Aid Effectiveness: New Instrument, New Results?

Stockholm Institute of Transition Economics (SITE)  Stockholm School of Economics  Box 6501  SE-113 83 Stockholm  Sweden
Stockholm Institute of Transition Economics
WORKING PAPER
April 2011
No. 11
Aid Effectiveness:
New Instruments, New Results?
Emmanuel Frot and Maria Perrotta
Working papers from Stockholm Institute of Transition Economics (SITE) are preliminary by nature, and are
circulated to promote discussion and critical comment. The views expressed here are the authors’ own and
not necessarily those of the Institute or any other organization or institution.

Aid Effectiveness: New Instrument, New Results?
Emmanuel Frot∗
Maria Perrotta†
First version, May 2009. This version, April 2010
Abstract
Despite a voluminous literature on the topic, the question of whether aid
leads to growth is still controversial. To observe the pure effect of aid, re-
searchers used instruments that must be exogenous to growth and explain well
aid flows. This paper argues that instruments used in the past do not satisfy
these conditions. We propose a new instrument based on predicted aid quan-
tity and argue that it is a significant improvement relative to past approaches.
We find a significant and relatively big effect of aid: a one standard devia-
tion increase in received aid is associated with a 1.6 percentage points higher
growth rate.
PRELIMINARY, DO NOT CITE.
1 Introduction
Foreign assistance has been disbursed for decades and is today still seen as a major
tool of development policy, and while all promises of increasing aid flows are likely
not to be fulfilled, the trend is clearly towards an expansion. If there seems to be
near unanimity among policy makers about the positive role of aid,1
the academic
∗
SITE, SSE, P.O. Box 6501, SE-113 83 Stockholm, Sweden. Email: emmanuel.frot@hhs.se.
†
SITE, SSE, P.O. Box 6501, SE-113 83 Stockholm, Sweden. Email: maria.perrotta@hhs.se. The
authors wish to thank Ethan Kaplan, Jakob Svensson, Rajeev Dehejia, Philippe Aghion, Pamela
Campa, Martin Berlin, all the participants at the IIES and Economics Department seminars at
Stockholm University as well as three anonimous referees.
1
For instance, the Monterrey Consensus, adopted by Heads of State and Government after the
2002 United Nations International Conference on Financing for Development, states that “Official
Development Assistance (ODA) [...] is critical to the achievement of the development goals and
targets of the Millennium Declaration”, that “we recognize that a substantial increase in ODA and
1

community has not found any robust evidence that aid contributes to development.2
The aid effectiveness literature is large and mostly inconclusive. The results vary
widely in size and sign, and have often been proven not to be robust and often re-
versed by new estimations. The so-called third generation of aid and growth studies,
which established some influential and widely cited results in the 90s, has recently
been criticized, mainly on two points: the unsatisfactory instrumentation strategies
and the “black box” way in which they use General Method of Moments (GMM)
estimations.3
These two points relate to the two fundamental issues the researcher
must confront when designing an empirical strategy to deal with the question of aid
effectiveness. The first is the identification of the causal effect of aid on growth,
unconfounded by simultaneity and reverse causality. The second is the consistent
estimation in a dynamic panel setting. We offer our main contributions on these two
points.
We propose a new instrument and argue that it is a significant improvement rel-
ative to past approaches. It takes the “supply side” approach, that makes use of
variables linked to the aid allocation process (mostly historical and political vari-
ables), one step further. Our identification strategy is similarly based on predicted
aid flows; however, unlike existing studies, we exploit a source of variation that we
argue not to be subject to the same criticisms, namely that of being directly corre-
lated with the outcome. This source of variation is related to the temporal order in
which donor-recipient partnerships are established: Frot (2009) shows that when a
partnership is established and how long it lasts are of importance for aid quantities.
In addition to being exogenous to growth, we show that our instrument is highly
correlated with actual aid levels.
On the second point, we keep our estimation strategy as simple and transparent
as possible. Given that standard panel estimators (fixed effect estimators) are biased
in dynamic settings, we make use of the GMM estimators in order to account for
individual level fixed effects. But we rely exclusively on our “external” instrument
for the identification of the aid coefficient. In addition, we test the validity of the
other resources will be required if developing countries are to achieve the internationally agreed
development goals and objectives, including those contained in the Millennium Declaration”, and
that “we urge developed countries that have not done so to make concrete efforts towards the target
of 0.7 per cent of gross national product (GNP) as ODA to developing countries”.
2
Many authors argue that aid failed to achieve growth. Easterly (2006) gives a detailed presen-
tation of the arguments. Easterly (2007) summarizes them in an article entitled “Was Development
Assistance a Mistake?”.
3
Bazzi and Clemens (2009) make this point very effectively and provide many examples. In
releasing his Stata package to perform GMM estimations, Roodman (2009a) warned about the
risks of using it unwittingly.
2

instruments created by the GMM procedure and, as a consequence, we are able to
comment on the validity of the GMM approach to estimate aid efficiency.
To give a preview of the results, we find a significant and moderate effect of aid
on growth: in our sample, a 1 percent increase in received aid is associated with a
0.06 to 0.13 percent higher growth rate.
The paper is organized as follows: in the next section, we spell out what are
the empirical challenges that the question of aid effectiveness presents, and highlight
how the literature has dealt with them in some important contributions. In Section
3 we describe in detail how our instrument is built; we then briefly discuss our
methodological choices in terms of estimators and present the results in Section 4.
In Section 5 the robustness of the results is assessed. Section 6 concludes the paper.
All variable definitions and data sources are to be found in a data appendix at the
end of the paper.
2 Estimation pitfalls and previous literature
A vast literature has focused on the effect of aid on GDP growth, controlling for
various variables. Some version of the following equation is implicitly or explicitly
derived from a standard growth model a la Solow, and brought to the data:
∆yit = αt + βyit−1 + γait−1 +
k
δkxkit + µi + ξit. (1)
In equation (1), i and t respectively index the countries and time periods (five-year
intervals, usually), y is the (natural logarithm of) GDP, and ∆ indicates its variation,
an approximation for the growth rate, α is a constant that might change over time,
γ is the coefficient of interest, the effect of aid a (also in logs), xk are additional
explanatory variables, and the error term consists of an unobserved country-specific
effect µi and a random noise ξit.4
To estimate this equation, researchers have to deal with the familiar problem of
reverse causality. Aid is to a larger extent allocated to low performing countries,
such that low growth ‘causes’ high aid quantities. This simple observation makes
the causal link from aid to GDP growth impossible to establish by looking at simple
partial correlations between these two variables. To observe the causal effect of aid,
researchers used instruments that must be exogenous to growth and explain aid flows
4
Most papers in the literature estimate the effect of aid, expressed as a share of GDP, on growth.
We prefer to use aid levels, for reasons exposed later, and for consistency with the literature also
run our regressions using aid as a share of GDP in Section 5.
3

Table 1: Instruments in the aid effectiveness literature
Boone (1996) Burnside and Dollar (2000) Hansen and Tarp (2001) Dalgaard et al. (2004)
Log population Log of initial income Egypt dummy Aid (-1)
Friends of US Policy index Arms imports (-1) Aid2
(-1)
Friends of OPEC Log population Policy (-1) Aid*inflation (-1)
Friends of France Arms imports/Tot. imports, (-1) Policy2
(-1) Aid*openness (-1)
Aid (-2) Sub-Saharan African dummy Policy*Log population Aid*share of land in tropics (-1)
Egypt dummy Policy*Initial GDP per capita M2/GDP (-1)
Franc zone dummy Policy*Initial GDP per capita2
Budget surplus (-1)
Central America dummy Policy*aid (-1) Inflation (-1)
Policy*aid2
(-1) Openness (-1)
Aid(-1)
Aid2
(-1)
Note: Instrumental variables for aid used in four influential papers. -1 and -2 indicate lags.
well. Rajan and Subramanian (2008) and Bazzi and Clemens (2009), among others,
review the past literature and question the validity of the instruments used in past
studies. Table 1 lists the instruments used in four influential papers.5
These papers typically instrument aid with many variables without any clear
identification strategy. Burnside and Dollar (2000) explain that theirs is based on the
aid allocation literature, the so-called supply-side approach, but it is difficult to argue
that any of their instruments satisfies the required exogeneity assumption. Deaton
(2010) criticizes the whole literature by mentioning that neither the Egypt dummy
nor population, though they are aid determinants, can plausibly be exogenous. These
variables are external to growth but assuming that they do not have any influence
on growth except through aid flows is not very plausible. Moreover, the Egypt
dummy is problematic as the source of variation is unlikely to teach us anything
about the effect of aid on growth in a general way. The variation between Egypt
and non-Egypt countries, or for that matter between Franc-zone countries and non
Franc-zone countries, is not very useful. Unfortunately, similar criticisms apply to all
instruments listed in Table 1. None of them is exogenous to growth. Even the fraction
of land in the tropics, used by Dalgaard et al. (2004), is correlated with institutions
which, in turn, affect long-run development, as shown by Acemoglu et al. (2001).
Lagged aid variables, either interacted with other exogenous regressors or not, also
constitute a dubious choice if growth is serially correlated. Similarly, the assumption
that a control such as policy has a contemporaneous effect on growth but none in
the next period, except through aid, is hard to defend.
5
The instruments used in Boone (1996) are found in Table 4 of his paper, those of Burnside and
Dollar (2000) in Table 1 and those of Hansen and Tarp (2001) in Table 1. Dalgaard et al. (2004)
reproduce previous specifications but their own set of instruments is found in Table 3 of their paper,
Clemens et al. (2004) use the same set of instruments as Hansen and Tarp (2001).
4

Rajan and Subramanian (2008) recognize these issues and adopt a slightly differ-
ent approach based on donor-recipient pair characteristics, instead of using recipients’
characteristics. Donors choose aid allocation based on poverty considerations, but
also because of history and influence. The authors here capture historical relation-
ships through colonial links and commonality of language. Influence is proxied by
the relative size of the donor and the recipient. The larger the donor, the larger its
influence. Relative size is also interacted with historical variables as influence is likely
to be further increased if historical links are strong. Aid quantities are estimated
at the donor-recipient level and then summed across donors to find the recipient
predicted aid quantity. Rajan and Subramanian (2008) then use this instrument to
revisit most of the past evidence on aid effectiveness and find little robust evidence
of any link between aid and growth.
This identification strategy improves upon past studies but is still not entirely
convincing. Historical variables are unlikely to be exogenous to growth and are cor-
related with traditional growth determinants, as shown by Bertocchi and Canova
(2002). Acemoglu et al. (2001) have also demonstrated how colonial origins are of
importance for growth through institutional quality. A second concern with the in-
struments of Rajan and Subramanian (2008) is their limited variation since historical
variables are simple dummies. In addition, they still include population in their set
of instrumental variables, despite its drawbacks. In fact, Bazzi and Clemens (2009)
show that their identification almost exclusively relies on population size because the
other instruments are weak, to the point of being irrelevant. Therefore, Rajan and
Subramanian (2008) face the same problem of invalid instruments as earlier papers.
A second challenge for the researcher is the fact that the process of economic
growth calls for a dynamic model, in which current values depend on past realiza-
tions. This is why the lag value of income figures as a regressor in equation (1). One
immediate problem in the estimation of such a model is that lagged values of the
dependent variable (and potentially of the other regressors) are correlated with the
fixed effect in the error term. This makes the OLS and 2SLS estimators inconsistent.6
Sure enough, the fixed effect estimator is consistent; but with five-year intervals over
forty years of data it is not possible to rely on asymptotic properties7
, although this
point has often been overlooked. To deal with this issue, researchers have made use
of a class of estimators built for the purpose, namely the GMM estimators. This
procedure consists of first-differencing the data, as opposed to the fixed effect trans-
6
Only the coefficient on income is plagued by this problem. On the other hand, the presence
of one inconsistent coefficient also biases the other coefficients in the regression, moreover in a
direction that is difficult to predict.
7
Asymptotics require t → ∞, while here we have t = 8 at most!
5

formation that demeans them (subtracts the sample mean). Endogenous variables
are then instrumented using their own lagged values. The main advantages of these
estimators are that they deal with individual level fixed effects without incurring the
bias to which standard panel estimators (chiefly the fixed effect transformation) are
subject in dynamic settings. Furthermore, they offer “internal” solutions for dealing
with endogenous regressors. In particular, the Arellano and Bond (1991) original
“difference” estimator instruments for current period differences in endogenous vari-
ables using their own multiple lagged levels. The more efficient Blundell and Bond
(1998) “system” estimator, which exploits the moment conditions from a system of
the differenced equation plus the original level equation, additionally instruments for
current period levels using lagged differences. This wealth of plausibly valid instru-
ments is never submitted to the standard weak-instrument diagnostics, so there is
no guarantee for their relevance; and the problems for inference of using many weak
instruments are very serious and very well known.8
Moreover, the exclusion restric-
tions on which these methods rely are more demanding than what is often assumed
(in particular for the “system” method; see Roodman (2009a) for a discussion of
these issues).
Our approach is hence to exclusively rely on our external instrument for the
identification of the aid coefficient. Endogenous variables for which we do not have
an external instrument9
, mainly income, are instrumented using their lagged values,
but we are very careful in keeping the number of instruments as low as possible by
collapsing the instrument matrix, as recommended in Roodman (2009a). Moreover,
in Section 5, we replicate the GMM instrumentation in a traditional IV setting, so
that we can use the whole standard battery of tests for instrument strength. In
the absence of a test for instrument strength in a GMM setting, this approach is
used by Bazzi and Clemens (2009), following Blundell and Bond (2000), Bun and
Windmeijer (2010) and Roodman (2009a). The “difference” estimator has often been
criticized on the grounds that it is biased because of weak instrumentation. It was
then recommended, as in Bond et al. (2001), to use the “system” estimator, which
is considered to be more robust to weak estimation. However, recent research (see
Bun and Windmeijer (2010) and Hayakawa (2007)) suggests that “system” GMM
estimators may not fare any better and can be seriously biased. An additional
contribution of the paper is therefore to assess the validity of the GMM approach
in the aid effectiveness literature. In addition to not taking instrument strength for
8
See Stock and Yogo (2005) and Staiger and Stock (1997). Stock and Wright (2000) and Bun
and Windmeijer (2010) look at this issue in the context of GMM estimators.
9
We use partnership characteristics to build instruments for aid but also for trade flows, see
sections 3 and 5.1.
6

granted, we also statistically test the exclusion restrictions on which the “system”
estimator relies. Papers on aid effectiveness typically eschewed these tests, whereas
the restrictions are far from trivial.10
Our results cast serious doubts on the ability
of GMM estimators to identify the relevant effects, and suggest that the (consistent)
two-stage least squares estimator, biased but free from weak instrumentation issues,
should be considered first.
3 The instrument
This section focuses on describing in more detail our new instrument, which is the
main contribution of this work.
3.1 Design
Total aid Ait to recipient i in year t can be decomposed as
Ait =
j
sijtDjt, (2)
where donors are indexed by j, Djt is j’s total aid budget in year t and sijt is the share
of this budget allocated to recipient i. Each donor-recipient pair (i, j) in a given year
t is characterized by two features: the date when the partnership was established,
and how long this partnership existed. The latter is the difference between t and the
entry date and is referred to as τijt. We call κij i’s entry date position in an ordered
sequence of all partnerships established by j. For instance, κij = 1 for recipients
that received aid from j in the first year j started to give aid, and so on.11
More
formally, define ηij as the first year j gives aid to i and πj as the first year the donor
disburses aid to any country. The entry date order κij is then defined as
κij = ηij − πj + 1. (3)
Donor portfolio expansion implies that aid shares are bound to fall on average. In
order to make aid shares neutral with respect to portfolio size we define normalized
10
On the other hand, Bond et al. (2001) argue that they must be satisfied when estimating a
Solow growth model.
11
To be precise, our data only starts in 1960, so the ordered sequence of recipients’ cohorts is
approximate. This is a data limitation which is akin to censoring, but on an independent variable;
the econometric literature has surprisingly little to say about how to deal with this issue; see Manski
and Tamer (2002) and Rigobon and Stoker (2009) for contributions on this issue.
7

aid shares σijt
σijt = sijt −
1
Njt
, (4)
where Njt is the number of recipients that have received aid from donor j at least
once before year t. Normalized shares are hence deviations from an equal sharing
rule among all recipients.
Predicted aid shares are then the OLS fitted values of
σijt = a + bκij + cτijt + uijt. (5)
Predicted aid shares for any observation (i.e. a given (i, j) pair in a given year)
are fully defined by their entry date order and partnership length. In other words,
to any partnership characterized by entry date of order κ and length τ we associate
a predicted aid share ˆσκτ ≡ â + ˆbκ + ˆcτ. ˆσκτ is not related to i, j, or t: it is the
typical share (in fact, the average share) that any recipient gets from a donor if their
partnership was established in the κth
year of activity of this donor, τ years ago.
The instrument for aid is the predicted aid quantity
Âit =
j
ˆσκijτijt
Djt. (6)
In words, we first estimate the predicted aid share each donor allocates to each
recipient, based on the pair characteristics. We then multiply these predicted aid
shares by the donors’ aid budgets to obtain a predicted aid quantity for each recipient.
The intuition is as follows. The instrument artificially recreates a situation where
a country receives more aid in a given period, independently of the “fundamentals”
of its economy, but rather for one or more of the following reasons: because it on
average had an earlier order of entry with respect to other recipients in the donors’
portfolio; because it was in the (average) partnership for a longer period of time;
finally, because the (average) donor’s budget for aid happened to be larger that year.
Unlike actual aid Ait, Âit is not influenced by shocks to economic performance in the
recipient country,12
so it is not affected by reverse causality; moreover, we will argue
in the following section that it is a strong instrument, relevant for predicting actual
12
On the other hand, it is affected by shocks to the donor’s economy, through the aid budget.
For example, a boom year for one or more donor countries can lead to larger aid budgets and at
the same time larger trade flows; if some of the recipients are also trade partners, which is often
the case, we might erroneously attribute to aid the beneficial effects that come from other channels.
However, we think that year effects do a good job of controlling for these instances. Moreover, in
the robustness checks, we control for trade, which we consider to be the main potential alternative
channel from having a partnership to growth.
8

aid flows, and that its only effect on growth occurs through the actual aid flows it
proxies.
3.2 Properties
For Âit to be a good instrument, it must be the case that entry date order and length
are strong determinants of aid shares. Frot (2009) shows that this is indeed the case,
and we reproduce some of his results here. Using data on aid recipients, we group
recipients into six cohorts based on entry dates: recipients with an entry date of one,
then with entry dates between two and five, six and ten, eleven and fifteen, sixteen
and twenty, and above twenty one. Figure 1 presents the average normalized share
received by recipients in each cohort in each year.13
In other words, Figure 1 shows
how much recipients in each cohort get in deviation from equal sharing.
Figure 1: Average aid share in deviation from equal sharing, by recipient cohort
As shown by the figure, early entrants into donors’ portfolios are on average
receiving larger aid shares. There is some convergence across cohorts but even many
13
Donors enter the market in different years, and sometimes exit the market. These changes
make comparing the cohort averages difficult, so for Figure 1 we restrict the sample to donors that
have been present from 1960 to 2007.
9

years after portfolios have been formed, it is still the case that entry dates and aid
shares are correlated. Stratification by cohorts is visible in any year, and seems to
have reached a certain persistence level.
Figure 1 does not alone offer enough evidence that entry dates play a decisive
role in determining aid shares, neither does it exclude the case that other factors are
behind the correlation between entry date order and aid receipts. It is likely that
donors created partnerships that prioritized poor countries and heavily populated
countries, and that such countries have received larger aid shares because of these
characteristics, and not because of their entry dates. However, Frot (2009) also
shows that the explanatory power of entry dates is robust to controlling for these
characteristics. In order to disentangle these different possible effects, the normalized
aid share of each recipient is regressed on a set of controls. The following equation
is estimated:
σijt = α + βτijt + γτ2
ijt + δκij + xijtϕ + εijt (7)
where κij is entry date order, τijt is the number of years the partnership has existed
(τijt = t − ηij + 1), xijt is a vector of controls including recipient GDP per capita,
recipient population size, a dummy variable for whether donor and recipient shared
a colonial relationship, and the distance between i and j, and εijt is an error term
uncorrelated with the independent variables. The variable τ2
ijt enters the equation
to allow for convergence among countries with different entry dates. The exact
functional form of the dependence of the normalized share σijt on κij is debatable.
Equation (7) assumes that it is linear. Figure 1 suggests something more complex,
with a falling effect of entry dates on aid shares (curves get closer when one moves
downward vertically). To capture such non-linearities we also estimate equation (7)
by adding κ2
ij as a regressor. Table 2 presents the results. Column (1) shows that
entry dates are indeed affected by recipient and recipient-donor characteristics, as
expected: donors did prioritize countries with a larger population, lower GDP per
capita, geographically closer to them and countries with which a colonial relationship
had been in place.
The remaining columns indicate that, as suggested by Figure 1, earlier entrants
indeed receive larger aid quantities, even after controlling for such recipient and
recipient-donor characteristics. Columns (4) and (5) acknowledge the censored na-
ture of aid shares that are bound to lie between 0 an 1, and thus present censored
regression estimates. The effects are sizable. Consider two hypothetical aid recipi-
ents A and B from the same portfolio. A and B’s characteristics are identical, except
that A’s entry date is one and B’s is ten (corresponding roughly to a one-standard
deviation difference). The difference in A and B’s aid shares in year 20 (20 years after
they started receiving aid) is 0.99 percent using estimates from column (3), and 1.45
10

Table 2: Determinants of aid shares
(1) (2) (3) (4) (5)
Entry Aid share Aid share Aid share Aid share
GDP per capita .00036*** -.00014*** -.00025***
(.000065) (.000018) (.0000075)
Population, mil -.012*** .0055*** .0059***
(.0010) (.0013) (.00013)
Colony -3.91*** 2.69** 2.96***
(1.04) (1.03) (.061)
Distance .17** -.057** -.083***
(.077) (.022) (.0040)
Entry -.12*** -.11*** -.17*** -.15***
(.016) (.019) (.0041) (.0054)
Entry, squared .0030*** .0032*** .0035*** .0036***
(.00048) (.00054) (.00015) (.00019)
Length .062*** .091*** .061*** .11***
(.0084) (.011) (.0033) (.0043)
Length, squared -.0011*** -.0018*** -.00091*** -.0019***
(.00017) (.00020) (.000079) (.000096)
Constant 6.98*** -.12 .019 -.44*** -.12**
(1.03) (.082) (.26) (.033) (.055)
Observations 71620 132798 71620 132798 71620
Recipients 113 130 113 130 113
Donors 29 56 29 56 29
R2
.057 .019 .098 .007 .028
Note: Robust standard errors clustered at the donor level in parentheses. Columns (4) and (5)
estimate a censored-normal regression. * p < 0.10, ** p < 0.05, *** p < 0.01.
11

percent from column (5). This is as large as between a quarter and 40 percent of the
standard deviation of the shares distribution. To put this number into perspective,
we compare it with the GDP differential that would result in such a difference. In
other words, for B to have the same aid share as A, how much smaller should its per
capita per capita GDP be? From the estimates of Table 2, B’s income per capita
would have to be USD 7071 to 5814 lower than that of A, using columns (3) and
(5), respectively. The mean income per capita in the sample is USD 1712, with a
standard deviation of USD 2043, so this difference is extremely large. This implies
that entry dates have a large effect when compared to per capita GDPs. The small
percentage difference is also significant in monetary terms, as it represents between
USD 14 and 20 million (in 2006 USD). Entry dates, together with partnership length,
are therefore good predictors of aid shares, on top of more traditional determinants
of aid. In the next section, we will report more evidence of predicted aid indeed
being a strong instrument for aid.
Returning to our question, we are ultimately interested in the effect of aid, as
predicted by entry date order, on growth. Hence, we also need to ensure that there
are no other confounding effects that go from entry dates to growth through other
channels than aid, i.e. that exclusion restrictions are satisfied. For example, it might
be the case that early entrants do not only receive more aid, but also larger trade
flows, which in turn affect growth. In such a case, we would erroneously attribute to
aid the better growth performance observed. A response to this concern is to control
for those potential factors correlated with entry dates and affecting growth in the
growth regression and show that aid has an independent effect on top of them. This
is done for trade flows.14
We also show that the direct correlation between entry
order and growth, although present, is very weak, and there is no strong evidence
against the claim that it might come entirely and only through aid.
14
An issue with directly including trade flows in the estimation of equation (1) is that they, too,
are affected by reverse feedback with the growth rate, the left-hand side variable. Our approach is
to instrument them, too, in a similar way as we did for aid flows, using entry dates and partnership
length. The predicted total trade flows are then included in the equation. Initially, we also took
the same approach for inward foreign direct investment flows, but then abandoned this part of the
analysis due to serious limitations in the bilateral FDI data.
12

4 Results
4.1 Preliminary stage
As mentioned above, our strategy consists of first estimating aid shares by regressing
actual shares on entry dates and partnership length (and their squares).15
We then
compute predicted aid quantities Âit by summing up predicted aid shares multiplied
by donors’ aid budgets. The predicted aid quantity is then used as an external
instrument in the “second stage” growth regression (i.e. in equation (1)).
4.2 Baseline results
Table 3 reports the OLS and IV estimation of equation (1) with and without country
fixed effects.16
The equation includes a number of controls which are frequently used
in the literature: population size; a measure of schooling17
; inflation as a measure
of macroeconomic policies; liquid assets (M2/GDP), commonly used as a measure
of financial depth; institutional quality, measured by the International Country Risk
Guide (ICRGE) index; the Sachs et al. (1995) index of openness. We also include
ethno-linguistic fractionalization and regional dummies for Sub-Saharan Africa and
quickly growing East Asia, when possible. These controls are those most commonly
used in the aid effectiveness literature, and allow us to draw comparisons with past
studies.
The log-log specification adopted in equation (1) implies that the coefficient on
aid is the elasticity of GDP with respect to aid. We start by not instrumenting the
aid variable, and present naive estimates, with and without country fixed effects in
Table 3. Column (1) confirms the traditional finding that, when not instrumented,
aid has no effect on GDP growth. The inclusion of country fixed effects only reinforces
this conclusion. However, as argued above, there is little to learn from regressions
where aid is not instrumented. We move on to columns (3) and (4) where aid is
instrumented using our instrument of predicted aid quantities. Because a major
concern in the literature is the weakness of instrumentation for aid, we provide two
statistics. The first is the p-value of the Angrist and Pischke (2009) test of excluded
15
The specification we use to predict aid shares corresponds to Table 2 column (4). The correlation
between predicted and actual shares is 46%, 48% between predicted and actual aid quantities.
16
All regressions in the paper include year effects. Refer to the data appendix for all variable
definitions and their sources.
17
This is the Barro and Lee (2010) average years of primary schooling. Whether we use primary
or secondary schooling does not make much difference.
13

Table 3: OLS and IV regressions
(1) (2) (3) (4)
OLS FE OLS 2SLS FE 2SLS
Log GDP, lagged -0.020 -0.23*** -0.030* -0.23***
(0.016) (0.047) (0.018) (0.050)
Log aid, lagged 0.018 0.017 -0.017 0.10***
(0.011) (0.017) (0.050) (0.039)
Log population 0.023 -0.16 0.052 -0.23**
(0.021) (0.12) (0.039) (0.10)
Inﬂation -0.10*** -0.11*** -0.11*** -0.10***
(0.025) (0.028) (0.025) (0.028)
Money, lagged 0.00069 0.0028** 0.0011 0.0029***
(0.00060) (0.0013) (0.00086) (0.0011)
Schooling 0.00029 -0.0013 -0.0028 0.033
(0.012) (0.036) (0.012) (0.037)
Institutional quality 0.013** 0.0077 0.014** 0.0042
(0.0055) (0.0073) (0.0056) (0.0070)
Openness 0.097*** 0.075*** 0.10*** 0.078***
(0.017) (0.027) (0.018) (0.028)
Ethno. fractionalization -0.083 -0.097
(0.057) (0.063)
East Asia 0.014 0.018
(0.026) (0.028)
Sub-Saharan Africa -0.020 -0.0086
(0.038) (0.047)
Observations 347 347 347 344
Countries 61 61 61 58
AP test (p-val) 0.046 0.00088
KP F stat 4.16 12.3
R2
0.32 0.38 0.29 0.28
Note: AP: Angrist-Pischke. KP: Kleibergen-Paap. DThe dependent variable is the growth rate.
All regressions include year eﬀects. Robust standard errors clustered at the recipient level in
parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
14

instruments.18
The second is the Kleibergen and Paap (2006) Wald statistic. Both
are tests of instrument weakness.
Column (3) is the two-stage least square (2SLS) specification. It fails to find any
significant effect of aid on GDP growth, but it is likely that omitted country fixed
characteristics make the error term not orthogonal to the control variables, biasing
the estimates. In addition, the Kleibergen and Paap Wald statistic is quite low.19
In
column (4), we include country fixed effects to avoid the bias due to their omission.
The consequence for the aid coefficient is quite dramatic. It is much larger than
in column (2) and comfortably passes the five percent significance threshold. The
weak instruments statistics now confirm that our instrument is highly correlated with
aid. The null hypothesis of the Angrist and Pischke test is strongly rejected, and
the Kleibergen and Paap Wald statistic is much higher than in column (3). These
results indicate that the inclusion of fixed effects is important for the validity of our
approach.20
The estimated effect implies an elasticity of GDP with respect to aid of
0.10. This elasticity is relatively moderate. Another way of interpreting the result is
that a 1 percent change in aid increases GDP growth by approximately 0.10 percent.
The first-stage regression for the fixed effect regression is shown in column (1) of
Table 4. It confirms that predicted aid is a strong predictor of actual aid.
The results in Table 3 are problematic because of the correlation between lagged
income and the error term, due to the strong persistence in income and the individual
specific component in the error term. We can sign this bias for the lagged income
coefficient, but not so easily for the other variables. It is nevertheless useful in
order to evaluate the performance of the GMM estimator. In the OLS setting, the
coefficient on lagged income is upward biased, whereas Nickell (1981) proved that the
within group estimator is downward biased. We know that the true coefficient lies
somewhere in this range, and this remark allows us to evaluate if the GMM estimator
succeeds in removing the bias. In columns (1) and (2) of Table (5), we rely on the
difference GMM estimator in order to remove the dynamic bias, in asymptotic terms.
This method estimates the model in differences, to get rid of the fixed effects. The
lags of endogenous regressors, which are exogenous to the first difference of the error
term, are used to instrument for their first difference. In column (1), we instrument
aid with its lags, as is usually done in the literature. In column (2), we use our
18
With a single endogenous regressor, this statistic is simply the F-statistic of the first stage.
19
Although critical values only exist for the Cragg-Donald Wald statistic, which is not robust to
heteroskedasticity, the 25% maximal IV size value is 5.53, which suggests that the Kleibergen-Paap
statistic is indeed low.
20
This test is based on the F-statistic of the first stage, so the stark improvement is not surprising:
the model including country fixed effects performs much better than that without.
15

Table 4: First stages
(1) (2) (3)
Aid Aid Trade
Log GDP, lagged -0.088 -0.11 1.07***
(0.27) (0.27) (0.13)
Log predicted aid, lagged 1.42*** 1.69*** -0.025
(0.41) (0.40) (0.13)
Log predicted trade, lagged -1.12*** 1.06***
(0.35) (0.21)
Log population 0.63 0.71 -0.31
(0.70) (0.69) (0.25)
Inflation -0.073 -0.078 0.0097
(0.10) (0.10) (0.048)
Money, lagged 0.0016 0.00067 0.0068***
(0.0052) (0.0052) (0.0025)
Schooling -0.28* -0.30* 0.047
(0.16) (0.16) (0.10)
Institutional quality 0.056*** 0.056*** -0.0099
(0.021) (0.019) (0.015)
Openness 0.053 0.023 0.11
(0.13) (0.13) (0.081)
Countries 58 58 58
R2
0.35 0.37 0.78
Observations 344 343 343
Note: Column (1) is the first stage of the regression in Table 3 column (4). Columns
(2) and (3) are the first stages of the regression in Table 7 column (4). The instruments
for aid and trade are built from fitted values of the preliminary stage estimated at the
bilateral level, and then aggregated at the country level. All regressions include country
and year effects. Robust standard errors clustered at the country level in parentheses. *
p < 0.10, ** p < 0.05, *** p < 0.01.
16

instrument for aid. Both coefficients are insignificant, but the estimates of the GDP
coefficient cast serious doubts on the validity of the approach. The first-differenced
GMM estimate is well below the within groups estimate of Table 3, which can already
be expected to be strongly downward biased, given the small time dimension of the
dataset. This signals that the GMM estimate is also biased, possibly because of weak
instruments.21
The first-differenced GMM estimator is therefore not very informative
and for this reason, we use the system GMM estimator in the next two columns.
This is a more efficient method, developed by Blundell and Bond (2000); it uses the
moment conditions from the same difference equation but also from the original level
equation at the same time. This method is valid under the assumption that the
GMM instruments (i.e. the lagged differences) are exogenous to the error term in
the level equation. This can be tested using a Hansen test, denoted in the regression
tables as “level eq.”; we report the test p-value. If this test fails, the validity of the
system GMM approach is questionable, and the results should be interpreted with
caution. Finally, the p-value of the Hansen J test of overidentification is reported;
its null hypothesis must not be rejected for the GMM exclusion restrictions to be
valid.
The GDP coefficient, both in columns (3) and (4), now lies in the expected range,
which confirms that system GMM estimators are more appropriate. Estimates in
column (3) do not make use of our aid instrument. The null hypothesis of the
exogeneity of the GMM instruments for the levels equation is not rejected by the
Hansen test. On the other hand, the number of instruments and countries is of the
same order of magnitude, such that the p-value of the test is likely to be upward
biased, as underlined by Roodman (2009b). Column (4) instruments aid with our
instrument. The coefficient of aid is now significant, although only with a p-value of
6.9 percent. It is also smaller than in Table 3. The Hansen tests of overidentification
restrictions and of exogeneity that the GMM instruments for the levels equation
fail to reject their null hypotheses, suggesting that the assumptions required for the
estimators to be valid are satisfied. Taken together, columns (4) of Tables 3 and 5
indicate an elasticity of GDP to aid between 0.057 and 0.10.
GMM estimators come with several caveats about their validity, however. The
first concerns the risk of having too many instruments. Roodman (2009b) showed
how Hansen tests tend to fail to reject the null hypothesis when the instrument count
is large. A rule of thumb is that instruments should not exceed the number of coun-
tries, which is the case in our estimations. Relying on our external aid instrument
in column (4) reduces the instrument count, but it still remains close to the number
21
Here we mean the GMM instruments. We do not rely on them for the aid variable, and we
know that our instrument for aid is actually strong.
17

Table 5: GMM regressions
(1) (2) (3) (4)
Diff. GMM Diff. GMM Sys. GMM Sys. GMM
Log GDP, lagged -0.38*** -0.54*** -0.016 -0.086*
(0.12) (0.14) (0.027) (0.050)
Log aid, lagged -0.014 0.016 0.018 0.057*
(0.030) (0.040) (0.017) (0.031)
Log population -0.073 -0.027 0.022 0.057
(0.14) (0.16) (0.033) (0.047)
Inflation -0.11*** -0.076*** -0.086** -0.080**
(0.033) (0.027) (0.034) (0.038)
Money, lagged 0.0019 0.0030** 0.0016** 0.0016*
(0.0012) (0.0012) (0.00077) (0.00090)
Schooling -0.052 -0.047 -0.0072 0.058
(0.050) (0.063) (0.027) (0.051)
Institutional quality 0.0095 0.014** 0.013** 0.019**
(0.0073) (0.0072) (0.0050) (0.0085)
Openness 0.080*** 0.088*** 0.11*** 0.11***
(0.031) (0.032) (0.022) (0.022)
Instruments 60 40 74 48
Hansen J test (p-val) 0.55 0.27 0.76 0.27
Hansen test (p-val), lev. 0.95 0.11
AR(1) 0.016 0.12 0.00081 0.0010
AR(2) 0.57 0.28 0.80 0.67
Note: Instruments for the differences equation are log GDP lagged twice in all specifications, and
log aid lagged twice in columns (1) and (3). Instruments for the levels equation are log GDP lagged
and differenced once in columns (3) and (4), and log aid lagged and differenced once in column
(3). In columns (2) and (4), log predicted aid is used as an instrument. All regressions include
year effects. Robust standard errors clustered at the country level in parentheses. * p < 0.10, **
p < 0.05, *** p < 0.01.
18

of countries. Roodman (2009b) recommends that the instrument count is reduced
as a robustness check. One way of doing this is to collapse the instrument matrix.
Estimates with this collapsed matrix are reported in Column (1) of Table 6. The
coefficient on aid is now smaller, and insignificant, but maybe more importantly, the
Hansen tests now strongly reject the overidentification restrictions and the validity
of the instruments for the level equation.22
This suggests that the p-value of these
tests in Table (5) were inflated by the number of instruments, and that system GMM
estimators are based on questionable assumptions.
There is one more concern: unlike IV regressions in Table 3, no test of instrument
strength is available in a GMM setting. Bazzi and Clemens (2009) argue that weak
instruments are a major concern with these estimators, and suggest a replication of
the GMM instrumentation in a traditional IV setting, where such tests exist.23
We
follow their advice and re-create the matrix of GMM instruments for the difference
and system equations, reporting the estimations in columns (2) and (3). We can now
report the Kleibergen-Paap statistics about instrument strength and the Kleibergen-
Paap LM test of underidentification. Column (2) shows that the Wald statistic
is very low for the difference equation, and that even the underidentification null
hypothesis cannot be rejected. Since we know from Table 3 that predicted aid is
not a weak instrument for aid, these signs of weak instrumentation must be due
to the GMM instruments. This implies, among other things, that lagged GDP
levels are very weak instruments for GDP differences. This is not very surprising,
given that the difference GMM estimators performed poorly. Such weakness usually
justifies the use of system GMM, as it is believed to be more robust. The fact that
difference GMM performed so poorly implies that the identification relies heavily on
the levels equation. Instrument strength in this equation is therefore crucial for the
whole system GMM. But column (3) actually reveals that the instrumentation of
this equation is even worse than for the difference equation.
All in all, from Table 6, we conclude that our system GMM estimates suffer
from two severe drawbacks. First, exogeneity tests are rejected when the set of
instruments is shrunk. Second, GMM instruments appear to be extremely weak.
These points lead us to infer that the GMM approach may not improve the fixed
effects specification. Instruments with this level of weakness imply that conclusions
about estimated coefficients are fragile. Given these results, Table 3 column (4)
remains our preferred specification.
22
Collapsing the instrument matrix when using the GMM instruments for aid also leads to the
rejection of these null hypotheses.
23
Blundell and Bond (2000), Bun and Windmeijer (2010), Hayakawa (2007) and Roodman
(2009a) make the same recommendation.
19

Table 6: Instrument collapsing and weak instruments
(1) (2) (3)
Collapse Difference System
Log GDP, lagged -0.044 -1.00*** 1.35
(0.062) (0.21) (8.47)
Log aid, lagged 0.023 0.054 -0.85
(0.043) (0.049) (6.08)
Log population 0.035 0.33 -0.71
(0.063) (0.26) (4.23)
Inflation -0.088** -0.075*** -0.93
(0.040) (0.019) (5.35)
Money, lagged 0.0018** 0.0043*** -0.000099
(0.00090) (0.0011) (0.012)
Schooling 0.013 0.067 -1.38
(0.059) (0.085) (8.99)
Institutional quality 0.012 0.018*** -0.12
(0.010) (0.0054) (0.84)
Openness 0.10*** 0.049* 0.13
(0.024) (0.027) (0.35)
Instruments 22
Countries 61 58 61
Hansen J test (p-val) 0.013
Hansen test (p-val), level 0.0044
AR(1) 0.0014
AR(2) 0.79
KP LM test (p-val) 0.24 0.88
KP F stat 2.05 0.011
Note: KP: Kleibergen-Paap. In column (1) system GMM is used, like in Table 5,
column (4), but the matrix of GMM-type instruments is collapsed. Column (2)
and (3) are 2SLS regressions where variables are instrumented using GMM-type
instruments. In column (2) all variables are differenced once, and instrumented
using log predicted aid and lagged log GDP levels. In column (3), instruments
are log predicted aid and differenced log GDP. Robust standard errors clustered
at the country level in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
20

5 Robustness
5.1 Instrument exogeneity
Exogeneity of our unique aid instrument cannot be statistically tested in the absence
of other valid instruments. Exogeneity will be violated if predicted aid affects GDP
growth through other channels than aid. This will happen if aid partnerships are cor-
related with other variables that influence GDP. Our concern is that our instrument
captures a larger effect, from many causes, with aid only being one of its components.
If we do not control for the other components, we will wrongly attribute the causal
effect in its entirety to aid. For instance, countries engaged in a long-term aid part-
nership may also exchange valuable information about innovation or technological
progress that have nothing to do with aid, but that reflect the specific nature of the
relationship between the two countries. It is very difficult to directly control for these
exchanges but other channels may capture these effects. An important variable very
likely to be influenced by partnership characteristics is trade. We would expect that
two countries engaged in a very strong aid partnership would also engage in other
economic exchanges, and that trade would be a prominent one. If our instrument is
just a correlate of trade, then it is likely that the effect we are measuring comes from
trade, but not from aid.
To control for this possibility, we include trade, defined as the sum of exports to-
ward and imports from donor countries, in the previous specifications. We construct
a trade instrument using the same strategy as for the aid instrument. Using aid en-
try dates, we compute a predicted trade quantity for each bilateral trade partnership
and obtain a predicted trade quantity by summing these up.24
Table 7 shows that controlling for trade only marginally changes the results.
The effect of aid in the 2SLS fixed-effect regression has a similar size and is sig-
nificant. Our trade instrument also appears to be strong, as is confirmed by the
Angrist-Pischke p-value of the first-stage regression for trade, and the relatively high
Kleibergen-Paap F statistic. The first two stages are presented in columns (2) and
(3) of Table 4. We also included our trade variable in the GMM estimations. As in
Table 6, these results cast serious doubts on the validity of the GMM approach in
this setting, but we gain no new insight from this exercise.25
A stronger concern would be that some unobserved trait of the recipient country
24
This is done because otherwise the simultaneity between trade and growth would once more
bias the estimations. A reason for using the aid partnership entry dates to instrument trade flows
is that we are especially interested in capturing the part of those flows that correlates with our aid
instrument.
25
Estimation tables are available in an appendix.
21

Table 7: OLS and IV regressions, with trade flows
(1) (2) (3) (4)
OLS FE OLS 2SLS FE 2SLS
Log GDP, lagged 0.020 -0.20*** 0.032 -0.33***
(0.023) (0.061) (0.090) (0.084)
Log aid, lagged 0.015 0.016 0.014 0.088***
(0.011) (0.017) (0.021) (0.033)
Log trade, lagged -0.050** -0.030 -0.065 0.092
(0.024) (0.040) (0.10) (0.059)
Log population 0.022 -0.17 0.022 -0.20*
(0.022) (0.12) (0.023) (0.10)
Inflation -0.11*** -0.11*** -0.11*** -0.10***
(0.023) (0.028) (0.025) (0.028)
Money, lagged 0.0014** 0.0027** 0.0016 0.0021*
(0.00069) (0.0012) (0.0016) (0.0013)
Schooling 0.0030 -0.0047 0.0037 0.023
(0.0100) (0.036) (0.012) (0.037)
Institutional quality 0.013** 0.0077 0.013** 0.0065
(0.0053) (0.0077) (0.0054) (0.0065)
Openness 0.093*** 0.075*** 0.092*** 0.069**
(0.016) (0.027) (0.021) (0.029)
Ethno. fractionalization -0.046 -0.034
(0.049) (0.099)
East Asia 0.039 0.045
(0.031) (0.055)
Sub-Saharan Africa -0.0090 -0.0055
(0.037) (0.039)
AP test (p-val), aid 0.000000061 0.00010
AP test (p-val), trade 0.030 0.0000036
KP F stat 2.49 12.3
R2
0.33 0.39 0.33 0.27
Note: AP: Angrist-Pischke. KP: Kleibergen-Paap. All regressions include year effects. Robust
standard errors clustered at the recipient level in parentheses. * p < 0.10, ** p < 0.05, ***
p < 0.01.
22

that promotes growth also has a direct effect on the starting date and/or the duration
of the donor-recipient relationship, i.e. the building blocks of our instrument. For
example, if donors are reluctant or unable to establish a partnership in places with
despotic rulers or in places with persistent conflicts, this could at the same time delay
the entry of those countries into donors’ portfolios and limit growth. This would
result in a negative correlation between entry date and growth, biasing upward the
coefficient on aid in the main regression. In the first column of Table 8 we see that,
indeed, countries with a later entry date did experience a lower growth rate. This
simple correlation disappears, though, after controlling for the initial level of GDP
and population size, arguably strong determinants of subsequent growth rates. In
column (3) we also control for total aid received. The idea would be to check if,
although the time of entry in a development cooperation partnership has an effect
on growth, this effect goes through aid and only through aid. The direct inclusion of
aid quantity in this regression is problematic, given the endogeneity of aid to growth,
so we do not put too much weight on this last model.
In the regressions reported in columns (1) to (3), the observations are at the
partnership level: this implies that each recipient country has many entry dates (one
for each donor) and only one growth rate for each time period. In columns (4) to (6),
we collapse the observations at the recipient country level, using the aid quantities
as weight for donor countries: therefore, each recipient will only have one average
entry date, which will be earlier if the most important donors in terms of aid given
started their partnership with this country earlier, and vice versa. Even the simple
correlation disappears in this setting. There results show that entrants with different
entry dates do not on average differ from a GDP growth point of view and thus, is
further suggestive evidence that our instrument is indeed exogenous.
5.2 Outliers
Easterly et al. (2004) showed how aid effectiveness results could be sensitive to the
exclusion of a few outliers. We make use of the Hadi (1992) procedure to exclude
outliers from the sample. Both with the within groups estimator and in the system
GMM regressions, we find larger effects of aid than when all observations are used.
The elasticity of GDP with respect to aid increases by 60 percent, with and without
controlling for trade.
Figure 2 shows the two partial regression plots of GDP growth on instrumented
aid, with and without outliers. We conclude that outliers tended to bias our estimates
downward and hence, the GDP elasticity with respect to aid is possibly much larger.26
26
Estimation tables are available in an appendix.
23

Figure 2: Partial regression plot of growth on aid, including and excluding outliers
24

Table 8: Correlation between entry date and growth
Whole Sample Collapsed
(1) (2) (3) (4) (5) (6)
Entry -0.00050** -0.00025 -0.00018 -0.0024 -0.0030 -0.0028
(0.00020) (0.00022) (0.00022) (0.0023) (0.0039) (0.0040)
Log GDP, lagged -0.0031** 0.0031* 0.00085 0.0034
(0.0015) (0.0018) (0.0072) (0.0085)
Log population 0.0054*** -0.011*** -0.0024 -0.0091
(0.0013) (0.0024) (0.0086) (0.012)
Log aid 0.021*** 0.0092
(0.0022) (0.013)
Observations 20974 20974 20974 812 812 812
Countries 112 112 112 112 112 112
R2
0.041 0.042 0.048 0.052 0.052 0.053
Note: The dependent variable is the growth rate over five years. All regressions include year effects. Columns (1)-(3)
include one observation for each recipient-donor pair every five years; observations in columns (4)-(6) are the weighted
average for each recipient and five-year period, where each donor is weighted with the total aid quantity donated to
that specific recipient during the five-year period. Robust standard errors in parentheses. * p < 0.10, ** p < 0.05, ***
p < 0.01.
5.3 Sample size
Our previous specifications include control variables that are commonly found in
the aid effectiveness literature. However, limited data availability sharply reduces
the sample size. Our dataset contains 130 countries but the regressions rely on 61
countries at most. Larger sample size comes at the cost of omitting some growth
determinants and hence, potentially biases the aid coefficient. On the other hand,
the aid instrument, if truly exogenous, should remove the correlation between aid
and the error term even in the presence of omitted variables. This provides an
indirect test of instrument validity, in addition to extending the estimation to many
more countries. The most parsimonious specification with only lagged GDP, aid, and
population as controls, allows us to use data on 108 countries, a dramatic increase.
Aid is not significant in any of the regressions.
Because we include as few controls as possible in these regressions, there may
be strong outliers in these specifications. We put this result to the test of exclud-
ing outliers, once more following the Hadi procedure. Table 9 confirms that these
data points strongly influence the results, despite representing a very small group
of observations (the procedure excludes 7 observations). This is visually confirmed
by the partial regression plots of growth on aid shown in the Appendix. First, aid
becomes significant, even when it is not instrumented. This result is not robust to
the inclusion of additional controls, as shown earlier, and thus has little meaning
25

in itself. More interesting is the within-groups estimate when aid is instrumented,
in column (4). The coefficient is significant, and its size almost the same as with
the controls (see Table 7 column (4)). This is further encouraging evidence of our
instrument being valid.27
Table 9: OLS and IV regressions excluding outliers, large sample
(1) (2) (3) (4)
OLS FE 2SLS FE-2SLS
Log GDP, lagged 0.0046 -0.21*** -0.0057 -0.21***
(0.0063) (0.039) (0.010) (0.038)
Log aid, lagged 0.022*** 0.023* -0.022 0.085**
(0.0073) (0.013) (0.033) (0.037)
Log population -0.011 0.022 0.021 -0.079
(0.0097) (0.089) (0.026) (0.11)
Countries 108 108 108 104
AP test (p-val) 0.00039 0.0000061
KP F stat 13.4 22.7
R2
0.073 0.23 0.025 0.18
Note: AP: Angrist-Pischke. KP: Kleibergen-Paap. All regressions include year effects.
Robust standard errors clustered at the country level in parentheses. * p < 0.10, **
p < 0.05, *** p < 0.01.
Finally, we use GMM estimators on the same large sample. The difference GMM
estimator once more fails to produce correct estimates of the lagged GDP coefficient;
while using system GMM, the aid coefficient is very close to the one in Table 5. This
once more tends to confirm that our results are robust. As before, though, GMM
estimates appear to be quite fragile. On the other hand, we find it encouraging that
all our system GMM specifications find an elasticity close to 0.05.
These robustness tests confirm our earlier results that aid has a significant and
positive impact on growth. The elasticity of GDP with respect to aid is found to
lie between 0.05 and 0.16, depending on the estimators used and the exclusion of
outliers from the regression sample.
27
In fact, the coefficient on aid is virtually unchanged even without controlling for population
and initial GDP. Tables can be obtained from the authors upon request.
26

5.4 Aid as a share of GDP
We depart from the aid effectiveness literature by measuring aid in constant dollars,
while past research traditionally used aid as a share of GDP.28
This departure was
done to avoid introducing additional endogeneity in the aid variable. It is indeed
peculiar to strive to remove reverse causality from GDP to aid by using instrumental
variables and then re-introducing GDP as a denominator. We prefer to instead use
aid quantities. This offers other advantages: first, the log-log specification directly
estimates the elasticity of GDP with respect to aid; moreover, since lagged log GDP
enters equation (1), the particular case with aid as a share of GDP can be seen as a
special case of equation (1), albeit in its log form, while our aid-quantity specification
would be the more general case.
Nevertheless, and despite the fact that instrumentation is likely to be more prob-
lematic, we feel that we cannot completely ignore the past convention and, in Table
10, we present results where the aid variable is expressed in GDP percentage points.
The trade variable is also computed as a share of GDP, while other controls are the
same as in previous tables.
Columns (1) and (2) are based on the whole sample, and columns (3) and (4)
exclude outliers identified by the Hadi procedure. The first two columns show that
aid has no effect on GDP, but the next two reveal that this is due to very few outliers
(only 13 observations are excluded from column (2) to column (4)). As in Table 3,
the aid coefficient differs significantly from zero only when instrumented. Removing
outliers does not only increase the aid coefficient, it also improves the identification,
as shown by the Angrist-Pischke test and the Kleibergen-Paap statistic.29
In Table 11, system GMM estimators are used to remove the bias induced by the
dynamic nature of the specification.30
Column (1) presents results based on the full
sample, and column (2) excludes the outliers. Columns (3) and (4) control for trade.
In both specifications, aid turns out to be significant once outliers are excluded, with
p-values of 6.1 and 7.8 percent in columns (2) and (4), respectively. The size of the
coefficient is smaller than with the within groups estimator. Although the Hansen
28
Another departure is the definition of the growth variable that can be measured between the
beginning and the end of the time period, or as an average of yearly growth rates. We return to
this point in Appendix 7.2, as the results are not affected by this change of definition.
29
We do not present results using OLS and 2SLS estimators, however aid coefficients are not
significantly different from zero in any of them, with and without outliers.
30
We focus on system GMM rather than difference GMM for the same reason as in Section 4.
The lagged log GDP coefficients with difference GMM are well below their FE estimates, such that
the difference GMM estimator must be severely biased and thus is not reliable. Tables are available
from the authors upon request.
27

Table 10: OLS and IV regressions, aid as a share of GDP
(1) (2) (3) (4)
FE FE 2SLS FE FE 2SLS
Log GDP, lagged -0.23*** -0.28*** -0.23*** -0.15**
(0.046) (0.053) (0.046) (0.065)
Aid, share of GDP 0.15 -1.19 0.21 2.15**
(0.25) (0.80) (0.31) (1.02)
Log population -0.15 -0.099 -0.16 -0.26***
(0.12) (0.15) (0.12) (0.081)
Inflation -0.11*** -0.12*** -0.12*** -0.11***
(0.027) (0.024) (0.028) (0.030)
Money, lagged 0.0028** 0.0023 0.0024* 0.0026**
(0.0013) (0.0015) (0.0012) (0.0010)
Schooling -0.0012 -0.061 0.0038 0.058
(0.034) (0.044) (0.032) (0.044)
Institutional quality 0.0085 0.0068 0.0066 0.0026
(0.0072) (0.0059) (0.0061) (0.0053)
Openness 0.075*** 0.075*** 0.064*** 0.060**
(0.027) (0.026) (0.023) (0.024)
AP test (p-val) 0.028 0.0011
KP F stat 5.08 11.8
R2
0.38 0.28 0.39 0.25
Note: AP: Angrist-Pischke. KP: Kleibergen-Paap. All regressions include year and coun-
try fixed effects. Outliers, identified through the Hadi procedure, are excluded from the
sample in columns (3) and (4). Robust standard errors clustered at the country level in
parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
28

tests do not reject the GMM approach, we remain wary of these estimations where
instrumentation is very weak.
Finally, in Table 12, we check that using aid as a share of GDP does not solve
the issue previously encountered in Table 6. We replicate those specifications using
the new aid variable. Column (1) runs the system GMM estimation collapsing the
instrument matrix, and fails to reject the validity of the system GMM assumption.
On the other hand, columns (2) and (3) show that the GMM instruments, both for
the difference and system equations, are very weak.31
Our conclusions are therefore mostly robust to the change in aid measurement.
When properly instrumented for, aid has a positive and significant effect on GDP.
Our estimates with this new variable range from 1.18 to 2.15. These can be related
to our former estimates. If γ1 and γ2 are the aid coefficients using log aid and aid as
a share of GDP, then computing marginal effects, we should have γ1 = At−1
Yt−1
γ2. The
mean of aid per GDP in the regression sample is 0.052, such that the corresponding
γ1 lies between 0.062 and 0.11. The actual estimates are between 0.057 and 0.16, so
the two specifications lead to similar results.
6 Conclusions
In this article, we proposed a new instrument for identifying the causal effect of aid
on growth. This instrument takes the supply side approach that relates to the aid
allocation decision a step further, for the first time using a source of variation that
is not just external but exogenous to growth. As far as possible, the instrument is
shown to be valid and strong. We claim that this is an improvement from a stream
of papers that relied on weak and non-exogenous instruments.
When it comes to the estimation strategy and the choice of estimator, we make
simple and clear methodological choices, explain and motivate them step by step and
probe their validity as best as we can. In particular, we do not take it for granted
that GMM estimators provide strong instruments and thus solve any dynamic bias.
On the contrary, we show that they should be used with much caution as the cure
may be worse than the disease. Instrument weakness is so prominent that estimates
are at best fragile, at worst misleading.
The effects uncovered by our identification strategy are statistically significant
and robust to various specifications. They indicate an elasticity of GDP with respect
to aid that lies around 0.10.
31
This is also the case when outliers are excluded.
29

Table 11: GMM regressions, aid and trade as shares of GDP
(1) (2) (3) (4)
Sys. GMM Sys. GMM Sys. GMM Sys. GMM
Log GDP, lagged 0.037 0.028 0.041 0.038
(0.041) (0.037) (0.034) (0.039)
Aid, share of GDP 0.94 1.18* 0.89 1.26*
(0.61) (0.63) (0.56) (0.71)
Trade, share of GDP -0.045 -0.060
(0.16) (0.21)
Log population -0.0082 0.0040 -0.017 -0.0056
(0.034) (0.026) (0.029) (0.034)
Inflation -0.11*** -0.10*** -0.11*** -0.11***
(0.022) (0.021) (0.022) (0.021)
Money, lagged 0.0015** 0.0012** 0.0015** 0.0011
(0.00061) (0.00063) (0.00076) (0.00080)
Schooling -0.013 0.00095 -0.018 0.0038
(0.029) (0.021) (0.028) (0.023)
(0.0055) (0.0054) (0.0050) (0.0061)
Openness 0.095*** 0.097*** 0.091*** 0.089***
(0.022) (0.024) (0.024) (0.028)
Instruments 48 48 49 49
Hansen J test (p-val) 0.62 0.83 0.68 0.83
Hansen test (p-val), level 0.57 0.61 0.65 0.51
AR(1) 0.00095 0.00015 0.00082 0.00012
AR(2) 0.93 0.81 0.94 0.76
Note: Instruments for the differences equation are log GDP lagged twice. Instruments for the
levels equation are log GDP lagged and differenced once. Log predicted aid and trade are used as
instruments in all regressions. Columns (2) and (4) exclude outliers. All regressions include year
effects. Robust standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
30

Table 12: Instrument collapsing and weak instruments, aid as share of GDP
(1) (2) (3)
GMM Collapse 2SLS-Difference 2SLS-System
Log GDP, lagged 0.20 -1.19*** 0.27
(0.20) (0.20) (0.22)
Aid, share of GDP 2.68 -0.57 4.04
(2.52) (1.06) (3.44)
Log population -0.12 0.44 -0.15
(0.14) (0.30) (0.15)
Inflation -0.14*** -0.066*** -0.23*
(0.051) (0.020) (0.13)
Money, lagged -0.00016 0.0039** -0.0016
(0.0019) (0.0015) (0.0025)
Schooling -0.023 0.066 0.0065
(0.048) (0.10) (0.065)
Institutional quality -0.0037 0.019*** -0.0066
(0.012) (0.0051) (0.016)
Openness 0.074* 0.045 0.020
(0.041) (0.035) (0.072)
Instruments 22
Countries 61 58 61
Hansen J test (p-val) 0.65
Hansen test (p-val), level 0.41
AR(1) 0.0032
AR(2) 0.86
KP F stat 1.99 1.20
Note: KP: Kleibergen-Paap. Column (1) presents GMM estimations, (2) and (3) are 2SLS re-
gressions where variables are instrumented using GMM-type instruments and log predicted aid.
Instruments for the differences equation are log GDP lagged twice. Instruments for the levels equa-
tion are log GDP lagged and differenced once. Log predicted aid is used as an instrument in all
the regressions. All the regressions include year effects. Robust standard errors clustered at the
country level in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
31

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7 Appendix
7.1 Data appendix
Time periods. Observations for all variables except GDP, aid and trade are five-year
arithmetic averages. Time period 1 represents years 1961-1965. The last period
(period 10) is 2001-2005.
Log aid. Aid is Official Development Assistance (ODA) and comes from the Donor
Assistance Committee (DAC) database of the OECD, Table 2a. Because predicted
aid is built from predicted aid shares, net ODA, which is the usual aid variable in the
aid effectiveness literature and which is potentially negative, cannot be used. Aid
is defined as gross ODA, minus gross debt relief. The latter is excluded because it
artificially inflates aid numbers in very recent years, where large debt cancellations
were granted. Aid is not averaged, but summed up over the time period. It is
34

expressed in millions of 2006 USD. Aid from all donors whose activity is reported by
DAC and to all developing countries, according to DAC definition, is considered.
Log trade. Trade at the bilateral level is defined as the sum of imports and
exports. At the recipient country level, it is summed across donor countries. Data
in current USD millions from the International Trade dataset, version 2.01, of the
Correlates of War Project. It is converted in 2006 USD by deflating it with the
Consumer Price Index of the US Bureau of Labor Statistics.
Aid and trade as shares of GDP. Data in current USD is divided by GDP in
current USD.
Log GDP. GDP in 2000 USD is from the World Development Indicators. GDP
is not averaged, but measured every fifth year (1965, 1970, 1975, etc.). We use this
instead of averaging to avoid introducing serial correlation.
GDP per capita. In 2000 USD. Source: World Development Indicators.
Growth. Growth is defined as the difference ln(y˜t) − ln(y˜t−5), where y˜t is GDP in
year ˜t. Note here that ˜t indexes year and not time periods.
Log population. Population is measured in millions. Source: World Development
Indicators.
Inflation. Natural logarithm of 1+consumer price inflation rate. Source: World
Development Indicators.
Money. Ratio of M2 to GDP. Source: World Development Indicators.
Schooling. Average years of primary schooling attained. Source: Barro and Lee
(2010).
Institutional Quality. Variable between 0 and 16, defined as the sum of “Corrup-
tion”, “Law and Order”, and “Bureaucracy Quality”, from the International Country
Risk Guide (ICRG) of the PRS Group. Data is not available before 1984. For earlier
years, data from the first available year is used. By doing so we follow the practice
in the literature (see Roodman (2007)).
Openness. Index constructed by Sachs et al. (1995) and Wacziarg and Welch
(2008).
Ethnic fractionalization. Ethnolinguistic Fractionalization index. Source: Roeder
(2001).
Regional dummies. Dummies for East Asia and Pacific, and Sub-Saharan Africa.
Region definitions are from the World Development Indicators.
Colony. Dummy variable equal to 1 if the pair has ever had a colonial link.
Source: CEPII.
Distance. Distance in thousands of kilometers between the two main cities of the
country. Source: CEPII.
35

Table A.1: Summary statistics and source of variables
Variable Mean s.d. Unit
Growth .18 .20 Percentage
Aid 1.86 3.28 Constant 2006 USD bn
Aid, GDP share .087 .12 Percentage
GDP 27.1 76.4 Constant 2000 USD bn
GDP per capita 1711 2043 Constant 2000 USD
Population 20.5 74.9 Millions
Inflation .15 .28 Annual change, perc. points
Openness .22 .39 0-1 index
Money 32.5 27.5 M2 as perc. of GDP
Trade 41.9 113.8 Constant 2006 USD bn
Schooling 2.98 1.65 Year
Institutional quality 6.55 .2.61 1-16 continuous variable
East Asia .12 .33 Identifier
Sub-Saharan Africa .35 .48 Identifier
Ethno-linguistic frac. .53 .27 Index (0 to 1)
Aid share 1.18 3.86 Percentage
Entry 8.84 9.07 year
Length 17.6 11.7 year
Colony .038 .19 Index (0 to 1)
Distance 8.41 3.84 Thousands of km
36

7.2 Definition of growth
As indicated in Appendix 7.1, growth is defined over five-year periods. The aid
effectiveness literature traditionally measures growth as the average yearly growth
rate during the time period, i.e. as 1
5
4
i=0
y˜t+i+1−y˜t+i
y˜t+i
. The two growth rates are highly
correlated so we do not expect this change to affect the results.32
On the other hand,
we want to ensure that our results are not driven by this modification, and for greater
comparability with the existing literature, we here replicate some of our results with
growth defined as the five-year average of yearly rates.
Panel A uses aid volumes, panel B aid as a share of GDP. To compare results
with the five-year growth rate and with the average yearly growth rate, one should,
using a first order approximation, multiply these by five. Column (1) of Table A.2
is the within groups estimator with aid instrumented. The coefficient on aid is still
significant, and its size multiplied by five is equivalent to the same coefficient in Table
3, column (4). Column (2) presents results with the system GMM estimator, and
once more they correspond to what we found with the five-year growth rate. The
next two columns exclude outliers. In A.3, which reports the same estimations but
with aid as a share of GDP, the aid coefficient is significant only after outliers are
excluded from the sample, similarly to the results in Section 5.4. Tables A.2 and
A.3 confirm that our findings are in no way driven by our alternative definition of
growth.
7.3 Additional robustness checks
7.3.1 Instrument exogeneity
In Table A.4, we include our trade variable in the GMM estimations. In column (1),
the GMM difference estimator is used: like in Table 5, the coefficient on lagged GDP
is too low for the estimator to be valid. In column (2) the system GMM estimator
is used, and the coefficient on aid is smaller than with the within groups estimator,
but still significant. The Hansen tests do not reject the required conditions. On the
other hand, the relatively large number of instruments is likely to decrease the power
of these tests. For this reason, we collapse the instrument matrix in column (3). The
Hansen tests are still valid, but the aid coefficient is no longer significant.
Collapsing the instruments is useful for having more accurate Hansen tests, but
since fewer moment conditions are used, the estimator becomes less efficient. Hence,
we take the following approach: we keep in mind from the collapsing exercise that the
32
The correlation is 0.99 in the data.
37

Table A.2: Growth as an average
(1) (2) (3) (4)
FE-2SLS Sys. GMM FE-2SLS Sys. GMM
Log GDP, lagged -0.047*** -0.013 -0.044*** -0.018*
(0.010) (0.011) (0.013) (0.0091)
Log aid, lagged 0.022*** 0.011* 0.033*** 0.011*
(0.0078) (0.0064) (0.012) (0.0060)
Log population -0.054** 0.0077 -0.057** 0.014
(0.021) (0.0094) (0.025) (0.0098)
Inflation -0.019*** -0.018* -0.019*** -0.016**
(0.0056) (0.010) (0.0064) (0.0073)
Money, lagged 0.00058** 0.00030* 0.00049** 0.00032*
(0.00023) (0.00017) (0.00025) (0.00019)
Schooling 0.0058 0.0074 0.0092 0.012*
(0.0075) (0.013) (0.0077) (0.0069)
Institutional quality 0.00066 0.0035** 0.000031 0.0037**
(0.0014) (0.0016) (0.0016) (0.0017)
Openness 0.016*** 0.023*** 0.016** 0.024***
(0.0058) (0.0044) (0.0068) (0.0046)
Instruments 48 48
Hansen J test (p-val) 0.27 0.29
Hansen test (p-val), level 0.10 0.059
AR(1) 0.00086 0.000086
AR(2) 0.92 0.52
AP test (p-val) 0.00088 0.0017
KP F stat 12.3 10.9
R2 0.27 0.081
Note: KP: Kleibergen-Paap. AP: Angrist-Pischke. For the GMM estimations, instruments
for the differences equation are log GDP lagged twice; instruments for the levels equation
are log GDP lagged and differenced once. Log predicted aid is used as an instrument in all
regressions. In columns (3) and (4), outliers are excluded using the Hadi procedure. All
regressions include year effects. Robust standard errors clustered at the country level in
parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
38

Table A.3: Growth as an average, aid as sh. of GDP
(1) (2) (3) (4)
FE-2SLS Sys. GMM FE-2SLS Sys. GMM
Log GDP, lagged -0.057*** 0.0072 -0.030** 0.0052
(0.011) (0.0076) (0.013) (0.0068)
Aid, share of GDP -0.23 0.17 0.46** 0.23**
(0.16) (0.11) (0.21) (0.11)
Log population -0.027 -0.0020 -0.060*** 0.0010
(0.030) (0.0068) (0.016) (0.0049)
Inflation -0.023*** -0.022*** -0.022*** -0.020***
(0.0048) (0.0044) (0.0059) (0.0041)
Money, lagged 0.00048 0.00028** 0.00053** 0.00025*
(0.00031) (0.00012) (0.00022) (0.00013)
Schooling -0.013 -0.0038 0.012 -0.00047
(0.0091) (0.0055) (0.0093) (0.0041)
(0.0012) (0.0011) (0.0011) (0.0011)
Openness 0.015*** 0.020*** 0.012** 0.020***
(0.0053) (0.0044) (0.0049) (0.0049)
Instruments 48 48
Hansen J test (p-val) 0.62 0.82
AR(1) 0.00070 0.000086
AR(2) 0.84 0.58
AP test (p-val) 0.028 0.0011
KP F stat 5.08 11.8
R2 0.29 0.24
Note: KP: Kleibergen-Paap. AP: Angrist-Pischke. For the GMM estimations, instruments
for the differences equation are log GDP lagged twice; instruments for the levels equation
are log GDP lagged and differenced once. Log predicted aid is used as an instrument in all
regressions. In columns (3) and (4), outliers are excluded using the Hadi procedure. All
regressions include year effects. Robust standard errors clustered at the country level in
parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
39

Table A.4: GMM regressions, with trade flows
(1) (2) (3) (4) (5)
Diff. GMM Syst. GMM GMM Collapse 2SLS-Diff. 2SLS-Sys.
Log GDP, lagged -0.50*** 0.038 0.45 -1.18*** 0.35
(0.17) (0.041) (0.40) (0.31) (0.25)
Log aid, lagged 0.016 0.041* 0.019 0.041 0.026
(0.040) (0.024) (0.10) (0.048) (0.052)
Log trade, lagged -0.032 -0.096** -0.41 0.11 -0.33
(0.081) (0.044) (0.35) (0.15) (0.26)
Log population -0.037 0.015 -0.12 0.44 -0.079
(0.17) (0.022) (0.13) (0.29) (0.071)
Inflation -0.078*** -0.095*** -0.13* -0.079*** -0.21*
(0.029) (0.031) (0.068) (0.020) (0.11)
Money, lagged 0.0029** 0.0025** 0.0052 0.0039*** 0.0037
(0.0012) (0.0012) (0.0047) (0.0013) (0.0035)
Schooling -0.034 0.013 -0.11 0.077 -0.074
(0.065) (0.022) (0.15) (0.090) (0.080)
Institutional quality 0.014* 0.014** 0.00094 0.017*** 0.0030
(0.0073) (0.0060) (0.017) (0.0056) (0.011)
Openness 0.078** 0.11*** 0.095** 0.051* 0.084**
(0.033) (0.031) (0.046) (0.030) (0.042)
Instruments 41 49 23
Countries 58 61 61 58 61
Hansen J test (p-val) 0.25 0.63 0.44
AR(1) 0.11 0.00070 0.0031
AR(2) 0.26 0.46 0.35
KP F stat 2.13 0.33
Observations 285 346 346 285 339
Note: KP: Kleibergen-Paap. Columns (1), (2), and (3) present GMM estimations, (4) and (5) are 2SLS regressions where variables
are instrumented using GMM-type instruments, log predicted aid, and log predicted trade. Instruments for the differences
equation are log GDP lagged twice. Instruments for the levels equation are log GDP lagged and differenced once. Log predicted
aid and trade are used as instruments in all regressions. All regressions include year effects. Robust standard errors clustered at
the country level in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
40

Hansen tests do not reject the system GMM assumptions, but when it comes to point
estimates, we consider those in column (2) as our preferred because they are more
efficient. In columns (4) and (5), we test the strength of the GMM-type instruments,
similarly to what is done in Table 6. We find that they are very weak, as shown by
the extremely low Kleibergen and Paap F statistic. The null of underidentification
cannot be rejected with a reasonable confidence level. As in Table 6, these results
cast some serious doubt on the validity of the GMM approach in this setting.
7.3.2 Outliers
In Table A.5, we focus on our key regressions and run them without the Hadi-
identified outliers in order to check their robustness. Columns (1) and (2) use the
within groups estimator and find larger effects of aid than when all observations are
used. The difference is sizable. The elasticity of GDP with respect to aid increases
by 60 percent in both specifications, with and without controlling for trade. System
GMM regressions in columns (4) and (5) yield similar results, but the aid coeffi-
cient becomes significant when controlling for trade. This is encouraging but we are
reluctant to draw any firm conclusions from regressions based on very weak instru-
mentations. We take away from Table A.5 that outliers tended to bias our estimates
downward, so that the GDP elasticity with respect to aid is possibly much larger.
7.3.3 Sample size
Table A.7 presents results from the most parsimonious specification with only lagged
GDP, aid, and population as controls.
Column (1) of Table A.7 shows that the difference GMM estimator once more
fails to produce correct estimates of the lagged GDP coefficient. Column (2) applies
the system GMM estimator, and the aid coefficient is very close to in Table 5. This
once more tends to confirm that our results are robust. Column (3) collapses the
instrument matrix, and reveals that the system GMM assumptions are likely to be
violated. As previously, the GMM estimates appear to be quite fragile. On the
other hand, we find it encouraging that all our system GMM specifications find an
elasticity close to 0.05.
Figure A.7 illustrates the change in the estimated aid coefficient of the within
group estimator when outliers are excluded from the sample. Figure A.7 reveals
that a few observations lie very far from the main group and so drive the result.
When these are excluded, the coefficient becomes positive and significant, as shown
in section 5.3 and Table 9.
41

Table A.5: Excluding outliers
(1) (2) (3) (4)
FE-2SLS FE-2SLS System GMM System GMM
Log GDP, lagged -0.21*** -0.33*** -0.099** 0.018
(0.063) (0.12) (0.049) (0.048)
Log aid, lagged 0.16*** 0.14*** 0.050 0.049**
(0.058) (0.045) (0.031) (0.020)
Log trade, lagged 0.10 -0.099*
(0.082) (0.052)
Log population -0.25** -0.21* 0.085 0.042
(0.12) (0.12) (0.053) (0.036)
Inflation -0.096*** -0.10*** -0.079** -0.094***
(0.033) (0.032) (0.035) (0.035)
Money, lagged 0.0025** 0.0018 0.0017 0.0025**
(0.0012) (0.0013) (0.0010) (0.0012)
Schooling 0.049 0.038 0.065* 0.035
(0.038) (0.038) (0.033) (0.028)
Institutional quality 0.00087 0.0030 0.020** 0.019**
(0.0082) (0.0073) (0.0094) (0.0076)
Openness 0.080** 0.069** 0.12*** 0.12***
(0.034) (0.035) (0.024) (0.026)
Instruments 48 49
Hansen 0.29 0.37
Hansen level 0.029 0.19
AR(1) 0.000094 0.000090
AR(2) 0.72 0.97
KP F stat 10.9 11.2
Note: KP: Kleibergen-Paap. Instruments for the differences equation are log GDP lagged twice.
Instruments for the levels equation are log GDP lagged and differenced once. Log predicted aid
and trade are used as instruments in all regressions. All regressions include year effects. Robust
standard errors clustered at the country level in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
42

Table A.6: OLS and IV regressions, large sample
(1) (2) (3) (4)
FE-2SLS FE-2SLS System GMM System GMM
Log GDP, lagged -0.21*** -0.33*** -0.099** 0.018
(0.063) (0.12) (0.049) (0.048)
Log aid, lagged 0.16*** 0.14*** 0.050 0.049**
(0.058) (0.045) (0.031) (0.020)
Log trade, lagged 0.10 -0.099*
(0.082) (0.052)
Log population -0.25** -0.21* 0.085 0.042
(0.12) (0.12) (0.053) (0.036)
Inflation -0.096*** -0.10*** -0.079** -0.094***
(0.033) (0.032) (0.035) (0.035)
Money, lagged 0.0025** 0.0018 0.0017 0.0025**
(0.0012) (0.0013) (0.0010) (0.0012)
Schooling 0.049 0.038 0.065* 0.035
(0.038) (0.038) (0.033) (0.028)
Institutional quality 0.00087 0.0030 0.020** 0.019**
(0.0082) (0.0073) (0.0094) (0.0076)
Openness 0.080** 0.069** 0.12*** 0.12***
(0.034) (0.035) (0.024) (0.026)
Instruments 48 49
Hansen 0.29 0.37
Hansen level 0.029 0.19
AR(1) 0.000094 0.000090
AR(2) 0.72 0.97
KP F stat 10.9 11.2
Note: KP: Kleibergen-Paap. Instruments for the differences equation are log GDP lagged twice.
Instruments for the levels equation are log GDP lagged and differenced once. Log predicted aid
and trade are used as instruments in all regressions. All regressions include year effects. Robust
standard errors clustered at the country level in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
43

Table A.7: GMM, large sample
(1) (2) (3)
Diff. GMM Sys. GMM GMM-Collapse
Log GDP, lagged -0.40** -0.0036 0.067
(0.18) (0.053) (0.053)
Log aid, lagged 0.071* 0.042** 0.0058
(0.040) (0.021) (0.035)
Log population 0.65* -0.013 -0.055
(0.37) (0.051) (0.060)
Instruments 44 53 19
Countries 106 108 108
Hansen J test (p-val) 0.50 0.24 0.066
AR(1) 0.13 0.012 0.011
AR(2) 0.52 0.25 0.22
Note: The dependent variable is the growth rate. Instruments for the differences equation are
GDP lagged twice in all the specifications. Instruments for the levels equation are GDP lagged and
differenced once. Predicted aid is used as an instrument. The matrix of instruments is collapsed in
column (3). All regressions include year effects. Robust standard errors clustered at the country
level in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.
44

Figure A.7: Partial regression plot of growth on aid, including (top plot) and exclud-
ing (bottom plot) outliers, larger sample
45

Table A.8: List of countries
Sample with controls Large sample
Algeria Malaysia Angola Palestinian Adm. Areas
Argentina Mali Barbados Rwanda
Bangladesh Mexico Belize Samoa
Bolivia Morocco Benin Saudi Arabia
Botswana Mozambique Bhutan Solomon Islands
Brazil Niger Burkina Faso St. Lucia
Cameroon Pakistan Burundi St.Vincent & Grenadines
Chile Panama Cambodia Sudan
Colombia Papua New Guinea Cape Verde Suriname
Congo, Dem. Rep. Paraguay Central African Rep. Swaziland
Congo, Rep. Peru Chad Timor-Leste
Costa Rica Philippines Comoros Tonga
Cote d’Ivoire Senegal Djibouti Vanuatu
Dominican Republic Sierra Leone Equatorial Guinea Viet Nam
Ecuador Sri Lanka Ethiopia
Egypt Syria Fiji
El Salvador Tanzania Grenada
Gabon Thailand Guinea
Gambia Togo Guinea-Bissau
Ghana Trinidad and Tobago Laos
Guatemala Tunisia Lebanon
Guyana Turkey Lesotho
Haiti Uganda Libya
Honduras Uruguay Madagascar
India Venezuela Maldives
Indonesia Yemen Mauritania
Iran Zambia Mauritius
Jamaica Zimbabwe Micronesia, Fed. States
Jordan Namibia
Kazakhstan Nepal
Kenya Nicaragua
Liberia Nigeria
Malawi Oman
Note: The large sample corresponds to the regressions where the only controls are lagged log GDP, lagged log aid, and log
population. Note that in addition to including more countries, the “large” sample also includes more observations for some
countries than the sample with controls.
46

Aid Effectiveness: New Instrument, New Results?

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