Aid and Two Gap Model

Aid and the Two Gap Model Aid is a burning issue these days. The question of countries accepting foreign aid has intrigued economists and the general public for a quite a while. Television discussions and newspaper articles have frequently focused on this issue while politicians try to fight this matter out in the parliaments. Furthermore, many are trying to unravel the enigma of aid and its effects on growth. This paper, in the little word space provided, will try to establish a relation between aid and growth.
It will do so by first defining aid and growth and then moving on to some of the important models which can be used to understand this link. We will discuss the two-gap model and then move on to the Solow and Harrod-Domar model, giving empirical examples in each case. Finally, we will analyze two countries and try to inspect the reasons for their different growth rates using the logic used in the discussed models. Aid can be defined as any voluntary transfer of resources. It can be either public (provided by donor countries or multilateral donor organization such as the IMF and The World Bank) or private (given by NGO’s. . The Organization for Economic Corporation and Development defines aid as any transfer of money or resource that fulfills the following criteria: a) The objective of the transfer should be noncommercial. b) It should be given for the purpose of economic development. c) The terms of the transfer should be concessional (interest rate should be less than the prevailing interest rate in the market OR the maturity period should be longer than usual). Aid should not be mixed with grant which is often used interchangeably with this term.
Aid is any transfer that has concessional terms while grant is a form of aid that does not require the repayment of the principal. In this paper, we will often measure aid in the from of official development assistance (ODA) which is a convenient indicator of international aid flow. On the other hand, we will measure growth by scrutinizing the percentage change in GDP. One of the most widely used framework for analyzing the effects of aid on growth is the two-gap model which holds a key position in policy decisions related to foreign assistance.

The two gap model is based on the Harrod Domar equation g = s/v where s is savings rate v is capital output ratio Capital output ratio is assumed to be constant. The two gap model assumes that a developing country faces either a savings gap or a foreign exchange gap. The savings gap occurs when a country faces a shortage of savings to match Investment in attaining an intended growth rate. In such a case, foreign borrowing or aid can supplement the savings and help bridge the gap between savings and investment. This allows a country to achieve the targeted growth rate. Ft < I – S (Savings gap)
A foreign exchange gap takes place when a country’s exports are not enough to finance its imports. In such situations, aid is handy as it fills the foreign exchange gap and provides countries with sufficient exchange to reach the required level of imports. At a given point in time, only one of the two gaps is binding. Ft < M – X (Foreign Exchange gap) Following this further, we fit empirical data into this model. Zambia is a developing country that has continuously received aid since the mid 1960’s. In 1992, almost 80% of Zambia’s investment was financed by foreign aid.
Since, Zambia has received aid over such a long period, the two gap model predicted that its per capita GDP would reach $2300 by the turn of the century. On the contrary, its GDP per capita in 2007 remained merely half of what was expected . i. e. $1300. The fig. below summarizes the analysis of the Zambian economy. To examine whether the Zambian case is an exception or does the model always fail to predict the reality, we scrutinize on various factors which could have blocked the path of growth for this country. Zambia has been infected by violence and instability right from its independence, with bloodshed and massacres a common feature.
In addition, economic growth has been hindered by the outbreak of civil war and influx of refugees from the neighboring countries. Corruption is another problem that has stalled growth which can be seen from the fact that Zambia is ranked 101 on the corruption perception index. Very recently, Sweden and Netherlands stopped aid to Zambia due to rampant corruption allegations. All these problems add to the ineffectiveness of aid on the growth of Zambian economy which can explain why the two-gap model failed to forecast the ineptness of aid.
The effect of aid on growth can also be explained using two basic but important models, namely Harrod Domar model and the Solow model. Although the upshot of aid on growth is a multidimensional and complex process we only take into account the effect of aid on variables defined in these two models. The main focus of our discussion will be the saving rate which comes out to be the most imperative variable in both these models. We start through the basic Harrod Domar model. Capital output ratio, capital labor ratio and labor output ratio are assumed to be constant.
Some of the important relations are as follows: S=s. Y (2) (3) (1) g= (s/v)-(? ) S=I Where: Y is income S is total saving I is Investment ? is depreciation of capital According to this model, growth can be increased by increasing s, decreasing v or decreasing ?. We shall mainly focus on the relation of aid on growth through the savings rate channel. Countries ask for aid mainly due to its perceived beneficial effect on the savings rate. As shown, saving equals investment in the Harrod-Domar model, subsequently an increase in savings will result in an increase in investment.
This increase is supposed to boost the growth rate of the recipient country. Michael P. Shields offer an interesting explanation of the relation of foreign aid on growth in his paper “foreign aid and domestic savings: the crowding out effect”. If foreign aid is expected to increase savings, then equation (3) becomes g=(s+fa)/v -? Where fa is foreign aid as a proportion of income (4) (s+fa) represents the total funds available for backing investment. According to this equation, an increase in foreign aid is supposed to increase the total saving funds and hence investment by an equal amount.
This suggests that an each additional dollar of foreign aid should result in a one dollar increase in investment in the economy of the recipient country. Reality however is not that perfect and it is too generous for anyone to assume such a one-to-one increase in investment from aid. Famous economist Edward Griffin offers a criticism of such approach. According to him foreign aid should be taken so as to supplement income rather than having a direct impact on savings. In such a case, an increase in income by the amount of foreign aid fa would increase consumption by (1-s). a, thus increasing the investment by s. fa. In such a case, domestic savings can be crowded out by foreign aid by the net amount –(1-s)fa which equals (s-1)fa. Markedly, foreign aid can crowd out private savings and investment, resulting in a decrease in growth as suggested by the Harrod Domar model. The main obstacle in the way of growth in the Harrod-Domar model is the phenomenon of aid filtering out into increased consumption (1-s). fa. Aid has to be spent on investment or has to increase the saving rate (both eventually come out to be the same) for a country to grow.
To see a practical example of this, we consider Pakistan, which is a country largely dependent on foreign aid. During the period 1952-2002, the total amount of aid given to Pakistan equaled 63703 million US dollars. Ghulam Mohey-ud-din examines in his paper “Impact of foreign aid on economic development in Pakistan”, the reasons for aid not resulting in the required growth for Pakistan. He states three main reasons for the failure of aid to account for growth. First of all, a staggering 58% of this total aid (approx. 6945 million US dollars) was tied to development of large projects while only 13% (approx 8281 million US dollars) accounted for non-food and BOP aid. Such a large portion of aid (58%) going towards consumption invariably meant that the effect on savings was going to be very minute. Thus, financial aid tended to crowd out saving and investment. Secondly, while the nominal aid gradually increased, in reality, aid as a percentage of gross national income fell from approximately 7. 6% in 1960 to nearly 3% in 2002. This meant that aid was not catching up to the required increase in the GNI of Pakistan.
Thirdly, along with the increase in aid came the burden of burgeoning foreign debt. This required huge amounts of debt servicing which reduced Pakistan’s current account. As previously explained, aid was already not resulting in much growth due to it crowding out savings and investment. An additional burden of debt servicing did the government no better. Accordingly, its GDP growth rate was subject to constant fluctuations and Pakistan could never attain sustainable growth. The growth rate reached a peak of 10. 22% in 1953 but since then, the average growth has gone down with the exception of one or two years.
In 2002, the GDP growth rate stood at 4. 73%. Aid during a whole half of a century could not result in sustained economic growth. Another approach that looks at the impact of foreign aid on growth is the poverty trap. Many poor developing countries face an inability to grow at reasonable rates due to getting stuck in a poverty trap, which can be defined as a self-reinforcing mechanism which causes poverty to persist. We use the Solow model to analyze how aid can be used to pull countries out of this poverty trap and onto the path of self-sustaining economic growth.
We assume the basic assumptions of Solow model to be true. Thus, we assume constant returns to scale production function and diminishing returns to capital. The final and important relation of the Solow model is ? k=s. y-(n+? ). k (5) k is capital per worker n is population growth Philipp Harms and Matthiaz Lutz depart from this conventional Solow model by assuming that people have to satisfy their basic consumption needs for which savings are zero until per capita income does not exceed a certain level. The modified Solow diagram is shown below
Two steady states are shown in the above figure. k* is an unstable steady state while k** is a stable steady state. If the country’s initial capital per worker is below the unstable steady state k*, then the country is stuck in a potentially dangerous poverty trap. Low income levels result in low saving which leads to lower investment in capital stock. Increasing depreciation ? of capital will further lower the capital per worker k and result in even lower income. This vicious cycle of poverty and lack of growth will keep re-enforcing each other unless the country is given a push start.
This push can be in the form of aid, which may impact the savings rate s as discussed in the extended Harrod Domar model. Furthermore, aid in the form of foreign capital inflow can also increase capital per worker, consequently pushing the country out the poverty trap. Now we come to the analysis of growth patterns in two Arab countries namely Egypt and Palestine. We will explore the amounts and type of aid given to these countries and then investigate their underlying effects on various growth variables based on the Solow and Harrod Domar models discussed earlier in the paper.
With this in mind, we turn to the empirical evidences which show that: 1. ODA/GNI ratio for Palestine has increased during the period 2000-2005, while that of Egypt has decreased during the same period. 2. ODA/Capita for Palestine has increased to $500 during the period 2000-2005, while ODA/Capita for Egypt has come down to $15 in 2003 from $179 in 1979. 3. In Egypt, 13% of the total aid was tied whereas in Palestine 8% was tied. 4. Technical aid provided to Egypt was 44% while that of Palestine was 16% of total aid during the period 2000-2004. 5.
In Egypt, education was given the highest priority among the aid allocated to the social sector. While in Palestine, Education was the second lowest recipient of aid allocated to the social sector. 6. In Palestine, growth rate of real GDP from 2003-2005 was 35. 50%, while the percentage change in real GDP for Egypt was 127. 46 for the same period. ODA/GNI ratio signifies the dependency of the recipient country on the donor for foreign aid. A large increase in the ODA/GNI ratio of Palestine meant that it was becoming more and more dependent on foreign aid for support, while the opposite was true for Egypt.
Consequently, Palestinian institutions kept weakening and were not given the incentive to develop due to their heavy reliance on outward help. On the other hand, Egypt’s lower dependency on foreign aid meant that it was getting increased opportunities to develop its institutions and stand up on its own feet. As the ODA/capita of Palestine increased to alarming heights, it signaled the reliance of Palestine on foreign donations. This could have created a moral hazard problem for the rulers of Palestine who knew that growth would result in drawing back of aid.
In such a scenario, the incentive to grow could have actually vanished. Conditional or tied aid has great disadvantages because the recipient government cannot spend the aid on their desired projects. Moreover, tied aid has to be spent on specific and predetermines projects. As discussed earlier in the paper, if foreign aid is diverted to such consumption, it has the tendency to crowd out investment and savings. Although Egypt had a greater share of tied aid than Palestine, however the small size and weak economy of Palestine meant that even 8% of tied aid had a profound effect on its growth.
Egypt was provided more technical aid than Palestine. Technical aid in turns translates into higher Theta in the extended Solow model. An important relation of this model is ?ke= s. ye-(n+? +theta) k Therefore higher technical aid for Egypt resulted in higher effective capital per labor and in turn higher growth than Palestine. The allocation of higher portion of aid to education by Egypt as compared to Palestine means that Egypt is contributing more to its human capital. This will in turn again stimulate theta in the extended Solow model, resulting in increase growth rate of Egypt.
In the light of above discussion, it can be said that the effect of aid on growth does not only depend on variables explained in the models above. Many other factors play a vital role in this link as well. As seen in the case of Zambia, the macroeconomic and political stability are pre-requisites which feed into this complex relation as well. The aid distribution plan should be effective and free of corruption of all sorts for it to have an impact on growth. A major chunk of aid should be distributed towards the saving and investment channel.
While our analysis has tried to determine a link between aid and development, it still carries some shortcomings. The assumptions used in the models such as a fixed capital output ratio are too stringent and do not carry much weight in the reality. Some variables such as savings rate s and productivity theta are determined exogenously, while the macro/microeconomic conditions determining these variables could also affect the impact of aid on growth. Nonetheless, the analysis provides useful insight into the complex relation of aid and growth.
Economicgrowth,
Capitalaccumulation,
Macroeconomics,
Grossdomesticproduct,
Investment,
Economicdevelopment,
Stockandflow,
EconomicsAid and the Two Gap Model Aid is a burning issue these days. The question of countries accepting foreign aid has intrigued economists and the general public for a quite a while. Television discussions and newspaper articles have frequently focused on this issue while politicians try to fight this matter out in the parliaments. Furthermore, many are trying to unravel the enigma of aid and its effects on growth. This paper, in the little word space provided, will try to establish a relation between aid and growth.
It will do so by first defining aid and growth and then moving on to some of the important models which can be used to understand this link. We will discuss the two-gap model and then move on to the Solow and Harrod-Domar model, giving empirical examples in each case. Finally, we will analyze two countries and try to inspect the reasons for their different growth rates using the logic used in the discussed models. Aid can be defined as any voluntary transfer of resources. It can be either public (provided by donor countries or multilateral donor organization such as the IMF and The World Bank) or private (given by NGO’s. . The Organization for Economic Corporation and Development defines aid as any transfer of money or resource that fulfills the following criteria: a) The objective of the transfer should be noncommercial. b) It should be given for the purpose of economic development. c) The terms of the transfer should be concessional (interest rate should be less than the prevailing interest rate in the market OR the maturity period should be longer than usual). Aid should not be mixed with grant which is often used interchangeably with this term.
Aid is any transfer that has concessional terms while grant is a form of aid that does not require the repayment of the principal. In this paper, we will often measure aid in the from of official development assistance (ODA) which is a convenient indicator of international aid flow. On the other hand, we will measure growth by scrutinizing the percentage change in GDP. One of the most widely used framework for analyzing the effects of aid on growth is the two-gap model which holds a key position in policy decisions related to foreign assistance.
The two gap model is based on the Harrod Domar equation g = s/v where s is savings rate v is capital output ratio Capital output ratio is assumed to be constant. The two gap model assumes that a developing country faces either a savings gap or a foreign exchange gap. The savings gap occurs when a country faces a shortage of savings to match Investment in attaining an intended growth rate. In such a case, foreign borrowing or aid can supplement the savings and help bridge the gap between savings and investment. This allows a country to achieve the targeted growth rate. Ft < I – S (Savings gap)
A foreign exchange gap takes place when a country’s exports are not enough to finance its imports. In such situations, aid is handy as it fills the foreign exchange gap and provides countries with sufficient exchange to reach the required level of imports. At a given point in time, only one of the two gaps is binding. Ft < M – X (Foreign Exchange gap) Following this further, we fit empirical data into this model. Zambia is a developing country that has continuously received aid since the mid 1960’s. In 1992, almost 80% of Zambia’s investment was financed by foreign aid.
Since, Zambia has received aid over such a long period, the two gap model predicted that its per capita GDP would reach $2300 by the turn of the century. On the contrary, its GDP per capita in 2007 remained merely half of what was expected . i. e. $1300. The fig. below summarizes the analysis of the Zambian economy. To examine whether the Zambian case is an exception or does the model always fail to predict the reality, we scrutinize on various factors which could have blocked the path of growth for this country. Zambia has been infected by violence and instability right from its independence, with bloodshed and massacres a common feature.
In addition, economic growth has been hindered by the outbreak of civil war and influx of refugees from the neighboring countries. Corruption is another problem that has stalled growth which can be seen from the fact that Zambia is ranked 101 on the corruption perception index. Very recently, Sweden and Netherlands stopped aid to Zambia due to rampant corruption allegations. All these problems add to the ineffectiveness of aid on the growth of Zambian economy which can explain why the two-gap model failed to forecast the ineptness of aid.
The effect of aid on growth can also be explained using two basic but important models, namely Harrod Domar model and the Solow model. Although the upshot of aid on growth is a multidimensional and complex process we only take into account the effect of aid on variables defined in these two models. The main focus of our discussion will be the saving rate which comes out to be the most imperative variable in both these models. We start through the basic Harrod Domar model. Capital output ratio, capital labor ratio and labor output ratio are assumed to be constant.
Some of the important relations are as follows: S=s. Y (2) (3) (1) g= (s/v)-(? ) S=I Where: Y is income S is total saving I is Investment ? is depreciation of capital According to this model, growth can be increased by increasing s, decreasing v or decreasing ?. We shall mainly focus on the relation of aid on growth through the savings rate channel. Countries ask for aid mainly due to its perceived beneficial effect on the savings rate. As shown, saving equals investment in the Harrod-Domar model, subsequently an increase in savings will result in an increase in investment.
This increase is supposed to boost the growth rate of the recipient country. Michael P. Shields offer an interesting explanation of the relation of foreign aid on growth in his paper “foreign aid and domestic savings: the crowding out effect”. If foreign aid is expected to increase savings, then equation (3) becomes g=(s+fa)/v -? Where fa is foreign aid as a proportion of income (4) (s+fa) represents the total funds available for backing investment. According to this equation, an increase in foreign aid is supposed to increase the total saving funds and hence investment by an equal amount.
This suggests that an each additional dollar of foreign aid should result in a one dollar increase in investment in the economy of the recipient country. Reality however is not that perfect and it is too generous for anyone to assume such a one-to-one increase in investment from aid. Famous economist Edward Griffin offers a criticism of such approach. According to him foreign aid should be taken so as to supplement income rather than having a direct impact on savings. In such a case, an increase in income by the amount of foreign aid fa would increase consumption by (1-s). a, thus increasing the investment by s. fa. In such a case, domestic savings can be crowded out by foreign aid by the net amount –(1-s)fa which equals (s-1)fa. Markedly, foreign aid can crowd out private savings and investment, resulting in a decrease in growth as suggested by the Harrod Domar model. The main obstacle in the way of growth in the Harrod-Domar model is the phenomenon of aid filtering out into increased consumption (1-s). fa. Aid has to be spent on investment or has to increase the saving rate (both eventually come out to be the same) for a country to grow.
To see a practical example of this, we consider Pakistan, which is a country largely dependent on foreign aid. During the period 1952-2002, the total amount of aid given to Pakistan equaled 63703 million US dollars. Ghulam Mohey-ud-din examines in his paper “Impact of foreign aid on economic development in Pakistan”, the reasons for aid not resulting in the required growth for Pakistan. He states three main reasons for the failure of aid to account for growth. First of all, a staggering 58% of this total aid (approx. 6945 million US dollars) was tied to development of large projects while only 13% (approx 8281 million US dollars) accounted for non-food and BOP aid. Such a large portion of aid (58%) going towards consumption invariably meant that the effect on savings was going to be very minute. Thus, financial aid tended to crowd out saving and investment. Secondly, while the nominal aid gradually increased, in reality, aid as a percentage of gross national income fell from approximately 7. 6% in 1960 to nearly 3% in 2002. This meant that aid was not catching up to the required increase in the GNI of Pakistan.
Thirdly, along with the increase in aid came the burden of burgeoning foreign debt. This required huge amounts of debt servicing which reduced Pakistan’s current account. As previously explained, aid was already not resulting in much growth due to it crowding out savings and investment. An additional burden of debt servicing did the government no better. Accordingly, its GDP growth rate was subject to constant fluctuations and Pakistan could never attain sustainable growth. The growth rate reached a peak of 10. 22% in 1953 but since then, the average growth has gone down with the exception of one or two years.
In 2002, the GDP growth rate stood at 4. 73%. Aid during a whole half of a century could not result in sustained economic growth. Another approach that looks at the impact of foreign aid on growth is the poverty trap. Many poor developing countries face an inability to grow at reasonable rates due to getting stuck in a poverty trap, which can be defined as a self-reinforcing mechanism which causes poverty to persist. We use the Solow model to analyze how aid can be used to pull countries out of this poverty trap and onto the path of self-sustaining economic growth.
We assume the basic assumptions of Solow model to be true. Thus, we assume constant returns to scale production function and diminishing returns to capital. The final and important relation of the Solow model is ? k=s. y-(n+? ). k (5) k is capital per worker n is population growth Philipp Harms and Matthiaz Lutz depart from this conventional Solow model by assuming that people have to satisfy their basic consumption needs for which savings are zero until per capita income does not exceed a certain level. The modified Solow diagram is shown below
Two steady states are shown in the above figure. k* is an unstable steady state while k** is a stable steady state. If the country’s initial capital per worker is below the unstable steady state k*, then the country is stuck in a potentially dangerous poverty trap. Low income levels result in low saving which leads to lower investment in capital stock. Increasing depreciation ? of capital will further lower the capital per worker k and result in even lower income. This vicious cycle of poverty and lack of growth will keep re-enforcing each other unless the country is given a push start.
This push can be in the form of aid, which may impact the savings rate s as discussed in the extended Harrod Domar model. Furthermore, aid in the form of foreign capital inflow can also increase capital per worker, consequently pushing the country out the poverty trap. Now we come to the analysis of growth patterns in two Arab countries namely Egypt and Palestine. We will explore the amounts and type of aid given to these countries and then investigate their underlying effects on various growth variables based on the Solow and Harrod Domar models discussed earlier in the paper.
With this in mind, we turn to the empirical evidences which show that: 1. ODA/GNI ratio for Palestine has increased during the period 2000-2005, while that of Egypt has decreased during the same period. 2. ODA/Capita for Palestine has increased to $500 during the period 2000-2005, while ODA/Capita for Egypt has come down to $15 in 2003 from $179 in 1979. 3. In Egypt, 13% of the total aid was tied whereas in Palestine 8% was tied. 4. Technical aid provided to Egypt was 44% while that of Palestine was 16% of total aid during the period 2000-2004. 5.
In Egypt, education was given the highest priority among the aid allocated to the social sector. While in Palestine, Education was the second lowest recipient of aid allocated to the social sector. 6. In Palestine, growth rate of real GDP from 2003-2005 was 35. 50%, while the percentage change in real GDP for Egypt was 127. 46 for the same period. ODA/GNI ratio signifies the dependency of the recipient country on the donor for foreign aid. A large increase in the ODA/GNI ratio of Palestine meant that it was becoming more and more dependent on foreign aid for support, while the opposite was true for Egypt.
Consequently, Palestinian institutions kept weakening and were not given the incentive to develop due to their heavy reliance on outward help. On the other hand, Egypt’s lower dependency on foreign aid meant that it was getting increased opportunities to develop its institutions and stand up on its own feet. As the ODA/capita of Palestine increased to alarming heights, it signaled the reliance of Palestine on foreign donations. This could have created a moral hazard problem for the rulers of Palestine who knew that growth would result in drawing back of aid.
In such a scenario, the incentive to grow could have actually vanished. Conditional or tied aid has great disadvantages because the recipient government cannot spend the aid on their desired projects. Moreover, tied aid has to be spent on specific and predetermines projects. As discussed earlier in the paper, if foreign aid is diverted to such consumption, it has the tendency to crowd out investment and savings. Although Egypt had a greater share of tied aid than Palestine, however the small size and weak economy of Palestine meant that even 8% of tied aid had a profound effect on its growth.
Egypt was provided more technical aid than Palestine. Technical aid in turns translates into higher Theta in the extended Solow model. An important relation of this model is ?ke= s. ye-(n+? +theta) k Therefore higher technical aid for Egypt resulted in higher effective capital per labor and in turn higher growth than Palestine. The allocation of higher portion of aid to education by Egypt as compared to Palestine means that Egypt is contributing more to its human capital. This will in turn again stimulate theta in the extended Solow model, resulting in increase growth rate of Egypt.
In the light of above discussion, it can be said that the effect of aid on growth does not only depend on variables explained in the models above. Many other factors play a vital role in this link as well. As seen in the case of Zambia, the macroeconomic and political stability are pre-requisites which feed into this complex relation as well. The aid distribution plan should be effective and free of corruption of all sorts for it to have an impact on growth. A major chunk of aid should be distributed towards the saving and investment channel.
While our analysis has tried to determine a link between aid and development, it still carries some shortcomings. The assumptions used in the models such as a fixed capital output ratio are too stringent and do not carry much weight in the reality. Some variables such as savings rate s and productivity theta are determined exogenously, while the macro/microeconomic conditions determining these variables could also affect the impact of aid on growth. Nonetheless, the analysis provides useful insight into the complex relation of aid and growth.

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