The Short Run Effects of Health Aid in Low Income Countries:Evidence from Panel Data Analysis

Background The debatable. This paper examines the short run effect of health aid on health status in low income countries of the world. Method The study estimates the short run effect of health aid on health status in low income countries. Infant mortality rate was used as a proxy for health status and a panel data was constructed from 34 countries for the period between 2000 and 2017. For the estimation, first difference GMM and System GMM were employed. Results The estimation results confirm the argument that health aid has a beneficial and statistically significant short run effect on the health status of low income countries: doubling health aid saves the lives of 20 infants per 10,000 live births. Conclusion From the findings of this paper it can be concluded that health aid could be one of the best tools with which the broader health status gap currently observed between high income and low income groups, could be eliminated and hence the target of Universal Health Coverage is met. However, recipient countries need to find ways of promoting domestic factors that have favorable impact on health sector as they cannot persistently relay up on external resources.

literature itself, there is disagreement concerning effect of health aid in low income countries. Some argue that health targeted aid improves health status in low income countries by improving resource availabilities for health service delivery.
For instance, Levine argue that health is an area aid effect is noticeable because health programs such as communicable disease prevention and control through safe and adequate water supply, effective sanitation, immunizations, and better nutrition are directly related to the sought health outcomes (3). Easterly argue that with appropriate accountability, external aid leads to the decrease of infant mortality significantly (4). Mishra and Newhouse provide a strong empirical evidence for this argument. Using donor commitments data of 118 countries between the period of 1973 and 2004, they observed significant effect of health aid on health status of population. According to their finding, an increase in 1% per capita health aid improves infant mortality rate by 2%, (5). Similarly, Chauvet Gubert and Mesple-Somps, using a panel data of 109 developing countries from 1987 to 2004, reported results that suggest health aid significant effect on health improvement (6). Ebeke, and Drabo (7) and Mishra and Newhouse (8), Chauvet and Guillaumont (9) also report similar finding that suggest health aid's significant effect on health outcome of developing world.
On the other hand, the authors emphasized that health targeted aid is more effective in recipients of low income countries. According to Gormanee, Girma and Morrissey, the impact of aggregate aid on health status of low income countries is more evident due to the fact that it bridges the gap between the available and required resources that results in remarkable changes through direct public health related projects that enables communicable disease prevention and controls; access to safe and adequate water supplies, improved sanitation, combating malaria by draining swamps to minimize mosquito breeding sites, immunization of vaccine preventable diseases (10). Likewise, the positive effect of aggregate aid on health status of developing courtiers is reported elsewhere (11,12).
In contrast, other scholars argue that there is no sufficient evidence to claim that health aid improves health status of the recipient countries. For instance, Williamson  periods shows that, health aid has no effect on recipient countries infant mortality rate (14).
The latter opponent group argues that health targeted aid is ineffective because recipient countries can transfer the resources to non targeted expenditures instead of being injected to the health sector for which it was targeted. According to Pettersson, such non targeted expenditures sourced from all development assistance are as high as 70% (15). Ineffectiveness of aid is also argued that it can negatively affect competitiveness of aid receiving countries, encourage dependency and disincentive adoption of good policies, and encourage corruption (16,17).
The above controversy forms a dilemma to policy makers as to whether to treat the health aid as a complementary tool or just to disregard it and concentrate on domestic factors. One root of the controversy is methodological deficiencies in empirical studies, specifically misspecification problems, both weak functional form and omitted variables problems, in health estimating equations. Besides this, a separate short run health aid effects are rarely emphasized while the size and significance of the estimated marginal effects are strongly dependent on such time spans. Therefore, this research attempts to fill this gap by employing well specified estimation equation that is consistent with sound theoretical framework grounded on utility maximizing human behavior. (18,19,20,21) Methods Framework of the study Grossman Where W j (t) are input variables and for j>k the variables are unobserved or not measured.
In constructing health capital model, Grossman suggested the application of utility maximization constrained with resources which may require application of optimal control analysis (20). Building on these views it is assumed here that households derive satisfaction from their health status and they strive to maximize their utility constrained by socioeconomic and demographic factors. The common and very important solution from such utility maximization problem is the constancy of marginal effects of the input variable. That is after taking total derivative of equation [1] [Due to technical limitations, this equation is only available as a download in the supplemental files section.] the marginal effects f' j s are constants. Based on the constancy of marginal effects one can integrate equation [2] to get Where A is some constant.
In fact, in empirical analysis, to maintain the result of optimal control analysis, i.e. constancy of the marginal effects-the input variables have to undergo some mathematical transformations like log transformation, exponential transformation depending on the measure of the input variable, otherwise the estimation equation will face mis-specification problem arising from wrong functional form.
In the specification of health estimating equation, besides the wrong functional form, one may face omitted variable problem, the case where a part of the input variables are unobservable or their data may not be available. From introductory econometrics we understand that ignoring these variables will make the coefficient estimates of the known variables unbiased. To deal with this issue here it is assumed that the omitted variables follow auto regressive of order two which can be Substituting equation [5] in equation [3] one gets the long run health function as Essentially equation [6] is long run health equation since it is grounded on the constancy of marginal effects of the input variables which holds true in the long run.
To drive the short run health function from equation [6], here Partial Adjustment Model (PAM) is adopted. Intuitively, it is clear that the possibility that the coefficients in the health status estimating equation [6] could be related to the level of change in health status before the input variables changes. That is, keeping all other things equal, a one percent change in an explanatory variable in a population with lower level of health status could have higher effect than when similar change takes place in another population with a higher level of health status. When the interest is to know the short run effect, this phenomenon demands us to control for previous level of health status. The PAM specifies the observed level of a given dependent variable as a weighted average of its level that existed in the previous time period and its equilibrium level at the present time, as if the system is already on its equilibrium path the regression assigns one to , that makes the transition path dynamics to have no effect in determining the level of H(t). But if the system is on the transition to equilibrium fully the regression assigns zero to , which makes the equilibrium path dynamics to have no effect in determining the level of H(t). In actual cases, is expected to lie between these two IMR was considered as a dependent variable of the current study. Though life expectancy is another alternative proxy variable for health status IMR was preferred in this study; first, it is more sensitive to economic changes of the population than life expectancy, implying that it is a better measure of improvement in low income groups of the society (5, 28). Second, infant mortality explains substantial improvements in life expectancy it's self in poor countries. Third, past studies indicate that in developing countries, improvement in infant mortality shows better access to; medical care, safe water and better sanitation, improved maternal and infant nutrition, literacy status especially that of female and increased per capita GDP and economic inequality. Fourth, data on infant mortality are available for a large set of countries and are more reliable than life expectancy. On these grounds this study considers IMR as a good proxy for health status (13).
According to World Bank (WB), IMR is defined as the number of infants dying before reaching one year of age, per 1,000 live births in a given year and the data was taken from WB (29).
HDA, the main variable of interest here is defined as an external source of health expenditure in a recipient country, measured in constant 2010 USD. External sources compose of direct foreign transfers and foreign transfers distributed by government encompassing all financial inflows into the national health system from outside the country. External sources either flow through the government scheme or are channeled through non-governmental organizations or other schemes, data for this variable was taken from WB (29).
GDPP was also taken from the World Bank (29) and the source defined it as "gross domestic product, in constant 2010 USD dollars, divided by midyear population".. It is obvious that higher level of income favors consumption of quality of goods and services, better nutrition, housing, and ability to pay for medical care services.
Therefore, GDPP is considered to be explanatory variable of health status of the population under the study.
HC index was taken from Feenstra et al. The source indicated that the HC was based on years of schooling and returns to education (30).
AFERT data was taken from the World Bank world development indicators (29) and it is defined as the number of births per 1,000 women aged between 15 and19 years.
The rates are based on data on registered live births from vital registration systems or, in the absence of such systems, from censuses or sample surveys. The estimated rates are generally considered reliable measures of fertility in the recent past.
Where no empirical information on age-specific fertility rates is available, a model is used to estimate the share of births to adolescents. EDEP data were taken from the World Bank (29) and the Bank defined the variable as the ratio of elderly  To estimate equation [9] the first difference generalized method of moments (GMM) developed by Arellano and Bond (23) is suitable. Furthermore, based on the nature of the error terms, system GMM developed by Blundel and Bond depending is recommended (24). However, in the cases of a weak instrument problem in a dynamic panel data model like equation [9], first differenced GMM estimator have been found to have a poor precision (25). Therefore, system GMM estimator is recommended to provide better accurate estimate in the current IMR equation (5, 8, 26, and 27). However, for comparison purpose, estimation results from both estimators will be considered in the current study. At the same time, the conventionally derived variance estimator for GMM estimation is employed for standard error vce (gmm).
To deal with omitted variables, it is assumed that the omitted variables follow auto regressive of order one, which is equivalent to assuming that they follow first order differential equations, whose solution will be function of time. On this ground instead of just assuming the variables away, log-time is used as a control variable representing all omitted variables in both short run and long run health equations.     ( Table 2). Moreover, as shown on Table 2, the coefficient estimate of log-HDA was -1.9818 and this was statistically significant (P = 0.0000). Similarly, statistically significant estimate was observed for the log-GDPP coefficient,-9.6007 (P = 0.0000). In the same way, the estimator gives -as a coefficient of expINST, 7.8092 (P = 0.0160). The estimator also gives -0.8945 as a coefficient estimate of expHC, which is statistically significant at 10% level of significance (P = 0.051).

Results
Sometimes the short run relative importance of the selected input variables together with their flexibility in policy decisions may be point of interest. Table -3 reports  (Table 3).
The table informs that decline in adolescent fertility, increase in health aid and increase in per capita income play major role in reducing infant mortality. In explicit terms, from the observed average annual IMR decline is due to increase in health aid; is due to increase in per capita income and is due to decline in adolescent fertility. If left unchecked governance quality and yield were found to play an adverse role in the efforts made to reduce IMR (Table 3). Moreover, from Table 3, it can be understood that 46% of the decline in IMR was due to the selected input variables.

Discussion
In the short run health function analysis of the current study, the coefficient of log-HDA by the system GMM estimate is -1.9818, and this is strongly significant( P = 0.000), suggesting, that HDA has a strong reverse effect on IMR. Accordingly, in the Similarly the table indicates that the coefficient estimate of log-GDPP is -9.6007, which is statistically significant, z = -4.2200, P = 0.0000, suggesting that raising per capita income growth contributes to the improvement of population health in low income countries. In line with this estimation result, Pritchett and summers (1996) argued, income is a crucial factor influencing health status, because higher income facilitates improvement in public health through infrastructures like safe water supply and improved sanitation (34). Better income also improves accessibility to health care service that reduces infant mortality. Preston also argued that the combined effect of changes in income, literacy and the supply of calories results in about a half of gain in life expectancy in developing countries (35). Similarly, Wang states that income is considered as a main explanatory input of health function (36).
The effect of cereal yield on IMR was found to be statistically insignificant in the short run. In the literature several writers argued that it has got significant effect on health. For example, Cutler et al (2006) argued that improved nutrition that results from improvements in agricultural yields to be one of the main factors that determine decline in mortality. They argue that better fed people resist most bacterial disease better, and recover more rapidly and more often. Fogel, based on historical evidences, also argues that improved nutrition results in mortality decline. The difference between the finding here and the once in the literature might be due to the attention given in the short run in the current study (37) Figure 1 Supplementary Files This is a list of supplementary files associated with the primary manuscript. Click to download.