Turning the paradigm of aid allocation on its head
Abstract
How should aid be allocated among countries? Past research efforts to answer this question
have followed three steps: (1) the definition of an objective function, (2) the characterization
of its functional form, and (3) the estimation of its parameters. Each step has been heavily
criticized. Yet, attempts to refine the objective function and its functional form have increased
complexity, placing a further burden on the already fragile parameterization step. We propose
an alternative model by reversing this paradigm. We start by examining what can be estimated
with “sufficient” credibility. We then define five key properties or axioms, which are justified
in terms of fairness, proportionality, country ownership, and encouragement of domestic
investments. Finally, we combine these elements into an allocation formula, which jointly
determines the aid budget needed to achieve certain development goals and how this aid budget
should be allocated across countries. The framework is applied to the allocation of development
assistance for health.
Keywords: Aid; Allocation; Axiomatic approach; Development Assistance for Health
JEL Classification: F35, O11, I15, H5
1
Introduction
The bulk of academic research on development aid either aims to empirically identify the
determinants of aid allocation, or to assess the impact of development interventions on socioeconomic outcomes. In contrast, normative research on how to allocate development aid is
surprisingly scarce. To be sure, the absence of normative research does not reflect the fact that
a consensus on the question has already emerged. As stated by Anderson and Waddington
(2007), there has been “continued disagreement about which criteria should be used in
determining the cross-country aid allocations”.
Thus far, normative research on how aid should be allocated has been built around the
pioneering work of Collier and Dollar (2001, 2002; CD henceforth). CD propose to allocate
aid to countries to maximize poverty reduction. Building on the seminal work of Burnside and
Dollar (2000), CD estimate that aid is more efficient at reducing poverty when government
effectiveness is higher. According to CD’s framework, aid should, therefore, be allocated in
priority to countries that are poor and well governed.
CD's framework is ingenious and has been highly influential on policymakers and donors
(Easterly, 2003; Easterly et al., 2004). In later research, CD’s “poverty-efficient” framework
has nevertheless been criticized on normative and empirical grounds, as further detailed in
Section 2. The growth regression relating aid to poverty, which forms the basis of the allocation
formula, has received particularly strong criticism, being labeled "reductionist" and "narrow"
(Cogneau and Naudet, 2007; McGillivray and Pham, forthcoming), and its estimation leading
to "fragile" or "ambiguous" results (see e.g. Hansen and Tarp 2001; Easterly, 2003; Easterly et
al., 2004; Dalgaard et al. 2004, Bourguignon and Sundberg, 2007). Pertinent extensions of
CD’s framework in response to normative critiques rely even more heavily on demanding
econometric estimates and parameterization (see e.g. Llavador and Roemer, 2001; Cogneau
and Naudet, 2007; Wood, 2008; or Guillaumont et al., forthcoming).
In this paper, we build a new framework that jointly determines the aid budget needed to
achieve certain development goals, and how this aid budget should be allocated across
countries. In response to the criticisms on the paradigm pioneered by CD, we reverse their
approach. Instead of defining an objective function, struggling to evaluate its functional form
and parameters, and obtaining an allocation formula that does not necessarily satisfy desired
2
properties, we turn this paradigm on its head. We start by examining what can be estimated
with “sufficient” credibility (Section 3). We then define desired properties – or axioms – that
the allocation framework should satisfy (Section 4). Finally, we combine these elements into
an allocation formula (Section 5). Our allocation framework relies on five axioms: (i) Needs:
everything else being equal, countries with strictly higher needs should not receive less aid per
capita; (ii) Financial capacity: everything else being equal, countries with strictly higher
domestic capacity should not receive more aid per capita; (iii) Level of aid: for countries
displaying the desired level of domestic effort, aid should top up government expenditure to
fund the costs of necessary investments in the development objective; (iv) Domestic financing:
the allocation formula should encourage domestic contribution of recipient countries targeted
at the objective; and (v) Proportionality: the elasticity of aid with respect to effort should be
equal to 1.
In Section 6, we apply the general framework to the allocation of development assistance for
health (DAH). We analyze how much DAH countries would receive according to the proposed
framework and calculate the total amount of DAH needed under different scenarios. In the
health sector, there is indeed scope for improvement in resource allocation based on transparent
and explicit criteria (Ottersen et al., 2013), as studies find a lack of alignment between disease
burden and funding (Dieleman et al. 2014). Ravishankar et al. (2009) highlight this discrepancy
by reporting a “33-fold difference between DAH received by Turkmenistan and Nicaragua,
two countries with similar disease burden”. International agencies in health have recently
expressed their willingness to reflect on their allocation mechanisms, as demonstrated by the
Equitable Access Initiative.1
Three disclaimers, all further discussed in later sections, are in order. First, the contribution of
this paper is not to criticize allocation frameworks building on CD's work. CD's framework
and its extensions made key contributions to the academic literature. These contributions are
appealing from a theoretical point of view and their influence on policy shows that their interest
extends beyond theory. We take the critiques as given and propose a new allocation framework
The Equitable Access Initiative (EAI) consists of nine major international agencies in health (the World
Health Organization; the World Bank; Gavi, The Vaccine Alliance; UNAIDS; UNICEF; UNDP; UNFPA;
UNITAID; and the Global Fund). It “aims to develop a health framework based on a broader set of economic
and health indicators to better inform decision making on health and development”, see
http://www.theglobalfund.org/en/equitableaccessinitiative/.
1
3
that responds to the critiques. The complexity of the question of how to allocate development
aid implies that our framework also suffers from limitations and problems of applicability. The
advantages and limits of the two approaches are different and should be weighed against the
priorities of donors.
Second, two assumptions should be discussed from the onset. First, our framework assumes
that countries should have access to a minimum bundle of goods and services if they contribute
their share from domestic resources. For such countries, aid should fill the gap between what
countries can reasonably afford to pay and the total cost of the minimum bundle. This ethical
stance implies that our framework defines no budget constraint for donors, but rather allows us
to calculate a total budget needed to achieve a development goal. Second, our framework is
anchored in the principles of country ownership and democratic decision-making: countries
themselves have to determine their priorities, taking into account their preferences, their degree
of development, and their vulnerabilities. We believe that it is not the role of an allocation
framework to explicitly account for the myriad of factors – often unknown – explaining
heterogeneity between countries. Instead, development aid aims at supporting governments in
realizing their development objectives. Recognizing that errors are possible and that citizens
are responsible for holding their government accountable, our framework does not penalize
countries that have implemented bad policies in the past. This choice also avoids creating or
reinforcing a poverty trap. Instead, our framework assumes that development aid should be
proportional to the current domestic efforts of countries. The framework and its axioms can be
adapted to alternative normative viewpoints of international agencies and researchers.
Finally, our paper offers a general theoretical framework, which is then applied to the allocation
of DAH. It is beyond the scope of this paper to incorporate the many real-world implementation
constraints into the model. For example, our framework does not take into account the
absorptive capacity of recipient countries (Carter, 2014), crisis situations and humanitarian aid
(Collier & Hoeffler, 2004), or coordination problems between different stakeholders
(Bourguignon and Platteau, 2015; Dreher et al., 2015). These constraints should be reflected
upon by policymakers if they are interested in adapting the framework, or by scholars in future
research.
2
Review of existing frameworks
4
The allocation framework of CD and the papers following this approach consist of three core
elements: (1) the definition of an objective function; (2) the definition of its functional form;
and (3) the estimation of its parameters.
The objective function of CD (2001, 2002) minimizes current poverty. Formally, CD propose
to distribute a total amount of aid 𝐴̅ in t=0 to foster countries’ economic growth such as to
minimize aggregate poverty in t=1:
min ∑𝑖 𝐻𝑖1 ⇔ max ∑𝑖 𝛼𝑖 𝑔𝑖1 𝐻𝑖0
𝐴𝑖0
(1)
𝐴𝑖0
subject to: ∑𝑖 𝐴𝑖0 = 𝐴̅
where subscript 𝑖 identifies countries and subscript t identifies time periods, 𝐴𝑖0 = total aid,
𝐻𝑖𝑡 = total poverty, 𝛼𝑖 = elasticity of poverty reduction with respect to income, 𝑔𝑖1 = growth of
income per capita, 𝐴̅ = total aid to be allocated.
In the second step, CD postulate that income growth is a non-linear function of aid and policy
environment:
𝐴
𝐴
2
𝐴
𝑔𝑖1 = 𝑐 + 𝑏1 𝑋𝑖0 + 𝑏2 𝑃𝑖0 + 𝑏3 (𝑌𝑖0 ) + 𝑏4 (𝑌𝑖0 ) + 𝑏5 (𝑌𝑖0 ) × 𝑃𝑖0 + 𝑢𝑖0
𝑖0
𝑖0
𝑖0
(2)
where 𝑌𝑖0 = total GDP, 𝑃𝑖0 = the level of policy and Xit = exogenous conditions. Combining
equations (1) and (2), the solution of the maximization program is straightforward to derive:
𝑌
𝜆 𝑌𝑖0
𝐴𝑖0 = − 2𝑏𝑖0 {𝑏3 + 𝑏5 𝑃𝑖0 − 𝛼
4
𝑖
𝐻𝑖0
}
(3)
where 𝜆 is the shadow value of aid.
The last step is to estimate the parameters of this equation, in line with the work of Burnside
and Dollar (2000). CD assume that the elasticity 𝛼𝑖 is constant across countries and equal to 2.
The parameters 𝑏3 , 𝑏4 and 𝑏5 are evaluated by estimating the growth equation (2) using a panel
dataset. CD’s estimates, shown in Column 1 of Table 1, suggest that 𝑏4 is negative, implying
diminishing marginal returns to aid. Their estimate of 𝑏5 is positive, suggesting that aid is more
efficient in a good policy environment. From equation (3), they conclude that aid should be
higher in countries with good policy and high initial poverty.
Table 1: Estimation of growth equation (2) by Collier and Dollar (2002) (Column 1) and
replication for health (Columns 2 & 3).
(1)
5
(2)
(3)
Growth rate of
per capita GNP
Initial national income per capita (log)
Δlog DALYs lost per 100,000
0.67
(1.08)
Initial DALYs lost per 100,000 (log)
0.0114
(0.25)
-0.146***
(-4.14)
-0.143***
(-3.65)
Policy
0.46*
(1.65)
-0.306**
(-2.39)
-0.367**
(-2.53)
Aid (% of national income)
-0.54
(1.40)
-0.130*
(-1.95)
-0.188***
(-2.92)
Square of aid (% of national income)
-0.02
(1.60)
-0.00603*
(-1.95)
-0.00847***
(-2.79)
0.31***
(2.94)
-0.0253**
(-2.01)
-0.0309**
(-2.23)
349
0.37
125
0.298
116
0.358
Interaction
Policy x aid in % national income
Observations
R-squared
Robust t-statistics in parentheses. * p<0.10, ** p<0.05, *** p<0.01. Column 1 is a replication
of the Column 1 of Table 1 of Collier and Dollar (2002). Policy is measured by the CPIA index.
Aid in percentage of national income is measured as ODA/GDP. The regression includes
regional dummies (South Asia, East Asia, Sub-Saharan Africa, Middle East/North Africa,
Europe/Central Asia) as well as the ICRGE indicator of institutional quality. Column 2
considers Category I DALYs per 100,000 and DAH in percentage of GNI. Policy is measured
by the government effectiveness indicator of the World Bank WGI. Aid in percentage of
national income is measured as ODA/GDP in column 1, and as DAH/GNI in column 2. The
regression includes regional dummies. Column 3 further controls for GDP per capita in PPP in
2000 from the Penn World Table. Afghanistan, Cuba, Eritrea, Guyana, Libyia, Papua New
Guinea, Solomon Islands, South Sudan and Timor are excluded from column 3 due to lack of
data.
The framework of CD has been criticized on three grounds. First, from a normative perspective,
the objective function of CD is “debatable in terms of fairness” because “it allows the
persistence of big inequalities in poverty risk between people living in countries whose
structural disadvantages are very different” (Cogneau and Naudet, 2007). Countries with bad
policies and the poor people living in them are clearly penalized (McGillivray, 2004). This
critique reflects the “uncomfortable trade-off between need and effectiveness” (McGillivray
and Pham, forthcoming) and the “fundamental disagreement about what is meant by a fair or
equitable allocation” (Anderson and Waddington, 2007).
In response to this critique, the frameworks of Llavador and Roemer (2001) and Cogneau and
Naudet (2007) propose to equalize growth opportunities among recipient countries. Anchored
6
in theories of justice, their frameworks distinguish between a country’s effort, which is within
its control and should be rewarded, and circumstances, which are beyond a country’s control
and should be compensated for. Formally, the objective is to equalize the part of expected
poverty at date T that is “purely circumstantial” and “effort-free”. The equalization process
follows Rawls’ minimax system, as recommended by Roemer (1998):
𝑒
minmax ∑𝑖 𝐻𝑖𝑇
(4)
𝐴𝑖0
subject to: ∑𝑖 𝐴𝑖0 = 𝐴̅
𝑒
The expected poverty 𝐻𝑖𝑇
is a function of aid, which looks similar to equation (2). However,
𝑒
𝐻𝑖𝑇
depends on ex-ante expected effort and growth, contrary to ex-post poverty 𝐻𝑖𝑇 which is a
function of ex-post observed effort and growth (Cogneau and Naudet, 2007).
Another normative critique was offered by Wood (2008), who argues that “[…] donors and
people care—for intellectually and morally defensible reasons—about both current and future
levels of poverty”. However, CD’s framework focuses on reducing current poverty, rather than
the discounted flow of future poverty. In response, Wood (2008) proposes to minimize the
discounted sum of future poverty, such that equation (1) is replaced by the following objective
function:
min ∑𝑖 ∑𝑡
𝐴𝑖0
𝐻𝑖𝑡 (𝐴𝑖0 )
(5)
(1+𝑟)𝑡
The second critique of the framework of CD relates to its operationalization. As put by Wood
(2008), “to operationalize any allocation model, it is clearly necessary to choose a specific
form, but the choice matters greatly for the results”. The growth equation of CD was criticized
for being “reductionist” and not “sufficiently nuanced” (McGillivray et al., 2016), assuming
that “aid can only reduce poverty by increasing growth” (Lensink and White, 2000), and
“ignoring a lack of human capital and economic vulnerability in recipient countries”
(McGillivray et al., 2016). A few scholars proposed various avenues for generalizing equation
(2) in response to this critique. For example, Guillaumont et al. (forthcoming) expand equation
(2) to account for the impact of aid, economic vulnerability, human capital and their
interactions on growth.
The third critique relates to the estimation of the model’s parameters. Panel data analyses of
the relationship between aid and growth, i.e. equation (2), yielded fragile and ambiguous results
(see e.g. Hansen and Tarp, 2001; Easterly, 2003; Easterly et al., 2004; Dalgaard et al., 2004;
7
Bourguignon & Sundberg, 2007). As summarized by Wood (2008), “there is much
disagreement about the effects of aid on poverty reduction: how big, how rapid, and
conditional on what characteristics of recipient countries, aid instruments, and donor
behaviour?” We formalize this empirical challenge, building on a general model in which
countries invest efforts to improve a development outcome 𝑑𝑖𝑡 . This outcome depends on a
country’s effort, circumstances and income, as well as on the level of aid that it receives. Effort
and circumstances are difficult to measure. The observable part of these variables is labeled
with a superscript o. The unobservable part is labeled with superscript u. In equation (6)
summarizes this general model:
𝑑𝑖𝑡+1 = 𝑑(𝑦𝑖𝑡 , 𝑒𝑖𝑡𝑜 , 𝑒𝑖𝑡𝑢 , 𝑐𝑖𝑡𝑜 , 𝑐𝑖𝑡𝑢 , 𝑎𝑖𝑡 )
(6)
𝑗
𝑗
where 𝑦𝑖𝑡 = income per capita, 𝑎𝑖𝑡 = aid per capita, 𝑒𝑖𝑡 = effort, 𝑐𝑖𝑡 = circumstances.
Circumstances may include the lagged outcome variable 𝑑𝑖𝑡 . The distribution of 𝑒𝑖𝑡𝑢 and 𝑐𝑖𝑡𝑢 is
unknown.
Equation (6) is a general form of equation (2). This equation is expected to be difficult to
estimate for three main reasons. First, the estimation of equation (6) is subject to the usual
endogeneity issues of omitted variables, reverse causality and mismeasurement (Rajan &
Subramanian, 2008; Clemens et al., 2012; Museru et al., 2013). Because unobserved variation
is likely to vary over time, estimations including fixed effects are also expected to be biased.
In this context, randomization is impossible, and finding credible instrumental variables for all
factors interacting with aid in equation (6) is extremely complicated. Second, many variables
entering in equation (6) are unobservable. The variance of the OLS estimator is proportional to
the variance of the error term, which is expected to be massive in this case. Finally, the
functional form of equation (6) is unknown (Clemens et al., 2012; Dalgaard & Hansen, 2001;
Hansen & Tarp, 2001). The difficulty of estimating this functional form using theory or data
mining is magnified by the first difficulty – that is, the fact that many variables of equation (6)
are unobservable.
The coefficients of the CD regression are indeed imprecisely measured and likely to be biased.
For example, the 95% confidence interval of the coefficient associated with the interaction term
in Column 1 of Table 1 is [0.10, 0.52]. The upper bound is more than five times larger than the
lower bound. Several scholars have revisited the results of Burnside and Dollar (2000) and
Collier and Dollar (2001, 2002); see, for an early overview, Burnside and Dollar (2004). For
8
instance, Easterly et al. (2004) conclude, using the same definitions and estimation methods on
a slightly extended country and time sample, that the interaction term of aid and policy “[…]
is not robust to alternative equally plausible definitions of aid and policy, or to alternative
period lengths”. Also in the case of health, Stuckler et al. (2013) report highly contested effects
of aid on health, “[…] with proponents on all sides adhering strongly to their competing
interpretations”. The authors find substantial methodological weaknesses, including
confounding extraneous factors correlated with aid, adverse selection, issues with time lags
and low power biasing towards the null hypothesis.
In Columns 2 and 3 of Table 1, we replicate the estimation of equation (2) for the health
outcome measure of Disability Adjusted Life-Years (DALYs) lost due to communicable,
maternal, perinatal and nutritional conditions per 100,000. DALYs are a standardized metric
that allow for direct comparison of burdens of different diseases across countries and over time.
Conceptually, one DALY lost is the equivalent of losing one year in good health because of
either premature mortality or disability (Murray et al., 2015). Assessing health outcomes by
both mortality and morbidity provides a more encompassing view on health outcomes than
only looking at mortality or life expectancy alone. Data is available for all countries for 2000
and 2012. The Government Effectiveness Index used in the estimation is published by the
World Bank as part of the Worldwide Governance Indicators. The index captures perceptions
of the quality of public services, the quality of the civil service and the degree of its
independence from political pressures, the quality of policy formulation and implementation,
and the credibility of the government's commitment to such policies.2 Data on DAH flows was
published by the Institute for Health Metrics and Evaluation (2016). 3 Regressions include
countries for which data is available. As expected, the coefficient associated with the
interaction term between government effectiveness and DAH/GNI is negative, indicating that
these two variables are complementary factors explaining the reduction in DALYs. This
coefficient is significant at the 5% threshold, but the 95% confidence interval is relatively large
([-0.05, -0.0004] in column 2 and [-0.014, -0.002] in column 3). A legitimate question is
whether imprecision and biases are too large to be used for aid allocation.
2
CPIA data is only available from 2005 onwards and we were, therefore, not able to use it here.
3
We thank Joseph Dieleman and Nafis Sadat for providing this data via email.
9
We propose a fourth original critique: the framework of CD and its extensions do not explicitly
differentiate needs and financial capacity. A country’s financial capacity to invest in
development outcomes is not explicitly modeled, implying that richer countries with high needs
(i.e. high poverty) are not made accountable for their situation. Instead, two countries with
similar level of poverty and quality of policies will receive the same amount of aid, even though
one of them may be much richer than the other. The fact that needs and financial capacity are
not clearly distinguished in the framework of CD is rooted in the fact that needs (i.e. poverty
reduction) and financial capacity (i.e. national income growth) are perfectly multicollinear in
their benchmark framework, as the elasticity of poverty with respect to income 𝛼𝑖 is assumed
to be constant across countries and equal to 2. In the case of health, needs (i.e. health outcomes)
and financial means (i.e. national income) can and should be distinguished.
As shown in this literature review, the research extending CD’s pioneering work mostly
focused on the first two critiques. These extensions are ingenious and important: they
contribute to the literature by making CD's framework more general. However, making the
objective function (equation 1) and the growth equation (equations 2 and 6) more general
comes at a cost: the extended frameworks are even more complex to estimate. While
progressing on the first two critiques, the extended frameworks have disregarded the third
critique. For example, the operationalization of the framework of Cogneau and Naudet (2007)
not only requires the estimation of income elasticities 𝛼𝑖 in each country and of a growth
equation, as for the CD approach, but also requires the estimation of growth prospects without
aid, and the estimation of the policy effort function, which depends on “pure effort”, initial
poverty and circumstances. The framework of Wood (2008) further requires estimating the
impact of current aid on future poverty decline. By considering a more general growth
equation, Guillaumont et al. (forthcoming) multiply the number constraints on the functional
form as well as the number of parameters that should be estimated.
Hence, we propose a fundamental rethinking of the common approach to respond to the four
critiques altogether. It is most likely impossible to define a single objective function
summarizing the multidimensionality of aid objectives. Moreover, the principle of country
ownership4 further imposes limits on donors’ priorities. It would also be unrealistic to think
The principle of country ownership was endorsed by the international community at the 2005 Paris
Declaration, and then in 2008, at the Accra Agenda for Action. The Paris Declaration on Aid Effectiveness
4
10
that more rigorous econometrics could lead to a precise estimation of the objective function,
and present a basis for development policy and aid allocation.
In response, we propose to reverse the process followed by CD-type frameworks. Instead of
building an elegant but complex theoretical framework, and then struggling to estimate its
parameters, we first determine what parameters can be credibly estimated (Section 3). We then
determine key properties, or axioms, that should be satisfied (Section 4). Finally, we build the
allocation framework upon these elements (Section 5).
3
What can be estimated?
In this section, we propose three important elements that can be estimated with reasonable
precision: (1) an efficiency frontier characterizing the best level of development outcomes
attainable for given national income; (2) the budget needed by countries on the frontier to reach
the desired development objective; and (3) the share of their budget that countries can be
expected to allocate to the desired development objective.
We argue that the existence of a “development frontier” based on equation (6) is the first
element that can be estimated with reasonable precision.5 We start by noting that aid 𝑎𝑖𝑡 is also
the outcome of an unknown allocation process that depends on effort, circumstances and
income:
𝑎𝑖𝑡 = 𝑎(𝑦𝑖𝑡 , 𝑒𝑖𝑡𝑜 , 𝑒𝑖𝑡𝑢 , 𝑐𝑖𝑡𝑜 , 𝑐𝑖𝑡𝑢 )
(7)
Equations (6) and (7) can hence be combined to obtain the following reduced form equation:
𝑑𝑖𝑡+1 = 𝑟(𝑦𝑖𝑡 , 𝑒𝑖𝑡𝑜 , 𝑒𝑖𝑡𝑢 , 𝑐𝑖𝑡𝑜 , 𝑐𝑖𝑡𝑢 )
(8)
While a full characterization of the function 𝑟 using econometrics is impossible, we argue that
countries with the highest level of outcome 𝑑𝑖𝑡+1 for their given financial capacity 𝑦𝑖𝑡 can be
identified using efficiency frontier analysis. These countries display the most favorable
circumstances and the highest level of effort for given financial capacity 𝑌𝑖𝑡 . The idea is not to
(2005) proposes the following definition of country ownership: “Partner countries exercise effective
leadership over their development policies, and strategies and co-ordinate development actions.”
If the number of countries is sufficiently large, the distribution of countries in the space {𝑦𝑖𝑡 , 𝑒𝑖𝑡𝑜 , 𝑒𝑖𝑡𝑢 , 𝑐𝑖𝑡𝑜 , 𝑐𝑖𝑡𝑢 }
can be approximated by a continuous density function whose frontiers can be identified with precision. The
larger the sample of countries, the more precise are the estimates of the frontier and the smaller the
confidence intervals.
5
11
measure a causal relationship, but rather to identify a function characterizing this specific group
of countries. We denote this "development frontier" as: 𝑑𝑖𝑡+1 = f(𝑦𝑖𝑡 ).
The estimation of the development frontier can be illustrated in the context of DAH. As
outcome variable, we use the disability-adjusted life years lost to communicable, maternal,
perinatal and nutritional conditions per 100,000 (Group I DALYs).6 We measure the domestic
capacity of countries using gross national income (GNI) per capita expressed in 2011
international $ (int-$) sourced from the World Bank (Anand and Bärnighausen, 2004). Sterck
et al. (forthcoming) show that the relationship between GNI per capita and DALYs lost due to
the disease burden of Group I is best captured by a log-log function.
Our efficiency analysis is based on quantile regression 7 to limit the influence of outlying
observations and mismeasurement problems (Liu et al., 2008). The sample includes all
countries for which data on DALYs and GNI per capita are available (140 countries for 2000
and 119 countries for 2000). Figure 1 shows the quantile regression line based on the first
quartile between Group I DALYs (log) on GNI per capita (log). The slope of the regression
line is negative and close to -1. Regression results are presented in Table 2. This table shows
that regression coefficients associated with GNI per capita (log) are very precisely estimated.
In column 1, the t-statistic of GNI per capita (log) is equal to -28.8, and the confidence interval
is [-0.99, -0.87]. As data are available for the years 2000 and 2012, we can test whether the
relationship between Group I DALYs (log) and GNI per capita (log) is stable over time. We
find a very comparable coefficient when we use data for 2012 (Column 1) or 2000 (Column
2). By pooling the years, we can see that neither the intercept nor the slope of the regression
line changed significantly over time (Column 3).
Three categories of health conditions are distinguished: (1) Group I DALYs lost due to communicable,
maternal, perinatal and nutritional conditions; (2) DALYs lost due to non-communicable diseases; and (3)
DALYs lost due to injuries. Our analysis focuses on Group I DALYs. This part of the burden of disease is the
most important in our context, as only 1.5% of all DAH is directed towards DALYs lost to non-communicable
diseases (Dieleman et al., 2015). Moreover, since Group I DALYs can be effectively contained with a wellfunctioning health system, their correlation with log GNI per capita is much higher (Sterck et al.,
forthcoming).
7 We chose to run quartile regression based on the 25th percentile. The method can be easily applied with
other percentiles or using Data Envelopment Analysis.
6
12
Figure 1 – The health development frontier.
We call this quartile regression line the “health development frontier” (HDF). Importantly, the
HDF does not capture a causal relationship between health outcome and financial capacity.
The HDF characterizes the levels of health outcomes that can be achieved by countries
displaying favorable circumstances and good level of effort, given their financial capacity.
Countries that are above the HDF are either penalized by unfavorable circumstances or do not
display high level of effort (or both). This analysis cannot and does not seek to distinguish
which of the two explanations explicates deviations from the frontier.
13
Table 2 – Quartile regressions between Group I DALYs lost per 100,000 (in log) and GNI per
capita (in log)
(1)
(2)
(3)
Dependent variable: Group I DALYs lost per 100,000 (log)
Year
GNI per capita (log)
2000
-0.931***
(0.0323)
2012
-0.988***
(0.0672)
Year = 2012
-0.988***
(0.0693)
-0.468
(0.817)
Interaction: GNI per capita (log) x Year =
2012
0.0487
(0.0829)
Constant
16.82***
(0.300)
17.35***
(0.676)
17.35***
(0.691)
Observations
Robust standard errors in parentheses
* p<0.10, ** p<0.05, *** p<0.01
149
119
238
The second element, which can be estimated with relative precision, is the budget needed by
efficient countries, i.e. on the development frontier, to invest in the desired development
objective.8 By this are meant accounting estimates of providing particular public services, be
they (primary) education, basic poverty relief – or, in our application, basic healthcare. We
denote c the budget needed by a country on the development frontier to move toward the
realization of the objective 𝑑. There is a great deal of literature on needs and cost estimates
associated with different development objectives. These works provide reasonable estimates
of the cost of reaching an objective provided that money is used efficiently. For instance, total
financing needs to meet basic education (including universal primary education) have been
estimated by UNESCO (2007), and further calculations exist for the broader range of Education
For All (EFA) objectives, as established in Dakar in 2000 (GCE, 2008). Important for our
objective, these estimates do not assume or are not based on elasticities of how much particular
programs contribute to reaching a development objective. Thus, they are intrinsically different
from the estimated coefficient of a growth regression. Moreover, when new estimates become
available, the allocation formula can easily be updated.
This quantity is expected to be more difficult to calculate for countries that are not on the development
frontier. These latter countries are characterized by unfavorable circumstances, lack of effort, or both, and
the cost of investments in the development objective is expected to vary with these factors in complex ways.
8
14
In the case of healthcare, Article 25 of the 1948 Universal Declaration of Human Rights
declares that “[e]veryone has the right to a standard of living adequate for the health and wellbeing of himself and of his family […]”, which includes medical care in the event of sickness
and disability, where “[m]otherhood and childhood are entitled to special care and assistance”
(see also Sachs, 2012). The Taskforce on Innovative International Financing for Health
Systems (2009) has provided an estimate of the costs of providing basic health goods and
services. These services include, among others, the cost of treating AIDS, TB and malaria,
immunizations, treatment of acute respiratory infections, diarrheal diseases, maternal and
perinatal conditions, and malnutrition (for the entire list, see Appendix 1 of the publication by
the Taskforce). These costs are calculated as an average across 49 low-income countries for
the year 2005. By adjusting for price differences across countries and over time, we calculate
c, the cost of the minimum health bundle in 2012, which amounts to 198.7 int-$ per person per
year (see Appendix 1). We do not claim that, with this amount, countries automatically have
the lowest level of 𝑑. It can take time for recurrent investments to materialize.
As the third element, we propose that the desired level of financial effort that countries should
exert to reach the development objective can be set ex ante by policymakers. The financial
effort of a government, denoted by ℎ𝑖𝑡 , is measured by the government expenditures on the
relevant program, whether education, poverty relief or social expenditures, or health, as a share
of GDP. The indicator of financial effort has two key advantages compared to other existing
policy indicators, such as the Country Policy and Institutional Assessment (CPIA), the
Worldwide Governance Indicators (WGI), or the corruption perception index (CPI). First,
government spending can be distinguished by program, depending on the objectives of the
donor. Government prioritization of specific sectors can, therefore, be taken into account when
allocating aid. Second, the indicator of financial effort is a continuous variable whose changes
can be instantaneously reflected in the data. As briefly discussed before, however, financial
effort does not necessarily entail effectiveness in reaching an objective. Using financial effort
minimizes the risk of path dependency and poverty traps.
We set a target ℎ∗ for the financial effort. There are international norms about budget
allocation. For education, for example, the UNESCO (2014) has argued that countries should
commit to spending 6% of their GNP or 20% of their government expenditures on education,
with 50% on primary education. In the case of health, we follow McIntyre and Meheus (2014),
15
who state that governments should spend 5% of GNI on health goods and services. Also, the
World Health Report 2010 notes that “[…] those countries whose entire populations have
access to a set of services usually have relatively high levels of [mandatory] pooled funds – in
the order of 5-6% of gross domestic product” (WHO, 2010).
4
Axioms for the allocation of aid
Building on the three measurable quantities defined in Section 3, this section defines axioms
for the allocation of aid. We formalize the axioms by considering two hypothetical countries i
and j. The axioms are then combined into an allocation formula in Section 5. The first two
columns of Table 3 summarize the variables that are used in this section.
We explicitly distinguish between needs and financial capacity using axioms (i) and (ii). These
axioms can be justified on the basis of fairness. Aid should be provided with a particular
development objective in mind. Therefore, aid per capita should depend on the needs of
countries in terms of these objectives. On the other hand, countries with more available
financial means, other things being equal, can and should be held more accountable for their
development outcomes, implying that they should not receive more aid per capita.
Axiom (i) on needs: everything else being equal, countries with strictly higher needs should
not receive less aid per capita.
𝑦𝑖𝑡 = 𝑦𝑗𝑡 , ℎ𝑖𝑡 = ℎ𝑗𝑡 and 𝑑𝑖𝑡 > 𝑑𝑗𝑡 
𝑎𝑖𝑡 ≥ 𝑎𝑗𝑡
(9)
Axiom (ii) on financial capacity: everything else being equal, countries with strictly higher
domestic capacity should not receive more aid per capita.
𝑑𝑖𝑡 = 𝑑𝑗𝑡 , ℎ𝑖𝑡 = ℎ𝑗𝑡 and 𝑦𝑖𝑡 < 𝑦𝑗𝑡 ⇒
𝑎𝑖𝑡 ≥ 𝑎𝑗𝑡
(10)
Axioms (i) and (ii) address the distribution of aid between countries, but do not provide
information about the level of aid that countries should receive. Given a budget needed to
deliver a certain development objective, we assume that donors should complement
government expenditures in order to allow countries to reach this budget as long as countries
are efficient, i.e. on the development frontier, and exert the desired level of financial effort
themselves. We denote 𝑔𝑖𝑡 as the government expenditures per capita allocated to the
16
development objective and ℎ𝑖𝑡 as the share of GNI allocated by the government to the
development objective (𝑔𝑖𝑡 /𝑦𝑖𝑡 ).
Axiom (iii) on the level of aid: for countries on the development frontier and displaying the
desired level of domestic financial effort ℎ𝑖𝑡 = ℎ∗ , aid should top up government expenditure
to fund the costs of necessary investments in the development objective 𝑐:
𝑎𝑖𝑡 = max(𝑐 − 𝑔𝑖𝑡 , 0) = max(𝑐 − ℎ∗ 𝑦𝑖𝑡 , 0)
(11)
Given the objective of aid to improve certain development outcomes, the allocation of the aid
should not crowd out domestic funding (see e.g. Morrissey, 2015; Prichard, 2016). Rather, the
formula should encourage domestic contributions.
Axiom (iv) on domestic financing: the allocation formula should encourage the domestic
contribution of recipient countries targeted at the objective.
Here, we opt for the wording “encourage” instead of “maximize” on purpose. Designing aid
allocation to maximize the domestic contribution of a country would require knowing how
government expenditure targeted at the objective varies as a function of the allocation formula
(e.g. Svensson, 2000; 2003). This reaction function is unknown, as it depends on the unknown
objective function and budget constraints of the government. Therefore, while maximizing
domestic contribution in the strict sense seems infeasible, we aim to design an allocation
formula that encourages domestic contribution.
To encourage domestic funding, the amount of aid allocated should increase with government
𝜕𝑎
expenditure targeted at the objective (𝜕ℎ𝑖𝑡 > 0, with 𝑎𝑖𝑡 = 0 if ℎ𝑖𝑡 = 0). In other words, the
𝑖𝑡
allocation formula should be defined as a counterpart financing rule, which we denote as 𝛿𝑖𝑡 .
We define 𝛿𝑖𝑡 as the share of government health expenditures relative to total health
expenditure, with 0 ≤ 𝛿𝑖𝑡 ≤ 1:
𝛿𝑖𝑡 ≡ 𝑔
𝑔𝑖𝑡
(12)
𝑖𝑡 +𝑎𝑖𝑡
𝑔
Denoting ℎ𝑖𝑡 as the ratio 𝑦𝑖𝑡, we can rewrite equation (12) as follows:
𝑖𝑡
𝛿𝑖𝑡 ≡ ℎ
ℎ𝑖𝑡 𝑦𝑖𝑡
(13)
𝑖𝑡 𝑦𝑖𝑡 +𝑎𝑖𝑡
Given needs and financial effort, the relationship between counterpart financing 𝛿𝑖𝑡 and
17
national income 𝑦𝑖𝑡 is given by:
𝜕 𝛿𝑖𝑡
𝜕𝑦𝑖𝑡
=
ℎ𝑖𝑡 (𝑎𝑖𝑡 −
𝜕𝑎𝑖𝑡
𝜕𝑦𝑖𝑡
𝑦𝑖𝑡 )
(ℎ𝑖𝑡 𝑦𝑖𝑡 +𝑎𝑖𝑡 )²
≥ 0 as 𝑎𝑖𝑡 ′ ≤ 0 following axiom (ii)
(14)
This derivative is strictly positive for countries receiving aid (as ℎ𝑖𝑡 > 0 ⇔ 𝑎𝑖𝑡 > 0 ) .
Following equation (14), we see that counterpart financing is higher when 𝑦𝑖𝑡 is larger, for
given financial effort and needs. In other words, a dollar of aid will lead to more domestic
expenditure if this dollar is given to a richer country. Thus, if donors want to encourage
domestic expenditure for given financial effort and needs, they should allocate aid to the richest
of two countries with the same levels of needs and financial effort:
𝑑𝑖𝑡 = 𝑑𝑗𝑡 , ℎ𝑖𝑡 = ℎ𝑗𝑡 and 𝑦𝑖𝑡 < 𝑦𝑗𝑡 ⇒
𝑎𝑖𝑡 ≤ 𝑎𝑗𝑡
(15)
The last axiom pertains to countries not complying with the desired level of financial effort
(ℎ𝑖𝑡 ≠ ℎ∗ ).
Axiom (v) on proportionality: the elasticity of aid with respect to financial effort is equal to
1.
𝜕𝑎𝑖𝑡 / 𝑎𝑖𝑡
𝜕ℎ𝑖𝑡 /ℎ𝑖𝑡
=1
(16)
Axiom (v) implies that aid should be proportional to domestic financial effort: a doubling of
domestic financial effort should double the amount of aid.
This axiom is grounded in the recognition that the priorities of government may not be exactly
aligned with those of the international community. The principle of country ownership,
acknowledged in both the Paris Declaration on Aid Effectiveness (2005) and the Accra Agenda
for Action (2008), affirms that receiving countries should have sufficient autonomy to set their
development priorities and define their own strategies (see e.g. Bigsten and Tengstam, 2015).
Country ownership allows receiving countries to decide on the national strategies that fit with
their knowledge of local contexts and needs (Bourguignon and Sundberg, 2007; Bourguignon
and Platteau, 2015; forthcoming). As governments are responsible for their own strategies,
citizens can hold their government accountable, incentivizing the government to be responsive
to local needs (Deaton, 2013).
18
To foster the desired level of investment in the development objective (ℎ𝑖𝑡 = ℎ∗ ), an extreme
allocation rule would consist in a lump-sum transfer equal to max (𝑐 − ℎ∗ 𝑦𝑖𝑡 , 0) for countries
satisfying ℎ𝑖𝑡 = ℎ∗ , while aid would be equal to zero if ℎ𝑖𝑡 < ℎ∗ .9 This allocation would satisfy
axioms (i) to (iii) while minimizing total aid. Axiom (v) argues that the “sanction” of not
complying with the objective ℎ𝑖𝑡 = ℎ∗ should not be as dramatic. Countries should have the
discretionary space to not fully comply with the objective ℎ𝑖𝑡 = ℎ∗ , for example when dealing
with shocks or having other priorities. It seems unreasonable and unfair to force them to comply
with the objective ℎ𝑖𝑡 = ℎ∗ through a conditional lump-sum transfer. Such an allocation would
potentially lead to volatile and procyclical allocation of DAH. Axiom (v) postulates that the
“sanction” for “non-compliance” should rather be proportional to the exerted domestic
financial effort.10
The counterpart financing rule of the U.S. President's Emergency Plan for AIDS Relief
(PEPFAR) and of the Global Fund to Fight AIDS, Tuberculosis and Malaria (GFATM) also
respect the proportionality axiom.11
Equation (16) imposes a constraint on the functional form of the counterpart financing rule 𝛿𝑖𝑡 .
Following equation (13), the derivative of counterpart financing 𝛿𝑖𝑡 with respect to financial
effort ℎ𝑖𝑡 is given by:
𝜕𝛿𝑖𝑡
𝜕ℎ𝑖𝑡
=
𝑦𝑖𝑡 𝑎𝑖𝑡 −
𝜕𝑎𝑖𝑡
𝜕ℎ𝑖𝑡
ℎ𝑖𝑡 𝑦𝑖𝑡
(ℎ𝑖𝑡 𝑦𝑖𝑡 +𝑎𝑖𝑡 )²
=
𝑦𝑖𝑡 (𝑎𝑖𝑡 −
𝜕𝑎𝑖𝑡
𝜕ℎ𝑖𝑡
ℎ𝑖𝑡 )
(17)
(ℎ𝑖𝑡 𝑦𝑖𝑡 +𝑎𝑖𝑡 )²
Taken together, equations (16) and (17) imply the following equality:
𝜕𝛿𝑖𝑡
𝜕ℎ𝑖𝑡
=0
(18)
In other words, the counterpart financing rule 𝛿𝑖𝑡 (ℎ𝑖𝑡 ) would be non-continuous and equal to 0
everywhere except in ℎ𝑖𝑡 = ℎ∗ .
10 This axiom is hence aligned with the principle of proportionality in law. This principle is usually applied
on the grounds of fairness. It entails that an imposed sanction should stand in relation to the severity of the
illicit act (see e.g. Shavell, 2009).
11 PEPFAR requires counterpart financing of 25% by governments (Vassall et al., 2013). The GFATM defines
counterpart financing thresholds as a function of a country’s income classification. The minimum threshold
is 5 per cent for LICs, 20 per cent for Lower LMICs, 40 per cent for Upper LMICs, and 60 per cent for UMICs.
9
19
Table 3 – Definition of variables and operationalization
Variable
Definition
Operationalization (for allocation of DAH)
𝑎𝑖𝑡
Level of aid per capita
DAH per capita, in int-$ (𝐷𝐴𝐻𝑖𝑡 )
𝑦𝑖𝑡
National
income
per
capita
(corrected
for
price Gross national income per capita, in int-$ (𝐺𝑁𝐼𝑖𝑡 )
differences)
𝑑𝑖𝑡
The development objective
Burden of disease as measured by Group I DALYs lost per
100,000 (𝐷𝐴𝐿𝑌𝑖𝑡 )
𝑔𝑖𝑡
Government expenditures per capita allocated to the Government health expenditures per capita (𝐺𝐻𝐸𝑖𝑡 ) in int-$
development objective
ℎ𝑖𝑡
Share of GNI allocated by the government to the Share of government health expenditures in GNI (𝐺𝐻𝐸𝑖𝑡 )
𝐺𝑁𝐼𝑖𝑡
development objective (𝑔𝑖𝑡 /𝑦𝑖𝑡 )
𝛿𝑖𝑡
Counterpart financing: share expenditures allocated to the Share
development objective paid domestically (𝑔
𝑑𝑖𝑡+1 = f(𝑦𝑖𝑡 )
𝑔𝑖𝑡
𝑖𝑡 +𝑎𝑖𝑡
of
𝐺𝐻𝐸𝑖𝑡
)
(𝐺𝐻𝐸
𝑖𝑡 +𝐷𝐴𝐻𝑖𝑡
total
health
expenditures
paid
)
̂0 + 𝛽
̂1 log(𝐺𝑁𝐼𝑖𝑡 ) with
log(𝐷𝐴𝐿𝑌𝑖𝑡 ) = 𝛽
Development frontier
̂0 = 16.9 and 𝛽
̂1 = −0.94
𝛽
c
Per capita cost of tackling the development objective
Per capita cost of basic healthcare (198.7 int-$)
ℎ∗
Desired level of domestic financial effort
5%
20
domestically
Four remarks are in order before deriving the allocation formula from these axioms. First, we
purposely did not define a budget constraint, i.e. a limit to the total amount of aid that the
international community is ready to pay for the development objective. In line with the
objective of Universal Health Coverage (UHC) (Moreno-Serra and Smith, 2012; O’Connell et
al., 2014), our ethical position is that countries should have access to a minimum bundle of
health goods and services as long as they contribute their share, as formalized in axiom (iii).
For such countries, aid should fill the gap between what countries can reasonably afford
themselves and the total cost of the minimum bundle. We therefore have the ambition to study
how much aid is needed, as well as how this aid should be allocated. Another possible starting
point, corresponding to a different research question, would be to exogenously define a budget
constraint and determine how this aid budget should be distributed. In this case, either the
parameters 𝑐 or ℎ∗ , or axioms (iii) to (v), would have to be revised. Such adaptation is a good
topic for future research.
Second, government policies are taken into account in the axioms, but in a different way to
CD. Rather than punishing past behavior of governments that implemented bad policies, our
framework encourages future investments in the development objective. In doing so, we anchor
the framework in the principles of country ownership and democracy: countries have to
determine their priorities themselves, depending on their preferences and circumstances
(development, vulnerabilities, human capital, external or internal threats, etc.). An allocation
framework cannot explicitly account for the countless factors explaining heterogeneity in
development outcomes between countries. Instead, aid should support governments in
realizing their own development plans. Development is a difficult and uncertain endeavor with
no magic bullet. Most developing countries are now democracies in construction and,
ultimately, it is their citizens that should be responsible for holding their government
accountable, not donor agencies. This choice also avoids creating or reinforcing a poverty trap.
Instead, our framework assumes that development aid should be proportional to the current
domestic efforts of countries.
Third, the seeming contradiction between expressions (10) and (15) is not a flaw in the
framework (these are not strict inequalities), but rather a logical consequence of axioms (ii)
and (iv), which allows us to solve the model exactly. On the one hand, donors want to give
more aid to poorer countries ceteris paribus, as emphasized in axiom (ii). On the other hand,
donors want to maximize the return on their investment by encouraging domestic financing.
21
The allocation formula is, therefore, defined as a counterpart financing rule, which is an
increasing function of national income. In other words, every dollar of aid invested in a richer
country ceteris paribus should be backed by more domestic financing. Together, equations (10)
and (15) imply that countries with a similar disease burden and a similar level of domestic
financial effort should receive a similar amount of DAH per capita:
𝑑𝑖𝑡 = 𝑑𝑗𝑡 , ℎ𝑖𝑡 = ℎ𝑗𝑡 and 𝑦𝑖𝑡 < 𝑦𝑗𝑡 ⇒
𝑎𝑖𝑡 = 𝑎𝑗𝑡
(19)
This result may seem unfair: the two countries receive the same amount of aid, despite the fact
that one is much richer. Anticipating results from the next sections, let us examine an example
justifying this result. Botswana and Tanzania have about the same level of DALYs – about
32,000 per 100,000 (Botswana is heavily affected by the HIV epidemic). The GNI per capita
of Botswana is, however, much higher than the GNI per capita of Tanzania. If the governments
of the two countries invest 5% of their GNI in health, they will receive the same amount of aid
per capita, in line with equation (19). However, our framework also concludes that the
counterpart financing rule should be 43% for Tanzania and 83% for Botswana. Hence, every
dollar invested in health by the government of Tanzania will entail 1.34$ of aid, while every
dollar invested by the government of Botswana will lead to 0.21$ of aid. In other words, every
dollar of aid should be backed by 75 cents of government expenditure in Tanzania, but 4.8$ of
government expenditure in Botswana. From the point of view of donors, investing a dollar of
aid in Botswana is likely to have a much bigger impact, as long as the cost-effectiveness of
development programs is not massively different in the two countries. In this case, aid is also
likely to decrease at a faster pace in Botswana.
Finally, by no means do we claim that our list of axioms is definitive. While axioms (i) and (ii)
are very intuitive and probably unavoidable, axioms (iii) to (v) could be subject to revision –
for example, if more data become available on the preferences and the reaction functions of
governments and donors.
5
Allocation formula
We build on what is observable (Section 3) and on axioms (Section 4) to derive the allocation
formula.
22
Countries on the development frontier
From axiom (iv) we have:
𝑎𝑖𝑡 =
1−𝛿𝑖𝑡
𝛿𝑖𝑡
𝑔𝑖𝑡 =
1−𝛿𝑖𝑡
𝛿𝑖𝑡
ℎ𝑖𝑡 𝑦𝑖𝑡 ↔ 𝛿𝑖𝑡 = 𝑎
ℎ𝑖𝑡 𝑦𝑖𝑡
𝑖𝑡 +ℎ𝑖𝑡 𝑦𝑖𝑡
(20)
∗
From axiom (iii), we have for countries putting financial effort ℎ𝑖𝑡
in the development
objective:
𝛿𝑖𝑡 = min (
ℎ∗ 𝑦𝑖𝑡
𝑐
, 1)
(21)
Because of equation (18), we obtain that equation (21) also defines the counterpart financing
rule for countries characterized by a different level of financial effort than ℎ∗ . Equation (21)
shows that the counterpart financing ratio for countries on the development frontier is a linear
function of a country’s financial capacity, which depends on national income, 𝑦𝑖𝑡 , and on the
share of national income that is expected to be allocated to the development objective, ℎ𝑖𝑡 . The
counterpart financing ratio is an inverse function of the expected per capita cost of financing
the development objective, c.
Countries above the development frontier
To facilitate reasoning, we abstract from time and compare the level of DAH that should be
allocated to two fictive countries E and I, which have the same initial level of development
(𝑑𝐸 = 𝑑𝐼 ) and the same percentage of domestic expenditure on the development objective
(ℎ𝐸 = ℎ𝐼 = ℎ∗ ). However, country E is on the development frontier (𝑑𝐸 = 𝑓(𝑦𝐸 )) while
country I is richer and, hence, not on the frontier.
Since country E is on the development frontier, its level of aid per capita is given by equation
(11). Equation (11) can be rewritten by imputing the function of the development frontier:
𝑎𝐸 = max(𝑐 − ℎ𝐸 𝑓 −1 (𝑦𝐸 ),0)
(22)
Countries E and I have the same level of development and the same percentage of government
expenditure on the development objective. Equations (13), (19) and (22) can, therefore, be
combined to obtain the amount of aid that country I should be entitled to:
23
𝑎𝐸 = 𝑎𝐼
↔ max(𝑐 − ℎ𝐸 𝑓 −1 (𝑦𝐸 ),0) =
1−𝛿𝐼
↔
𝛿𝐼
↔
1
1−𝛿𝐼
𝛿𝐼
ℎ𝐼 𝑦𝐼
𝑐
= 𝑦 max (ℎ∗ − 𝑓(𝑑𝐸 ), 0)
𝐼
𝛿𝐼 = max (
𝑦𝐼
𝑐
𝑦𝐼 + ∗ −𝑓 −1 (𝑑𝐼 )
ℎ
, 0)
Because 0 ≤ 𝛿𝑖𝑡 ≤ 1, we have:
𝑦𝐼
𝑐
𝑦𝐼 + ∗ −𝑓 −1 (𝑑𝐼 )
ℎ
𝛿𝐼 = min (max (
, 0) , 1)
(23)
This last equation gives the counterpart financing rule for any country, which is not on the
development frontier, as a function of its national income 𝑦𝐼 and its development level 𝑑𝐼 .
6
Application to development assistance for health
In this section, we apply the framework to the allocation of DAH between countries. The third
column in Table 3 lists how each variable of the general framework is operationalized for the
allocation of DAH.
The counterpart financing rule for a country on the HDF is a function of its national income
(𝑦𝑖𝑡 ) and of parameters c and ℎ∗ (equation (20)). National income is measured by GNI per
capita (Anand and Bärnighausen, 2004). The per capita costs of providing basic healthcare 𝑐
and the share of national income that is expected to be allocated to the development objective
ℎ∗ were determined in Section 3 (𝑐 = 198.7 int-$, ℎ∗ = 0.05). The counterpart financing rule
for countries on the HDF is, therefore, given by:
0.05 𝑦
𝑦
𝛿𝐸 = min (max (198.7 int𝐸 $ , 0) , 1) = min (max (3,974𝐸int $ , 0) , 1)
𝑐
We have 𝛿𝐸 = 1 when the ratio ℎ∗ =
198.7 int $
0.05
(24)
= 3,974 int-$. This ratio, therefore, defines the
GNI per capita threshold, above which a country on the frontier is deemed to possess sufficient
domestic resources to fund basic healthcare domestically.
Some countries are artificially below the HDF because the frontier was estimated using a
quartile regression (to minimize problems of outliers and mismeasurement). It would seem
24
unfair to penalize these countries for being more efficient than the frontier. For these countries,
the counterpart financing ratio is, therefore, also determined by equation (24).
For countries above the HDF, the allocation framework additionally accounts for the
development needs of each country (equation (23)), as measured by Group I DALYs per
100,000. Using the parameters of the development frontier derived in Section 3, and
substituting 𝑐 with the costs of basic healthcare and ℎ∗ with the expected domestic contribution
yields:
𝑦
𝛿𝐼 = min (max (𝑦 +3,974 int $−𝑒 (log𝐼 (𝐷𝐴𝐿𝑌𝐼 )−16.9 )/0.94 , 0) , 1)
𝐼
(25)
We apply these formulas for the 140 countries for which GNI per capita and Group I DALYs
data are available. The map in Figure 2 shows the counterpart financing rule 𝛿𝑖𝑡 (all countries
with 𝛿𝑖𝑡 < 1 are shown). The resulting counterpart financing rule is also visualized in Figure
3, as a function of GNI per capita and Group I DALYs lost.
By construction, all axioms defined in Section 4 are satisfied. Here we provide intuition,
making use of Figure 3. Above the HDF, counterpart financing increases for any downward
move on Figure 3, in line with axiom (i) on needs. In line with axiom (ii), counterpart financing
requirements decrease for every move to the right in Figure 3. As can be seen from Figure 3,
the allocation formula is continuous: there is no discontinuity between countries on and just
above the development frontier, or any other thresholds, thereby avoiding fiscal cliffs. While
axiom (iii) determines the counterpart financing rule on (and below) the HDF, axioms (ii) to
(iv) jointly determine the slope of the contour lines. Axiom (v), on proportionality, cannot be
visualized in Figure 3. It determines how aid varies with the level of financial effort. This latter
axiom is discussed below when exploring country examples.
25
Figure 2 – Counterpart financing: Share of the domestic contribution (𝜹𝒊𝒕 ) to public spending
on health according to the allocation framework. Shown is the world region with all countries
for which 𝜹𝒊𝒕 < 𝟏𝟎𝟎%.
Based on the counterpart financing ratios, we calculate the total amount of DAH to be allocated
across countries. Following axioms (iv) and (v), the amount of DAH a country receives
depends on the reaction of its government to the new framework. We consider three different
scenarios.
In the business-as-usual scenario (BAU), countries do not increase domestic contributions in
reaction to the new framework.12 Under this scenario, the total amount of DAH is estimated at
36.7 billion US-$.
In the exact-cost scenario (EC), we assume that countries choose the level of government health
expenditures (GHE) to be able to exactly finance universal primary healthcare with the help of
DAH. The sum of GHE per capita and DAH per capita is set to be equal to the estimated cost
of universal primary healthcare; that is, 77.5 US-$ or 198.7 int-$ per capita for all countries.
The total amount of DAH under this scenario is estimated at 76.3 billion US-$.
The indicator of government health expenditures per capita (GHE per capita provided by the WHO) used
to produce these estimates partly includes development assistance for health (DAH). These estimates are,
therefore, upper-bound estimates of the cost of the business-as-usual scenario.
12
26
In the optimistic scenario (5P), we assume that countries increase government health
expenditures to 5% of GNI per capita. Under this scenario, the total amount of DAH is 111.2
billion US-$.
In comparison, aggregate DAH was equal to 32.1 billion US-$ in 2012. 13 Sachs (2012)
estimated that 40 billion US-$ per year would be needed from the donor world to achieve
universal health coverage in low-income settings. Ottersen et al. (2014) estimated that the total
need for DAH ranges between 79 to 436 billion US-$, depending on different scenarios.
Figure 3 – Counterpart financing rule in the allocation of development assistance for health
(DAH). The shaded areas show the share of domestic contribution of total health expenditure.
From this amount, only 8.3 billion US-$ was channeled to governments, while the rest was allocated to
non-governmental organizations.
13
27
Figure 4 compares the current government expenditures and development assistance on health
to the allocation of DAH under different scenarios. To illustrate the allocation rule, we consider
the following five country cases, all of which are highlighted in Figure 3: Malawi, Rwanda,
China, Kenya, and South Africa.
Malawi, Rwanda, and China were chosen because they are very close to the HDF, but have
very different GNI per capita. Malawi is poor (𝑦 = 726 int-$): according to the counterpart
financing rule 𝛿𝐸 , Malawi should finance 726 int-$/3,974 int-$ = 18.2% domestically. In the
5%-scenario, Malawi is spending 5% of its GNI on government health expenditures, or 726*
5% = 36.3 int-$ per capita. It will be entitled to 162.4 int-$ DAH per capita, or 100.6 US-$.
From axiom (v) it follows that DAH is proportional to ℎ𝑖 . Thus, if Malawi were to spend only
2.5% of its GNI on government health expenditures, it would receive half of the 162.4 int-$
DAH per capita, or 50.3 US-$.
Rwanda has a higher GNI per capita (1,463 int-$) than Malawi. According to the counterpart
financing rule, Rwanda should domestically finance 1,463 int-$/3,974 int-$ = 36.8% of total
health expenditures. If Rwanda spends 5% of its GNI on government health expenditures, it
will be entitled to 125.6 int-$ or 54.9 US-$ DAH per capita.
Finally, China is much richer than Malawi and Rwanda. As China’s GNI per capita (10,040
int-$) is above the minimum GNI per capita of finance basic healthcare, it will contribute 100%
domestically to its health expenditures.
Kenya and South Africa were selected as examples because both countries suffer from high
levels of disease burden (34,731 and 34,994 per 100,000, respectively), although Kenya is
much poorer than South Africa. The allocation formula indicates that the domestic counterpart
financing is equal to 46.7% for Kenya and 79.8% for South Africa. If both countries invest 5%
of their GNI per capita in government expenditure for health, both countries will receive about
152 int-$ per capita of DAH (62.2 and 96.6 US-$ for Kenya and South Africa, respectively).
To obtain this amount of aid, South Africa will have to invest much more domestically
compared to Kenya: every dollar of aid should be backed by 0.88 dollar of government health
expenditure in Kenya, and 3.96 dollar in South Africa.
28
Figure 4 – The current allocation of DAH, and the amount of DAH and government spending
on health under three different scenarios.
A number of conclusions can be drawn from comparing our allocation results to the current
one. First, aid is given to fewer countries in our framework than is currently the practice.
According to our allocation framework, there are 51 countries that would receive DAH. This
contrasts with 84 countries, which received DAH in 2012 according to the IHME.
Second, our framework tends to be more generous than the current allocation of DAH. Of the
countries which will receive DAH according to our framework, only Laos and Timor are
currently characterized by a lower share of domestic financing than their counterpart financing
𝐺𝐻𝐸
ratio ( 𝑇𝐻𝐸𝑖𝑡 < 𝛿𝑖𝑡 ). For 27 countries, the counterpart financing ratio 𝛿𝑖𝑡 is lower than 50%,
𝑖𝑡
29
while only three countries currently have their share of government expenditures in total health
𝐺𝐻𝐸
expenditures, 𝑇𝐻𝐸𝑖𝑡 , below 50% (Mozambique, Laos and Burundi).
𝑖𝑡
Finally, the new framework incentivizes domestic funding in absolute amounts. As can be seen
from Figure 4, health expenditures in absolute terms increase under the EC and 5P scenarios.
7
Discussion and conclusion
Academic endeavors to derive an allocation formula have been dominated by a paradigm
introduced in the seminal work of CD (2001; 2002). This paradigm consists of defining an
objective function, conducting a growth regression to estimate parameters, and making an expost assessment as to whether face validity is achieved. Multiple authors have extended and
nuanced the original objective function and growth equation, criticizing the original framework
for being incomplete or unfair. Another recurring point of criticism has been the fundamental
econometric problems underlying the growth regression. Although widely expressed as a
severe hindrance, this empirical critique has not been taken on board in the allocation formula
literature, ironically even though CD (2001) end their paper by stressing: “Please do not take
the point estimates too seriously”. To these critiques, we add that existing allocation formulas
do not distinguish needs from domestic capacity of recipient countries.
In this paper, we constructed an allocation framework in a fundamentally different fashion. We
first determined what parameters can be credibly estimated and what key properties, or axioms,
a fair allocation framework should satisfy. With these building blocks, we derived an allocation
formula taking the form of a counterpart financing rule, which we then applied to DAH. The
total amount of DAH to be allocated among countries based on our formula ranges between 37
and 111 billion US-$, depending on how countries respond to the framework.
Our approach is less demanding in terms of data and operationalization, which is a key
advantage for its application. In particular, it does not rely on the estimation of a growth
equation. The single econometric estimation to be conducted is the derivation of the
development frontier between national income and the development objective. The only
required indicators are national income per capita, the development objective (e.g. DALYs),
and the share of income allocated by the government to the development objective. Necessary
estimates of per capita cost of delivering a development objective, as well as the desired level
30
of domestic financial efforts by the government, can be taken from existing studies and can be
refined when new data is available.
The new approach also has the advantage of being easily implementable, replicable, and
adaptable. In our selection of axioms, the distinction between needs and domestic capacity
plays a pivotal role, and the formula is defined as a proportional counterpart financing rule to
boost domestic financing. However, given the wide variety of normative viewpoints – not in
the last place by donors, who ultimately are the implementers of allocation formulas – the
framework can easily be adapted. Our allocation formula is not based on discrete income
threshold, as is often the case in current allocation formulas of donor organizations, to reduce
the risk that countries face a fiscal cliff with multiple donor withdrawal when graduating from
one income category to another (Saxenian et al., 2015; Sumner, 2011). This risk is particularly
worrying for health systems, as positive health outcomes can be reversed when investments in
health are stopped, even if only for a short period (Piot et al., 2015).
The limits of our framework should also be emphasized. Our paper offers a general theoretical
framework with an application to the allocation of DAH. Of course, the devil is in the details
when it comes to the practical implementation of aid-allocation frameworks, given real-world
constraints. For example, it is beyond the scope of this paper to study possible coordination
problems between donors, competition between different sectors of aid, distinctions between
development and humanitarian aid, or limits to the absorptive capacity of recipient countries.
Future research by policymakers and scholars needs to reflect upon these real-world
constraints.
Our framework can be applied to other development objectives, such as poverty relief or
education, as long as estimates of per capita costs of delivering the development objective and
the desired level of domestic financial efforts by the government are available. Our list of
axioms is by no means definitive, and the framework can be further refined, for instance by
introducing dynamics such as in Wood (2008), or by incorporating a budget constraint, or by
considering how inclusive domestic financial efforts are.
31
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34
Appendix 1. The price of the minimum bundle of health goods and
services
The Taskforce on Innovative International Financing for Health Systems (2009) estimated the
cost of a basket of services and goods that are necessary to provide basic health services. The
Appendix 1 of the publication by the Taskforce provides the complete list of health
interventions costed in the ‘WHO normative approach’.
The included health services include both, the cost of preventive and treatment interventions:
– Preventive interventions taken into account include immunizations, postpartum care
and counselling, mosquito nets, communication targeted at behavioral change, among
others.
– Treatment interventions include the treatment of AIDS, TB, and malaria, acute
respiratory infections, maternal and perinatal conditions, diarrheal diseases, and
malnutrition.
– Also taken into account in the cost estimate is the cost of childbirth and antenatal care.
Of the total sum of costs, 40% are allocated to capital investment while the remaining 60% are
allocated to recurrent costs.
The Taskforce calculates the costs of this basket of health goods and services as an average
across 49 low-income countries for the year 2005. The price of this bundle of goods and
services given by the Taskforce is 54 US-$ in 2005 prices. This consumption bundle has a nontraded part (62%) and a traded part (the remaining 38%).
We first convert the price of this consumption bundle into 2012 US-$. Meheus and McIntyre
(2014) report a 59% price increase between 2005 and 2012 in the 49 low-income countries,
which we use to adjust the price of the non-traded part. For the traded part we take into account
US-$ inflation as reported by the OECD, which reports an 18% price increase (CPI) between
2005 and 2012.
(54 𝑈𝑆$ × 0.38) × (1 + 0.18) + (54 𝑈𝑆$ × 0.62) × (1 + 0.59)
= 77.45 𝑈𝑆$ (𝑖𝑛 2012 𝑝𝑟𝑖𝑐𝑒𝑠)
We then calculate the population weighted average price level ratio of the PPP conversion
factor (GDP) to market exchange rate for the benchmark year of the latest International
Comparison Program, which was 2011. The data for this are taken from the World Bank’s
World Development Indicators. For the 49 countries, this ratio relative to the US is 0.39, so
that the price of the minimum bundle of health goods and services is (77.45 US$)/0.39=198.73
international-$.
35