Foreign aids and economic growth in Africa: Does third-country effect matter?

Abstract Different regions are linked through different factors such as climate, and border sharing. Apart from this, African countries have developed significant links as a result of globalisation, economic integration, and trade liberalisation. Since any country’s economic growth is influenced by the performance of its neighbours, these ties have resulted in spatial dependence among these countries. On this basis, the significance of spatial interactions between countries cannot be overemphasised. It is for this reason that the study investigated spatial dependence between African countries. The study employed non-spatial (FE, GMM) and spatial (SDM, SAM, and SEM) econometrics techniques and data ranging from 1996 to 2019 to examine the impact of ODA on Economic growth in Africa and its spill-over effects. Based on the graphs and the Moran I test, the findings reveal that (i) there is spatial dependence among African countries (ii) The GMM results indicate that the ODA impact was positive and statistically significant but smaller in magnitude compared to the magnitude of the spatial models’ coefficients. This suggests that not controlling for space heterogeneity will possibly underestimate the real impact of ODA on GDP. Secondly, the study found that the weighted GDP was positive and statistically significant, which indicates that an increase in the GDP of a certain country has a positive and statistically significant impact on their neighbour’s economic growth. Based on the findings of the study, it is suggested that countries should improve their relationships and partnerships if they want ODA to provide the desired benefits across Africa.

like decreased foreign demand, inflation, higher borrowing costs, and extreme weather (United Nations, 2023). In African countries, literature attributes growth (or lack thereof) to numerous factors such as imports, exports, gross capital formation, gross domestic savings, foreign aid, and human capital (Batrancea, Rathnaswamy, & Batrancea, 2021;Gingras, 2018;Oyebowale & Algarhi, 2020). However, no one conclusion has been reached regarding how these factors affect growth in individual African countries. Others have a detrimental impact on growth, while others have a favourable impact (see, for example, Aslan & Altinoz, 2021;Tefera & Odhiambo, 2022). The impact on the growth of specific African countries is mostly determined by a country's macroeconomic policies.
Spatial externalities are equally important for the advancement of growth in African countries. For instance, having democratic neighbours assists a country's growth, while unstable governments in the region's neighbours have the opposite impact (Ganau, 2017). According to Zall e (2017), this phenomenon referred to as the spatial multiplier effect occurs when a country's political risk affects a country's economic growth and the economic growth of other countries that are geographically close. For example, employing a spatial dependency framework, Chih, Kishan, and Ojede (2022) observed that FDI has a significant influence on growth when sub-Saharan African nations are more open to international trade. The international trade and growth nexus has long been investigated. For example, Ramirez and Loboguerrero (2002) employed spatial econometrics to estimate a cross-country interdependence growth model in which a country's economic growth is influenced by its neighbours' growth rates. The analysis was based on a three-decade sample of 98 countries (1965-75, 1975-85, 1985-95). The analysis emphasised the importance of cross-national spatial relationships, which indicated that a country's economic growth is influenced by its neighbours' performance, which is then influenced by its geographical location. Moreira (2005) used two expanded versions of the reduced form Papanek-type regression to investigate the relationship between ODA and economic growth in 48 emerging economies. This method presumes that the contribution of aid to growth in all developing nations is essentially the same. The study covered the years 1970-1998, and instead of annual data, six sub-period averages were used. The findings revealed a positive relationship between ODA and developing country economic growth. Shaikh (2011) investigated the relationship between ODA and economic growth in Pakistan from 1972 to 2008 using cointegration and OLS estimation. The cointegration results revealed a long-term positive relationship between ODA and economic growth. T€ uzemen and T€ uzemen (2015) used the Johansen cointegration test and error correction model to examine the relationship between ODA and economic growth in Turkey from 1967 to 2013. The study found a nonlinear relationship between foreign aid and economic growth. Siddique et al. (2018) studied the impact of ODA on economic growth in a panel of South and East Asian countries from 1995 to 2013. The dynamic panel estimation technique was utilised in the study, and the results demonstrated a positive relationship between ODA and economic growth for the countries. Yiew and Lau (2018) studied the role and impact of ODA on economic growth in 95 developing countries from 2005 to 2013. Pooled OLS, Random Effects, Fixed Effects, and Fixed Effects Robust Models Regression techniques were employed for the analysis. The results revealed that ODA and economic development have a U-shaped relationship. Foreign aid initially harms a country's growth, but it progressively positively contributes to economic growth. Amidi and Madiji (2020) used a spatial dynamic panel data framework to investigate economic growth in terms of "bilateral trade flow" and "geographical distance" for 25 EU nations over the period 1992-2016. The findings of the study revealed spatial and spill-over effects in these countries. This led to the conclusion that a country's growth rate is influenced by the growth rates of its neighbours. Parent and Zouache (2009) investigated the growth of Africa and the Middle East from 1990 to 2005. The Bayesian Model Averaging method, which generates estimates as a weighted average of Spatial Autoregressive estimates for all feasible variable combinations was employed. According to one of the paper's conclusions, including spatial dependencies has a direct impact on the determinants of growth in Africa and the Middle East. Nwaogu and Ryan (2015) investigated the influence of foreign direct investment (FDI), foreign aid, and remittances on the economic growth of 53 African and 34 Latin American and Caribbean countries using a dynamic spatial framework. A panel data set with eight separate 5-year periods spanning the years 1970-2009 was employed. Results from both regions emphasised the importance of spatial interdependence in explaining economic growth because one country's growth is influenced by the growth of its neighbours. However, this study uses only the SAR, ignoring in this case the spatial effects of the control variables such as FDI, ODA, and remittances. Tait, Siddique, and Chatterjee (2016) investigated the impact of ODA on economic growth in twenty-five Sub-Saharan African countries from 1970 to 2012. According to the findings of a fixed effect panel data analysis, aid has a strong positive long-term influence on per capita GDP growth. Yahyaoui and Bouchoucha (2021) investigated the relationship between ODA and economic growth in the presence of governance using FMOLS and DOLS techniques for the period 1996-2014 in 48 African countries. They found a negative effect of foreign aid on economic growth. Gichanga (2018) investigated the relationship between economic growth and ODA inflows in Kenya for the period 1970-2016. The ADRL Bounds test approach was used. The results showed a positive but insignificant relationship between ODA and economic growth. Veledinah (2014) investigated the ODA-Growth relationship in Kenya using the VECM estimation technique for the period 1970-2012. The findings from the study showed a positive contribution of ODA to economic growth in the short run, although it was not statistically significant. Gichanga (2018) also examined the relationship between economic growth and ODA inflows in Kenya from 1970 to 2016 using ADRL Bounds test. According to the results, ODA and economic growth have a positive but insignificant relationship. Yahyaoui and Bouchoucha (2021) employed FMOLS and DOLS techniques to investigate the relationship between ODA and economic growth in the context of governance in 48 African countries between 1996 and 2014. The findings revealed a negative influence of foreign aid on economic growth. Fasanya and Onakoya (2012) examined the impact of ODA on Nigerian economic growth from 1970 to 2010 using the neoclassical modelling analytical framework. The findings revealed a significant impact of aid flows on Nigeria's economic growth. Suphian and Kim (2016) studied the impact of ODA on economic growth in Tanzania, Uganda, and Kenya from 1980 to 2014 using the autoregressive distribution lag was applied (ARDL). In the long run, the estimated ODA results of all countries suggested a positive and significant impact on their economic growth. Seck et al. (2022) assessed the regional growth potential of regional economic communities in Africa using a spatial dynamic panel data model. These included SADC, ECOWAS, COMESA, ECCAS, and AMU. The paper demonstrated that national economic growth in Africa is aided by growth in surrounding countries due to trade links rather than geographic proximity. The findings also revealed hidden significant heterogeneity among regional economic communities, with SADC, ECOWAS, and COMESA registering significant positive spill-over effects across their respective members, while ECCAS and AMU showed no significant spatial correlation, due to the improving their bilateral trade flows.
In conclusion, more studies on ODA and economic growth are realising the importance of spatial dependence as another determinant of economic growth. This is reflected in the growing body of literature on African countries. Nonetheless, most research on ODA, economic growth, and spatial dependence in Africa ignores the heterogeneity of these countries and assumes cross-country homogeneity and spatial independence. This assumption is incorrect as it may result in model misspecification and inaccurate outcomes. Therefore, this study contributes to the body of knowledge by taking into consideration cross-country heterogeneity in estimating the relationship between ODA and economic growth, as well as spatial dependence in African countries.

Econometric model specification
The study benchmarks its theoretical growth nexus on the neoclassical Solow growth model (Solow, 1956). The model presumes that the long-run economic growth rate is characterised by exogenous technological advancement and the stable steady state is achieved by an endogenous change in capital accumulation. The Cobb-Douglas technology notes that the total output is governed by rising inputs and the exogenous advancement in technology. Hence, the model specification is the resultant of the augmented human capital Cobb-Douglas production function. This function undertakes output to be a function of capital and labour inputs, and its original form may be written out as follows: where Y is output, K conveys domestic capital input, L suggests labour input, A indicates the positive parameter that measures the inputs' productivity, a and b are the elasticities of production with respect to K and L, respectively, and e u is the multiplicative disturbance term.
In Equation (1), the output is measured by real GDP (2010 ¼ 100) (in US$), human capital is measured by the number of years of schooling, and labour is measured by the number of people engaged (in millions). This study is undertaken under the assumption that the above production function presents constant returns to scale, consequently, the sum of the mentioned above production elasticities is equal to one (i.e., aþb¼1).
Bearing in mind that the model presented by Equation (1) is linear in logarithmic functional form, we can transform it by applying natural logarithms on both sides of it. The resulting log-log model below depicts the link between the stated above inputs and economic growth in the country i at time t.
where log is the natural logarithm, log(Y it ) is the GDP over time across countries i (i.e., economic growth), b 0 ¼ log ðAÞ is the model intercept, the subscript ið¼ 1, :::, MÞ is the cross-section dimension that represents African countries, the subscript t(¼1, … ,T) is the time-series dimension that represents years, X is the set of the stated above input variables, the b j ðj ¼ 1, 2Þ are partial regression coefficients, a is the non-observed effect and u is the random error term. Furthermore, in attempting to achieve the aim of this research and the belief that aid plays a part in the process of national welfare creation, we include foreign aid on the right-hand side of the model, and Equation (2) becomes as displayed below.
where F it conveys foreign aid measured by ODA in US$ as a percentage of GDP, and k is the respective coefficient.
To be thorough, we comprise the following control variables on the right-hand side of Equation (3): human capital, money supply, institutions quality, social infrastructures, and population. In this context, Equation (3) can be re-written as given below.
where Z is the set of the mentioned above control variables, d k ðk ¼ 1, :::, 6Þ is the set of the control variables' coefficients, and all other variables, parameters, and subscripts are as defined before. Assumed the functional form applied to Equation (4), all the added regressors discussed in the previous paragraph are inserted in logarithmic form, except the social infrastructures' variable, since it takes the minimum value of zero, as shown in summary statistics presented in Table 1.
In the augmented growth model given by Equation (4), human capital is measured by the number of years of schooling, the money supply is measured by the M 2 monetary aggregate (in US$), institutions quality is measured by the principal component index of 5 institutional measurers (to be further discussed in details), the social infrastructures variable is measured by the mobile phones subscribers per 100 people and population is measure in millions.
The subscript it designates that Equation (4) is a panel data model, so the number of observations is provided by MT, were M is the number of African countries, and T is the number of years that are included in this study (i.e., period).

Estimation strategy
To estimate the impact of ODA on economic growth in Africa as a function of selected non-spatial and spatial variables, we employ two different methods: (i) non-spatial techniques (FE, RE, and GMM) and (ii) spatial techniques; Spatial Autoregressive (SAR), Spatial Durbin Model (SDM) and Spatial Error Model (SEM). To be more specific, we first ignore the neighbouring effect of ODA and estimate Equation 4 by different non-spatial techniques. Furthermore, the first law of geography as firstly provided by Tobler (1970) argues that no region is isolated from others. Nonetheless, the law finds its base on the spatial econometrics framework where it explores and analyses the link that may suggest a spatial dependence. When there is strong evidence of spatial dependence, estimating the model by non-spatial techniques may lead to biased results, to avoid biases it is recommendable to employ spatial techniques (Getis, 2007). As can be noted and discussed earlier, the Equation (4) model specification is solely a panel data model that does not consider spatial characteristics. Moreover, as Anselin (2010) argues, the standard panel data models: FE, RE, GMM cannot address biases triggered by the existence of spatial dependence among or between countries. Thus, there is a need to apply spatial econometrics techniques, therefore, the study built on that and employed spatial econometrics methods to examine the impact of ODA on economic growth in Africa.
The standard spatial econometrics models that are generally estimated in empirical studies are SAR, SDM, and SEM. Building on (Elhorst, 2014;Espoir & Sunge, 2021), we start by estimating the SDM model as this is more general and it allows the spatial lag of the dependent and independent variables (in this study we only considered the lag on the variable of interest, ODA). The choice of SDM has its foundation in the fact that if we restrict some of its parameters to zero, we can easily get the SAR and SEM. Therefore, we extend the specification in Equation (4) by adding the variables with the spatial weighting matrix on the right-hand of the Equation and it is displayed as shown below.
where all other variables denote the same as Equation (4) and the subscript q indicates the expected parameter to capture the SAR effect and u is the expected parameter to capture the effect of ODA of neighbouring countries on the economic growth of a given country. This parameter is also known as the Spatial Autocorrelation (SAC) coefficient. The W nt is the spatial weighting matrix defining the neighbouring link between different African countries. By applying the likelihood ratio (LR) and the Wald test restriction tests as suggested by LeSage and Pace (2009), Equation (5) is reduced into SAR and SEM. More specifically, both tests examine two hypotheses, these are: H 0 :u s ¼ 0: By applying this restriction test we examine if Equation (5) can be reduced into a SAR model. Furthermore, if H 0 :u s þ qn ¼ 0 then the model specified in Equation (5) can be reduced into SEM.

Spatial Weight Matrix (W)
The spatial weight matrix is the pillar of the spatial econometric model and a core element that distinguishes spatial econometrics from other econometrics techniques such as time series. This is formally expressed by a spatial framework of n areas, for instance, M ¼ fM i g n iÀ1 , and a neighbour relation M & Px, where M can be a province, region, country, Historiographically, the majority of neighbouring countries are former British and French colonies, with a few other former European colonies unlikely to be neighbours. This must reveal something about the non-geographical neighbouring effect. Nonetheless, despite this acknowledgement, some sources argue that geographical borders matter more than non-geographical ones (see also Espoir &Sunge, 2021 andZall e, 2017). Therefore, to capture geographical neighbouring, in this paper, we adopted a weight matrix in a form of contiguity, and we assume first-order contiguity. 1 Furthermore, we also refine our weight by considering only a matrix Queen 2 rather than a Rock.

Data
The estimation of the final model given by Equation (5) used panel data on each of the model variables. The data were collected annually from the World Development Indicators (i.e., money supply, institutions quality, and social infrastructures), African Development Bank (i.e., ODA), and Penn World Tables (i.e., real GDP capital, labour, and human capital), for the period covered by this study . Table 1 displays the data characteristics of the selected 14 non-transformed variables that are included in the final model specified in the previous section. In the study, we used the following features, mean, which is used to determine the central point of relative distribution frequency. The standard deviation depicts the spread of several observations and finally, we use minimum and maximum values.
The table shows that GDP has a mean of 100372.9 US dollars with the least developed countries exhibiting a minimum of 1367.426 US dollars and the relatively ahead countries showing a value of about 1287589 US dollars. With regards to the variable of interest, ODA, it is found that it has a mean value of 858.059 US dollars that Africa ever received with a minimum and maximum of 18.41 and 11879.08 US dollars, respectively. The described statistics indicate no observable outliers among the selected variables, and therefore, they are suitable for further analysis.

Results of principal component analysis
As earlier mentioned, the study computed the principal component analysis as a preliminary analysis of the data on the African continent before moving to the main regression analysis. The 5 government dimensions that the study used to measure institutions' quality are more likely to suffer from multicollinearity. To address the problem, the study employed a principal component analysis to derive the correspondent institution quality index. Table 2 exhibits the results from the PCA analysis, here the study considered only the component associated with an eigenvalue greater than one and variables whose loading factor exceeded 0.30 in absolute value. As the results below show, a single factor (eigenvalue ¼ 4.191) from the PCA overall affects the total variance by about 83.8%. Therefore, we used only the first component which appears to be the only one retaining approximately 80% of the variance in the initial data. The first component comprises all institutions quality variables using as references the Rule of law (RL), Governance effectiveness (GE), Regulatory quality (RQ), Control of Corruption (CC), and finally Political instability (PI). The followed order is driven by the impact of each variable on the overall PCA index, see for example panel B in Table 2. A 1% percent increase in the RL has a bigger impact as compared to its counterparts, followed by the GE, RQ, CC finally the PI. We also show the Scree plot of eigenvalue after PCA and both panels reveal that the PCA has well converged with no sign of structural breaks, see Figure 1 (Appendix).

Non spatial panel models results
The empirical results followed two different approaches. The study starts by reporting the results from the nonspatial model as shown in Table 3. To estimate the effect of ODA on economic growth in a step-wise way we start by analysing the effect of ODA on economic growth. Due to bias that might arise due to the omitted variables, we subsequently add other control variables as per columns 2, 4, 6, and 8 in Table 3. We first estimate a baseline regression using the ordinary least square (OLS) regression and the results in the first OLS indicate that a 1% increase of ODA yields an economic growth of 0.59% and its level of significance shows how important this is in driving the African economic growth, see also Yiew and Lau (2018). Something notable is that the OLS results seem to be sensitive to the model specification, this is exhibited by the change in its impact on economic growth. As it seems, a 1% increase in ODA reduces economic growth by about 0.07%. Although this is a relatively small reduction, it is highly significant which shows that it plays a role. Furthermore, other factors that drive economic growth include capital, labour, human capital, population, and institutions quality. With exception of the surprising result of the impact of labour, all mentioned factors indicate a positive and statistically significant impact on economic growth. This implies that a 1% increase in capital, human capital, population, and institutions quality will lead to an increase in the economic in about 0.51%, 0.29%, 0.95% and 0.08%, respectively.
Contrary to these factors, labour seems to be harmful to growth. For example, the results above show that a 1% increase in labour reduces growth by about 0.41%. The uncommon result is suspected to be due to the spatial effect that is not taken into   account. The results also indicate that money supply, as well as social infrastructure, are statistically not significant. Implying that they do not play a significant role in economic growth.
The panel data settings indicate that each unit in the panel has its characteristic where some are time-invariant. Using a simple OLS triggers biased results originating from the heterogeneity characteristics between the units within the panel as well as the timeinvariant that are not controlled for. To correct those potential biases one is to use either Fixed effect (FE) or Randon effect (RE). Table 3 also summarises the results of those estimations, whereby the estimated coefficient of ODA is positive for the first model of FE and RE. However, it is only statistically significant for the RE model. The inclusion of the control variables in model 2 for each estimation does not significantly alter the effect of ODA on growth with the estimated coefficients showing a nonsignificant effect of the variable of interest on growth, the results corroborate with those by (Moreira, 2005;Siddique et al., 2018). This shows that controlling for the heterogeneity effect as well as the time-invariant characteristics play a significant role and produces robust results compared to OLS. Like the OLS estimated coefficients, capital, population, and institutions quality remained positive and statistically significant, see also Gichanga (2018). Indicating that so far, their overall impact on growth is not spurred by any kind of estimation technique. Moreover, human capital, money supply as well as social infrastructure changed their overall impact on welfare creation. For example, while labour and human capital were statistically significant in the baseline estimates, they are no longer significant with the human capital being significant at 5% in the RE estimation. Along the same lines, money supply, as well as the social infrastruture, have become statistically significant across the analysed estimations techniques. However, although statistically significant, the magnitude of the social infrastructures is so small that it partially cancels its level of significance on growth. The same cannot be said about money supply, its magnitude indicates that a 1% increase leads to a decrease in the economic growth of about 0.02% and 0.01% in the FE and RE estimations, respectively. This supports the macroeconomics theory which indicates that an expansionary monetary policy leads to a price increase, which thereafter translated into inflation and consequent growth slowdown. The effect of the expansionary monetary policy can be emphasised more under the fixed exchange rate regime where it becomes ineffective in responding to any shock which can thereafter boost the economy.
Although FE and RE already account for almost the critical issues that could trigger bias such as the heterogeneity across African countries, the results can only be robust under a static panel setting. In the event of a dynamic panel setting and time series persistent effect, using either FE or RE will produce inconsistent results. Therefore, we attempt to report results that meet panel dynamic settings. To do so we estimated a system GMM that controls for the past values of the dependent variable, as well as the possible initial conditions and the results, which are summarised in Table 3. Although normally the inclusion of the past values in the model generally trumps the level of significance of all other factors, ODA remains consistent either for GMM model I or GMM model II. As it shows, a 1% increase in the ODA increases GDP by 0.01% both for GMM models I and II. As expected, the past values of the dependent variable highly affect the present values. For instance, a 1% increase in the first lag of GDP yields an increase in the current GDP by about 0.995% and 0.86%, respectively. Same as before, capital, labour, and institutions quality are statistically significant, indicating that they drive the economic growth in the selected African countries. Due to different biases that occur due to different events, we consider the GMM results more robust and therefore our interpretation is biased to the system GMM estimators.

The role of space
To begin with, we analyse the role of space utilising Moran's I test and the results are summarised in Table 4 (Appendix). Conveniently we present the Moran's I for ODA and GDP for two different periods, 1996 and 2019. The results show that overall the values of the tests are statistically significant for both variables across time which in turn one can be argued that there is significant spatial dependence across countries in Africa.
Although we have tested the role of space using the Moran I test, this does not show the spatial agglomeration triggered by dependence levels between and among countries. Therefore, to assess the spatial agglomeration the study plots the contour map of GDP and ODA for two different data points, 1996 and 2019. The choice of the years is to allow us to see the trends over time between the beginning and the end of our time span. Figure 2 presents the different spatial agglomerations among countries throughout 1996 and 2019. As the figures exhibit, the level of spatial disparity is weak in 1996 compared to 2019. This might be due to different ties that African countries started having as time went by. On the one hand, it presents a range ODA of a minimum of 95% and 1% for 1996 and 2019 respectively. Furthermore, it shows the other hand that African countries received a maximum ODA of 135% and 42%, for 1996 and 2019, respectively. This implies that the dependence ratio of African countries on their donors is decreasing over time.
As the maps display, there is strong evidence of spatial agglomeration in 2019. This indicates that as the world gets more globalised, any shock in one country directly or indirectly affects other countries that belong to the same cluster like the one hit by the shock. See for example the later year of 2019 countries such as South Africa, Swaziland, Lesotho, Botswana, Zimbabwe, and Zambia are in the higher neighbouring effect cluster; followed by Mozambique, Tanzania, Uganda, and Democratic.
Along the same lines, GDP maps present the same patterns as the ODA. The spatial agglomeration is lower in 1996 compared to 2019. Implying that any shock in one country within a certain cluster would more likely severely affect other countries in 2019 compared to 1996. However, we also have some clusters suggesting otherwise in 1996. See for instance Botswana, Zambia, Democratic Republic of Congo, Uganda and Gambia followed by Mauritania, Mali, Niger, Burkina Faso, and Benin. These two clusters show a very strong spatial dependence between these countries. This indicates that contrary to ODA, economic growth has long been integrated. In other words, good and sustainable economic growth in a certain country within the same cluster affected the growth of their counterparts. Similarly, countries such as Sudan, Ethiopia, Kenya, Tanzania, Democratic Republic of Congo, and Malawi, followed by South Africa, Lesotho, Botswana, Mozambique, Zimbabwe as well as Zambia, and finally Morroco, Argelia, Niger, Burkina Faso, and Benin also follow the same pattern as the first cluster.
Overall the four maps suggest that there is an increasingly strong agglomeration between and among countries which suggests that the spatial dependence between neighbouring countries increased from 1996 to 2019. Not taking into account the spatial dependence will result in misleading results and hence wrong policy implications.
We also presented the Moran I scatter plot for ODA and GDP to see the quadrants where most African countries are located. This is displayed in Figures 3 and 4 which show the respective quadrants where most countries are situated. As can be visualised, the two years show different impacts. While in 1996 the overall impact was negative with the Moran I test of 0.020, in 2019 the impact is positive with the Moran I test of 0.046. This shows that in 1996 most countries were located in the first and second quadrants while in 2019 they were located in the first and third quadrants. Unlike ODA, GDP tends to present a negative impact for both panels. For example, the GDP Moran's I for 1996 indicates that an overall has been located in the first and second quadrant. This implies that if one has to look at individual impact perhaps countries located in the second and fourth quadrants would exhibit a negative impact triggered by their neighbour's economic growth. Along

Spatial Empirical results
After exploring the role of space using the Mora I test, Maps as well as the Mora I plot. We further perform different spatial models such as the spatial fixed effect-SDM, spatial fixed effect SAM, and spatial fixed effect-SEM. The results summarised in Table 4 were all obtained using the contiguity weighting matrix and fixed effects maximum likelihood estimators. Same as the non-spatial models, in a stepwise way we controlled for other variables in column two for each model. Controlling for space improved the results, this is exhibited by the fact that while most of the GMM results are statistically insignificant, the spatial models show that other factors also play a significant role in explaining a certain country's economic growth. For example, in column two of the SDM, contrary to GMM results, money supply, population, and social infrastructure are statistically significant. Following the same thought, in the remaining models, SAM and SEM, human capital also is statistically significant. This suggests that GMM does not give a real picture of the impact of those variables on the welfare creation in a certain country. Same as GMM in Table 2, ceteris paribus, GDP increase in a certain country has a positive and statistically significant impact on the neighbours' GDP growth across all the regressions. The coefficient of ODA shows that it is positive and statistically significant both in the country and in the neighbour. The effect of ODA in GMM is lower (0.014) than those of spatial models (0.049, 0.019, 0.040, and 0.019) for all the models, respectively. This implies that by not controlling for spatial dependence we underestimate the real impact of ODA on GDP, see also (Amidi & Madiji, 2020;Nwaogu & Ryan, 2015;Ramirez & Loboguerrero, 2002).

Robustness check
In Table 5 we check for the sensitivity of the results by adding on the right hand of the equation the interaction term of the Institution principal component and ODA. Although the coefficient of the interacted term is small and statistically insignificant, the overall  results seem to be consistent without major changes. This shows suggested that the above results in Table 4 are reliable and yield good policy implications.

Conclusion
The study employed different econometric techniques, the non-spatial models comprised of OLS, fixed effect, random effect, GMM, and spatial models such as fixed effect-SDM, fixed effect-SAM, and fixed effect-SEM to investigate the impact of ODA on GDP in selected African countries in the period spanning from 1996 to 2019.
To perform the spatial models, it was first defined how two or more countries can be neighbours by using contiguity weighting matrix. Furthermore, the effect of space was explored by using Moran I, maps as well as the Moral I plot. The existence of space heterogeneity was proven to be important when analysing the impact of ODA on Economic growth. For example, the maps exhibited strong spatial evidence by showing a large number clustering together both in 1996 and 2019 for ODA and GDP. Along the same line, the Moran I plot showed that the impact is different from zero, also suggesting the existence of spatial dependence between countries and among countries belonging to the same cluster.
Empirically, among other findings, the study concluded that the ODA impact in GMM estimation, although positive and statistically significant, was smaller in magnitude compared to the magnitude of the spatial models' coefficient. This suggests that by not controlling for space heterogeneity we are more likely to underestimate the real impact of ODA on GDP. Secondly, it was also found that the weighted GDP was positive and statistically significant which indicates that an increase in the GDP of a certain country has a positive and statistically significant impact on their neighbour's economic growth. Likely, the impact of ODA appeared to be positive in a certain country and positively affected the neighbours or the countries within the same cluster.
Robustness checks were also performed by adding an interaction term to see if the results were sensitive to the model specification and concluded that they continued to be stable and therefore could be used for policy recommendations. Concerning spatial heterogeneity, it is recommended that countries should strengthen their relationship as well as a partnership if they want to have ODA yielding the desired results. By strengthening their relationship and partnership, they will ensure that almost all those belonging to the same cluster adopt similar policies or measures and therefore yield similar results.

Extension of the study
We acknowledge that, while geographical borders appear to be more crucial than nongeographic ones (culture or being a former colony of the same country), the latter can also play a role in the spatial impact of ODA. As a result, looking beyond geographical boundaries will be an extension of this study or any future study. Also, consider splitting the sample into periods of weak and strong growth in Africa.

Notes
1. The first order contiguity considers two regions to be neighbours if they share a direct border. In other words, a neighbour of the neighbour is not a neighbour of yours. 2. Two regions are considered neighbour if only share borders. In other words, different from Rock, in the Queen matrix is not considered neighbour if two regions are only sharing corners.

Disclosure statement
No potential conflict of interest was reported by the author(s).