EU Strategy for Africa” in which
increased aid was required to achieve a significant boost in growth. See also the United Nations (2006) report for a
detailed review on related estimates for Africa.
2
1
question. Are aid flows to developing countries excessive or insufficient? In other words, we aim at
answering whether there exists an aid threshold, above which the growth impact of aid changes critically.
To this end, we use the threshold regression model developed by Hansen (2000) and Caner and Hansen
(2004) for estimating variants of standard growth specifications in a panel of 42 aid recipients covering
the period 1970-2000. Our central finding is that there is a threshold level of aid, above which the growth
impact of aid becomes unambiguously positive. In particular, we find that low levels of aid (measured as a
percentage of the recipients’ GDP) exert a negative or insignificant effect on growth. However, the growth
impact of aid becomes positive for recipients where aid flows exceed a critical threshold, amounting
roughly to 3.4% of their GDP.
Our results obviously coincide with recent calls for a major scaling up of aid aiming at helping poor
countries achieve the Millennium Development Goals. In particular, Sachs et al. (2004) and Sachs (2005)
have put forward an idea that goes back to Rostow (1960), according to which poor countries are stuck in
low-saving poverty traps and that a major intervention (‘big push’) is required to eliminate poverty. One
simplifying idea behind these calls is that investment is inadequate in developing countries due to low
savings (triggered, for instance, by the needs for subsistence consumption) and poor productivity. As a
result, these countries converge to a low-growth equilibrium, a situation that is aggravated under credit
market imperfections. Alternatively, potential non-convexities in the production process, such as
increasing returns on infrastructural capital or threshold effects in human capital, suggest that a large aidinduced rise in domestic investment would have a strong long-run growth impact. In this vein, aid
recipients could benefit from a massive inflow of aid oriented towards savings and capital accumulation.
It is noteworthy that actual experience and associated empirical evidence have not provided
overwhelming support for these mechanisms until now. Although Azariadis and Stachurski (2005) have
noted that generally poverty-trap models seem to be lacking testable quantitative implications, some
studies have attempted to investigate their predictions in the context of aid flows. Easterly (2006) has
claimed that the stylized facts are not consistent with a low-income poverty trap due to insufficient aid, as
growth is lower in aid-intensive countries than in similar developing countries that get little aid. In
2
addition, aid to Africa has risen over time (measured as a percent of income), but Africa’s growth rate has
fallen at the same time. Kraay and Raddatz (2007) have recently tested whether the savings and increasing
returns patterns predicted by poverty-trap models are supported by the data. The authors show that there is
no supporting evidence either in the behavior of savings and per capita income, or technological
nonconvexities, in favor of a poverty trap. The authors also fail to provide evidence for the existence of a
high-growth high-equilibrium that countries might be able to attain with appropriately large aid inflows.
Against such a background, the results presented in the current paper seem to offer, for the first time,
some compelling evidence that large-scale aid flows can have a significant growth impact over the long
run. This empirical regularity is supported by the recent findings of Herzer and Morrissey (2009) who
have established that there is substantial heterogeneity in the output effects of aid among 59 recipients:
although the estimated long-run effect of aid is negative, almost one-third of the countries examined have
enjoyed a positive growth effect. Indeed, the United Nations (2006) report has mentioned several cases of
aid success, where aid flows have resulted in boosting domestic investment and growth over the last
decades. For instance, the East Asian miracle economies, notably the Republic of Korea and Taiwan,
received enormous amounts of aid during the initial and early stages of their development.3 In Africa, both
Botswana and Mauritius received remarkably large amounts of aid at key strategic moments in their
development as earlier did Tunisia.4 These examples indicate that, despite the often-cited failure of aid in
boosting development in recipients, large amounts of well-targeted aid can, in conjunction with other
factors, produce remarkable success stories in terms of growth.
The present paper belongs to the newer generation of empirical studies that have attempted to
investigate heterogeneous policy effects on growth. For instance, Kourtellos et al. (2007) have shown that
countries that belong to a growth regime characterized by levels of ethnolinguistic fractionalization above
3
The nearly $6 billion in US economic aid to South Korea between 1946 and 1978 was only marginally lower than
the US total aid to Africa in the same period ($6.9 billion). A similar pattern was found in Taiwan, where although
its big push began on the back of a greater degree of domestic resource mobilization, aid still accounted for nearly
40% of gross domestic capital formation in the 1950s and was over $4 billion between 1949 and 1967 with per capita
aid being higher than that of Korea.
4
Botswana enjoyed initially a very high aid to GDP ratio, which dropped sharply following a sustained period of
rapid growth, whereas a similar pattern was found in Mauritius.
3
a threshold value experience a negative partial relationship between aid and growth, while those belonging
to the regime with fractionalization below the threshold do not experience any growth effects from aid.
Yet, the authors also find that the typology of these regimes may be alternatively well-characterized by
institutions or macroeconomic policies, and not just ethnolinguistic fractionalization. Instead, our
approach identifies the threshold level of aid that triggers differences in its growth impact. Investigating
threshold effects of aid on growth in conjunction with other variables, such as ethnolinguistic
fractionalization, or key aggregates, such as inflation or the domestic fiscal stance, seems therefore to
offer a promising route for future research.
The rest of the paper is structured as follows. Section 2 briefly outlines the empirical methodology and
describes the specification utilized and the dataset at hand. Section 3 presents the empirical results and
section 4 concludes the paper.
2. Empirical methodology and data
The threshold regression model treats the sample split value (threshold parameter) as unknown by
internally sorting the data on the basis of some threshold determinants into groups of observations, each of
which obeys the same model. The threshold regression approach is parsimonious, but also allows for
increased flexibility in functional form and it is not as susceptible to the curse of dimensionality problems
as nonparametric methods. Chan (1993) showed that the asymptotic distribution of the threshold estimate
is a function of a compound Poisson process. This distribution is too complicated for inference as it
depends on nuisance parameters. Using a concentrated least squares (TR-CLS) approach, Hansen (2000)
developed a more useful asymptotic distribution theory for estimating both the threshold parameter and
the regression slope coefficients in a cross-section of observations, as opposed to simple parametric
approaches that set the threshold exogenously.5
In particular, assume that { yi , xi , q, ui }in=1 is strictly stationary, ergodic and ρ-mixing, and that
5
Masanjala and Papageorgiou (2004) point out that the exogeneity assumption in determining the threshold effect is,
in fact, constrained to the estimation of dynamic linear panel data models, which is not the case in the context of the
present analysis.
4
Eu i |F i−1  = 0 , where yi is the dependent variable (growth), xi is a p × 1 vector of covariates (including
aid), and qi is a threshold variable (aid). Consider then the following threshold regression with threshold
for aid:
yi = xi′ β1 + u1i ,
qi ≤ γ
(1)
yi = xi′ β 2 + u2i ,
qi > γ
(2)
Equations (1) and (2) describe the relationship between the variables of interest in each of the two regimes
with γ being the sample split (aid threshold). Note that qi is observed but the sample split is unknown. Τhe
variance covariance matrix of the errors (u1i , u2 i )′ has the following properties: Eu 1i , u 2i  = 0 ,
Eu 21i  = σ 21 > 0 , Eu 22i  = σ 22 > 0 . In general, if the model involves exogenous slope variables then
estimation is based on Concentrated Least Squares (Hansen, 2000). In turn, the heteroskedasticityconsistent Lagrange Multiplier (LM) test introduced by Hansen (1996) is employed to verify whether
there is indeed evidence of a sample split; the null hypothesis of the test is that there is no threshold effect
and the corresponding p-values are computed by a bootstrap analog. Using a similar set of assumptions,
Caner and Hansen (2004) study the case of endogeneity in the slope variables and propose a concentrated
two stage least squares estimator (IVTR-C2SLS) for the threshold parameter and a GMM estimator for the
slope parameters.
To estimate equations (1) and (2) we use data from 42 aid-recipient countries over the period 19702000. Although the sample size is relatively small compared to related studies due to data limitations, it is
representative of the population of aid recipients.6 Since our emphasis is on the long-run growth impact of
aggregate aid without the inclusion of country fixed effects that traditionally help capture the impact of
worldwide business cycles, we estimate long-run horizon cross-country regressions using alternatively
6
The countries included are: Burkina Faso, Bolivia, Brazil, Botswana, Chile, Côte d'Ivoire, Cameroon, Congo Rep.,
Colombia, Costa Rica, Dominican Republic, Ecuador, Egypt Arab Rep., Ethiopia, Ghana, Gambia, Guinea-Bissau,
Guatemala, Honduras, Indonesia, Jamaica, Kenya, South Africa, Sri Lanka, Madagascar, Mexico, Mali, Malawi,
Malaysia, Niger, Nicaragua, Peru, Philippines, Paraguay, Singapore, Sierra Leone, El Salvador, Thailand, Trinidad
and Tobago, Uganda, Venezuela, and Yemen.
5
whole-period and ten-year averages, rather than four-year averages as is common in a strand of the
relevant literature. Hence, growth volatility, which is far higher in poorer countries (Pritchett, 2000), and
cyclical factors are unlikely to affect our estimates. In turn, we follow the empirical specification adopted
by Dalgaard et al. (2004, Table 3), which allows for a parsimonious representation of the long-run growth
equation with aid as one of the determinants. However, we also experiment with additional potential
control variables to assess the robustness of our empirical results. Data come from the World Bank
database unless otherwise specified. The dependent variable of the estimated regressions is the average
growth rate of real per capita GDP. To capture convergence effects the logarithm of initial GDP per capita
in constant 1985 dollars (source: Heston et al., 2006) is included as a control variable. Dalgaard et al.
(2004) have established that the growth impact of aid is far smaller in the tropical region. In line with
these authors, the importance of (non-political) structural characteristics on aid effectiveness is assessed
using the fraction of a country’s area that is located in the tropics (source: Gallup and Sachs, 1999). A
measure of institutional quality that captures security of property rights and efficiency of the government
bureaucracy also enters growth regressions; data are drawn from Knack and Keefer (1995).7 Turning to
macroeconomic policy variables and in line with Burnside and Dollar (2000) and Dalgaard et al. (2004),
we use the budget surplus as a percentage of GDP to capture fiscal policy in addition to inflation and the
revised trade openness dummy variable introduced by Sachs and Warner (1995) and updated by Easterly
et al. (2004) and Wacziarg and Welch (2008).8
Regarding data on aid flows, we employ in benchmark regressions ordinary data on Effective
Development Assistance (EDA) measured as a percentage of real GDP (constant 1985 dollars) drawn
from Roodman (2007). Using EDA allows comparison of our empirical results with studies that have
employed EDA as a measure of aid; see, among others, Burnside and Dollar (2000), Dalgaard et al.
7
The dummies for East Asia and Sub-Saharan Africa, which are routinely included in empirical growth
specifications, cannot be identified in a threshold regression framework.
8
Sachs and Warner (1995) define closed economies as those having average tariffs on machinery and materials
above 40%, or a black market premium above 20%, or pervasive government control of key tradables.
6
(2004), Kourtellos et al. (2007) and Economides et al. (2008).9
A prevalent criticism of aid-growth regressions involves the likely endogeneity of aid as it is often
argued that donors might reward countries that have used aid well in the past or, conversely, help
countries that have experienced natural disasters, thus inducing a spurious correlation between aid and
growth. To avoid endogeneity-induced problems and account solely for the exogenous component of aid,
we follow the instrumentation strategy introduced by Rajan and Subramanian (2008). This approach picks
instruments directly at the level of the donor, rather than the recipient country, and hence precludes any
direct association of excluded instruments with growth rates. In turn, the choice of aid instruments relies
on two assumptions: the first assumption is that the greater the extent of historic relationships between a
donor and a recipient the more likely it is that a donor will want to give this country aid. This idea
introduces colonial links and common language in the aid supply regression. The second assumption is
that donors are more likely to want to give aid the more they expect to have influence over the recipient.
Thus, the relative size of the donor and the recipient, and also the interaction terms between the relative
country size and the colonial links are included in the set of instruments in order to construct the
exogenous part of aid flows.10
To assess the relationship between actual and fitted aid for the period 1970-2000 we regress actual aid
on fitted aid and the full set of growth covariates. We find that the relationship between actual and fitted
aid is remarkably strong, with a t-statistic that exceeds 6. Figure 1, which depicts the residuals from
regressions of actual and fitted aid on the growth covariates, indicates that the correlation coefficient is
9
Notice that EDA corresponds to nearly 1.9% of the recipients’ GDP on average, a figure that is close to our study’s
average. An alternative measure of aid flows is Net Official Development Assistance (Net ODA). However, as
illustrated by Chang et al. (1998), Net ODA focuses on the net flow of grants and concessional loans (entailing a
grant element of at least 25%), therefore leading to systematic overestimates of the concessionality of official loans
especially after mid-1980s. EDA, on the other hand, captures the overall grant element of all official financial flows,
therefore allowing meaningful comparisons between recipients and donors. Net ODA in our sample amounts, on
average, to around 6% of the recipient’s GDP and often exceeds 7%, whereas in the population of recipients it ranges
from -0.5% to 12% of GDP with only 3% of the recipients (Comoros, Cape Verde, Djibouti, and Liberia) exceeding
the maximum value of our study (7%) over the period 1970-2000.
10
In fact, the authors model the supply of aid based on the bilateral (donor-recipient) relationship and then aggregate
up the predicted values of aid received from each donor over all donors in order to get a precise measure of aid flows
as a percentage of each recipient’s GDP. See Rajan and Subramanian (2008) for more details on the instrumentation
strategy.
7
high and statistically significant, reaching almost 0.65. Thus, we can safely infer that, as in Rajan and
Subramanian (2008), fitted aid contains a great amount of information about actual aid, which cannot be
attributed to growth factors that affect both variables simultaneously.
Another important issue in the present context involves the potential endogeneity of institutional
quality since more developed countries can simply afford better institutions or because both growth and
institutions might be affected by the same factors. In this vein, Acemoglu et al. (2001) have used
European settler mortality as a source of exogenous variation in institutions.11 Following this rationale, we
adopt the Acemoglu et al. (2001) approach to address the likely endogeneity of institutions and we use
their dataset on settler mortality.12 These data correspond to estimates of mortality rates (expressed in
logarithms) faced by European soldiers, bishops and sailors in the colonies in the 17th, 18th and 19th
centuries. However, the settler mortality instrument is available for a subset of countries that were
colonized, which reduces our sample to 36 countries.
Table 1 summarizes the descriptive statistics of the variables at hand. Actual aid flows for the 42 aid
recipients analyzed here have on average been 1.5% of their GDP ranging between nearly zero and almost
7%. In contrast, the estimated exogenous component of aid amounts to almost 5% of the recipients’ GDP
and varies widely between -4.4% and 30%. The annual growth rate of the recipients’ real per capita GDP
hardly reaches 1.5%, but in some extreme cases it may exceed 7%. Institutional quality is at medium
levels and average inflation amounts to 20%. Average budget surplus is close to zero and almost half of
the recipient counties have closed economies, according to the definition of Sachs and Werner (1995).
Ninety per cent of the recipients’ land is located in the tropics. Descriptive statistics for settler mortality
11
During colonization in the previous three centuries, Europeans pursued different policies depending on the
mortality rate faced by the settlers. Specifically, Europeans were more likely to set up extractive institutions when
faced with high mortality, and it is possible that the differences in institutions have persisted to create differences in
institutional qualities across countries in the late twentieth century. Notice that this instrumentation approach and its
empirical implementation have been criticized by Albouy (2011). Acemoglu et al (2011) provide an extensive reply
to Albouy's comments.
12
Estimates of mortality rates correspond to potential settler mortality, measured in terms of deaths per annum per
1,000 “mean strength” (raw mortality numbers are adjusted to what they would be if a force of 1,000 living people
were kept in place for a whole year, e.g., it is possible for this number to exceed 1,000 in episodes of extreme
mortality as those who die are replaced by new arrivals). For more details on the construction of the mortality rate
index, see Acemoglu et al. (2001).
8
implies that in ex-colonies nearly one-quarter of European settlers would die per annum due to
unfavourable disease environments.13
3. Empirical findings
In this section we present the empirical results of the methodology developed in the previous section. For
comparison reasons, we also report results obtained from OLS and 2SLS regressions. As a benchmark we
use ordinary aid data (first four columns of Table 2) to assess the growth impact of aid flows. Although
this dataset is not purged from endogeneity, we nevertheless report findings to allow comparison with the
relevant literature. Column (1) presents estimates obtained from a pooled OLS regression that confirm
some standard results of the literature. The control variables appear with expected coefficients, although
the majority of them are statistically insignificant. In particular, institutional quality, budget surplus and
trade openness are positively signed as expected, but only the latter variable is statistically significant at
1% level. Initial income appears with a negative and statistically significant coefficient, thus confirming
the standard convergence hypothesis. In accordance with Dalgaard et al. (2004), inflation and the share of
a country’s land located in the tropics enter with negatively signed coefficients, although both are
statistically insignificant. Interestingly, for our purposes, the coefficient on aid is negative and statistically
insignificant, thus confirming the broad picture from the empirical literature on the aid-growth nexus.
To detect any non-linearities in the aid-growth relationship we follow the standard empirical strategy
and we augment the linear growth regression of column (1) by adding an aid-squared term. The inclusion
of this additional variable improves OLS estimation while leaving intact the effects of the control
variables (see column 2 of Table 2). Aid now exerts a statistically significant negative effect on growth,
but this adverse effect is progressively weakened at higher aid levels, as indicated by the statistically
significant positive coefficient of the squared term. Thus, when using ordinary aid data one finds
significant evidence that the marginal growth effect of aid is not uniform across recipients, but rather
13
The extreme value of this variable corresponds to Mali, for which estimated mortality rates exceed 1,000, i.e. all
living settlers and also new-born settlers are expected to die in one-year period. Another case with estimated
mortality rates above 1,000 is Gambia for which the index reaches 1470.
9
depends on the amount of aid received.
Given the aforementioned evidence in favour of aid non-linearities, in columns (3) and (4) of Table 2
we estimate threshold regressions using the same dataset of ordinary aid data. The control variables have
the expected signs and are now mostly significant. In particular, in major aid recipients (column 4) the
fraction of land in tropics exerts a largely negative effect on growth whereas the budget surplus affects
growth positively. For both subgroups of countries trade openness retains its positive significance and the
standard convergence hypothesis is validated empirically. Regarding aid, the heteroskedasticity-consistent
Lagrange-multiplier (LM) test (Hansen, 1996) reported in the lower part of Table 2 indicates that, when
ordinary aid data are employed, there is no threshold of aid above which aid is beneficial for growth.
The right panel of Table 2 highlights the main point of the paper. In particular, in columns (5)-(10) we
report estimates using endogeneity-free aid data. First, column (5) reports the results obtained from the
standard OLS regression. Again, the control variables appear with the expected signs and trade openness,
budget surplus and initial income exert a statistically significant growth effect. The OLS coefficient on aid
is statistically insignificant, although now it is positively signed. As in the case of ordinary aid data, we let
a quadratic term of endogeneity-free aid enter an alternative growth regression in order to detect nonconstant marginal effects of aid (column 6). The results remain virtually the same, but the coefficient of
aid becomes now negative (although insignificant), whereas the statistically significant positive coefficient
of the squared term indicates that the reverse growth effect of aid is moderated at higher aid levels. In light
of this evidence, we move on to threshold regression estimation. The picture here changes starkly: there is
an aid threshold below which the growth impact of aid is negative and statistically insignificant, but above
which it becomes positive and statistically significant. This result provides prima facie evidence that the
adverse growth impact of aid typically reported in the literature is driven by low aid flows, as in the
present analysis it is evidently reversed in higher aid levels. In columns (9) and (10) of Table 2 we
perform a similar exercise using ten-year averages to test the robustness of the aforementioned results in
the medium-run horizon. Our unbalanced sample of 42 countries now consists of 114 observations where
10
endogeneity-free aid data are obtained following the same instrumentation methodology.14 The main
picture survives and is now in fact more striking. The estimated aid coefficient above the threshold
remains positive and statistically significant, whereas the coefficient below the threshold is found negative
and statistically significant. In accordance with these findings, the values of the LM test indicate that one
can safely reject the null hypothesis of no threshold at 1% significance level. Thus, we obtain significant
evidence in favor of the existence of an aid threshold effect when both cross-sectional and panel data are
employed and when endogeneity of aid is controlled for.15 Regarding the rest of the controls, we find that,
as in column (1), the fraction of land in the tropics turns out a growth deterrent in major aid recipients,
whereas budget surplus exerts an adverse effect for countries below the aid threshold and a positive effect
for those above the threshold.
We next address the potential endogeneity of institutions discussed in the previous section by using
settler mortality data as instruments. Due to data availability our sample is now reduced to 36
observations.16 Column (1) in Table 3 reports results obtained via Two-Stage Least Squares estimation.
Evidently, the instrumentation of institutions does not affect the growth impact of aid. The coefficient of
aid turns out negative and insignificant, validating the findings of the literature. However, when we
account for the presence of a threshold in the growth effect of aid the picture is again different (columns 2
and 3). There is a threshold for aid above which the growth impact of aid is positive and statistically
significant, whereas it is insignificant below the threshold.17 Thus, we confirm that the existence of an aid
threshold is not affected by the endogeneity of institutions. We also address the endogeneity of institutions
using 10-year averages, which reduces our sample to 101 observations. Estimation results are reported in
14
We do not report estimation results of the corresponding OLS regressions, since they are similar to those reported
in columns (5) and (6).
15
In order to test and correct for potential threshold endogeneity and omitted-variable bias we use Heckman’s
correction method. In the lower part of Table 2 we provide estimates of the Inverse Mills ratio (lambda coefficient),
as well as the corresponding probability levels for each set of threshold regressions, where the null hypothesis is that
the aid threshold is exogenous. As can be readily seen, the lambda coefficients are always statistically insignificant,
thereby validating our finding that the growth impact of aid turns unambiguously positive at above-threshold levels.
16
Botswana, Guinea-Bissau, Malawi, Philippines, Thailand, and Yemen are excluded due to missing observations.
17
The LM test for no threshold is not applicable in the case of endogenous regressors. We also note that the budget
deficit is not included in specifications (2)-(3) because it is highly correlated with institutional quality in high aid
recipients, which causes numerical problems in the cross-section regression with endogenous institutions.
11
columns (4) and (5) of Table 3. Although the threshold regressions indicate that the coefficient of aid
above the threshold is now insignificant, its sign changes again from significantly negative to positive
above the threshold.
As a final step, to eliminate the possibility of omitted-variable bias and to test the robustness of our
results to the inclusion of additional explanatory variables, we follow the recent study by Alvi et al. (2008)
and we augment the model by first adding ethnic fractionalization to the benchmark regression. Ethnic
fractionalization denotes the probability that two individuals will not belong to the same ethnic group and
data correspond to 1960 values as provided by Easterly and Levine (1997). Columns (1)-(2) and (5)-(6) of
Table 4 report the results for both exogenous and endogenous institutions. Ethnic fractionalization has a
negative effect on growth in high aid-recipient countries. Our main finding persists across the estimated
specifications. The coefficient on aid is found to be negative below the threshold and significantly positive
above the threshold. Following Alvi et al. (2008), we also replicate estimation using money supply as a
share of GDP as a control variable (source: World Bank). Again the regressions corroborate our evidence
on the positive growth impact of aid for high aid recipients.18
We close the presentation of our empirical findings by noting that their main implication is that there
is a threshold of aid flows, above which their growth impact becomes significantly positive. We stress,
however, that when endogeneity-free aid data are employed, the reported threshold parameters do not
correspond to actual aid disbursements. Still, one can draw valid inference about the minimum amount of
EDA flows needed to make aid work by simply classifying countries into below- and above- threshold
groups. Thus, after controlling for endogeneity of aid and institutions (columns 5-6 of Table 4), we find
that Effective Development Assistance should exceed 3.4% of a recipient’s GDP, in order to boost
domestic growth. Countries exceeding this threshold level (Burkina Faso, Gambia, Guinea-Bissau, Mali,
18
We also experimented with the following additional variables. We introduced assassinations and an interaction
term with ethnic fractionalization, but both variables turned out insignificant, whereas the coefficient of aid was not
substantially affected. Also, following Clemens et al. (2004) we augmented the model by adding the logarithm of life
expectancy at birth in 1970. However, the estimation of this specification generated numerical problems because,
although initial log life expectancy is not very strongly correlated with initial log GDP (the correlation coefficient
is around 0.7), the correlation between these variables reaches 0.95 for high aid levels.
12
Malawi, Niger, Nicaragua) have benefited from aid during the time period under investigation by enjoying
higher growth rates. By contrast, in all remaining recipients aid has had a negligible growth effect.
4. Concluding remarks
One major issue in international development is the failure of aid to boost growth in recipient countries.
The negative or, at best, insignificant growth effect of aid supported by the majority of studies lies in the
central assumption that the relationship between aid and growth is uniform across countries. Using a datadriven threshold regression approach, this paper aimed at investigating whether the growth impact of aid
changes beyond a critical threshold. We showed that in standard OLS and Two-Stage Least Squares
regressions aid is found to be ineffective in enhancing growth in recipient countries. However, when a
threshold regression approach is used we found that high aid flows affect growth positively.
We close the paper with a word of caution. Given that most recipients are classified below the
estimated threshold, our evidence provides some indication why aid flows have so far been insufficient in
terms of exerting a significantly positive effect on the growth rate of recipients. Hence, the evidence
seems to favor the view that a substantial increase of aid flows is required for making aid work.
Nevertheless, the present approach cannot identify the generating mechanisms and channels through
which this growth effect takes place, but only aims at highlighting a robust empirical fact that warrants
further exploration. Recently, Ouattara and Strobl (2008) have shown that the negative growth effect of
aid comes mainly from financial program aid, whereas project aid affects growth positively but with
diminishing returns. Minoiu and Reddy (2010) find that developmental aid has a positive and large effect
on growth, while non-developmental aid is mostly growth-neutral. In this spirit, investigating the role of
various aid forms on growth through a more refined analysis warrants further investigation.
13
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17
Table 1. Descriptive statistics (42 aid-recipient countries, 1970-2000)
Mean
Std. dev.
Minimum
Maximum
Real per capita GDP growth
1.39
1.91
-1.93
7.13
Aid (EDA)
1.42
1.50
-0.01
6.73
Aid (endogeneity-free data)
4.77
5.10
-4.39
29.99
Institutional quality
4.62
1.53
2.50
8.94
Fraction of land in tropics
0.90
0.25
0.04
1.00
Budget surplus
-0.04
0.04
-0.22
0.05
Initial GDP per capita (log)
7.26
0.74
5.69
8.96
Inflation
0.20
0.20
0.03
0.91
Sachs-Warner openness
0.45
0.26
0.13
1.00
Settler mortality rates*
284.42
533.38
15.50
2940.00
Note:
*
Descriptive statistics for settler mortality rates correspond to a sub-sample of 36 aidrecipients for which data are available.
18
Table 2. Growth OLS and aid threshold regressions
ordinary aid
endogeneity-free aid
OLS
TR
OLS
≤ 1.37
TR
>1.37
TR
>3.32
≤3.32
CI = [1.29, 1.87]
CI = [2.81, 6.48]
≤ 6.18
> 6.18
CI = [5.32, 8.10]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Aid
-0.33
(0.32)
-1.20**
(0.50)
-1.21**
(0.53)
0.15
(0.29)
0.05
(0.05)
-0.05
(0.07)
-0.06
(0.06)
0.25***
(0.06)
-0.26***
(0.09)
0.08**
(0.04)
Institutional quality
0.20
(0.14)
0.18
(0.14)
0.35***
(0.11)
-0.02
(0.32)
0.11
(0.16)
0.15
(0.16)
-0.18*
(0.11)
0.02
(0.21)
0.10
(0.16)
1.06***
(0.29)
Fraction of land in tropics
-1.12
(1.19)
-1.13
(1.35)
1.06*
(0.60)
-7.26***
(1.58)
-1.51
(1.22)
-1.37
(1.28)
-0.71
(0.44)
-1.50
(2.06)
-0.83
(0.85)
-19.51***
(5.53)
Budget surplus
7.86
(10.50)
13.01
(10.68)
3.86
(6.21)
18.30*
(10.16)
17.26**
(8.64)
-0.08
(0.36)
0.99**
(0.42)
Initial GDP per capita (log)
-0.93**
(0.40)
-1.31*** -1.28*** -2.54***
(0.35)
(0.41)
(0.91)
Dependent variable: per capita growth
Inflation
-0.45
(1.26)
Sachs-Warner openness
3.68*** 3.19***
(1.03)
(0.93)
-0.56*
(0.30)
-0.59*
(0.31)
-0.15
(0.10)
-0.79**
(0.37)
-2.61
(7.19)
-11.24
(9.40)
-0.62
(0.87)
3.78
(2.50)
-0.41
(1.53)
-0.16
(1.60)
-0.55
(0.41)
2.12
(1.61)
-2.73***
(0.63)
-3.84***
(0.85)
2.44***
(0.86)
4.28***
(1.33)
4.08***
(0.96)
3.61***
(0.94)
5.75***
(0.49)
3.16***
(0.82)
0.71
(0.48)
-0.84
(0.73)
0.16**
(0.07)
Aid Squared
R-squared
-0.19
(1.14)
22.22** -29.38*** 41.17***
(10.65)
(4.50)
(10.71)
0.01*
(0.00)
0.54
0.58
-
-
0.53
0.55
-
-
7.69
(0.00)
12.72
(0.00)
-
-
5.81
(0.00)
5.94
(0.00)
-
-
-
-
0.25
-
-
0.00
0.01
42
42
42
42
Inverse Mill’s ratio (Prob)
-
-
42
2.32
(0.39)
-
-
42
0.30
(0.87)
42
-1.79
(0.42)
No. of observations
42
42
F-statistic on joint-significance (Prob)
LM test for no threshold: Bootstrap P-value
No of countries
24
18
42
16
26
78
36
Notes:
All regressions include a constant. Robust standard errors are in parentheses. *** denotes significance at 1%, ** at 5%, and * at 10%. In regressions (1)-(4) aid
data correspond to Effective Development Assistance (EDA), while in regressions (5)-(10) endogeneity-free aid data are employed as in Rajan and
Subramanian (2008). Variables in columns (1)-(8) are time-averages for 1970-2000 and variables in columns (9)-(10) correspond to 10-year averages. TR and
CI denote Hansen (2000) Threshold Regression and the 95% Confidence Interval, respectively. For the heteroscedasticity-consistent Lagrange-multiplier (LM)
test for no threshold the null hypothesis is that there is no threshold effect (Hansen, 1996).
19
Table 3. Growth 2SLS and aid threshold regressions: endogenous institutions
2SLS
TR
≤ 5.41
TR
> 5.41
CI = [5.28, 6.49]]
Dependent variable: Real
per capita GDP growth
≤ 4.87
> 4.87
CI = [0.14, 6.00]
(1)
(2)
(3)
(4)
(5)
Endogeneity-free Aid
-0.17
(0.15)
-0.15
(0.11)
0.38**
(0.16)
-0.29**
(0.13)
0.74
(0.69)
Institutional quality
1.53
(1.06)
1.00
(2.75)
1.55***
(0.30)
0.69
(0.79)
3.84
(3.96)
Fraction of land in tropics
1.14
(2.16)
-0.02
(3.50)
-59.41***
(15.88)
0.03
(0.98)
-28.68
(24.86)
Budget surplus
-7.50
(20.57)
-
-
-12.60
(8.06)
-48.63
(63.15)
Initial GDP per capita (log)
-1.06
(0.69)
-1.53
(2.55)
0.36
(0.31)
-0.55
(0.84)
-0.17
(1.15)
Inflation
0.12
(1.45)
1.73
(8.13)
-4.71***
(1.00)
-2.95***
(0.65)
-5.68
(3.74)
Sachs-Warner openness
1.82
(2.15)
3.03
(2.37)
-2.33
(1.89)
0.43
(0.72)
-0.96
(2.26)
F-statistic on jointsignificance (Prob)
1.68
(0.16)
-
-
No of countries
36
36
36
No. of observations
36
15
21
58
43
Notes:
For the Two-Stage Least Squares estimation heteroscendasticity-consistent robust standard
errors are reported. In columns (2)-(5) the Caner and Hansen (2004) regressions are used
and a heteroskedasticity corrected asymptotic 95% confidence interval for the threshold
estimate is computed using a quadratic polynomial as in Hansen (2000). Institutional
quality is instrumented using log settler mortality as in Acemoglu et al. (2001). See also
Table 2.
20
Table 4. Aid threshold regressions: robustness tests
exogenous institutions
≤ 5.76
> 5.76
CI = [2.82, 6.49]
Dependent variable: Real
per capita GDP growth
≤ 3.32
(2)
(3)
-0.18***
(0.07)
0.43*
(0.25)
-0.08
(0.06)
Institutional quality
-0.03
(0.13)
0.16
(0.42)
Fraction of land in tropics
-1.20*
(0.73)
-10.76***
(3.18)
Budget surplus
-2.41
(10.04)
Initial GDP per capita (log)
-0.51
(0.35)
-0.48*
(0.25)
-0.12
(0.10)
Inflation
-1.92
(1.34)
-1.13
(2.04)
Sachs-Warner openness
3.25***
(0.85)
1.56
(1.86)
Ethnic fractionalization
0.25
(0.74)
-3.70***
(0.45)
(4)
No of countries
28
> 6.37
CI = [5.28, 6.49]
≤ 6.37
> 6.37
CI = [5.28, 6.49]
(6)
(7)
(8)
0.27***
(0.06)
-0.16
(0.24)
0.58***
(0.15)
-0.22
(0.92)
0.44
(0.29)
-0.21*
(0.11)
-0.05
(0.25)
1.61
(6.13)
0.67*
(0.36)
2.02
(20.26)
1.18
(0.79)
-0.48
(0.42)
-2.10
(2.37)
0.92
(8.29)
-70.47***
(9.38)
0.89
(19.21)
-69.11***
(14.29)
-
-
-
-
-1.00**
(0.45)
-2.39
(5.84)
0.59
(0.41)
-2.14
(13.60)
0.12
(1.20)
0.06
(0.60)
2.59
(2.03)
4.64
(22.44)
-6.11***
(0.96)
4.56
(55.49)
-4.19***
(0.46)
5.68***
(0.49)
2.41*
(1.33)
3.38
(2.48)
1.93
(2.39)
2.56
(10.53)
-4.38
(8.62)
-2.52
(7.31)
-3.42**
(1.53)
-0.02
(0.33)
0.08
(0.07)
0.02
(0.01)
LM test for no threshold:
Bootstrap P-value
≤ 6.37
(5)
35.67*** -26.91*** 42.36***
(12.76)
(2.67)
(10.50)
M2
No. of observations
> 3.32
CI = [2.82, 6.49]
(1)
Endogeneity-free Aid
endogenous institutions
0.03
(0.04)
0.09
0.01
-
-
41
42
36
36
13
16
Notes:
See Tables 2 and 3.
21
26
25
11
25
11
Figure 1. Conditional relationship between Actual and Fitted Aid, 1970-2000
Residuals of Actual Aid (% of GDP)
2
NER
NIC
BWA
MLI
TTO
GMB
1
VEN
SLV
YEM
HND BFA
BOL
MDG GHA
EGY
CIV GTM
PER
JAM
UGA
CMR
ZAF
COL
PHL ECU
THA
SLE
MYS
GNB
SGP
CHL
MWI
0
MEX
CRI
-1
IDN
PRY
COG
DOM
KEN
ETH
LKA
BRA
-2
-5
0
5
10
Residuals of Fitted Aid (% of GDP)
15
Note:
The figure plots the first-stage relationship between actual and fitted aid, conditional on all the
covariates that enter the second-stage growth regression.
22