Many studies show that FA impacts the macro-economy of recipient countries. Some of them show a positive effect of FA on the recipient country’s economy. Domar (1946) argued that FA was necessary for economic development in low-income nations. This viewpoint is supported by later studies. Hansen and Tarp (2001) found that international aid could promote economic growth in recipient countries. Karras (2006) also found a positive effect based on the data from 71 recipient nations from 1960 to 1997. Levy (1988) revealed a significantly positive relationship between FA and investment, and economic development during 1968–1982 in Sub-Saharan African regions. Juselius, Møller and Tarp (2014) demonstrated the same relationship in the longer period of 1960 to 2007 in 36 African countries. In developing Asian countries, Asteriou (2009), investigated the presence of long-term relationships using panel unit tests, showing a positive effect.

In fact, FA is not as efficient as expected. Some scholars have explored the factors that impact poverty reduction. For example, Urtuzuastigui (2019) and Akobeng (2020) suggested that economic growth was subject to the institutional quality in aid-dependent countries. Wako (2018) and Maruta, Banerjee and Cavoli (2020) agreed with this point of view. In addition, Biscaye, Reynolds and Anderson (2017) argued that the effectiveness of FA was determined by the quality of other macro-economic determinants. Furthermore, Dreher, Fuchs and Langlotz (2019) showed that an increasing emigration rate contributed to more aid for the original nations of migrants. Sullivan, Blanken and Rice (2018) demonstrated that aid was being moved towards the conservation of global public services and products.

By contrast, some research uncovers that FA has only an insignificant or side effect on the recipient country’s economy. Mallik (2008) revealed that FA negatively impacts national economic growth in the long run by assessing 35 years in six African countries. Wafula, Odondo and Obange (2019) revealed an insignificant contribution to economic development in the short and long run during 1974–2017 in Kenya. These results have been confirmed by Bird and Choi (2020), showing a more ambiguous impact of FA. Additionally, FA essentially affects the institutional policies, resulting in more corruption in recipient counties, which inevitably restrains economic growth. Ali et al. (2019) examined the relationship between FA and corruption in Asian nations and revealed a remarkable negative effect on the corruption perception index in the recipient countries, showing that more FA results in more corruption. This finding is supported by Brautigam and Knack (2004) and Economides, Kalyvitis and Philippopoulos (2008).

Some studies revealed more complex results. For instance, Azam and Feng (2022) employed both fixed-effects and robust squares estimators to assess the relationship between FA and economic growth in 37 developing nations, from 1985 to 2018, and suggested that FA could contribute to economic development, but that the association was very weak in low-income nations where economic development mainly depended on exports. Additionally, FA had less positive effect on economic development in upper- middle income nations. Moreover, Abate (2022) used a generalised method of momentary assessing the effect in developing countries, and uncovered an inverted U-shaped association between FA and economic performance, indicating a negative effect when the governmental quality index and economic freedom were below the threshold value, otherwise finding a positive effect.

A controversial relationship exists between FA and poverty reduction. Some literature found that FA could contribute to poverty reduction (Alvi & Senbeta 2012; Bahmani-Oskooee & Oyolola 2009; Mahembe & Odhiambo 2020b), while others found this effect insignificant (Boone 1996; Arvin & Barillas 2002; Briggs 2017). On the contrary, Rajan and Subramanian (2011) showed an adverse effect of FA on poverty reduction, and suggested that the real exchange rate increases because of aid inflows, thus the aid-recipient countries lose their export competence. This finding partly explains why FA may not contribute to poverty reduction.

The negative effect is partially attributed to aid volatility that is harmful to the economic sustainability of the recipient countries (Houndonougbo 2017). The negative effect manifests in different ways. Bulir and Hamann (2008) argued that aid volatility could distort public investment and fiscal plans, supported by others (Celasun & Walliser 2008; Hudson 2015). Kumi et al. (2017) uncovered that aid volatility in industry significantly reduces industrial production, while Chauvet and Guillaumont (2009) revealed that aid volatility could result in economic volatility, which would interrupt the economic sustainability of the aid-dependent countries. Later studies (Boateng et al. 2021; Markandya et al. 2011) supported this viewpoint. Furthermore, the performance of governance is damaged by the range of volatility (Kangoye 2013). Meanwhile, Hudson and Mosley (2008) found that the effect is complex, given the two kinds of aid volatility (negative and positive), showing that negative volatility is more harmful to the macro-economy than positive. Therefore, the unpredictability of aid volatility may account for the fluctuation in the national economies and public welfare systems of aid-recipient countries.

To sum up, in a wide range of literature the relationship between FA and a recipient country’s economy is discussed, but few of them shed light on the effects on health poverty in the recipient countries. This research bridges that gap; it employs the RF methodology of machine learning to investigate the conductive effect, assessing to what extent aid volatility affects the health poverty of aid-dependent nations.

Although the impact of volatility in FA has on the recipient country’s economy is known, how this volatility affect residential life quality in recipient countries, observed from the micro-perspective, has not really been thoroughly researched. Thus, in this study the conductive effect is further researched. Generally speaking, FA flows into three domains: industry (f_e), household (f_h), and government (f_g).

Taking a recipient country’s (i) FA scale (Aid_i,t) in year t and its initial aid scale (Aid_i,0), the following equation is constructed.

Aidi,t=Aidi,0(1+ΔAidvoli,t)|Aidi,t,Aidi,0>0[Eqn 1]

ΔAidvol_i,t is the aid volatility in year t. ΔAidvol_i,t ≥ 0, or ΔAidvol_i,t ≤ 0. The FA increment (ΔAid_i,t) can be written as follows:

ΔAidi,t=ΔAidi,tfe+ΔAidi,tfh+Aidi,tfg[Eqn 2]

The three independent variables refer to the aid volatility in industry, the household, and the government, respectively.

Figure 1 outlines the theoretical framework of the conductive effect of positive aid volatility on health poverty in three ways. When a recipient nation receives a given amount of FA from others, there is always aid variance (ΔAid_it) compared to the initial aid amount, and this amount is distributed between the three areas mentioned before (f_e, f_h, f_g).

In terms of increasing aid, some money will be directly allocated to the residents, and this increases household income (ΔAidfhi,t>0); as a result, the residential life quality, including life health, is improved (Bayale 2020). Further, a certain amount of the aid fund is invested in industry (ΔAidfei,t>0) to relieve industrial capital shortages; industrial development results in economic growth, regardless of whether the aid volatilises negatively or positively, because ΔAid_it > 0. Subsequently, the growing of the economy in a recipient country will increase the household income, which may contribute to residential life health and consequently decrease health poverty. The government will also use a certain amount of the aid for public expenditures and infrastructure in order to drive the national economy (ΔAidfgi,t>0), which will eventually improve the national living standards, including medical treatment, although in institution-deficient countries, a considerable amount of aid is kept by the government (Ali et al. 2019).

Regardless of the ways in which the aid is distributed, it will eventually increase the household income. In this context, residents’ health will be improved. Better health could reduce medical expenditures, empower human capital, and thus increase household income, and eventually promote economic development (Banerjee, Deaton & Duflflo 2004), meaning the level of health poverty improve. Therefore, life health is crucial for sustainable economic development in a recipient country.

However, if the aid volatilises negatively, the residents will have to cut their daily expenditures, which may decrease their household income and life quality; that is, poor health + income poverty = health poverty. Additionally, volatile aid may potentially impact industrial yields and worsen the national economy, which leads to social issues, including detrimental life health. Meanwhile, negative aid volatility results in declining government expenditures in the public health system. As Hudson (2015) suggested, negative aid volatility may distort governmental expenditures, and all kinds of social issues may emerge. Therefore, negative aid volatility worsens residential life health, and consequently health deteriorates.

In conclusion, the mechanism of the impact of aid volatility on health poverty in recipient nations is complex. Aid funds are allocated to a variety of recipients in three main areas (industry, household, and government). Regardless of the area, the aid fund is ultimately to be used to improve local residents’ health, as a healthy workforce is the most fundamental and sustainable resource for economic development in a country. However, when aid fluctuates significantly, it interrupts the existent poverty reduction system, and could even break the economic sustainability of recipient countries, particularly the most aid-dependent ones, meaning the resource will be damaging at first. Therefore, aid volatility initially worsens health poverty and the recipient country’s economy.

Foreign aid volatility measurement: Following Hodrick and Prescott (1997), this study employs the HP filter method calculating the trends and periodic components of FA volatility (see Figure 2). The data-smoothing technique, used primarily in macro-economics, is used to reduce the short-run fluctuations resulting from the business cycle so as to identify long-term trends. This basic model is denoted as below.

yt=gt+ct[Eqn 3]

y_t represents the original signals series, g_t stands for the low trend component, and c_t refers to the higher-frequency period and is called the cyclical component. The series y_t consists of two components: a low trend component g_t and a cyclical component c_t. With an appropriate coefficient λ, the trend component can be calculated by:

ming{∑t=1T(yt−gt)2+λ∑t=2T−1[(gt+1−gt)−(gt−gt−1)]2}[Eqn 4]

λ refers to the penalty parameter. The first part stands for the total squared deviations of c_t, namely the cyclical component. The next part is the total squared value of the difference of the trend component (g_t), which is multiplied by λ, showing variations in the growth rate of the trend component. The HP filter may detect the cyclical component c_t from y_t via the extent of the good fit that the trend component tracks the original series y_t, against the prescribed smoothness in g_t.

Evaluating the effects of aid fluctuation on health poverty, this study proposes the dependent variables of public health level denoted by child death, maternal mortality, along with public life expectancy. As these variables have lag effects on public health, the lagged vectors are included as control variables. Aid volatility is proposed as an explanatory variable, and the aid scale is taken into account as a control variable. Following Alvi and Senbeta (2012) and Chong, Gradstein and Calderon (2009), a basic regression is developed as below.

Pit=f(Pi,t−1,Aidit,Aidvolit,X′it,εit)[Eqn 5]

P_it refers to the health poverty level of an aid-dependent nation i in time t. P_it-1 refers to the lagged health level in the recipient country. Following Clarke and Erreygers (2020), health poverty is measured by health status and life expectancy. Goal 3 of the Sustainable Development Goals of the United Nations aims to improve the global health status by reducing the global maternal and under-5 child mortality ratios to less than 70/100 000 live births, and 25/1000 live births, respectively. Thus, this study measures health status via two variables: the maternal death rate and death rate of children under 5 years old.

Aid_it stands for the FA rate (measured by the received aid amount / the GDP) of the recipient country i in year t. Aidvol_it refers to the aid volatility rate (measured by the HP filter method, as elaborated above). ε_it refers to random errors. X′it represents some other variables. According to Alvi and Senbeta (2012), Chong et al. (2009), and Mahembe and Odhiambo (2020a), and considering the data availability, this incorporates five more health-related variables into the regression model, which are economic level (GDP per capita), openness, inflation, age dependency ratio, and social institutions (corruption perception index). Table 1 outlines the measurements of the variables and data sources.

As regression methods test whether the relationship between foreign volatility and health poverty is statistically significant, but cannot examine the magnitude of the effect, machine learning methods do not require strong assumptions and could observe the magnitude of the effect aid fluctuations have on poverty from a predictive perspective, we introduce a RF model to assess the magnitude. Comparing the advantages between RF and K-Nearest Neighbor (KNN),Gradient Boosting Regression and Support Vector Machine (SVM), respectively, we found that the RF model was more robust and altogether better than others. Therefore, the RF method was used along with econometric methods to address the research question.

The RF method means a machine learning technique commonly used to deal with complex classification and regression problems with large datasets. It draws a final result and increases the decision precision based on the multiple outputs of clustered decision trees (Breiman 2001). For instance, Sohnesen and Stender (2017) have demonstrated that the RF method is more accurate than many commonly used stepwise and lasso regressions, and does facilitate better poverty predictions than regression models. Therefore, this approach was adopted to predict the potential effect of aid volatility on health poverty based on the regression results.

Supposing the relationship between a target (or response) variable Y and a number of predictors (or features), X₁, X₂, …, X_p.

Y=f(X1,X2,…,Xp)+e[Eqn 6]

e means an error value. The value of E (Y − Ŷ)² refers to the expected squared prediction error denoted as the value of the reducible error, calculated by E[f(X1,X2,…,Xp)—f^(X1,X2,…,Xp)]2. The machine learning technique may minimise the reducible error and estimate f.

The value of the response variable ŷR_j is calculated by a function of the regression tree estimator, f^tree (A) = Σ_j∈J ŷ R_j 1 {A ∈ R_j}, in which A = (X₁, X₂, …, X_p) represents the vector of the predictors, 1{.} stands for the indicator function, and (Rj)j∈J are the regions of the predictor space obtained by minimising RSS, identifying by the mean values of the variables within the same region R_j. Therefore, denoting the number of bootstrap samples as H and using the decision tree index calculated in the sample h ∈ H by f ^tree (A|h), the RF index is estimated using the equation below.

f^RF(X)=1H∑h=1Hf tree(A|h)[Eqn 7]

The RF method is useful in predicting the effects of aid volatility on health poverty. Firstly, as an alternative to linear regression models, RF achieves higher accuracy in predicting poverty, particularly at the national level (Sohnesen & Stender 2017). Secondly, it accurately quantifies the value of the influence of particular factors, which allows its users to develop more targeted health administrations. Thirdly, the marginal effects of aid volatility on health poverty are observed in the partial dependency graphs, and this has policy and economic implications for the recipient governments.

Using the HP filter method, it has been calculated that the FA volatility for the period 1989 to 2017 presents the most significant findings in some recipient countries. As Figure 3 shows, there was remarkable aid volatility in most African countries during the entire period, particularly in Burundi, Central Africa, Cabo Verde, Congo, Ethiopia, Comoros, Guinea-Bissau, Sudan and Liberia. The volatility directly interrupted the economic sustainability and affected the health poverty reduction in these recipient countries.

Table 2 shows that both the FA (Aid) and aid volatility (Aidvol) have a significant association with health poverty. Columns (1) to (6) show the negative relationships between FA and child mortality, and maternal mortality, respectively, while columns (7) to (9) show the positive association between FA and life expectancy. This result means that a growing quantity of FA may reduce both child and maternal mortality rates and promote life expectancy. However, the positive connect of aid volatility with both child and maternal mortality rates reveals that the higher the aid volatility, the higher the child and maternal mortality. By contrast, the negative association of aid volatility with life expectancy shows that significant aid volatility reduces life expectancy.

The lagged coefficients of child and maternal mortality and life expectancy indicate that the health poverty level is significantly determined by the conditions in previous years, because the differences between the columns control variables are very slight, and there were no significant changes when including other variables. For example, we derived the following values: lagged child mortality (0.989, 0.994, 0.964), maternal mortality (0.984, 0.945, 0.960), and life expectancy (1.006, 0.985, 0.988).

Moreover, this table shows that GDP per capita has a significant association with maternal mortality and life expectancy. Inflation has no significant association with life health level. Openness is related to maternal mortality only. Age dependency influences child mortality, and the perception of corruption is connected with maternal mortality and life expectancy.

Table 3 outlines the lagged effects of aid volatility on child and maternal mortality, as well as life expectancy, in the next 2 years. Although the lagged effects are significant in columns 2–6, the connections become fewer in the following years, because these coefficients decline over the 3 years. For instance, the aid volatility coefficient decreases from 6.322 in column (3) to 5.161 in column (4). Nevertheless, both FA and aid volatility still have significant effects on health poverty in the following 2 years.

As the aid volatility may be positive or negative, these two kinds of contrary fluctuation will have different effects on the public health. Table 4 presents the results regarding the heterogeneity between positive and negative aid volatility. The coefficient (0.077) in column (1) shows that aid volatility has no significant effect on the child mortality rate when it fluctuates negatively (volatility < 0), while the coefficient (0.293) in column (2) indicates a significant effect when volatility > 0. This finding suggests that this effect on child death can mainly be attributed to positive aid volatility. By contrast, the coefficients (1.844 and 1.763) in columns (3) and (4) show that aid volatility may result in significant maternal mortality when volatility < 0, and that the opposite pertains when it does not, which suggests that the effect on pregnant women’s death could be attributed to negative aid volatility. Furthermore, the coefficients (–0.195 and –0.215) in columns (5) and (6) suggest that the aid volatility may significantly reduce life expectancy, regardless of whether it volatilises positively or negatively.

Studies have shown that bilateral and multilateral aid have different effects on economic growth (Jeanneney & Tapsoba 2012; Ram 2003, 2004). It is supposed that these kinds of aid should have different effects on public health. Therefore, the HP filter method was adopted to investigate how these two kinds of aid and aid volatility affect health poverty in aid-dependent countries.

Table 5 presents the results. Generally, multinational aid volatility has greater an impact than bilateral volatility. Both bilateral and multilateral aid volatility have a significant positive effect on child and maternal mortality, which means that the two kinds of aid volatility increase the child and maternal mortality probability; therefore, multilateral aid volatility (2.378, 13.744) is riskier than the bilateral kind (2.509, 11.626). The two kinds of aid volatility have a negative effect on life expectancy, which means that volatility may result in a decline in life expectancy, while multilateral aid is stronger (–0.796) than the bilateral kind (–0.688).

Meanwhile, this table indicates that reductions in the two kinds of FA will result in more child and maternal deaths and a declining life expectancy. Similarly, multilateral FA has more significant effects on public health than the bilateral kind.

The aforementioned results have demonstrated the effect of aid volatility on child and maternal mortality, as well as life expectancy. In this study the RF method to evaluate the extent of these effects has been developed further.