The relationship between aid and economic growth of developing countries: Does institutional quality and economic freedom matter?

Abstract Foreign aid is an important means of finance for governments of developing countries. The current study investigates whether too much inflow of aid to developing countries is beneficial or harmful to their economy and whether institutional quality and economic freedom matters in aid–growth relationship. To this base, a panel data covering the period 2002–2019 was collected from 44 developing countries of the world. System generalized method of moment was employed to examine the nature of relationship between foreign aid and economic growth, and dynamic panel threshold regression is utilized to uncover the mediating role of institutional quality and economic freedom. The result thus obtained reveals that the relationship between foreign aid and economic growth takes inverted U shape indicating the existence of optimal level of aid equal to 9.7% of GNI. The result from dynamic panel threshold regression shows that the effect of aid on economic growth is negative when arithmetic mean of institutional quality index is less than or equal to −0.614 and the overall index of economic freedom is less than or equal to 60.521. Above the indicated thresholds, the effect of aid on economic growth is positive which means institutional quality and economic freedom matters in aid–growth relationship. Drawing on the results obtained, the study suggest that developing countries should not receive huge amount of aid from donors, reform their institutions for the better, and improve economic freedom if they want to reap the benefit of aid.


PUBLIC INTEREST STATEMENT
Analysis of the aid-growth nexus attracted researchers' attention across the globe after the 1947 US's marshal plan to rebuild Europe. Several studies have documented positive contribution of aid to economic growth while there are also cases against this. Moreover, the jury is still out on the role of institutional quality in shaping the relationship between aid and economic growth. With this background, the current study employed panel threshold regression and generalized method of moment to investigate the link between aid and economic growth on one hand and the role of institutional quality and economic freedom on the other in panel of 44 developing countries. The study findings reveal that the impact of aid on economic growth is conditional on the amount of aid received, institutional quality, and economic freedom. Specifically, the impact of aid on economic growth is positive if aid is below 9.7% of GNI, institutional quality index is greater than −0.614, and economic freedom index is greater than 60.521. positive which means institutional quality and economic freedom matters in aidgrowth relationship. Drawing on the results obtained, the study suggest that developing countries should not receive huge amount of aid from donors, reform their institutions for the better, and improve economic freedom if they want to reap the benefit of aid.

Introduction
Most probably, the only agenda that countries across the globe share in common is that of achieving higher rate of economic growth. However, there might be differences in way of getting there. Apart from different political ideologies, there are different economic theories, backed by empirical evidences, as to what constitutes source of economic growth. Capital that can be internally generated and/or obtained from outside sources can be considered as a source of economic growth . Importance of capital in economic growth is undisputed, though conditions necessary for its effectiveness could be cited.
It is true that Africa is resource abundant continent (Jalloh, 2013;Mulwa & Mariara, 2016). What is interesting here is, however, the nature of these resources-they are under the ground. Lowincome African countries finance simple infrastructural developments with aid (Lee & Alemu, 2015). For developing nations, foreign capital is the last resort in face of commitments to reduce the alarming poverty and meager opportunities to mobilize resources from internal sources. This poses one important question: does foreign a capital thus obtained by any means available promotes economic growth as anticipated or are there chances of failure. Had aid and funds from multilateral creditors been panacea for development problems of developing countries, poverty would not have been an agenda on international summits for the past 70 years. This rationalizes to revisit the role of foreign capital in the economy of recipient country.
Foreign aid constitutes an important aspect of foreign policy of developed countries toward developing countries (McArtur & Werker, 2016). As far as developing countries are concerned, government plays a significant role in economy through its national plans. In order to achieve wellstated development objectives, however, governments of developing countries have to mobilize the necessary resources. In case domestic resources fall short of what have to be raised (the fact on ground in developing countries), it is rational to seek capital (aid) from foreign sources. The implication is that foreign aid positively contributes to economic growth of developing countries through provision of capital for investment. This assertion is also supported by economic theories, a famous one being that of Chenery and Strout (1966), which is of the idea that foreign aid fills to gaps for developing countries, namely, saving gap and foreign exchange gap.
The issue of aid-growth relationship is, however, a contested issue in empirical field (Clemens et al., 2012), as the result from previous empirical works is mixed (see Moolio & Kong, 2016;Sothan, 2018;Tang & Bundhoo, 2017). In addition to varied results as regards to the relationship between the variables, difference in functional specification (linear versus non-linear) is also observed. Non-linear specification dominates contemporary research works on the subject. Negative and insignificant effect of aid on economic growth in earlier empirical studies renders aid-growth relationship skepticism about importance of absorptive capacity of aid receiving country which is commonly referred to as aid effectiveness in this research area. For example, the role of aid in economic growth is contingent on institutional quality (Hussen & Lee, 2012) and macroeconomic policies (Burnside & Dollar, 2000). Following this, it has been recognized that foreign capital per se is not adequate in influencing economic growth positively. In order to channel foreign capital toward economic growth, the absorptive capacity of the recipient country is an important issue.
Of course, test of linearity and the role of absorptive capacity concerning aid-growth relationship are not new in aid literature. However, novelty of the current study lies in its attempt to consider relatively large panel of developing countries from all over the world and examination of mediating role of economic freedom (to the best knowledge of the author, this issue has not been studied yet). Put in other words, the study objectives are to (1) answer whether or not the relationship between foreign aid and economic growth is linear and (2) whether foreign aid can positively contribute to economic growth under better institutions and economic freedom. The rest of the paper is organized as follows. In Section 2, review of available related literature is made both at theoretical and empirical levels. In Section 3, the detail of material and method adopted in order to achieve scientifically the stated objective is provided followed by result and discussion in Section 4. Finally, the conclusion of the study findings is given along with description of policy implication.

Theoretical literature review
There are many theories as to what drives economic growth. One of such well known in the field of economics is that of  and Domar (1946). According to these authors, it is a certain percentage of national income saved which accelerates economic growth through capital accumulation. This is indicated in Eq. (1) below where "g"represents the growth of national income, "s" represent the percentage of national income saved and invested, and "k" represents the capital output ratio. The straightforward implication of the model is, therefore, the now less developed countries will be developed if they could retain more proportion of their national income and then invest it. This raises an important question: is it possible for them? The fact on ground in less developed countries shows that low level of income, extreme poverty, high population growth, high unemployment, and so on will result in only meager amount of saving and hence, limited investment which ultimately result in slower rate of economic growth. Thus, less developed countries face shortfall of domestic saving below the target level of investment and this is called the saving gap in growth literature If we assume that an aid equals to b percent of national income of a typical less developed country received from a generous donor country, Eq. (1) will become Suppose a given less developed country planned to attain growth rate of national income equal to g* with a given level of k, the rate of capital accumulation (c) required to attain g* will be g*/k. Therefore, the saving gap is the excess of this capital accumulation (c) over saving (s) and the gap will be financed by aid (b).
According to Chenery and Strout (1966), there is another constraint which less developed countries face in addition to the saving gap, which is known as foreign exchange gap. The foreign exchange gap implies that the foreign currency they obtain from their export (mainly primary goods) is inadequate when they come to pay for their import (mainly investment goods). In this case, foreign capital in the form of aid will be made available to less developed countries so that they can cover foreign exchange shortage to pay for imports. In general, the proposition that foreign aid can contribute to economic growth of the recipient country has strong economic theoretical foundation.
Nevertheless, assessment of donors' motives behind aid to less developed countries is crucial in light of aid-growth relationship. When we look at some of motivations for developed countries to advance a certain amount of aid, they seem rational economic agents maximizing their own gain than supporting economy of developing countries. For instance, aid "tying" refers to the situation where aid recipient country is required to purchase goods from donor country (Kwakye, 2010). This shows donors aim to create or widen market for their export than supporting economy of the recipients. The gulf states of Saudi Arabia, Kuwait, and United Arab Emirates favor Muslim states adding to literature religious dimension of motivation to provide aid (Villanger, 2007). In any ways, it is difficult to link this motive in support of economy of recipient countries. Motivation behind aid outflow from USA is mainly political, strategic consideration, and governance situation in the recipient country although in some extent, humanitarian assistance. For instance, USA's aid to Egypt and Israel stems from a desire to influence Middle East politics. On the other hand, countries like France direct their aid toward their previous colonies while the two world's largest financial institutions, world bank and international monetary fund, demand some economic reforms in the recipient country. From this, we observe that there is a significant element of self-interest behavior when donors provide aid to recipient countries, which might coincide with or diverge from economic interest of the recipient countries. In the former case, aid is likely to contribute to economic growth while in the latter case it may not.

Empirical literatures
The issue of foreign aid, an important external source of finance for governments of developing countries, has attracted attention of researchers across the globe in contemporary economic research works. A massive literature on foreign aid has been focusing on the effect of aid on economic growth of the recipient countries. As far as literature on aid is concerned, studies conducted so far presents mixed results about aid-growth relationship. In terms of scope, aidgrowth relationship had been studied at both country level and cross-country level. Even though most of the studies adopted econometric models, estimation techniques vary considerably. As of functional form regarding aid-growth modeling, earlier studies has estimated linear equations while most of the recent papers favored non-linear specification.
Large number of studies found positive effect aid on economic growth. The result obtained by Lee and Alemu (2015) from the study conducted on 39 African countries of which 19 are lowincome countries indicates that the effect of aid on economic growth is positive for low-income countries than middle-income countries. Using annual data collected from 71 aid-receiving countries over the period covering 1960-1997, Karras (2006) found positive effect of aid on economic growth. Evidence from 36 African countries over the period spanning 1960-2007 as obtained by Juselius et al. (2014) also shows positive aid-growth relationship. The authors claim that the hypothesis of detrimental effect of aid on economic growth does not hold empirically. Moolio and Kong (2016) studied aid-growth relationship on panel of four Asian countries, namely, Cambodia, Lao PDR, Myanmar, and Vietnam from 1997 to 2014 and found positive effect of aid on economic growth. Evidence from study conducted in case of the eight WAEMU countries from 2002 to 2013 also indicates the favorable effect of aid on economic growth (Aboubacar et al., 2015).
On the other hand, there are also empirical findings against effectiveness of aid in bringing about economic growth. Mallik (2008) studied the effect of foreign aid on economic growth in six highly indebted poor African countries. His findings indicate that while there is no significant short run relationship between aid and economic growth, there is negative long run relationship between the variables in five out of six countries. Yiew and Lau (2018) find the non-linear nature of aid-growth relationship from study conducted on 95 developing countries. In their study, they obtained surprising U-shaped relationship between the variables, which implies that too much aid to developing countries is a blessing. The meaning of U-shaped relationship between aid and economic growth is that the effect of aid on economic growth is negative at lower level of aid inflow and turns out to be positive at higher level. Similarly, Gyimah-Brempong et al.
(2012) obtained U-shape relationship between aid and economic growth. Based on data collected on panel of 77 countries, they stated the threshold amount of aid at which aid starts to affect economic growth positively between 6.6 and 14.4% of GNI. Mbah and Amassoma (2014) studied aid-growth relationship in Nigeria. The result they obtained from time series analysis reveals negative effect of aid on economic growth. Negative effect of aid on economic growth is also obtained by Tiwari (2011) from study conducted on panel of 28 Asian countries.
The mixed results obtained by prior studies, especially those with negative effect of aid on growth, raise an important question: why? This necessitated revisiting conditions in the recipient countries, which is commonly referred to as "absorptive capacity" in aid-growth research works. Drawing on data collected from 10 African countries over a period covering 1990 to 2012, Tang and Bundhoo (2017) find aid per se is not significant in affecting economic growth in statistical terms, but positively significant when accompanied with good policy environment. Fashina et al. (2018) studied aid-growth relationship in case of Nigeria from 1984 to 2016. They included square of aid in their model to explore the nature of relationship between aid and economic growth. In their study, aid and square of aid were found statistically significant with positive and negative coefficients, respectively, and this confirms the hypothesis of inverted U-shaped relationship between the variables. Furthermore, they found that aid promotes economic growth when made available to fund education. According to Udvari and Ampah (2018), aid enhances economic growth via stimulating innovation. As to another evidence about the role of institutional quality in mediating the aid-growth relationship, Adusei (2020) find that institutional quality plays no significant role in mediating aid-growth relationship while aid standing alone has positive effect on economic growth. The study is based on data collected from a panel of 42 African countries from 1983 to 2018. On contrary, Hussen & Lee (2012) found that aid effectiveness is conditional on institutional quality from their study in Ethiopia from 1971 to 2010. Table 1 provides summary of empirical literature made in this study.

Data
In order to achieve the purpose of the study, the relevant variables such as growth rate of real GDP per capita, institutional quality, economic freedom, aid, trade openness, population growth, inflation, government expenditure, investment, and schooling were selected. The variables were selected based on theories of economic growth determinants. Then an annual strongly balanced panel data on 44 world countries from the year spanning 2002-2019 was collected. These countries (the list is given in appendix) constituting the sample were selected based on World Bank country classification. According to the World Bank, high-income countries are those with GNI per capita exceeding 12,535US$ in 2019. Countries considered by the study, therefore, those countries with income level less than the indicated GNI per capita. The study period was selected based on data availability on all of the variables considered by the study with an aim of obtaining strongly balanced panel dataset. The data were sourced from different sources such as world development indicators (WDI), worldwide governance indicators (WGI), heritage foundation, and United Nations development program (UNDP).
GDP per capita growth is used as a measurement for economic growth and aid is measured by net official development assistance (ODA) received by a sampled country at time t in percent of GNP of that country. As a measure of inflation, consumer price index is employed. The variable trade openness is measured by the sum of import and export as a percent of GDP. In the same manner, government expenditure and investment are also expressed in percent of GDP. In an attempt to include human capital variable in to the analysis, average years of schooling is used.
Another important independent variable, institutional quality, is produced by World Bank Group. Accordingly, there are six governance and institutional indicators. These are control of corruption, political stability, and absence of violence, regulatory quality, and government effectiveness, rule of law and voice and accountability. Each of these indicators ranges from2.5 (weak governance and institutional quality) to + 2.5 (strong governance and institutional quality). In this study, the arithmetic mean of the six indicators is used as a single institutional quality variable since all indicators are equally important. Examination of conditionality of the relationship between aid and economic growth on institutions of the recipient country is as old as the influential work of Burnside and Dollar (2000). However, contribution of the current study is estimation of the threshold value of institutional quality below and above which the effect of aid on economic growth vary, which has an important policy implication. Economic freedom is considered by the current study to find out whether it plays a mediate role in aid-growth relationship. Sourced from the heritage foundation, economic freedom is compiled by Fraser institute. The index of economic freedom of the world is a measure of degree of governments' control over domestic economy. The overall economic freedom index of world countries is produced by averaging scores on 12 specific components of economic freedom, each of them computed from different sub variables. The overall economic freedom thus obtained is graded on scale a scale from 0 to 100. Higher scales show more liberal the economy while lower scales are an indicative of suppressed economy. It is important to examine the mediating role of economic freedom in the relationship between aid and economic growth. First, it might be a prerequisite for developing countries to be qualified for aid or to receive more aid. This is especially true in case the donor countries act opportunistically. Second, an increase in economic freedom takes allocation problem out of governments hand gives it to the market. In case government sector is inefficient, therefore, economic freedom can cause growth impact of aid to be favorable.

Empirical model
In this particular study, three models are specified for estimation purpose. In the first specification, the impact of aid along with control variables on economic growth is stated. In the second specification, the impact of aid on economic growth is reexamined by controlling for institutional quality. In the second specification, therefore, the direct impact of institutional quality on economic growth is tested. In the third specification, the interaction term between institutional quality and economic growth is added to the second specification to explore whether institutional quality improves the impact of aid on economic growth. Thus, based on variables indicated in Table 2, economic growth of a recipient country i at a given point in time t is modeled as follows.
Inclusion of square of aid as independent variable in aid-growth analysis is necessary because of two reasons. First, aid is capital and there is diminishing marginal productivity of capital (Yahyaoui & Bouchoucha, 2020). Second, loan is an important part of aid when we see its composition (see Dreher et al., 2021). Even though loans (for aid) are provided on concessional terms, huge volume of loans would be burdensome so to repay in the long run. In this situation, the relationship between foreign aid and economic growth will be non-linear taking inverted U shape if the coefficient of variable aid is positive and significant while aidsq is negative and significant. If this is the case, it implies that too much aid to developing countries is a curse. On the other hand, if the sign of coefficients on aid and aidsq are negative and positive, respectively, then our conclusion will be too much aid to developing countries is blessing. Open is trade openness, pop is population growth rate, inf is rate of inflation, gov is government expenditure, school is schooling, instn is institutional quality and instn X aid is the interaction term between institution and aid. α; β 1 ; β 2 ; β 3 . . . β 11 , are parameters to be estimated. θ i is unobservable country specific effect, u t is time fixed effect, and e i;t is the idiosyncratic error term. Only GDP growth rate is expressed in logarithmic form among variables considered by this study.

System generalized method of moment
Application of ordinary least square estimator (pooled OLS) to models specified above, besides being static estimator, is inappropriate as some of the basic assumptions specially, the "zero correlation assumption" remain unfulfilled in growth models (Wooldridge, 2001). The use of fixed effect models will surely overcome some of limitations of OLS estimators as they control for effects of some variables that changes across countries (countries specific effects) and that evolves over time, but not across countries (time-specific effects).
As far as aid-growth analysis is concerned, the effect of fixed effects is more likely to be relevant. For example, the sampled countries are heterogeneous concerning colonial relationship with donors, geographic location, strategic importance, and political ideology just to mention some. More or less, level of human capital of developing countries is similar, but an investment in schools and health sectors mostly with development assistance is expected to improve it over time (time fixed effect). This implies that fixed effect models generate better estimates than pooled OLS. However, fixed effect models themselves are subject to some flaws. First, they do not capture the issue of dynamism-they are static models. Next, there might be reverse causality, i.e. economic growth causing aid (Galiani & Knack, 2016). In such a situation, consistency of parameter estimates is seriously affected.
An estimation framework that accommodates issues raised above satisfactorily is generalized method of moment (GMM) model. The model is feasible to use in this study, as the cross-sectional dimension is larger relative to time dimension. Based on how variables are instrumented with the aim of accounting for problems like endogeneity and serial correlation, there are two estimation methods within the framework of GMM. One is called difference GMM and it was developed by Arellano and Bond (1991). The difference GMM method uses levels of independent variables lagged at least two periods. Even though the model performs well than models indicated above, some studies attest that there is a problem with difference GMM estimation when persistence of variable(s) is detected, which is more likely in growth studies leading to the problem of weak instrument (see Borrego & Arellano, 1999). In order to account for the problem of weak instruments, Arellano and Bover (1995) and Blundell and Bond (1998) came up with the second method referred to as system GMM. System GMM takes lags of endogenous variables in addition to that of variables in level. The additional moment conditions with system GMM also improve efficiency.
Running system GMM requires performing post estimation specification tests to check for validity of instruments used. Accordingly, two such tests, namely, Hansen and Sargan test of over identification and second order serial correlation test are employed in this study following available literatures on the subject. In both of the tests, the null hypothesis states the validity of instrument variables. Therefore, the probability values associated with the tests should be greater than 5% for the model output to be acceptable. According to Roodman (2009), number of groups (countries in this case) should not exceed the number of instruments and this is checked.

Panel threshold regression
The essence of running panel threshold regression in this study is to examine whether conditions in the recipient countries matters in explaining aid-growth relationship. Accordingly, two of such conditions are selected in this study; these are institutional quality and economic freedom. Of course, the interaction term between aid and institutional quality specified in Eq. (5) above captures the role of institutional quality in aid-growth relationship. However, panel threshold regression is required here as it is helpful to check robustness of results in system GMM and also it provides the threshold value of institutional quality below and above which the effect of aid on economic growth varies.
Panel threshold regression in the realm of econometric estimation is based on a pioneering work of Hansen (1999). It is currently becoming popular as applied to inflation studies, financial development studies, public debt studies, mobile penetration studies, etc. The original panel threshold model proposed by Hansen is applicable only to static panel where covariates and/ threshold variables are required to be exogenous. An attempt has been made to extend original work of Hansen (1999) to dynamic panel threshold. For example, Kremer et al. (2013) have provided framework for dynamic panel threshold estimation. However, a problem with their work is imposition of too restrictive assumption about exogeneity of threshold variable in case of the former and even covariates in case of the latter. Seo and Shin (2016) proposed a dynamic panel threshold that overcomes the restriction on the nature of covariates and threshold variables. The estimation framework is applicable even when there are endogenous covariates. Since the problem of endogenous covariates and reverse causality is believed to be common in growth literature, the currents study employs this threshold model and it is given below. The estimator is based on first-difference generalized method of moment estimator of Arellano and Bond (1991).
Definition of Eq. (6) is as follows. Y it is the dependent variable, X 0 it is a K 1 � 1 vector of time varying repressors including one period lagged dependent variable and aid, 1 � f g is an indicator function, q it is threshold variable (in this case, institutional quality and economic freedom),δ is the threshold parameter,φ 1 and φ 2 are the coefficients associated with the lower and upper regime, respectively, μ it is the unobserved individual fixed effect, and ε it is the idiosyncratic random error. Table 3 provides the result of descriptive analysis. The descriptive analysis is based on 792 observations on all of the variables considered except for trade openness, which is based on 791 observations. The result reveals that GDP per capita growth rate averaged 2.903 with standard deviation of 0.19, which indicates low variability in spread of data. The minimum value of −0.43 for the variable is observed on Madagascar in 2002, while the maximum value (3.43) is observed on Mongolia in 2011. Economic depression of Madagascar in 2002 was the outcome of socio-political crises (Rajemison et al., 2014). The surprising growth experience of Mongolia in the indicated year had been driven by transportation and construction sector (World Bank, 2011). The mean value foreign aid (2.85) is closer to mean of lnGDP per capita growth rate. Higher variability of data also characterizes the variable as shown by minimum and maximum values of the respective variables (given in Table 3). Among macroeconomic variables considered by this study, standard deviation of trade openness (30.89) is the highest indicating greater variability of data.

Descriptive statistics and correlation analysis
When it comes to institutional quality, index of governance indicators averaged −0.38. This shows poor quality of governance indicators characterizes the sampled countries. As indicated by standard deviation (0.41), there is lower variability of data for the variable. Among countries considered in this study, the lowest institutional quality (−1.58) is occurred in Haiti 2004 while the highest (0.88) occurred in Botswana in 2003. On average, economic freedom index of the sampled countries is 59.11. According to economic freedom index of the world's classification of economies based on the score, the sample would be classified as "mostly unfree". As regards to shape of distribution of data, none of the variable is normally distributed as indicated by Jarque Bera test. However, lack of normality is of a little concern in generalized method of moment (GMM).
Pairwise correlation analysis is given in Table 4. Concerning correlation between the explanatory variables, high positive correlation is obtained only between aid and aid square (0.84). The result shows that except economic freedom, government expenditure, and population growth the rest of control variables are positively correlated to economic growth. (3)

Dynamic panel regression result
The result from dynamic panel data regression is given in Table 5. The table reports estimation results of the three equations specified above. Under column 2, result of system GMM model for the first equation (equation without controlling for institutional quality and its interaction term with aid) is reported. Column 3 reproduces the same, but now by controlling for the direct effect of institutional quality on growth while column 4 presents the estimation results after incorporating the interaction term. In all of the GMM estimation, the Wald statistics is strongly significant indicating that the models are significant jointly. Furthermore, the number of instruments used is less than the number of group. Although the null of serial correlation is not rejected at first order auto regression (A1), it is rejected at second order auto regression (A2). As regards to test of over identification, the null hypothesis of over identification is rejected in case of both Hansen and Sargan. As the result reveals, the one period lagged log of GDP per capita growth rate has positive significant effect on GDP per capita growth rate throughout the regression models. The implication of the result is that countries with fastest growth rate in the past continue to grow faster in the future, which confirms the divergence theory. The finding is consistent with that of Asafo (2019), Bekere and Bersisa (2018), and Hayat (2019) but contradict with findings of Sala and Trivín (2014), Van Bon (2019), and Zekarias (2016).
Among the control variables considered by this study, inflation, institutional quality, government expenditure, and total investment are found significant consistently throughout the models with slight variability of coefficients for each model. The sign of inflation is negative as expected. The negative effect of inflation on economic growth is understandable as, for instance, inflation creates uncertainty about business environment. The result is similar to what was found by Adaramola and Dada (2020). The result obtained concerning investment is also in line with that of Uddin (2014). The sign of government expenditure is negative unexpectedly and consistent with finding of Al Gifari (2015) and Amusa and Oyinlola (2019). With the expected sign, population growth is significant only in the last specification (column 4). Average years of schooling, a proxy for human capital, are not significant in explaining economic growth of nations in this study. The positive and significant sign of institutional quality shows economy of a country grow faster when institutional quality is improved.
Our variable of interest (aid) is significant with positive sign in the entire models, which indicates aid is important to stimulate economic growth of developing countries. The result further shows that the impact of aid (other things remaining constant) is a bit stronger when institutional quality is controlled for (0.091 versus 0.097). It can also be seen from Table 5 that the influence of aid on economic growth gets stronger when the interaction term between aid and economic growth is included. Square of aid is also a significant variable affecting economic growth surprisingly without change of sign and coefficient throughout the three specifications of GMM estimator.
Based on the result from system GMM model, therefore, it is established in this study that the relationship between aid and economic growth is non-linear as aid and square of aid have positive and negative significant coefficient, respectively. This shows that the relationship between aid and economic growth takes inverted U-shape indicating the impact of aid on economic growth is favorable only when kept below certain threshold above which it is detrimental to the economy. Therefore, too much aid harms economic growth of developing countries. The result is in line with that of Ali and Isse (2005); Fiodendji and Evlo (2013) but contradicts with that of Yiew and Lau (2018) and Gyimah-Brempong et al. (2012). Since the dependent variable is expressed in logarithm, we multiply coefficients of all of the explanatory variables including aid by 100 before interpreting the result. Accordingly, we can compute the effect of aid on economic growth by taking the first order derivative of Eqs. (4) and (5) with respect to aid as follows: Equation (5) gives direct effect of aid on economic growth while Eq. (6) gives the effect of aid on economic growth conditional on institutional quality. Evaluating Eqs. (5) and (6) at the mean value of aid (2.859) and institutional quality (−0.383) after multiplying the respective coefficients by 100, we get the effect of aid on economic growth for Eqs. (3), (4) and (5), respectively, as 6.241, 6.841, and 6. This indicates that a percentage point increase in aid to GDP ratio increases GDP per capita growth rate by about 6.3% without controlling for institutional quality, by about 6.9% when controlling for institutional quality and by 6% when controlling for institutional quality and interaction term. In order to explore if aid contribute well to economic growth under better institutional quality, we evaluate Eq. (4) at minimum (−1.587) and maximum (0.88) value of institutional quality and compare the result. Accordingly, with minimum institutional quality index of −1.587 and maximum institutional quality index of 0.88,

Economic growth
Aid (% of GNI) 9.7 a 1% percent increase in net inflow of aid to GDP ratio increases economic growth by about 2.75% and 9.42%, respectively. As the result indicates, the effect of aid on economic growth is different between models with and without the interaction term between aid and institutional quality. Even for a model with interaction term (column 4), the effect of aid on economic growth varies as the value of institutional quality index varies. Hence, institutions matter in aid-growth relationship unlike the findings of Dreher et al. (2021).
The fact that the aid-growth relationship is non-linear implies that there is a tipping point of aid where the effect of aid on economic growth becomes zero. Put in other words, the tipping point shows the maximum the level of aid inflow at which the effect of aid on economic growth is just zero. This is computed by taking the first order derivative of Eqs. (3), (4) and (5) with respect to aid, setting it equal to zero, and solving for aid. Accordingly, the tipping points for the equations are 9.1, 9.7, and 8.86, respectively. Figure 1 shows the tipping point of aid with respect to economic growth by controlling for institutional quality. Table 6 reports the result from dynamic panel threshold regression propounded by Seo and Shin (2016). The reported result is obtained by implementing STATA command xthenreg in STATA version 15. Our aim here is to examine whether or not the effect of aid on economic growth vary for values of institutional quality and economic freedom index being below and above certain threshold level. Since the non-linear relationship between aid and economic growth has already been established by using system GMM estimator and the corresponding threshold value is calculated for aid, we proceed by examining that of institutional quality and economic freedom. As indicated in the table, the result reveals that the effect on economic growth indeed varies depending on institutional quality and economic freedom since the respective threshold values are statistically and strongly significant. Specifically, the effect of aid on economic growth is negative (positive) when institutional quality and economic freedom indexes are below (above) −0.614 and 60.521, respectively. Therefore, the findings of the current study support the idea that absorptive capacity of aid recipient countries is crucial for aid effectiveness.

Conclusion and policy implication
In addition to external debt, foreign direct investment, and remittance, foreign capital flows in to developing countries in the form of foreign aid. However, the direction of impact of foreign aid on economic growth on the one hand and the nature of the relationship (linear or non-linear) between the variables is inconclusive in light of previous studies. There is also mixed results regarding the conditionality of foreign aid on institutional quality of the recipient countries and no recent study at all concerning the role of economic freedom in shaping the relationship between aid and economic growth. In order to fill the observed knowledge gap, the current study was undertaken based on data collected from credible sources over the period spanning 2002-2019 on 44 developing countries across the world.
Employing system GMM method with quadratic specification, currently a popular method in regressions involving endogenous variables, the study detected non-linear relationship between aid and economic growth where by the contribution of aid to economic growth is positive only at lower level (no more than 8-9% of GDP) and become harmful at a higher level. By employing dynamic panel regression model, it is also shown that institutional quality and economic growth are of utmost importance in shaping the relationship between aid and economic growth. In order for aid to stimulate economic growth in the sampled countries, the average institution quality indicators should be fairly above −0.614 while the overall measure of economic growth should exceed 60.521. The implication of results found is that developing countries should keep net inflow of aid toward them at lower level (under 10% of their GDP) and improve their institutional quality and ease government control over political and economic environment so that they can reap the benefits that foreign aid confers. The current study established threshold level of aid below and above which the effect of aid on economic growth vary for all of the 44 countries taken together. However, it would be better to see if the threshold level varies with income level and regions by considering even larger panel dataset.
Other than institutional quality and economic freedom, there might be significant mediator/ moderator variables like human capital and financial development in the relationship between aid and economic growth. Therefore, future similar studies can build on these to widen further the literature on aid and economic growth nexus.